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ŲV_numNaNsV_numINFsV_npnts@<V_nterms@V_nheldV_startRowV_endRow@;V_startColV_endCola_Si?į`õäKjb_Si?Ų“ĒĮaėgmu_Si@Pffffgoneminusnu_Si?ŃG®zįHlambda?šĮR8-sea_Ge?ā ń€ }beta?šĮR8-sef_misfit?„Lüœ[Ō@nu_Si?Ńė…øQģmixed?ē______f_misfit_Si?„Lüœ[Ō@b_Ge?Ł™‰‚“ä—f_misfit_Ge?¤s/ōĆ mh_thickness@Minimum?į&u£Maximum@>V_Root@¼#i‘ŗBŃV_YatRootV_FlagV_numRoots?šhc@*v¾č³mēK60?į8eŽŁįra_SiGe?į…ś€d>nb_SiGe?ŲČ!“Ųź f_misfit_SiGe?”ŻŽ0•ĢņGe_concentration?ə™™™™šnu_Ge?Ńė…øQģmu_Ge@Pffffgnu_SiGe?Ńė…øQģmu_SiGe@PffffgGrowth_Temp@‰øGrowth_rate?ąKn=ø$ŠÉwƒKm@²\/Ÿ³œV_notD5ÆxµŒ@tc@ QJNz…V_ODEStepCompleted@0V_ODEStepSize?ÖAŌ VV_ODETotalSteps@`V_ODEMinStep?l}8X_%¬V_ODEFunctionCalls@§ˆttD?Ni{}@ŠdNdt=‘ ? čøõä:V_startLayerV_endLayerV_startChunkV_endChunkc_ratio_Ge?Ų1&éxÕc_ratio_Si?ŲÆO „Ma_parameter@I…šoiEc_parameter@|„µÜĘ?x_Ge?čšŌ,<žķc_ratio?Ų.Š GNa_relax@f‘‡@nyShiftæŧ.ŪÄĄstrain_x_rayæt¾ś£°ö-x_Ge_exp?č›FņŠŲ…a_Si_x_ray@¹XbMÓF0?®ėQr$šBupper@$fudge?ģĢĢĢĢĢĶconcentration_variable?ągrowth_rate_variable?ątarget_strain>äųµˆćhńwidth@RĄAnnealing_time@ĒpRelaxation>TŌ7éZ@øSeparation>z×ņš¼ÆHInitial_dislocations>å‹`1SæiInitial_relaxation>åDųÉÅ&Östrain_limit>äųµˆćhńhc_Bai@±sb|¾rV_siga@Ā—ķÖ1éV_sigb@ %yWĪća2nthread=Ū‚Ź} ÕMisfit_density_Re@V€final_relaxation?`ņ4,ģśłAnneal_Temp@tPMisfit_density_growth_Re@’Ąstrain_limit_growth?/uMUkMisfit_density_anneal_Re@Sample_thickness@rvQė…ølinear>Wƒ"æquadratic?`Ųż÷“hN_not_original>,ĪYzpindex@ betaangle?šĮR8-setemporary?õ«jēÕfŠS_info’źą?ņ8ŸJłčæ’ėĮ–DATE=Tue, Jul 1, 2008;TIME=7:59:14 AM;FUNCTION=line;AUTODESTWAVE=fit_Log_N_not_wave;YDATA=root:Log_N_not_wave;XDATA=root:Inverse_Temp_growth_samples,;S_waveNamesņ8ŸJłčæ’ėĮ Volkert_time;Volkert_relaxation;S_pathamesņ8ŸJłčæ’ėĮ9Macintosh HD:Users:jose:Documents:Papers:Houghton theory:S_fileNameņ8ŸJłčæ’ėĮVolkert_data.txtS_nameameņ8ŸJłčæ’ėĮGraph14T1ameameņ8ŸJłčæ’ėĮ325*Y^„Rename textWave0,Sample; Rename wave0,Freq; Rename wave1,D_Freq; ;DelayUpdate „Rename wave2,Strain; „Make/O/N=6 D_Freq = 521-Freq „Make/O/N=6 Strain = (100)*D_Freq/758 „Make/O/N=6 D_Freq = 521-Freq „Make/O/N=6 Strain = D_Freq/758 „Rename wave0,Thick_nm; „Make/O/N=6 StrainRel = 0.042 - Strain „AppendToTable StrainRel „Make/O/N=6 StrainRel = 1 - (Strain/0.042) „Make/O/N=6 D_Freq = 521-Freq „Make/O/N=6 Strain = D_Freq/758 „Make/O/N=6 StrainRel = 1 - (Strain/0.042) „Make/O/N=6 StrainRel = 100*(1 - (Strain/0.042)) „ „Make/O/N=6 D_Freq = 521-Freq „Make/O/N=6 Strain = D_Freq/758 „Make/O/N=6 StrainRel = (1 - (Strain/0.042)) „ „Make/O/N=6 D_Freq = 521-Freq „Make/O/N=6 Strain = D_Freq/758 „Make/O/N=6 StrainRel = 1*(1 - (Strain/0.042)) „Display StrainRel vs Thick_nm „SetAxis/A left „Label bottom "\\f01\\Z18 t (nm)" „Label left "\\f01\\Z18\\F'Arial'Strain Relaxation" „ModifyGraph mode=3,marker=19,rgb=(0,0,0) „ModifyGraph msize=4 „ModifyGraph msize=5 „SetAxis left 0,1 ;DelayUpdate „SetAxis bottom 2,16 „ModifyGraph noLabel=0 „K0 = 0;K1 = 0; „CurveFit/H="110" poly 3, StrainRel /X=Thick_nm /D fit_StrainRel= poly(W_coef,x) W_coef={0,0,0.0049336} V_chisq= 0.68526; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0,0,0.00172} Coefficient values ± one standard deviation K0 = 0 ± 0 K1 = 0 ± 0 K2 = 0.0049336 ± 0.00172 „K0 = 0;K1 = 0; „CurveFit/H="110" poly 3, StrainRel /X=Thick_nm /D fit_StrainRel= poly(W_coef,x) W_coef={0,0,0.0049336} V_chisq= 0.68526; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0,0,0.00172} Coefficient values ± one standard deviation K0 = 0 ± 0 K1 = 0 ± 0 K2 = 0.0049336 ± 0.00172 „K1 = 0; „CurveFit/H="010" poly 3, StrainRel /X=Thick_nm /D fit_StrainRel= poly(W_coef,x) W_coef={0.35387,0,0.0029958} V_chisq= 0.223807; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0.142,0,0.00125} Coefficient values ± one standard deviation K0 = 0.35387 ± 0.142 K1 = 0 ± 0 K2 = 0.0029958 ± 0.00125 „CurveFit poly 3, kwCWave=W_coef, StrainRel /X=Thick_nm /D fit_StrainRel= poly(W_coef,x) W_coef={-0.2689,0.19552,-0.0073124} V_chisq= 0.0209297; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0.123,0.0363,0.00195} Coefficient values ± one standard deviation K0 = -0.2689 ± 0.123 K1 = 0.19552 ± 0.0363 K2 = -0.0073124 ± 0.00195 „CurveFit poly 3, kwCWave=W_coef, StrainRel /X=Thick_nm /D fit_StrainRel= poly(W_coef,x) W_coef={-0.2689,0.19552,-0.0073124} V_chisq= 0.0209297; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0.123,0.0363,0.00195} Coefficient values ± one standard deviation K0 = -0.2689 ± 0.123 K1 = 0.19552 ± 0.0363 K2 = -0.0073124 ± 0.00195 „SetAxis left 0,1.2 „Display Thick_nm vs StrainRel „SetAxis/A left „CurveFit poly 3, kwCWave=W_coef, StrainRel /X=StrainRel /D fit_StrainRel= poly(W_coef,x) W_coef={5.4123e-16,1,1.1657e-15} V_chisq= 4.1003e-31; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={4.32e-16,1.85e-15,1.65e-15} Coefficient values ± one standard deviation K0 = 5.4123e-16 ± 4.32e-16 K1 = 1 ± 1.85e-15 K2 = 1.1657e-15 ± 1.65e-15 „CurveFit poly 3, kwCWave=W_coef, Thick_nm /X=StrainRel /D fit_Thick_nm= poly(W_coef,x) W_coef={3.1279,-7.9446,19.327} V_chisq= 6.3416; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={1.7,7.29,6.48} Coefficient values ± one standard deviation K0 = 3.1279 ± 1.7 K1 = -7.9446 ± 7.29 K2 = 19.327 ± 6.48 „W_coef[1] = 0; „CurveFit/H="010" poly 3, kwCWave=W_coef, Thick_nm /X=StrainRel /D fit_Thick_nm= poly(W_coef,x) W_coef={1.5629,0,12.487} V_chisq= 8.84934; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={1.07,0,1.89} Coefficient values ± one standard deviation K0 = 1.5629 ± 1.07 K1 = 0 ± 0 K2 = 12.487 ± 1.89 „Make/O/N=6 Thick_Square = (Thick_nm)^2 „AppendToTable Thick_Square „Display StrainRel vs Thick_Square „SetAxis/A bottom „Label bottom "\\f01\\Z18 t\\S2\\M (nm)" „CurveFit/H="010" poly 3, kwCWave=W_coef, StrainRel /X=Thick_Square /D fit_StrainRel= poly(W_coef,x) W_coef={0.44397,0,9.4028e-06} V_chisq= 0.348451; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0.158,0,5.84e-06} Coefficient values ± one standard deviation K0 = 0.44397 ± 0.158 K1 = 0 ± 0 K2 = 9.4028e-06 ± 5.84e-06 „CurveFit/H="010" poly 3, kwCWave=W_coef, StrainRel /X=Thick_Square /D fit_StrainRel= poly(W_coef,x) W_coef={0.44397,0,9.4028e-06} V_chisq= 0.348451; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0.158,0,5.84e-06} Coefficient values ± one standard deviation K0 = 0.44397 ± 0.158 K1 = 0 ± 0 K2 = 9.4028e-06 ± 5.84e-06 „CurveFit poly 3, kwCWave=W_coef, StrainRel /X=Thick_Square /D fit_StrainRel= poly(W_coef,x) W_coef={0.18316,0.011042,-3.0793e-05} V_chisq= 0.0663043; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0.1,0.00309,1.15e-05} Coefficient values ± one standard deviation K0 = 0.18316 ± 0.1 K1 = 0.011042 ± 0.00309 K2 = -3.0793e-05 ± 1.15e-05 „ „Make/O/N=6 D_Freq = 521-Freq „Make/O/N=6 Strain = D_Freq/758 „Make/O/N=6 StrainRel = 1*(1 - (Strain/0.042)) „Make/O/N=6 Thick_Square = (Thick_nm)^2 „Make/O/N=6 Log_TS = log(Thick_Square) „AppendToTable Log_TS „RemoveFromGraph fit_StrainRel „K1 = 0; „CurveFit/H="0100" poly 4, StrainRel /X=Thick_nm /D fit_StrainRel= poly(W_coef,x) W_coef={0.14237,0,0.01682,-0.00084461} V_chisq= 0.054486; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0.121,0,0.0056,0.000339} Coefficient values ± one standard deviation K0 = 0.14237 ± 0.121 K1 = 0 ± 0 K2 = 0.01682 ± 0.0056 K3 = -0.00084461 ± 0.000339 „CurveFit poly 4, kwCWave=W_coef, StrainRel /X=Thick_nm /D fit_StrainRel= poly(W_coef,x) W_coef={-0.6075,0.36798,-0.030178,0.00084154} V_chisq= 0.0106841; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0.267,0.129,0.0166,0.000608} Coefficient values ± one standard deviation K0 = -0.6075 ± 0.267 K1 = 0.36798 ± 0.129 K2 = -0.030178 ± 0.0166 K3 = 0.00084154 ± 0.000608 „W_coef[3] = 0; „CurveFit/H="0001" poly 4, kwCWave=W_coef, StrainRel /X=Thick_nm /D fit_StrainRel= poly(W_coef,x) W_coef={-0.2689,0.19552,-0.0073124,0} V_chisq= 0.0209297; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0.151,0.0444,0.00239,0} Coefficient values ± one standard deviation K0 = -0.2689 ± 0.151 K1 = 0.19552 ± 0.0444 K2 = -0.0073124 ± 0.00239 K3 = 0 ± 0 „Display Strain vs Thick_nm „SetAxis/A left „CurveFit/H="0001" poly 4, kwCWave=W_coef, Strain /X=Thick_nm /D fit_Strain= poly(W_coef,x) W_coef={0.053294,-0.0082119,0.00030712,0} V_chisq= 3.69201e-05; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0.00635,0.00187,0.0001,0} Coefficient values ± one standard deviation K0 = 0.053294 ± 0.00635 K1 = -0.0082119 ± 0.00187 K2 = 0.00030712 ± 0.0001 K3 = 0 ± 0 BUG: In CoefficientsTab::setInitialGuessesFromWave, number of points in coefficients wave does not match the number of rows in the Coefficients List „CurveFit poly 3, Strain /X=Thick_nm /D fit_Strain= poly(W_coef,x) W_coef={0.053294,-0.0082119,0.00030712} V_chisq= 3.69201e-05; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0.00518,0.00152,8.19e-05} Coefficient values ± one standard deviation K0 = 0.053294 ± 0.00518 K1 = -0.0082119 ± 0.00152 K2 = 0.00030712 ± 8.19e-05 „W_coef[1] = 0; „CurveFit/H="010" poly 3, kwCWave=W_coef, Strain /X=Thick_nm /D fit_Strain= poly(W_coef,x) W_coef={0.027137,0,-0.00012582} V_chisq= 0.000394796; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0.00598,0,5.27e-05} Coefficient values ± one standard deviation K0 = 0.027137 ± 0.00598 K1 = 0 ± 0 K2 = -0.00012582 ± 5.27e-05 „CurveFit poly 3, kwCWave=W_coef, Strain /X=Thick_nm /D fit_Strain= poly(W_coef,x) W_coef={0.053294,-0.0082119,0.00030712} V_chisq= 3.69201e-05; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0.00518,0.00152,8.19e-05} Coefficient values ± one standard deviation K0 = 0.053294 ± 0.00518 K1 = -0.0082119 ± 0.00152 K2 = 0.00030712 ± 8.19e-05 „CurveFit poly 3, kwCWave=W_coef, StrainRel /X=Thick_nm /D fit_StrainRel= poly(W_coef,x) W_coef={-0.2689,0.19552,-0.0073124} V_chisq= 0.0209297; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0.123,0.0363,0.00195} Coefficient values ± one standard deviation K0 = -0.2689 ± 0.123 K1 = 0.19552 ± 0.0363 K2 = -0.0073124 ± 0.00195 „CurveFit poly 3, kwCWave=W_coef, StrainRel /X=Thick_nm /D fit_StrainRel= poly(W_coef,x) W_coef={-0.2689,0.19552,-0.0073124} V_chisq= 0.0209297; V_npnts= 6; V_numNaNs= 0; V_numINFs= 0; V_startRow= 0; V_endRow= 5; V_startCol= 0; V_endCol= 0; W_sigma={0.123,0.0363,0.00195} Coefficient values ± one standard deviation K0 = -0.2689 ± 0.123 K1 = 0.19552 ± 0.0363 K2 = -0.0073124 ± 0.00195 „TextBox/C/N=text0/F=0/A=MC " \tR = -0.2689 + (0.19552 ± 0.0363)*t - (0.0073124 ± 0.00195)*t\\S2" „TextBox/C/N=text0 "\\Z10\\f01R = -0.2689 + (0.19552 ± 0.0363)*t - (0.0073124 ± 0.00195)*t\\S2" „TextBox/C/N=text0/B=1 „ModifyGraph rgb=(0,0,0) „TextBox/C/N=text1/F=0/B=1/A=MC "\\Z12\\f01StrainRel = (1 - (Strain/0.042))" „Edit „Rename wave0,Energy; „Rename wave0,eps_r; Rename wave1,eps_i; „Differentiate eps_r/X=Energy/D=eps_r_DIF „AppendToTable eps_r_DIF „Differentiate eps_i/X=Energy/D=eps_i_DIF „AppendToTable eps_i_DIF „Display eps_r_DIF,eps_i_DIF vs Energy „SetAxis/A left „SetAxis/A bottom „ModifyGraph mode=0,rgb(eps_r_DIF)=(65280,0,0),rgb(eps_i_DIF)=(0,0,0) „ModifyGraph lsize=3,lstyle=1 „Legend/C/N=text0/F=0/B=1/A=MC „AppendToGraph wave1 vs wave0 „ModifyGraph lsize(wave1)=2,rgb(wave1)=(0,0,65280) „Legend/C/N=text0/J "\\s(eps_r_DIF) eps_r_DIF\r\\s(eps_i_DIF) eps_i_DIF" „TextBox/C/N=text1/F=0/B=1/A=MC "488 nm" „Edit „Differentiate e1_Si/X=eV_Si/D=e1_Si_DIF „Differentiate e2_Si/X=eV_Si/D=e2_Si_DIF „AppendToTable e1_Si_DIF,e2_Si_DIF „SetAxis left -100,100 ;DelayUpdate „SetAxis bottom 2,3.3 „AppendToGraph e1_Si_DIF,e2_Si_DIF vs eV_Si „ModifyGraph mode=0 „Label left "\\f01\\Z18\\F'Arial'First Derivative" „Label bottom "\\f01\\Z18 E (eV)" „ModifyGraph rgb(e1_Si_DIF)=(0,0,65280),rgb(e2_Si_DIF)=(16384,65280,16384) „ModifyGraph rgb(e1_Si_DIF)=(65280,0,0),rgb(e2_Si_DIF)=(0,0,0) „ModifyGraph lsize(e1_Si_DIF)=3,lsize(e2_Si_DIF)=3 „Legend/C/N=text0/J "\\f01\\Z12\\s(eps_r_DIF) e1_Si50Ge50_DIF\r\\s(eps_i_DIF) e2_Si50Ge50_DIF\r\\s(e1_Si_DIF) e1_Si_DIF\r\\s(e2_Si_DIF) e2_Si_DIF" „Legend/C/N=text0/J "\\f01\\Z10\\s(eps_r_DIF) e1_Si50Ge50_DIF\r\\s(eps_i_DIF) e2_Si50Ge50_DIF\r\\s(e1_Si_DIF) e1_Si_DIF\r\\s(e2_Si_DIF) e2_Si_DIF" „KillWaves W_coef,W_sigma,W_ParamConfidenceInterval,fit_Thick_nm,fit_Strain;DelayUpdate „KillWaves Energy,eps_r,eps_i,eps_r_DIF,eps_i_DIF,textWave0,wave0,wave1,eV_Si;DelayUpdate „KillWaves e1_Si,e2_Si,e1_Si_DIF,e2_Si_DIF „Variable /G a_Si=5.43086 „Variable /G b_Si=sqrt(2)*a_Si/2 „Print b_Si 3.8402 „Variable /G a_Si=5.43086 „Variable /G b_Si=sqrt(2)*a_Si/2 „Variable /G mu_Si=51.1 „Variable /G oneminusnu_Si=0.27 „Variable /G lambda=pi/3 „Print sin(lambda) 0.866025 „ Print cos(lambda) 0.5 „Variable /G a_Si=5.43086 „Variable /G a_Ge=5.6568 „Variable /G b_Si=sqrt(2)*a_Si/2 „Variable /G mu_Si=51.1 „Variable /G oneminusnu_Si=0.27 „Variable /G lambda=pi/3 „Variable /G beta=pi/3 „Variable /G f_misfit=(a_Ge-a_Si)/a_Si „Print f_misfit 0.041603 „Make/N=1000/D Thickness „SetScale/I x 0,100,"", Thickness „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G b_Si=sqrt(2)*a_Si/2 „Variable /G mu_Si=51.1 „Variable /G oneminusnu_Si=0.27 „Variable /G lambda=pi/3 „Variable /G beta=pi/3 „Variable /G f_misfit=(a_Ge-a_Si)/a_Si „Duplicate Thickness rho_eq „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G b_Si=sqrt(2)*a_Si/2 „Variable /G mu_Si=51.1 „Variable /G oneminusnu_Si=0.27 „Variable /G nu_Si=1-oneminusnu_Si „rho_eq=f_misfit/(b_Si*cos(lambda)) „rho_eq=f_misfit/(b_Si*cos(lambda))-(b_Si/(8*pi*Thickness*(cos(lambda))^2)) „rho_eq=f_misfit/(b_Si*cos(lambda))-(b_Si/(8*pi*Thickness*(cos(lambda))^2))*((1-nu_Si*(cos(beta))^2)/(1+nu_Si))*ln(4*Thickness/b_Si) „Display rho_eq vs Thickness „Edit rho_eq „rho_eq=f_misfit/(b_Si*cos(lambda)) „rho_eq=f_misfit/(b_Si*cos(lambda))-(b_Si/(8*pi*Thickness*(cos(lambda))^2))*((1-nu_Si*(cos(beta))^2)/(1+nu_Si)) „Print nu_Si 0.73 „AppendToTable Thickness „rho_eq=f_misfit/(b_Si*cos(lambda))-(b_Si/(8*pi*x*(cos(lambda))^2))*((1-nu_Si*(cos(beta))^2)/(1+nu_Si))*ln(4*x/b_Si) „Display rho_eq „Print b_Si*cos(lambda)*0.214664 0.0412176 „Make/N=5/D Parameters „Rename Parameters,Parameter; „Variable /G mu_Si=51.1 „Variable /G oneminusnu_Si=0.27 „Variable /G nu_Si=1-oneminusnu_Si „Variable /G lambda=pi/3 „Variable /G beta=pi/3 „Variable /G f_misfit=(a_Ge-a_Si)/a_Si „Parameter[0]= b_Si „Parameter[1]= f_misfit „Parameter[2]=lambda „Parameter[3]=nu_Si „Parameter[4]=beta „Edit Parameter „Make/N=1000/D Critical_Function „SetScale/I x 0,100,"", Critical_Function „Critical_Function=1 „Critical_Function=CriticalThickness(Parameter,x) „Display Critical_Function „ModifyGraph mode=0,lsize=1 „SetAxis bottom 0,10 „SetAxis bottom 0,2 „SetAxis left -10,10 „Edit Critical_Function.id „Critical_Function=CriticalThickness(Parameter,x) „SetAxis bottom 0,0.5 „Critical_Function=CriticalThickness(Parameter,x) „SetScale/I x 0,10,"", Critical_Function „Critical_Function=CriticalThickness(Parameter,x) „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Redimension/N=4 Parameter „Parameter[0]= b_Si „Parameter[1]= f_misfit „Parameter[2]=lambda „Parameter[3]=mixed „Parameter[0]= b_Si „Parameter[1]= f_misfit „Parameter[2]=lambda „Parameter[3]=mixed „Critical_Function=CriticalThickness(Parameter,x) „Critical_Function=CriticalThickness(Parameter,x) „Critical_Function=CriticalThickness(Parameter,x) „Parameter[0]= b_Si „Parameter[1]= f_misfit „Parameter[2]=lambda „Parameter[3]=mixed „Critical_Function=CriticalThickness(Parameter,x) „Critical_Function=CriticalThickness(Parameter,x) „Critical_Function=CriticalThickness(Parameter,x) „Critical_Function=CriticalThickness(Parameter,x) „Parameter[0]= b_Si „Parameter[1]= f_misfit „Parameter[2]=lambda „Parameter[3]=mixed „ „Critical_Function=CriticalThickness(Parameter,x) „Critical_Function=CriticalThickness(Parameter,x) „Critical_Function=CriticalThickness(Parameter,x) „ Print mixed 0.472543 „Critical_Function=CriticalThickness(Parameter,x) „Critical_Function=CriticalThickness(Parameter,x) „SetAxis left -2,2 „ModifyGraph grid(left)=2 „SetAxis bottom 0,1 „SetAxis left -1,1 „SetAxis left -0.5,0.5 „Critical_Function=CriticalThickness(Parameter,x) „Critical_Function=CriticalThickness(Parameter,x) „SetAxis bottom 0,10 „Critical_Function=CriticalThickness(Parameter,x) „Parameter[0]= b_Si „Parameter[1]= f_misfit „Parameter[2]=lambda „Parameter[3]=mixed „Critical_Function=CriticalThickness(Parameter,x) „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G b_Si=sqrt(2)*a_Si/2 „Variable /G mu_Si=51.1 „Variable /G oneminusnu_Si=0.27 „Variable /G nu_Si=1-oneminusnu_Si „Variable /G lambda=pi/3 „Variable /G beta=pi/3 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_Si=(a_Ge-a_Si)/a_Si „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G b_Si=sqrt(2)*a_Si/2 „Variable /G b_Ge=sqrt(2)*a_Ge/2 „Variable /G mu_Si=51.1 „Variable /G oneminusnu_Si=0.27 „Variable /G nu_Si=1-oneminusnu_Si „Variable /G lambda=pi/3 „Variable /G beta=pi/3 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_Si=(a_Ge-a_Si)/a_Si „Variable /G f_misfit_Ge=(a_Si-a_Ge)/a_Ge „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G b_Si=sqrt(2)*a_Si/2 „Variable /G b_Ge=sqrt(2)*a_Ge/2 „Variable /G mu_Si=51.1 „Variable /G oneminusnu_Si=0.27 „Variable /G nu_Si=1-oneminusnu_Si „Variable /G lambda=pi/3 „Variable /G beta=pi/3 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_Si=(a_Ge-a_Si)/a_Si „Variable /G f_misfit_Ge=-(a_Si-a_Ge)/a_Ge „Parameter[0]= b_Ge „Parameter[1]= f_misfit_Ge „Parameter[2]=lambda „Parameter[3]=mixed „Critical_Function=CriticalThickness(Parameter,x) „Parameter[0]= b_Ge „Parameter[1]= f_misfit_Ge „Parameter[2]=lambda „Parameter[3]=mixed „Critical_Function=CriticalThickness(Parameter,x) „Parameter[0]= b_Ge „Parameter[1]= f_misfit_Ge „Parameter[2]=lambda „Parameter[3]=mixed „Critical_Function=CriticalThickness(Parameter,x) „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „Critical_Function=CriticalThickness(Parameter,x) „Print mixed*b_Si/(8*pi*cos(lambda)) 0.0144406 „ Print mixed*b_Si/(8*pi*f_misfit_Si*cos(lambda)) 0.347105 „b_Si=0.4 „nu_Si=0.28 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „ Print mixed*b_Si/(8*pi*f_misfit_Si*cos(lambda)) 0.555902 „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G b_Si=sqrt(2)*a_Si/2 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Print mixed*b_Si/(8*pi*f_misfit_Si*cos(lambda)) 0.533694 „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G b_Si=sqrt(2)*a_Si/2 „Variable /G b_Ge=sqrt(2)*a_Ge/2 „Variable /G mu_Si=51.1 „Variable /G nu_Si=0.72 „Variable /G lambda=pi/3 „Variable /G beta=pi/3 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_Si=(a_Ge-a_Si)/a_Si „Variable /G f_misfit_Ge=-(a_Si-a_Ge)/a_Ge „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „Critical_Function=CriticalThickness(Parameter,x) „Critical_Function=CriticalThickness(Parameter,x) „Critical_Function=CriticalThickness(Parameter,x) „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G b_Si=sqrt(2)*a_Si/2 „Variable /G b_Ge=sqrt(2)*a_Ge/2 „Variable /G mu_Si=51.1 „Variable /G nu_Si=0.72 „Variable /G lambda=pi/3 „Variable /G beta=pi/3 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_Si=(a_Ge-a_Si)/a_Si „Variable /G f_misfit_Ge=-(a_Si-a_Ge)/a_Ge „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „Critical_Function=CriticalThickness(Parameter,x) „ Print mixed*b_Si/(8*pi*f_misfit_Si*cos(lambda)) 0.350191 „b_Si=0.4 „ Print mixed*b_Si/(8*pi*f_misfit_Si*cos(lambda)) 0.364763 „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G b_Si=sqrt(2)*a_Si/2 „Variable /G b_Ge=sqrt(2)*a_Ge/2 „Variable /G mu_Si=51.1 „Variable /G nu_Si=0.28 „Variable /G lambda=pi/3 „Variable /G beta=pi/3 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_Si=(a_Ge-a_Si)/a_Si „Variable /G f_misfit_Ge=-(a_Si-a_Ge)/a_Ge „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „Critical_Function=CriticalThickness(Parameter,x) „Critical_Function=CriticalThickness(Parameter,x) „Duplicate Critical_Function Total_energy „Variable /G h_thickness=10 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Display Total_energy „ModifyGraph mode=0,lsize=1 „SetScale/I x 0,0.2,"", Total_energy „Variable /G h_thickness=10 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „SetAxis left 0,4 „Variable /G h_thickness=9 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=5 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „SetAxis/A left „Variable /G h_thickness=4 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=3 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=2 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=1.5 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „Critical_Function=CriticalThickness(Parameter,x) „Edit Total_energy.id „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „Critical_Function=CriticalThickness(Parameter,x) „Variable /G h_thickness=1.49 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=1.48 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=1.47 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=1.46 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=1.45 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=1.44 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=0.5 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=0.4 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=0.3 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=0.2 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=0.15 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=0.13 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=0.12 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Variable /G h_thickness=0.10 „Total_energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si)+x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Duplicate Total_energy Elastic_Energy,Dislocation_Energy „Variable /G h_thickness=0.10 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „AppendToGraph Elastic_Energy,Dislocation_Energy „ModifyGraph mode=0,lsize(Dislocation_Energy)=1;DelayUpdate „ModifyGraph rgb(Dislocation_Energy)=(24576,24576,65535) „ModifyGraph lsize(Total_energy)=2 „Legend/C/N=text0/F=0/A=MC „Variable /G h_thickness=0.15 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „Variable /G h_thickness=1 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „SetAxis bottom 0,0.2 „Variable /G h_thickness=2 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „AppendToTable Elastic_Energy,Dislocation_Energy „Variable /G h_thickness=0.1 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „Print ln(4*h_thickness/b_Si) 0.0407705 „Variable /G h_thickness=0.05 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „Print ln(4*h_thickness/b_Si) -0.652377 „Variable /G h_thickness=0.06 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „Print ln(4*h_thickness/b_Si) -0.470055 „Variable /G h_thickness=0.07 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „Print ln(4*h_thickness/b_Si) -0.315904 „Variable /G h_thickness=0.09 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „Print ln(4*h_thickness/b_Si) -0.0645901 „Variable /G h_thickness=0.1 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „Print ln(4*h_thickness/b_Si) 0.0407705 „Variable /G h_thickness=0.11 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „Print ln(4*h_thickness/b_Si) 0.136081 „Variable /G h_thickness=0.12 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „Print ln(4*h_thickness/b_Si) 0.223092 „SetAxis left 0,0.06 „Variable /G h_thickness=0.13 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „Print ln(4*h_thickness/b_Si) 0.303135 „Print 4*h_thickness/b_Si 1.3541 „Variable /G h_thickness=0.10 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „Print 4*h_thickness/b_Si 1.04161 „Variable /G h_thickness=0.13 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „Print 4*h_thickness/b_Si 1.3541 „Label bottom "\\Z24Dislocation density \\F'Symbol'r" „Label left "\\Z24Energy" „TextBox/C/N=text1/F=0/A=MC "\\Z24h=0.1" „Variable /G h_thickness=0.11 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „Variable /G h_thickness=0.10 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „Variable /G h_thickness=0.12 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „TextBox/C/N=text1 "\\Z24h=0.12" „Variable /G h_thickness=0.14 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „TextBox/C/N=text1 "\\Z24h=0.14" „Print 4*h_thickness/b_Si 1.45826 „Variable /G h_thickness=0.2 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „SetAxis/A left „Variable /G h_thickness=1 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „TextBox/C/N=text1 "\\Z24h=1.0" „Variable /G h_thickness=1.3 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „TextBox/C/N=text1 "\\Z24h=1.3" „Variable /G h_thickness=1.44 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „TextBox/C/N=text1 "\\Z24h=1.44" „Variable /G h_thickness=1.5 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „Variable /G h_thickness=1.6 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „TextBox/C/N=text1 "\\Z24h=1.6" „Variable /G h_thickness=2 „Elastic_Energy=2*mu_Si*(1+nu_Si)*h_thickness*(F_misfit_Si-x*b_Si*cos(lambda))^2/(1-nu_Si) „Dislocation_Energy=x*ln(4*h_thickness/b_Si)*mu_Si*(b_Si)^2*(1-nu_Si*(cos(beta))^2)/(2*pi*(1-nu_Si)) „Total_energy=Elastic_Energy+Dislocation_Energy „TextBox/C/N=text1 "\\Z24h=2.0" „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „Critical_Function=CriticalThickness(Parameter,x) „SetAxis bottom 0,3 „ModifyGraph grid=2 „Label bottom "\\Z24Thickness" „Label left "\\Z24Zeros of critical thickness" 1.87373 „Print (b_Si*mixed/(8*pi*f_misfit_Si*cos(lambda))) 0.533694 „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „Variable/G Minimum=b_Si*mixed/(8*pi*f_misfit_Si*cos(lambda)) „Variable/G Maximum=30 „FindRoots /L=(Minimum) /H=(Maximum) CriticalThickness, Parameter Possible root found at 1.44832 Y value there is -4.44089e-16 „Print V_root 1.44832 „FindRoots /L=(Minimum) /H=(Maximum) CriticalThicknessRoot, Parameter Possible root found at 1.44832 Y value there is -4.44089e-16 „Make/N=200/D Critical_Thickness „SetScale/I x 0.0001,0.1,"", Critical_Thickness „Display Critical_Thickness „Critical_Thickness=CriticalThickness(Parameter,x) „ModifyGraph mode=0,lsize=1 „SetAxis bottom 0,0.05 „ModifyGraph log(left)=1 „SetAxis bottom 0.0001,0.05 „ModifyGraph grid(bottom)=1,log=1 „ModifyGraph grid=1 „ModifyGraph lsize=2 „Legend/C/N=text0/F=0/A=MC „Label bottom "\\Z24Strain mismatch" „Label left "\\Z24Critical Thickness (nm)" „Make/N=1000/D Dislocation_density „SetScale/I x 0,100,"", Dislocation_density „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*b_Si*mixed/(8*pi*x*(cos(lambda))^2) „Display Dislocation_density „ModifyGraph mode=0,lsize=2 „Edit Dislocation_density „SetScale/I x 0.001,100,"", Dislocation_density „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*b_Si*mixed/(8*pi*x*(cos(lambda))^2) „SetScale/I x 0.01,100,"", Dislocation_density „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*b_Si*mixed/(8*pi*x*(cos(lambda))^2) „SetAxis left 0,1 „Duplicate Dislocation_density Dislocation_density_2 „Dislocation_density_2=(1-CriticalThickness(Parameter,f_misfit_Si)/x )*f_misfit_Si/(b_Si*cos(lambda)) „AppendToGraph Dislocation_density_2 „ModifyGraph rgb(Dislocation_density_2)=(24576,24576,65535) „Legend/C/N=text0/F=0/A=MC „AppendToTable Dislocation_density_2 „SetAxis bottom 0,20 „Edit Dislocation_density.id „AppendToTable Dislocation_density_2 „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*b_Si*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density_2=(1-CriticalThickness(Parameter,f_misfit_Si)/x )*f_misfit_Si/(b_Si*cos(lambda)) „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*mixed/(8*pi*x*(cos(lambda))^2) „SetAxis left 0,0.3 „Label bottom "\\Z24Dislocation linear density" „Label left "\\Z24Dislocation linear density" „Label bottom "\\Z24Thickness (nm)" „Dislocation_density=max(0,Dislocation_density) „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*mixed/(8*pi*x*(cos(lambda))^2) „Print CriticalThickness(Parameter,f_misfit_Si) 1.44832 „Variable /G hc „hc=CriticalThickness(Parameter,f_misfit_Si) „Dislocation_density=(x>hc)*f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*mixed/(8*pi*x*(cos(lambda))^2) „Print hc 1.44832 „Dislocation_density=(x>hc) „Dislocation_density=(x>hc)*f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density=(x>hc) „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density=(x>hc)*Dislocation_density „Duplicate Dislocation_density Strain_theory „Strain_theory=f_misfit_Si-Dislocation_density*b_Si*cos(lambda) „Display Strain_theory „ModifyGraph mode=0,lsize=2 „SetAxis bottom 0,20 „SetAxis left 0,0.05 „AppendToGraph Strain vs Thick_nm „ModifyGraph marker=19,mode(Strain)=3 „ModifyGraph rgb(Strain)=(0,0,0) „Label bottom "\\Z24Layer thickness (nm)" „Label left "\\Z24Strain" „ModifyGraph lowTrip(left)=0.01,notation(left)=1 „ModifyGraph ZisZ(left)=1 „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G b_Si=sqrt(2)*a_Si/2 „Variable /G nu_Si=0.28 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_Si=(a_Ge-a_Si)/a_Si „Variable /G hc „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_Si) „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density=(x>hc)*Dislocation_density „Strain_theory=f_misfit_Si-Dislocation_density*b_Si*cos(lambda) „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G b_Si=sqrt(2)*a_Si/2 „Variable /G nu_Si=0.30 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_Si=(a_Ge-a_Si)/a_Si „Variable /G hc „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_Si) „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density=(x>hc)*Dislocation_density „Strain_theory=f_misfit_Si-Dislocation_density*b_Si*cos(lambda) „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G b_Si=sqrt(2)*a_Si/2 „Variable /G nu_Si=0.27 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_Si=(a_Ge-a_Si)/a_Si „Variable /G hc „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_Si) „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density=(x>hc)*Dislocation_density „Strain_theory=f_misfit_Si-Dislocation_density*b_Si*cos(lambda) „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G b_Si=sqrt(2)*a_Si/2 „Variable /G nu_Si=0.28 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_Si=(a_Ge-a_Si)/a_Si „Variable /G hc „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_Si) „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density=(x>hc)*Dislocation_density „Strain_theory=f_misfit_Si-Dislocation_density*b_Si*cos(lambda) „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable/G factor=1 „Variable /G b_Si=factor*sqrt(2)*a_Si/2 „Variable /G nu_Si=0.28 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_Si=(a_Ge-a_Si)/a_Si „Variable /G hc „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_Si) „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density=(x>hc)*Dislocation_density „Strain_theory=f_misfit_Si-Dislocation_density*b_Si*cos(lambda) „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable/G factor=1.2 „Variable /G b_Si=factor*sqrt(2)*a_Si/2 „Variable /G nu_Si=0.28 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_Si=(a_Ge-a_Si)/a_Si „Variable /G hc „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_Si) „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density=(x>hc)*Dislocation_density „Strain_theory=f_misfit_Si-Dislocation_density*b_Si*cos(lambda) „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable/G factor=1.3 „Variable /G b_Si=factor*sqrt(2)*a_Si/2 „Variable /G nu_Si=0.28 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_Si=(a_Ge-a_Si)/a_Si „Variable /G hc „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_Si) „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density=(x>hc)*Dislocation_density „Strain_theory=f_misfit_Si-Dislocation_density*b_Si*cos(lambda) „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable/G factor=0.9 „Variable /G b_Si=factor*sqrt(2)*a_Si/2 „Variable /G nu_Si=0.28 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_Si=(a_Ge-a_Si)/a_Si „Variable /G hc „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_Si) „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density=(x>hc)*Dislocation_density „Strain_theory=f_misfit_Si-Dislocation_density*b_Si*cos(lambda) „ModifyGraph rgb=(0,0,0) „ModifyGraph msize(Strain)=4 „TextBox/C/N=text0/F=0/A=MC "\\Z36\\f01Si/Ge" „Label bottom "\\Z24 Si layer thickness (nm)" „SavePICT/E=-5/B=288 „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density_2=(1-CriticalThickness(Parameter,f_misfit_Si)/x )*f_misfit_Si/(b_Si*cos(lambda)) „Duplicate Strain_theory Strain_theory_2 „Dislocation_density_2=(1-hc/x )*f_misfit_Si/(b_Si*cos(lambda)) „Dislocation_density_2=(x>hc)*Dislocation_density „Dislocation_density_2=(1-hc/x )*f_misfit_Si/(b_Si*cos(lambda)) „Dislocation_density_2=(x>hc)*Dislocation_density „Duplicate Dislocation_density_2 Test „AppendToTable Test „Test=(x>hc) „Dislocation_density_2=(1-hc/x )*f_misfit_Si/(b_Si*cos(lambda)) „Dislocation_density_2=(x>hc)*Dislocation_density_2 „Strain_theory_2=f_misfit_Si-Dislocation_density_2*b_Si*cos(lambda) „AppendToGraph Strain_theory_2 „ModifyGraph rgb=(0,0,0),mode(Strain_theory_2)=0,lstyle(Strain_theory_2)=2 „Rename Thick_nm,Thick_RBS_nm; „Rename wave0,Thick_TEM_nm; „AppendToGraph StrainRel vs Thick_TEM_nm „Display StrainRel vs Thick_TEM_nm „RemoveFromGraph StrainRel „AppendToGraph Strain vs Thick_TEM_nm „ModifyGraph rgb=(0,0,0),mode(Strain#1)=3,marker(Strain#1)=8 „ModifyGraph msize(Strain#1)=4,mrkThick(Strain#1)=1,opaque(Strain#1)=1 „Make/O/N=6 Strain = D_Freq/733 „Make/O/N=6 freq_Conf = 602/((4*Thick_RBS_nm/0.5431) + 1)^2.46 „Make/O/N=6 freq_Conf = 602/((4*Thick_RBS_nm/0.5431) + 1)^2.46 „AppendToTable freq_Conf „Make/O/N=6 D_Freq = 521-(Freq + freq_Conf) „Make/O/N=6 freq_Conf = 602/((4*Thick_RBS_nm/0.5431) + 1)^2.46 „Make/O/N=6 D_Freq = 521-(Freq + freq_Conf) „Make/O/N=6 Strain = D_Freq/733 „Make/O/N=6 StrainRel = (1 - (Strain/0.042)) „Make/O/N=6 StrainRel = (1 - (Strain/0.042)) „Make/O/N=6 freq_Conf = 602/((4*Thick_RBS_nm/0.5431) + 1)^2.46 „Make/O/N=6 D_Freq = 521-(Freq + freq_Conf) „Make/O/N=6 Strain = D_Freq/733 „ „Make/O/N=6 StrainRel = (1 - (Strain/0.042)) „Make/O/N=6 StrainRel = 100*(1 - (Strain/0.042)) „ErrorBars Strain Y,wave=(wave0,wave1) „ErrorBars/L=2 Strain Y,wave=(wave0,wave1) „ErrorBars/T=2/L=2 Strain Y,wave=(wave0,wave1) „Rename wave1,Strain_error_minus_RBS; „Rename wave0,Strain_error_plus_RBS; „Print b_Si 0.345618 „SavePICT/E=-5/B=288 „Duplicate Dislocation_density Dislocation_density_SiGe „Duplicate Strain_theory Strain_theory_SiGe „Equilibrium_strain() „Equilibrium_strain() „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G a_SiGe=(a_Si+a_Ge)/2 „Variable/G factor=1//This fake factor is to see what is the effect of changing the parameters „Variable /G b_SiGe=factor*sqrt(2)*a_SiGe/2 „Variable /G nu_Si=0.28//This needs to be changed SiGe, but the difference is small „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_SiGe=(a_Ge-a_SiGe)/a_SiGe „Variable /G hc „Parameter[0]= b_SiGe „Parameter[1]= f_misfit_SiGe „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_SiGe) „Dislocation_density_SiGe=f_misfit_SiGe/(b_SiGe*cos(lambda))-ln(4*x/b_SiGe)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density_SiGe=(x>hc)*Dislocation_density „Strain_theory_SiGe=f_misfit_SiGe-Dislocation_density*b_SiGe*cos(lambda) „Display Strain_theory_SiGe „Edit Strain_theory_SiGe.id „AppendToTable Strain_theory.id „SetAxis/A bottom „Print hc 4.17235 „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable/G factor=1//This fake factor is to see what is the effect of changing the parameters „Variable /G b_Si=factor*sqrt(2)*a_Si/2 „Variable /G nu_Si=0.28 „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_Si=(a_Ge-a_Si)/a_Si „Variable /G hc „Parameter[0]= b_Si „Parameter[1]= f_misfit_Si „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_Si) „Dislocation_density=f_misfit_Si/(b_Si*cos(lambda))-ln(4*x/b_Si)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density=(x>hc)*Dislocation_density „Strain_theory=f_misfit_Si-Dislocation_density*b_Si*cos(lambda) „Print hc 1.44832 „Print A_SiGe 0.554383 „AppendToTable Dislocation_density_SiGe.id „Dislocation_density_SiGe=0 „Dislocation_density_SiGe=f_misfit_SiGe/(b_SiGe*cos(lambda))-ln(4*x/b_SiGe)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density_SiGe=(x>hc)*Dislocation_density „Print f_misfit_SiGe 0.0203776 „Strain_theory_SiGe=f_misfit_SiGe-Dislocation_density*b_SiGe*cos(lambda) „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G a_SiGe=(a_Si+a_Ge)/2 „Variable/G factor=1//This fake factor is to see what is the effect of changing the parameters „Variable /G b_SiGe=factor*sqrt(2)*a_SiGe/2 „Variable /G nu_Si=0.28//This needs to be changed SiGe, but the difference is small „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_SiGe=(a_Ge-a_SiGe)/a_SiGe „Variable /G hc „Parameter[0]= b_SiGe „Parameter[1]= f_misfit_SiGe „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_SiGe) „Dislocation_density_SiGe=f_misfit_SiGe/(b_SiGe*cos(lambda))-ln(4*x/b_SiGe)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density_SiGe=(x>hc)*Dislocation_density „Strain_theory_SiGe=f_misfit_SiGe-Dislocation_density*b_SiGe*cos(lambda) „Print hc 4.17235 „RemoveFromTable Strain_theory.id „Print f_misfit_SiGe 0.0203776 „Print (1>hc) 0 „Print (5>hc) 1 „Print Dislocation_density_SiGe[0] 0 „Print Dislocation_density_SiGe[2] -0 „Print b_SiGe*cos(lambda) 0.196004 „Print Dislocation_density_SiGe[2]*b_SiGe*cos(lambda) -0 „Print f_misfit_SiGe-Dislocation_density_SiGe[2]*b_SiGe*cos(lambda) 0.0203776 „Print Dislocation_density_SiGe[15] 0 „Print Dislocation_density_SiGe[15]*b_SiGe*cos(lambda) 0 „Print f_misfit_SiGe-Dislocation_density_SiGe[2]*b_SiGe*cos(lambda) 0.0203776 „Make/N=1000/D misfit „misfit=100 „AppendToTable misfit.id „misfit=f_misfit_SiGe „Strain_theory_SiGe=misfit-Dislocation_density*b_SiGe*cos(lambda) „Strain_theory_SiGe=misfit-Dislocation_density_SiGe*b_SiGe*cos(lambda) „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G a_SiGe=(a_Si+a_Ge)/2 „Variable/G factor=1//This fake factor is to see what is the effect of changing the parameters „Variable /G b_SiGe=factor*sqrt(2)*a_SiGe/2 „Variable /G nu_Si=0.28//This needs to be changed SiGe, but the difference is small „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_SiGe=(a_Ge-a_SiGe)/a_SiGe „Variable /G hc „Parameter[0]= b_SiGe „Parameter[1]= f_misfit_SiGe „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_SiGe) „Dislocation_density_SiGe=f_misfit_SiGe/(b_SiGe*cos(lambda))-ln(4*x/b_SiGe)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density_SiGe=(x>hc)*Dislocation_density „misfit=f_misfit_SiGe „Strain_theory_SiGe=misfit-Dislocation_density_SiGe*b_SiGe*cos(lambda) „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G a_SiGe=(a_Si+a_Ge)/2 „Variable/G factor=1//This fake factor is to see what is the effect of changing the parameters „Variable /G b_SiGe=factor*sqrt(2)*a_SiGe/2 „Variable /G nu_Si=0.28//This needs to be changed SiGe, but the difference is small „Variable /G mixed=(1-nu_Si*(cos(beta))^2)/(1+nu_Si) „Variable /G f_misfit_SiGe=(a_Ge-a_SiGe)/a_SiGe „Variable /G hc „Parameter[0]= b_SiGe „Parameter[1]= f_misfit_SiGe „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_SiGe) „Dislocation_density_SiGe=f_misfit_SiGe/(b_SiGe*cos(lambda))-ln(4*x/b_SiGe)*mixed/(8*pi*x*(cos(lambda))^2) „Dislocation_density_SiGe=(x>hc)*Dislocation_density_SiGe „misfit=f_misfit_SiGe „Strain_theory_SiGe=misfit-Dislocation_density_SiGe*b_SiGe*cos(lambda) „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G Ge_concentration=0.5 „Variable /G a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „Variable/G factor=1//This fake factor is to see what is the effect of changing the parameters „Variable /G b_SiGe=factor*sqrt(2)*a_SiGe/2 „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G Ge_concentration=0.5 „Variable /G a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „Variable/G factor=1//This fake factor is to see what is the effect of changing the parameters „Variable /G b_SiGe=factor*sqrt(2)*a_SiGe/2 „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G Ge_concentration=0.5 „Variable /G a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „Variable/G factor=1//This fake factor is to see what is the effect of changing the parameters „Variable /G b_SiGe=factor*sqrt(2)*a_SiGe/2 „Variable /G nu_Si=0.28 „Variable /G nu_Ge=0.27 „Variable /G mu_Si=51.1 „Variable /G mu_Ge=40.13 „Variable /G nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „Variable /G mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „Variable /G mixed=(1-nu_SiGe*(cos(beta))^2)/(1+nu_SiGe) „Variable /G f_misfit_SiGe=(a_Si-a_SiGe)/a_SiGe „Variable /G hc „Parameter[0]= b_SiGe „Parameter[1]= f_misfit_SiGe „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_SiGe) „Print hc 0 „ „Variable /G lambda=pi/3 „Variable /G beta=pi/3 „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G Ge_concentration=0.5 „Variable /G a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „Variable/G factor=1//This fake factor is to see what is the effect of changing the parameters „Variable /G b_SiGe=factor*sqrt(2)*a_SiGe/2 „Variable /G nu_Si=0.28 „Variable /G nu_Ge=0.27 „Variable /G mu_Si=51.1 „Variable /G mu_Ge=40.13 „Variable /G nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „Variable /G mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „ „Variable /G mixed=(1-nu_SiGe*(cos(beta))^2)/(1+nu_SiGe) „Variable /G f_misfit_SiGe=(a_Si-a_SiGe)/a_SiGe „Variable /G hc „Parameter[0]= b_SiGe „Parameter[1]= f_misfit_SiGe „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_SiGe) „ „Print hc 0 „Print mu_SiGe 45.615 „Print F_misfit_SiGe -0.0203776 „Variable /G f_misfit_SiGe=abs((a_Si-a_SiGe)/a_SiGe) „Variable /G hc „Parameter[0]= b_SiGe „Parameter[1]= f_misfit_SiGe „Parameter[2]=lambda „Parameter[3]=mixed „hc=CriticalThickness(Parameter,f_misfit_SiGe) „ „Print hc 4.20235 „Make/D wave1,wave2 „SetScale/I x 0,4,"", Critical_Function „SetScale/I x 0,4,"", wave1,wave2 „wave1=x „wave2=1.1*ln(10*x) „Display wave1,wave2 „SetScale/I x 0,10,"", wave1,wave2 „wave1=x „wave2=1.1*ln(10*x) „Print cos (60) -0.952413 „Print cos (pi*60/180) 0.5 „Make/N=1/D Conc_wave „Variable /G Growth_Temp= 700 //This is the growth temperature in K „Variable /G Growth_rate=1 // This is the growth rate in nm/s „Variable /G Ge_concentration=0.5 //This is the Ge concentration „Conc_wave[0]=Ge_Concentration „Variable /G hc=CriticalThicknessHoughton(Ge_concentration) „Print hc 0.110575 „Print Ge_Concentration 0.5 „Print w[0] 0.5 „FindRoots CriticalThicknessHoughtonRoot, w Possible root found at 0.110575 Y value there is 3.20422e-08 „Make/N=1000/D Root_test „SetScale/I x 0,10,"", Root_test „Root_test=(0.55/w[0])*ln(10*x)-x „Display Root_test „Duplicate Root_test Root_test_1,Root_test_2 „Root_test=(0.55/w[0])*ln(10*x)-x „Root_test_1=(0.55/w[0])*ln(10*x) „Root_test_2=x „Display Root_test_1,Root_test_2 „FindRoots CriticalThicknessHoughtonRoot, w Possible root found at 0.110575 Y value there is 3.20422e-08 „FindRoots CriticalThicknessHoughtonRoot, w Possible root found at 0.110575 Y value there is 3.20422e-08 „Variable /G hc=CriticalThicknessHoughton(Ge_concentration) „Print hc 4.07938 „Variable /G Ge_concentration=1 //This is the Ge concentration „Conc_wave[0]=Ge_Concentration „Variable /G hc=CriticalThicknessHoughton(Ge_concentration) „Print hc 0 „Variable /G hc=CriticalThicknessHoughton(Ge_concentration) „Print hc 0 „Root_test=(0.55/w[0])*ln(10*x)-x „Root_test_1=(0.55/w[0])*ln(10*x) „Root_test_2=x „Print Ge_Concentration 1 „KillWaves w „Variable /G hc=CriticalThicknessHoughton(Ge_concentration) „Print hc 0 „Edit w.id „FindRoots /L=1 /H=10 CriticalThicknessHoughtonRoot, w Possible root found at 1.48325 Y value there is 2.25132e-09 „Variable /G hc=CriticalThicknessHoughton(Ge_concentration) „Print hc 1.48325 „Variable /G Ge_concentration=0.5 //This is the Ge concentration „Conc_wave[0]=Ge_Concentration „Variable /G hc=CriticalThicknessHoughton(Ge_concentration) „Print hc 4.07938 „Variable /G Growth_Temp= 700 //This is the growth temperature in K „Variable /G Growth_rate=1 // This is the growth rate in nm/s „Variable /G Ge_concentration=0.5 //This is the Ge concentration „Conc_wave[0]=Ge_Concentration „Variable /G Kn=1e18*(cos(pi*35/180)*exp(-2.5/(8.617e-5*Growth_Temp))*(1+nu_SiGe)/(1-nu_SiGe))^2.5 „Variable /G Kn=1e18*(cos(pi*35/180)*exp(-2.5/(8.617e-5*Growth_Temp))*(1+nu_SiGe)/(1-nu_SiGe))^2.5 „Variable V_not=4e18 „Variable /G Kn=1e18*(cos(pi*35/180)*exp(-2.5/(8.617e-5*Growth_Temp))*(1+nu_SiGe)/(1-nu_SiGe))^2.5 „Variable /G V_not=4e18 „Variable /G Km = V_not*b_SiGe*cos (lambda) „Variable /G Km = V_not*b_SiGe*cos (lambda)*exp(-2.25/(8.617e-5*Growth_Temp)) „Variable /G Km = V_not*b_SiGe*cos (lambda)*exp(-2.25/(8.617e-5*Growth_Temp))*((1+nu_SiGe)/(1-nu_SiGe))^2 „Make /D/O/N=(500,2) System „SetScale /P x 0,10,System „SetDimLabel 1,0,N,System „SetDimLabel 1,1,epsilon,System „Make/N=6/D Houghton_wave „Houghton_wave[0]=Kn „Redimension/N=7 Houghton_wave „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Variable /G hc=CriticalThicknessHoughton(Ge_concentration) „Variable /G tc=hc/Growth_rate „Houghton_wave[5]=tc „Houghton_wave[6]=Growth_rate „System[0][%N]=1e-17 „System[0][%epsilon]=0 „Display System[][%N] „AppendToGraph System[][%epsilon] „IntegrateODE Derivatives,Houghton_wave, System „Edit System.id „System=0 „System[0][%N]=1e-17 „System[0][%epsilon]=0 „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=tc „Houghton_wave[6]=Growth_rate „IntegrateODE Derivatives,Houghton_wave, System „System=0 „System[0][%N]=1 „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „System=0 „System[0][%N]=1 „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „Edit Houghton_wave.id „Variable /G Kn=1e18*(cos(pi*35/180)*exp(-2.5/(8.617e-5*Growth_Temp))*(1+nu_SiGe)/(1-nu_SiGe))^2.5 „Houghton_wave[0]=Kn „Variable /G Kn=1e18*(cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^2.5*exp(-2.5/(8.617e-5*Growth_Temp)) „Houghton_wave[0]=Kn „System=0 „System[0][%N]=1 „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System ODE integration aborted; completed calculation for element 1 „System=0 „System[0][%N]=1 „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „System=0 „System[0][%N]=1 „System[0][%epsilon]=0 „System=0 „System[0][%N]=1 „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System ODE integration aborted; completed calculation for element 359 „System=0 „System[0][%N]=1 „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „System=0 „System[0][%N]=1 „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „System=0 „System[0][%N]=1 „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „System=0 „System[0][%N]=1 „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „System=0 „System[0][%N]=1e-10 „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „System=0 „System[0][%N]=1e-10 „System[0][%epsilon]=0 „Variable /G tt=0 „Variable /G D „D=Houghton_wave[3]-0.55*ln(4*Houghton_wave[6]*(Houghton_wave[5]+tt)/Houghton_wave[4])/(Houghton_wave[6]*(Houghton_wave[5]+tt)) „Print D -0.00272107 „Variable /G tt=0 „Variable /G D „Variable /G dNdt „dNdt=Houghton_wave[0]*((Houghton_wave[2]-System[0][%epsilon])*D)^2.5 „Print dNdT NaN „Print System[0][%epsilon] 0 „dNdt=Houghton_wave[0]*((Houghton_wave[2]-System[0][%epsilon])*D)^2.5 „Print dNdt NaN „Print Houghton_wave[0] 2.49137 „Print (Houghton_wave[2]-System[0][%epsilon]) 0.0203776 „Print Houghton_wave[2] 0.0203776 „Print tc 4.07938 „Variable /G tt=10 „Variable /G D „Variable /G dNdt „D=Houghton_wave[3]-0.55*ln(4*Houghton_wave[6]*(Houghton_wave[5]+tt)/Houghton_wave[4])/(Houghton_wave[6]*(Houghton_wave[5]+tt)) „ „Print D 0.305949 „tc=5 „Houghton_wave[5]=tc „Houghton_wave[6]=Growth_rate „Variable /G tt=0 „Variable /G D „Variable /G dNdt „D=Houghton_wave[3]-0.55*ln(4*Houghton_wave[6]*(Houghton_wave[5]+tt)/Houghton_wave[4])/(Houghton_wave[6]*(Houghton_wave[5]+tt)) „Print D 0.0674574 „Variable /G tc=hc/Growth_rate „Houghton_wave[5]=1.01*tc „Variable /G tt=0 „Variable /G D „Variable /G dNdt „D=Houghton_wave[3]-0.55*ln(4*Houghton_wave[6]*(Houghton_wave[5]+tt)/Houghton_wave[4])/(Houghton_wave[6]*(Houghton_wave[5]+tt)) „ „Print D 0.000928102 „dNdt=Houghton_wave[0]*((Houghton_wave[2]-System[0][%epsilon])*D)^2.5 „Print dNdt 3.87534e-12 „System=0 „System[0][%N]=1e-10 „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „ModifyGraph rgb(System#1)=(1,16019,65535) „Legend/C/N=text0/F=0/S=3/A=MC „Print b_SiGe 0.392008 „Variable /G V_not=4e20 „Variable /G N_not=5e-11 //This is the density of incipient nuclei at time zero. It could be taken as //the number of dislocations at time zero, but other defects may also act as nucleation sites for //dislocations. „Variable /G Qv=2.25 //This is in eV. „Variable /G B_disloc=1e18 „Variable /G Qn=2.5 //This is in eV. „Variable /G n_exponent= 2.5 „Variable /G m_exponent=2 „Variable /G Kn=B_disloc*N_not*((cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Variable /G Km = V_not*b_SiGe*cos (lambda)*exp(-Qv/(8.617e-5*Growth_Temp))*((1+nu_SiGe)/(1-nu_SiGe))^2 „Variable /G Growth_Temp= 700 //This is the growth temperature in K „Variable /G Growth_rate=0.5 // This is the growth rate in nm/s „Variable /G Ge_concentration=0.5 //This is the Ge concentration „Conc_wave[0]=Ge_Concentration „Variable /G hc=CriticalThicknessHoughton(Ge_concentration) „Variable /G tc=hc/Growth_rate „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „Variable /G b_SiGe=factor*sqrt(2)*a_SiGe/2 // Houighton uses a fixed 0.4 nm „Variable /G lambda=pi/3 „Variable /G nu_Si=0.28 „Variable /G nu_Ge=0.27 „Variable /G mu_Si=51.1 „Variable /G mu_Ge=40.13 „Variable /G nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „Variable /G mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „Variable /G V_not=4e20 „Variable /G N_not=5e-11 „Variable /G Qv=2.25 //This is in eV. „Variable /G B_disloc=1e18 „Variable /G Qn=2.5 //This is in eV. „Variable /G n_exponent= 2.5 „Variable /G m_exponent=2 „Variable /G Kn=B_disloc*N_not*((cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „ „Variable /G Km = V_not*b_SiGe*cos (lambda)*exp(-Qv/(8.617e-5*Growth_Temp))*((1+nu_SiGe)/(1-nu_SiGe))^2 „ „Variable /G f_misfit_SiGe=abs((a_Si-a_SiGe)/a_SiGe) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=1.01*tc „Houghton_wave[6]=Growth_rate „IntegrateODE Derivatives,Houghton_wave, System „Display System[][%N] „AppendToGraph System[][%epsilon] „ModifyGraph mirror(left)=0,standoff(left)=0 „RemoveFromGraph System#1 „AppendToGraph System[][%epsilon] „Display Critical_Function „AppendToGraph/R Critical_Thickness „Display System[][%N] „Display System[][%epsilon] „SetScale/P x 0,100,"", System „IntegrateODE Derivatives,Houghton_wave, System „SetScale/P x 0,1000,"", System „IntegrateODE Derivatives,Houghton_wave, System „SetScale/P x 0,10000,"", System „IntegrateODE Derivatives,Houghton_wave, System „SetScale/P x 0,100000,"", System „IntegrateODE Derivatives,Houghton_wave, System „Variable /G Growth_Temp= 823 //This is the growth temperature in K „Variable /G Growth_rate=0.5 // This is the growth rate in nm/s „Variable /G Ge_concentration=0.5 //This is the Ge concentration „Conc_wave[0]=Ge_Concentration „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „Variable /G b_SiGe=factor*sqrt(2)*a_SiGe/2 // Houighton uses a fixed 0.4 nm „Variable /G lambda=pi/3 „Variable /G nu_Si=0.28 „Variable /G nu_Ge=0.27 „Variable /G mu_Si=51.1 „Variable /G mu_Ge=40.13 „Variable /G nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „Variable /G mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „Variable /G V_not=4e20 „Variable /G N_not=5e-11 „Variable /G Qv=2.25 //This is in eV. „Variable /G B_disloc=1e18 „Variable /G Qn=2.5 //This is in eV. „Variable /G n_exponent= 2.5 „Variable /G m_exponent=2 „Variable /G Kn=B_disloc*N_not*((cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „ „Variable /G Km = V_not*b_SiGe*cos (lambda)*exp(-Qv/(8.617e-5*Growth_Temp))*((1+nu_SiGe)/(1-nu_SiGe))^2 „ „Variable /G f_misfit_SiGe=abs((a_Si-a_SiGe)/a_SiGe) „Make /D/O/N=(500,2) System „SetScale /P x 0,10,System „SetDimLabel 1,0,N,System „SetDimLabel 1,1,epsilon,System „System=0 „System[0][%N]=5e-11//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=1.01*tc „Houghton_wave[6]=Growth_rate „IntegrateODE Derivatives,Houghton_wave, System „SetScale /P x 0,5,System „IntegrateODE Derivatives,Houghton_wave, System „SetScale /P x 0,1,System „IntegrateODE Derivatives,Houghton_wave, System „Print hc 4.07938 „Print Growth_rate 0.5 „Print Growth_Temp 823 „mu_SiGe=64 „Variable /G Kn=B_disloc*N_not*((cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Variable /G Km = V_not*b_SiGe*cos (lambda)*exp(-Qv/(8.617e-5*Growth_Temp))*((1+nu_SiGe)/(1-nu_SiGe))^2 „ „Variable /G f_misfit_SiGe=abs((a_Si-a_SiGe)/a_SiGe) „Print mu_SiGe 64 „Variable /G mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „Print mu_SiGe 45.615 „IntegrateODE Derivatives,Houghton_wave, System „SetScale /P x 0,2,System „IntegrateODE Derivatives,Houghton_wave, System „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=1.001*tc „Houghton_wave[6]=Growth_rate „IntegrateODE Derivatives,Houghton_wave, System „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=1.002*tc „Houghton_wave[6]=Growth_rate „ „ „IntegrateODE Derivatives,Houghton_wave, System „System=0 „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=1.003*tc „Houghton_wave[6]=Growth_rate „ „ „IntegrateODE Derivatives,Houghton_wave, System „System=0 „System[0][%N]=5e-11//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=1.005*tc „Houghton_wave[6]=Growth_rate „ „ „IntegrateODE Derivatives,Houghton_wave, System „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=1.009*tc „Houghton_wave[6]=Growth_rate „ „ „IntegrateODE Derivatives,Houghton_wave, System „Print cos(pi*35/180) 0.819152 „Make/N=1000/D Houghton_relaxation „SetScale /P x 0,2,Houghton_relaxation „Duplicate Houghton_relaxation log_wave „log_wave=(f_misfit_SiGe*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe)) „log_wave=(f_misfit_SiGe*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))*(Ge_concentration-0.55*ln(10*Growth_rate*(tc+x)/(Growth_rate*(tc+x)))) „Houghton_relaxation=0.5*B_disloc*V_not*N_not*b_SiGe*cos(lambda)*exp(4.75/(8.617e-5*Growth_Temp))*(log_wave)^4.5 „AppendToGraph Houghton_relaxation „RemoveFromGraph Houghton_relaxation „Make /D/O/N=(500,2) System „SetScale /P x 0,2,System „SetDimLabel 1,0,N,System „SetDimLabel 1,1,epsilon,System „System[0][%N]=5e-11//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=1.009*tc „Houghton_wave[6]=Growth_rate „IntegrateODE Derivatives,Houghton_wave, System „log_wave=(f_misfit_SiGe*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))*(Ge_concentration-0.55*ln(10*Growth_rate*(tc+x)/(Growth_rate*(tc+x)))) „Houghton_relaxation=0.5*B_disloc*V_not*N_not*b_SiGe*cos(lambda)*exp(4.75/(8.617e-5*Growth_Temp))*(log_wave)^4.5 „AppendToGraph Houghton_relaxation „ModifyGraph mode(Houghton_relaxation)=3,marker(Houghton_relaxation)=19;DelayUpdate „ModifyGraph rgb(Houghton_relaxation)=(0,0,0) „AppendToTable Houghton_relaxation.id „log_wave=(f_misfit_SiGe*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))*(Ge_concentration-0.55*ln(10*Growth_rate*(1.009*tc+x)/(Growth_rate*(1.009*tc+x)))) „Houghton_relaxation=0.5*B_disloc*V_not*N_not*b_SiGe*cos(lambda)*exp(4.75/(8.617e-5*Growth_Temp))*(log_wave)^4.5 „AppendToTable log_wave.id „log_wave=(f_misfit_SiGe*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))*(Ge_concentration-0.55*ln(10*Growth_rate*(1.01*tc+x)/(Growth_rate*(1.01*tc+x)))) „log_wave=(f_misfit_SiGe*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))*(Ge_concentration-0.55*ln((4/b_SiGe)*Growth_rate*(1.009*tc+x)/(Growth_rate*(1.009*tc+x)))) „Print 4*Growth_rate*tc/b_SiGe 41.6255 „Duplicate Houghton_relaxation Houghton_Thickness „System=0 „System[0][%N]=5e-11//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=tc „Houghton_wave[6]=Growth_rate „ „ „IntegrateODE Derivatives,Houghton_wave, System „System=0 „IntegrateODE Derivatives,Houghton_wave, System „Thickness=hc+Growth_rate*x „Rename log_wave,Stress_Houghton_over_mu; „Stress_Houghton_over_mu=(f_misfit_SiGe*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))*(Ge_concentration-(0.55/Thickness)*ln(4*Thickness/b_SiGe)) „Houghton_relaxation=0.5*B_disloc*V_not*N_not*b_SiGe*cos(lambda)*exp(4.75/(8.617e-5*Growth_Temp))*(Stress_Houghton_over_mu)^4.5 „Houghton_relaxation=0.5*B_disloc*V_not*N_not*b_SiGe*cos(lambda)*exp(-4.75/(8.617e-5*Growth_Temp))*(Stress_Houghton_over_mu)^4.5 „System=0 „System[0][%N]=0//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=tc „Houghton_wave[6]=Growth_rate „IntegrateODE Derivatives,Houghton_wave, System „Houghton_relaxation=(x^2)*0.5*B_disloc*V_not*N_not*b_SiGe*cos(lambda)*exp(-4.75/(8.617e-5*Growth_Temp))*(Stress_Houghton_over_mu)^4.5 „SetAxis bottom 0,100 „SetAxis left 0,2e-05 „SetAxis bottom 0,300 „Houghton_relaxation=0.5*(x^2)*Kn*Km*(Stress_Houghton_over_mu)^4.5 „Variable /G Kn=B_disloc*N_not*((cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „ „Variable /G Km = V_not*b_SiGe*cos (lambda)*exp(-Qv/(8.617e-5*Growth_Temp))*((1+nu_SiGe)/(1-nu_SiGe))^2 „Houghton_relaxation=0.5*(x^2)*Kn*Km*(Stress_Houghton_over_mu)^4.5 „Houghton_relaxation=(x^2)*0.5*B_disloc*V_not*N_not*b_SiGe*cos(lambda)*exp(-4.75/(8.617e-5*Growth_Temp))*(Stress_Houghton_over_mu)^4.5 „Rename Stress_Houghton_over_mu,effective_concentration; „effective_concentration=Ge_concentration-(0.55/Thickness)*ln(4*Thickness/b_SiGe) „Houghton_relaxation=0.5*(x^2)*Kn*Km*(effective_concentration)^4.5 „Variable /G Factor=1.01 „Thickness=Factor*(hc+Growth_rate*x) „ „effective_concentration=Ge_concentration-(0.55/Thickness)*ln(4*Thickness/b_SiGe) „Houghton_relaxation=0.5*(x^2)*Kn*Km*(effective_concentration)^4.5 „SetAxis bottom 0,100 „AppendToTable Thickness.id „System=0 „System[0][%N]=0//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „Thickness=20 „ „effective_concentration=Ge_concentration-(0.55/Thickness)*ln(4*Thickness/b_SiGe) „ „effective_concentration=Ge_concentration-(0.55/Thickness)*ln(4*Thickness/b_SiGe) „ „Houghton_relaxation=0.5*(x^2)*Kn*Km*(effective_concentration)^4.5 „Thickness=10 „ „effective_concentration=Ge_concentration-(0.55/Thickness)*ln(4*Thickness/b_SiGe) „ „Houghton_relaxation=0.5*(x^2)*Kn*Km*(effective_concentration)^4.5 „Thickness=Factor*(hc+Growth_rate*x) „Houghton_relaxation=0.5*(x^2)*Kn*Km*(effective_concentration)^4.5 „Thickness=Factor*(hc+Growth_rate*x) „effective_concentration=Ge_concentration-(0.55/Thickness)*ln(4*Thickness/b_SiGe) „ „Houghton_relaxation=0.5*(x^2)*Kn*Km*(effective_concentration)^4.5 „ModifyGraph mode=0 „ShowInfo „Variable /G Growth_Temp= 773 //This is the growth temperature in K „Variable /G Growth_rate=0.5 // This is the growth rate in nm/s „Variable /G Ge_concentration=0.5 //This is the Ge concentration „Conc_wave[0]=Ge_Concentration „Variable /G hc=CriticalThicknessHoughton(Ge_concentration) „Variable /G tc=hc/Growth_rate „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „Variable /G b_SiGe=factor*sqrt(2)*a_SiGe/2 // Houighton uses a fixed 0.4 nm „Variable /G lambda=pi/3 „Variable /G nu_Si=0.28 „Variable /G nu_Ge=0.27 „Variable /G mu_Si=51.1 „Variable /G mu_Ge=40.13 „Variable /G nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „Variable /G mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „Variable /G V_not=4e20 „Variable /G N_not=5e-11 //This is the density of incipient nuclei at time zero. It could be taken as //the number of dislocations at time zero, but other defects may also act as nucleation sites for //dislocations. „Variable /G Qv=2.25 //This is in eV. „Variable /G B_disloc=1e18 „Variable /G Qn=2.5 //This is in eV. „Variable /G n_exponent= 2.5 „Variable /G m_exponent=2 „Variable /G Kn=B_disloc*N_not*((cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „ „Variable /G Km = V_not*b_SiGe*cos (lambda)*exp(-Qv/(8.617e-5*Growth_Temp))*((1+nu_SiGe)/(1-nu_SiGe))^2 „ „Variable /G f_misfit_SiGe=abs((a_Si-a_SiGe)/a_SiGe) „Variable /G Factor=1.01 „Thickness=Factor*(hc+Growth_rate*x) „Thickness=10 „ „effective_concentration=Ge_concentration-(0.55/Thickness)*ln(4*Thickness/b_SiGe) „ „Houghton_relaxation=0.5*(x^2)*Kn*Km*(effective_concentration)^4.5 „Variable /G Factor=1.01 „Thickness=Factor*(hc+Growth_rate*x) „ „ „effective_concentration=Ge_concentration-(0.55/Thickness)*ln(4*Thickness/b_SiGe) „ „Houghton_relaxation=0.5*(x^2)*Kn*Km*(effective_concentration)^4.5 „Print b_SiGe 0.395928 „effective_concentration=Ge_concentration-(0.55/Thickness)*ln(10*Thickness) „Houghton_relaxation=0.5*(x^2)*Kn*Km*(effective_concentration)^4.5 „SetAxis/A bottom „SetAxis/A left „RemoveFromGraph Houghton_relaxation „System=0 „System[0][%N]=0//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=tc „Houghton_wave[6]=Growth_rate „ „ „IntegrateODE Derivatives,Houghton_wave, System „SetScale /P x 0,10,System „System=0 „System[0][%N]=0//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=tc „Houghton_wave[6]=Growth_rate „ „ „IntegrateODE Derivatives,Houghton_wave, System „SetScale /P x 0,100,System „System=0 „System[0][%N]=0//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=tc „Houghton_wave[6]=Growth_rate „ „ „IntegrateODE Derivatives,Houghton_wave, System „SetScale /P x 0,10000,System „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=tc „Houghton_wave[6]=Growth_rate „IntegrateODE Derivatives,Houghton_wave, System „SetScale /P x 0,1000,System „System=0 „System[0][%N]=0//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_SiGe „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=tc „Houghton_wave[6]=Growth_rate „ „ „IntegrateODE Derivatives,Houghton_wave, System „Variable /G lambda=pi/3 „Variable /G beta=pi/3 „Variable /G nu_Si=0.28 „Variable /G nu_Ge=0.27 „Variable /G mu_Si=51.1 „Variable /G mu_Ge=40.13 „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G Growth_Temp= 773 //This is the growth temperature in K „Variable /G Growth_rate=0.5 // This is the growth rate in nm/s „Variable /G Ge_concentration=0.5 //This is the Ge concentration „Variable /G h_max=100 //This is the final thickness of the film „Variable /G nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „Variable /G mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „Variable /G a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „Variable /G f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „Variable /G b_SiGe=factor*sqrt(2)*a_SiGe/2 // Houighton uses a fixed 0.4 nm „Variable /G factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe „Variable /G factor=(8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „Variable /G factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „Print factor 0.576156 „SetScale/I x 0,6000,"", System „Redimension/N=8 Houghton_wave „System=0 „Variable /G lambda=pi/3 „Variable /G beta=pi/3 „Variable /G nu_Si=0.28 „Variable /G nu_Ge=0.27 „Variable /G mu_Si=51.1 „Variable /G mu_Ge=40.13 „Variable /G a_Si=0.543086 „Variable /G a_Ge=0.56568 „Variable /G V_not=4e20 „Variable /G Qv=2.25 //This is in eV. „Variable /G B_disloc=1e18 „Variable /G Qn=2.5 //This is in eV. „Variable /G n_exponent= 2.5 „Variable /G m_exponent=2 „Variable /G Growth_Temp= 773 //This is the growth temperature in K „Variable /G Growth_rate=0.5 // This is the growth rate in nm/s „Variable /G Ge_concentration=0.5 //This is the Ge concentration „Variable /G h_max=100 //This is the final thickness of the film „Variable /G N_not=5e-11 //This is the number of fixed sources in the material, preexisting defects in substrate or buffer. „SetScale/I x 0,h_max/Growth_rate,"", System „Variable /G nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „Variable /G mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „Variable /G a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „Variable /G f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „Variable /G b_SiGe=sqrt(2)*a_SiGe/2 // Houighton uses a fixed 0.4 nm „Variable /G factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „Variable /G Kn=B_disloc*N_not*((cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „ „Variable /G Km = V_not*b_SiGe*cos (lambda)*exp(-Qv/(8.617e-5*Growth_Temp))*((1+nu_SiGe)/(1-nu_SiGe))^2 „ „Variable /G hc=CriticalThicknessHoughton(Ge_concentration) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „ „IntegrateODE Derivatives,Houghton_wave, System „Variable /G Growth_Temp= 773 //This is the growth temperature in K „Variable /G Growth_rate=0.05 // This is the growth rate in nm/s „Variable /G Ge_concentration=0.5 //This is the Ge concentration „Variable /G h_max=100 //This is the final thickness of the film „Variable /G N_not=5e-11 //This is the number of fixed sources in the material, preexisting defects in substrate or buffer. „SetScale/I x 0,h_max/Growth_rate,"", System „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „IntegrateODE Derivatives,Houghton_wave, System „Make/N=500/D e_approx „SetScale/I x 0,h_max/Growth_rate,"", e_approx „e_approx=Kn*Km*((Ge_concentration-factor/hc)^(m_exponent+n_exponent))*(x^(m_exponent+n_exponent+2))/((m_exponent+n_exponent+1)*(n_exponent+1)) „AppendToGraph e_approx „ModifyGraph rgb(e_approx)=(0,0,0) „ShowInfo „ShowTools/A „Legend/C/N=text0/F=0/S=3/A=MC „Variable /G Growth_Temp= 773 //This is the growth temperature in K „Variable /G Growth_rate=0.5// This is the growth rate in nm/s „Variable /G Ge_concentration=0.5 //This is the Ge concentration „Variable /G h_max=100 //This is the final thickness of the film „Variable /G N_not=5e-11 //This is the number of fixed sources in the material, preexisting defects in substrate or buffer. „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Variable /G Growth_Temp= 773 //This is the growth temperature in K „Variable /G Growth_rate=0.5// This is the growth rate in nm/s „Variable /G Ge_concentration=0.5 //This is the Ge concentration „Variable /G h_max=100 //This is the final thickness of the film „Variable /G N_not=5e-11 //This is the number of fixed sources in the material, preexisting defects in substrate or buffer. „Variable /G Kn=B_disloc*N_not*((cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „ „Variable /G Km = V_not*b_SiGe*cos (lambda)*exp(-Qv/(8.617e-5*Growth_Temp))*((1+nu_SiGe)/(1-nu_SiGe))^2 „ „Variable /G hc=CriticalThicknessHoughton(Ge_concentration) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „ „ „SetScale/I x 0,h_max/Growth_rate,"", System „SetScale/I x 0,h_max/Growth_rate,"", e_approx „IntegrateODE Derivatives,Houghton_wave, System „e_approx=Kn*Km*((Ge_concentration-factor/hc)^(m_exponent+n_exponent))*(x^(m_exponent+n_exponent+2))/((m_exponent+n_exponent+1)*(n_exponent+1)) „Variable /G eta=0 //This is the pinning probability, apparently equal to 1/9 from JAP 66 5837 „Redimension/N=9 Houghton_wave „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=eta „System=0 „IntegrateODE Derivatives,Houghton_wave, System „RemoveFromGraph e_approx „Variable /G Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „ „Variable /G Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „ „ „Variable /G Kp = eta*Km/(b_SiGe*cos(lambda) „ „Variable /G hc=CriticalThicknessHoughton(Ge_concentration) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=eta „System=0 „IntegrateODE Derivatives,Houghton_wave, System „Variable /G Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „ „Variable /G Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „ „ „Variable /G Kp = eta*Km/(b_SiGe*cos(lambda)) „System=0 „IntegrateODE Derivatives,Houghton_wave, System „Print Km,Kn,Kp 554.887 1.98987e-12 0 „Print exp(-Qv/(8.617e-5*Growth_Temp)) 2.13777e-15 „Print exp(-Qn/(8.617e-5*Growth_Temp)) 5.01138e-17 „Print b_SiGe 0.392008 „Print Kn,Km,Kp 1.98987e-12 554.887 0 „System=0 „System[0][%N]=5e-11//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „Print hc 4.07938 „Variable /G Growth_Temp= 823 //This is the growth temperature in K „Variable /G Growth_rate=0.5// This is the growth rate in nm/s „Variable /G Ge_concentration=0.5 //This is the Ge concentration „Variable /G h_max=100 //This is the final thickness of the film „Variable /G N_not=5e-11 //This is the number of fixed sources in the material, preexisting defects in substrate or buffer. „Variable /G Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „ „Variable /G Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „ „ „Variable /G Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „System[0][%N]=5e-11//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „Variable /G Kn=B_disloc*N_not*((cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „ „Variable /G Km = V_not*b_SiGe*cos (lambda)*exp(-Qv/(8.617e-5*Growth_Temp))*((1+nu_SiGe)/(1-nu_SiGe))^2 „ „Variable /G f_misfit_SiGe=abs((a_Si-a_SiGe)/a_SiGe) „Print Kn, Km 6.10311e-08 4.03538e+06 „Variable /G Houghton_relax „Variable /G Houghton_time=h_max/Growth_rate „Houghton_relax=0.5*B_disloc*N_not*b_SiGe*cos(lambda)*((Houghton_time)^2)*((730/64000)^4.5)*exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)) „Print Houghton_relax 2.88977e-27 „Variable /G h_max=1000 //This is the final thickness of the film „Variable /G Houghton_relax „Variable /G Houghton_time=h_max/Growth_rate „Houghton_relax=0.5*B_disloc*N_not*b_SiGe*cos(lambda)*((Houghton_time)^2)*((730/64000)^4.5)*exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)) „Print Houghton_relax 2.88977e-25 „Print (730/64000)^4.5 1.80777e-09 „Print exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)) 8.15559e-30 „Print 0.5*B_disloc*N_not*b_SiGe*cos(lambda) 4.9001e+06 „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „SetScale/I x 0,h_max/Growth_rate,"", System „ „System=0 „System[0][%N]=5e-11//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „Make/N=1000/D D_wave „SetScale/I x 0,1000,"", D_wave „D_wave=Test_D(Houghton_wave,x) „Display D_wave „SetAxis left -0.1,0.5 „TextBox/C/N=text0/F=0/S=3/A=MC "epsilon" „TextBox/C/N=text1/F=0/S=3/A=MC "Dislocation density" „Variable /G Growth_Temp= 823 //This is the growth temperature in K „Variable /G Growth_rate=0.5// This is the growth rate in nm/s „Variable /G Ge_concentration=0.5 //This is the Ge concentration „Variable /G h_max=100 //This is the final thickness of the film „Variable /G N_not=5e-11 //This is the number of fixed sources in the material, preexisting defects in substrate or buffer. „SetScale/I x 0,h_max/Growth_rate,"", System „Variable /G nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „Variable /G mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „Variable /G a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „Variable /G f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „Variable /G b_SiGe=sqrt(2)*a_SiGe/2 „Variable /G Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „ „Variable /G Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „ „ „Variable /G Kp = eta*Km/(b_SiGe*cos(lambda)) „ „Variable /G hc=CriticalThicknessHoughton(Ge_concentration) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „SetScale/I x 0,h_max/Growth_rate,"", System „ „System=0 „System[0][%N]=5e-11//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „SetAxis left 0,1e-05 „h_max=50 „SetScale/I x 0,h_max/Growth_rate,"", System „ „System=0 „System[0][%N]=5e-11//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max/Growth_rate,"", e_approx „e_approx=Kn*Km*((Ge_concentration-factor/hc)^(m_exponent+n_exponent))*(x^(m_exponent+n_exponent+2))/((m_exponent+n_exponent+2)*(n_exponent+1)) „AppendToGraph e_approx „SetAxis bottom 0,10 „SetAxis left 0,1e-11 „h_max=1 „SetScale/I x 0,h_max/Growth_rate,"", System „ „System=0 „System[0][%N]=5e-11//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max/Growth_rate,"", e_approx „e_approx=Kn*Km*((Ge_concentration-factor/hc)^(m_exponent+n_exponent))*(x^(m_exponent+n_exponent+2))/((m_exponent+n_exponent+2)*(n_exponent+1)) „SetAxis left 0,1e-10 „e_approx=Kn*Km*(Growth_rate*(Ge_concentration-factor/hc)^(m_exponent+n_exponent))*(x^(m_exponent+n_exponent+2))/((m_exponent+n_exponent+2)*(n_exponent+1)) „SetAxis bottom 0,2 „SetAxis left 0,5e-11 „Label bottom "Time (s)" „Label left "Strain relaxation" „Legend/C/N=text1/F=0/S=3/A=MC „TextBox/C/N=text2/F=0/S=3/A=MC "h_max= 1 nm" „Duplicate/O e_approx e_Houghton „e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,x))^4.5 „AppendToGraph e_Houghton „e_Houghton=9.4e3*5000*x*x*((700/60000)^4.5)*exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)) „e_Houghton=9.4e10*5000*x*x*((700/60000)^4.5)*exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)) „Edit e_Houghton „e_Houghton=9.4e15*5000*x*x*((700/60000)^4.5)*exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)) „e_Houghton=9.4e3*5000*x*x*((700)^4.5)*exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)) „SetAxis left 0,1e-05 „h_max=10 „SetScale/I x 0,h_max/Growth_rate,"", e_Houghton „//e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,x))^4.5 „e_Houghton=9.4e3*5000*x*x*((700)^4.5)*exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)) „h_max=20 „SetScale/I x 0,h_max/Growth_rate,"", e_Houghton „//e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,x))^4.5 „e_Houghton=9.4e3*5000*x*x*((700)^4.5)*exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)) „SetAxis/A bottom „h_max=25 „SetScale/I x 0,h_max/Growth_rate,"", e_Houghton „//e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,x))^4.5 „e_Houghton=9.4e3*5000*x*x*((700)^4.5)*exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)) „h_max=30 „SetScale/I x 0,h_max/Growth_rate,"", e_Houghton „//e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,x))^4.5 „e_Houghton=9.4e3*5000*x*x*((700)^4.5)*exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)) „SetAxis/A left „System=0 „System[0][%N]=5e-11//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „h_max=1 „SetScale/I x 0,h_max/Growth_rate,"", System „System=0 „System[0][%N]=5e-11//Use 5000 cm-2. This is the starting density of dislocations. It could contain other sources. „System[0][%epsilon]=0 „IntegrateODE Derivatives,Houghton_wave, System „h_max=100 „SetScale/I x 0,h_max/Growth_rate,"", System „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „h_max=1 //This is the final thickness of the film „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „hc=CriticalThicknessHoughton(Ge_concentration) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „h_max=100 „SetScale/I x 0,h_max/Growth_rate,"", e_Houghton „e_Houghton=9.4e3*5000*x*x*((700)^4.5)*exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)) „SetScale/I x 0,h_max/Growth_rate,"", e_approx „e_approx=Kn*Km*(Growth_rate*(Ge_concentration-factor/hc)^(m_exponent+n_exponent))*(x^(m_exponent+n_exponent+2))/((m_exponent+n_exponent+2)*(n_exponent+1)) „SetAxis left 0,1e-05 „e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,h_max/Growth_rate))^4.5 „Print Km*Kn*0.5/N_not 840.554 „Print 0.5*B_disloc*N_not*v_not*b_SiGe*cos(lambda) 1.96004e+27 „Print 0.5*B_disloc*N_not*v_not*b_SiGe*cos(lambda)/((mu_SiGe)^4.5) 6.70317e+19 „Print 0.5*B_disloc*v_not*b_SiGe*cos(lambda)/((mu_SiGe)^4.5) 1.34063e+30 „Print mu_SiGe 45.615 „Print v_not 4e+20 „Print v_not/(mu_SiGe)^2 1.9224e+17 „Print v_not/1e6 4e+14 „Print v_not/(1e6*mu_SiGe^2) 1.9224e+11 „Print v_not/(1e6*(mu_SiGe*1e3)^2) 192240 „Print 0.5*B_disloc*(v_not/1e6)*b_SiGe*cos(lambda)/((mu_SiGe*1000)^4.5) 4.23946e+10 7.84016e+25 „Print 0.5*B_disloc*(v_not/1e6)*(b_SiGe*1e-6)*cos(lambda)/((mu_SiGe*1000)^4.5) 42394.6 „Print 0.5*B_disloc*(v_not/1e6)*(b_SiGe*1e-6)*cos(lambda)/((mu_SiGe*1000)^4.5) 42394.6 „Print 0.5*B_disloc*(v_not/1e6)*(b_SiGe*1e-6)*cos(lambda)/((64*1000)^4.5) 9236.02 „Print 0.5*B_disloc*(v_not/1e6)*(0.4*1e-6)*cos(lambda)/((64*1000)^4.5) 9424.32 „h_max=50 „SetScale/I x 0,h_max/Growth_rate,"", System „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „h_max=1 //This is the final thickness of the film „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „hc=CriticalThicknessHoughton(Ge_concentration) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max/Growth_rate,"", e_approx „e_approx=Kn*Km*(Growth_rate*(Ge_concentration-factor/hc)^(m_exponent+n_exponent))*(x^(m_exponent+n_exponent+2))/((m_exponent+n_exponent+2)*(n_exponent+1)) „SetScale/I x 0,h_max/Growth_rate,"", e_Houghton „e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,h_max/Growth_rate))^4.5 „e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,h_max/Growth_rate))^4.5 „RemoveFromTable Houghton_relaxation.id,effective_concentration.id,Thickness.id „AppendToTable e_Houghton.id „SetScale/I x 0,h_max/Growth_rate,"", e_Houghton „h_max=50 //This is the final thickness of the film „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „SetScale/I x 0,h_max/Growth_rate,"", System „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „hc=CriticalThicknessHoughton(Ge_concentration) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max/Growth_rate,"", e_approx „e_approx=Kn*Km*(Growth_rate*(Ge_concentration-factor/hc)^(m_exponent+n_exponent))*(x^(m_exponent+n_exponent+2))/((m_exponent+n_exponent+2)*(n_exponent+1)) „SetScale/I x 0,h_max/Growth_rate,"", e_Houghton „e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,h_max/Growth_rate))^4.5 „Print 0.5*B_disloc*(v_not/1e6)*(b_SiGe*1e-6)*cos(lambda)/((64*1000)^4.5) 9236.02 „e_Houghton=e_Houghton*9424.32/9236.02 „Print factor 0.570452 „e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,h_max/Growth_rate))^4.5 „e_Houghton=e_Houghton*9424.32/9236.02 „Print factor 0.570452 „hc=CriticalThicknessHoughton(Ge_concentration,factor) „Print hc 4.28797 „e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,(h_max-hc)/Growth_rate))^4.5 „Print mu_SiGe*f_misfit_Si_Ge 1.82192 „Print mu_SiGe*f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) 1.12496 „Print 3.88*(Ge_concentration-0.55*ln(h_max)/h_max) 1.77303 „h_max=75 //This is the final thickness of the film „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max/Growth_rate,"", e_approx „e_approx=Kn*Km*(Growth_rate*(Ge_concentration-factor/hc)^(m_exponent+n_exponent))*(x^(m_exponent+n_exponent+2))/((m_exponent+n_exponent+2)*(n_exponent+1)) „SetScale/I x 0,h_max/Growth_rate,"", e_Houghton „e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,(h_max-hc)/Growth_rate))^4.5 „e_Houghton=e_Houghton*9424.32/9236.02 „Print 3.88*(Ge_concentration-0.55*ln(h_max)/h_max) 0.653153 „Print hc 13.848 „Print h_max 75 „Print 3.88*(Ge_concentration-0.55*ln(10*h_max)/h_max) 0.587637 „Print mu_SiGe*f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) 0.425349 „Print mu_SiGe*f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe) 2.83232 „Print Test_D(Houghton_wave,(h_max-hc)/Growth_rate) 0.150177 „Print mu_SiGe*f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) 0.425349 „Print 64*f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) 0.556625 „Print 64*f_misfit_Si_Ge*cos(pi*35/180)*(1+0.28)/(1-0.28)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) 0.559045 „Print 64*f_misfit_Si_Ge*cos(pi*35/180)*(1+0.28)/(1-0.28)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) 0.562909 „Print 64*f_misfit_Si_Ge*cos(pi*35/180)*(1+0.28)/(1-0.28)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) 0.563795 „Print f_misfit_Si_Ge 0.0399413 „Print 64*0.0418*cos(pi*35/180)*(1+0.28)/(1-0.28)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) 0.590032 „h_max=50 //This is the final thickness of the film „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max/Growth_rate,"", e_Houghton „e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,(h_max-hc)/Growth_rate))^4.5 „e_Houghton=e_Houghton*(0.0418/f_misfit_Si_Ge)^4.5 „Print exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)) 8.15559e-30 „Print mu_SiGe*f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) 1.13289 „Variable /G Stress_Houghton=mu_SiGe*f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) „ „Stress_Houghton=64*0.0411*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) „Print Stress_Houghton 1.63561 „e_Houghton=9.4e3*(exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)))*(N_not*1e12)*(Stress_Houghton*1000)^4.5 „e_Houghton=9.4e3*(exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)))*(N_not*1e12)*((h_max-hc)/Growth_rate)^2*(Stress_Houghton*1000)^4.5 „Variable /G final_e_Houghton=9.4e3*(exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)))*(N_not*1e12)*((h_max-hc)/Growth_rate)^2*(Stress_Houghton*1000)^4.5 „ „Print final_e_Houghton 9.27325e-06 „Variable /G Stress_Houghton=mu_SiGe*f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) „e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,(h_max-hc)/Growth_rate))^4.5 „Stress_Houghton=64*0.0411*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) „Print Stress_Houghton 1.63561 „h_max=50 //This is the final thickness of the film „Growth_Temp= 850 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max/Growth_rate,"", e_approx „e_approx=Kn*Km*(Growth_rate*(Ge_concentration-factor/hc)^(m_exponent+n_exponent))*(x^(m_exponent+n_exponent+2))/((m_exponent+n_exponent+2)*(n_exponent+1)) „Stress_Houghton=64*0.0411*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) „Variable /G final_e_Houghton=9.4e3*(exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)))*(N_not*1e12)*((h_max-hc)/Growth_rate)^2*(Stress_Houghton*1000)^4.5 „ „Print final_e_Houghton 7.78433e-05 „h_max=30 //This is the final thickness of the film „Growth_Temp= 850 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max/Growth_rate,"", e_approx „e_approx=Kn*Km*(Growth_rate*(Ge_concentration-factor/hc)^(m_exponent+n_exponent))*(x^(m_exponent+n_exponent+2))/((m_exponent+n_exponent+2)*(n_exponent+1)) „Stress_Houghton=64*0.0411*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) „Print Stress_Houghton 1.4984 „Variable /G final_e_Houghton=9.4e3*(exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)))*(N_not*1e12)*((h_max-hc)/Growth_rate)^2*(Stress_Houghton*1000)^4.5 „ „Print final_e_Houghton 1.66037e-05 „h_max=20 //This is the final thickness of the film „Growth_Temp= 850 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max/Growth_rate,"", e_approx „e_approx=Kn*Km*(Growth_rate*(Ge_concentration-factor/hc)^(m_exponent+n_exponent))*(x^(m_exponent+n_exponent+2))/((m_exponent+n_exponent+2)*(n_exponent+1)) „SetScale/I x 0,h_max/Growth_rate,"", e_Houghton „e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,(h_max-hc)/Growth_rate))^4.5 „Stress_Houghton=64*0.0411*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) „Print Stress_Houghton 1.34253 „Variable /G final_e_Houghton=9.4e3*(exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)))*(N_not*1e12)*((h_max-hc)/Growth_rate)^2*(Stress_Houghton*1000)^4.5 „ „Print final_e_Houghton 3.78207e-06 „h_max=25 //This is the final thickness of the film „Growth_Temp= 850 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max/Growth_rate,"", e_approx „e_approx=Kn*Km*(Growth_rate*(Ge_concentration-factor/hc)^(m_exponent+n_exponent))*(x^(m_exponent+n_exponent+2))/((m_exponent+n_exponent+2)*(n_exponent+1)) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", e_approx „e_approx=Kn*Km*(Growth_rate*(Ge_concentration-factor/hc)^(m_exponent+n_exponent))*(x^(m_exponent+n_exponent+2))/((m_exponent+n_exponent+2)*(n_exponent+1)) „SetScale/I x 0,h_max/Growth_rate,"", e_Houghton „e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,(h_max-hc)/Growth_rate))^4.5 „Stress_Houghton=64*0.0411*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe)*Test_D(Houghton_wave,(h_max-hc)/Growth_rate) „Variable /G final_e_Houghton=9.4e3*(exp(-(Qn+Qv)/(8.617e-5*Growth_Temp)))*(N_not*1e12)*((h_max-hc)/Growth_rate)^2*(Stress_Houghton*1000)^4.5 „ „Print final_e_Houghton 8.85118e-06 „e_Houghton=0.5*Km*Kn*x*x*(Test_D(Houghton_wave,(h_max-hc)/Growth_rate))^4.5 „Label left "Dislocation density (nm\\S-2\\M)" „h_max=200 //This is the final thickness of the film „Growth_Temp= 850 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetAxis left 0,* „RemoveFromGraph e_approx „Make/N=1000/D Strain_thermal „SetScale/I x 2,9,"", Strain_thermal „SetScale/I x 0,h_max,"", Strain_thermal „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*factor*f_misfit_Si_Ge*(ln(4*x/b_SiGe))/x „Duplicate Strain_thermal Strain_kinetic „Print System(100) 4.93297e-10 „Print System[10][%epsilon] 1.92603e-09 „Print System(10)[%epsilon] 7.00943e-09 „Print System(10.7)[%epsilon] 9.97411e-09 „Print System(21.2)[%epsilon] 1.79537e-07 „Print System(21.5)[%epsilon] 1.79537e-07 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „AppendToGraph Strain_kinetic „h_max=200 //This is the final thickness of the film „Growth_Temp= 1000 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „h_max=200 //This is the final thickness of the film „Growth_Temp= 2000 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ModifyGraph mode(Strain_kinetic)=3 „Display Strain_thermal,Strain_kinetic „Edit Strain_thermal.id,Strain_kinetic.id „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „h_max=200 //This is the final thickness of the film „Growth_Temp= 1500 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „h_max=200 //This is the final thickness of the film „Growth_Temp= 850 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ModifyGraph mode=0 „ModifyGraph lstyle=0,rgb(Strain_kinetic)=(0,0,0) „Label bottom "\\Z24Thickness (nm)" „Label left "\\Z24Strain" „h_max=200 //This is the final thickness of the film „Growth_Temp= 850 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=1 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „SetAxis left 0,0.05 „SetAxis bottom 0,100 „AppendToGraph Strain „RemoveFromGraph Strain „AppendToGraph Strain_theory „RemoveFromGraph Strain_theory „h_max=10 //This is the final thickness of the film „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „SetAxis/A bottom „SetAxis/A left „h_max=10 //This is the final thickness of the film „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-10 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „h_max=10 //This is the final thickness of the film „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-19 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „h_max=10 //This is the final thickness of the film „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-9 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „h_max=10 //This is the final thickness of the film „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-8 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „h_max=10 //This is the final thickness of the film „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-7 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „h_max=10 //This is the final thickness of the film „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=3e-7 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „h_max=1000//This is the final thickness of the film „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „h_max=100//This is the final thickness of the film „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „h_max=100//This is the final thickness of the film „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-10 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „h_max=100//This is the final thickness of the film „Growth_Temp= 823 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-9 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „h_max=100//This is the final thickness of the film „Growth_Temp= 850 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-9 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „h_max=100//This is the final thickness of the film „Growth_Temp= 850 //This is the growth temperature in K „Growth_rate=0.1// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-9 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „h_max=100//This is the final thickness of the film „Growth_Temp= 850 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „h_max=100//This is the final thickness of the film „Growth_Temp= 900 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-11 //This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „h_max=100//This is the final thickness of the film „Growth_Temp= 900 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „KillWaves fit_StrainRel,Thick_Square,Log_TS,Thickness,rho_eq,Parameter;DelayUpdate „KillWaves Critical_Thickness,Strain_theory,Strain_theory_2,Test,wave1,wave2;DelayUpdate „KillWaves Conc_wave,Root_test,Root_test_1,Root_test_2,effective_concentration;DelayUpdate „KillWaves D_wave;DelayUpdate „KillWaves/A/Z „h_max=100//This is the final thickness of the film „Growth_Temp= 700 //This is the growth temperature in K „Growth_rate=0.5// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „h_max=100//This is the final thickness of the film „Growth_Temp= 700 //This is the growth temperature in K „Growth_rate=0.1// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=5e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „SetAxis left 0,2e-05 „h_max=100//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.1// This is the growth rate in nm/s „Ge_concentration=0.058 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „h_max=1000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.1// This is the growth rate in nm/s „Ge_concentration=0.058 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „h_max=10000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.1// This is the growth rate in nm/s „Ge_concentration=0.058 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=100000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.1// This is the growth rate in nm/s „Ge_concentration=0.058 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „Display Strain_kinetic „SetAxis left 0,1e-05 „h_max=300000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.1// This is the growth rate in nm/s „Ge_concentration=0.058 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=400000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.1// This is the growth rate in nm/s „Ge_concentration=0.058 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=500000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.1// This is the growth rate in nm/s „Ge_concentration=0.058 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=550000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.1// This is the growth rate in nm/s „Ge_concentration=0.058 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=520000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.1// This is the growth rate in nm/s „Ge_concentration=0.058 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=5000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=500//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=700//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=900//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1200//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1200//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „h_max=800//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1100//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1300//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1400//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1500//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1700//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1800//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1500//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1700//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1800//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1600//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1800//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=2000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=2200//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=2400//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=2500//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=2600//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=2700//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=3600//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=3800//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=4000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=4200//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=4400//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=8000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.3 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=8200//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.3 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=16000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=18000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=20000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-11//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=20000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=10000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=7000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=5000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=6000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=8000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=9000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=18000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=15000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=14000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=14500//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=25000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.3 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=30000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.3 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=28000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.3 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=56000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=60000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=65000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=70000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=68000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-12//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=600//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=500//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=450//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=480//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=800//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=700//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=900//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1100//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1200//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1150//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=1130//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=2000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.3 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=2100//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.3 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=2050//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.3 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=6050//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=8000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=7000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=5000//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=4900//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=4800//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-10//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=200//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=100//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=110//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=105//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=150//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=145//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=148//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.5 //This is the Ge concentration „N_not=1e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=205//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=225//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.4 //This is the Ge concentration „N_not=1e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max=400//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.3 //This is the Ge concentration „N_not=1e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max= 390//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.3 //This is the Ge concentration „N_not=1e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max= 700//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max= 800//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max= 850//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.2 //This is the Ge concentration „N_not=1e-9//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*b_SiGe*cos (lambda)*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^m_exponent)*exp(-Qv/(8.617e-5*Growth_Temp)) „Kp = eta*Km/(b_SiGe*cos(lambda)) „Houghton_wave[0]=Kn „Houghton_wave[1]=Km „Houghton_wave[2]=f_misfit_Si_Ge „Houghton_wave[3]=Ge_concentration „Houghton_wave[4]=b_SiGe „Houghton_wave[5]=hc „Houghton_wave[6]=Growth_rate „Houghton_wave[7]=factor „Houghton_wave[8]=Kp „ „//Now initialize and perform integration. „System=0 „System[0][%epsilon]=0 „System[0][%N]=N_not „IntegrateODE Derivatives,Houghton_wave, System „ „//Now calculate the strain thermal equilibrium and the kinetically limited strain. „ „SetScale/I x 0,h_max,"", Strain_thermal,Strain_kinetic „Strain_thermal=0 „Strain_thermal=f_misfit_Si_Ge*Ge_concentration*(xhc)*(factor*f_misfit_Si_Ge/x)*ln(4*x/b_SiGe) „ „Strain_kinetic=f_misfit_Si_Ge*Ge_concentration*(xhc)*f_misfit_Si_Ge*Ge_concentration-System((x-hc)/Growth_rate)[%epsilon] „ „//************************************************** „h_max= 30//This is the final thickness of the film „Growth_Temp= 703 //This is the growth temperature in K „Growth_rate=0.058// This is the growth rate in nm/s „Ge_concentration=0.6 //This is the Ge concentration „N_not=1e-8//This is the number of fixed dislocation sources in the material. „eta=0 // This is the pinning probability. Set to zero to neglect pinning. „ „//Now calculate different parameters needed. „nu_SiGe=Ge_concentration*nu_Ge+(1-Ge_concentration)*nu_Si „mu_SiGe=Ge_concentration*mu_Ge+(1-Ge_concentration)*mu_Si „a_SiGe=Ge_concentration*a_Ge+(1-Ge_concentration)*a_Si „f_misfit_Si_Ge=abs((a_Si-a_Ge)/a_Ge) „b_SiGe=sqrt(2)*a_SiGe/2 „factor=(1-nu_SiGe*(cos(beta))^2)*b_SiGe/ (8*pi*f_misfit_Si_Ge*cos(lambda)*(1+nu_SiGe)) „hc=CriticalThicknessHoughton(Ge_concentration,factor) „SetScale/I x 0,(h_max-hc)/Growth_rate,"", System „Kn=B_disloc*N_not*((f_misfit_Si_Ge*cos(pi*35/180)*(1+nu_SiGe)/(1-nu_SiGe))^n_exponent)*exp(-Qn/(8.617e-5*Growth_Temp)) „Km = V_not*