What is Fluctuation Microscopy?

Fluctuation Microscopy is a hybrid imaging/diffraction technique that is sensitive to the presence of medium range order (MRO) in amorphous materials.

In the transmission electron microscope, the Fluctuation Electron Microscopy (FEM) technique is a powerful method for studying atomically disordered materials such amorphous silicon, germanium, silica and carbon. The medium range ordering regime is here considered to be in the length range 0.5 – 2.0 nm.

The fluctuations being studied are the differences in structural arrangement and orientation between small sub-volumes within the thin sample. The width of the volume is defined by the resolution of the probing instrument, i,e, the point-spread function of the microscope. The volume depth is determined by the sample thickness.

There are two equivalent ways to conduct FEM experiments. The first method is to collect tilted dark field images from a thin amorphous sample using a small objective aperture, such as the image on the right. The small size of the objective aperture limits the resolution of the microscope, by broadening the point spread function to around ~1.5 nm diameter. In a disordered material, the image will tend to be speckly. This speckle (dark patches, as well as bright patches) arises because of variations in scattering intensity from regions whose width equals the point spread function. The speckle is not simply due to variations in thickness or density across the sample. It is due mainly to fluctuations in the coherence of the scattering between atoms within each 1.5 nm wide sub-volume in the sample. The fluctuations in coherence are either due to random (i.e. statistical) atom alignments, or because of local structural ordering.

The variance of the image intensity is a simple measure of the speckliness of an image. If the tilt of the illumination is changed, the total scattered intensity changes because the atomic scattering factor changes with angle. By dividing by the square of the mean image intensity, the normalized image intensity variance should be constant as a function of angle, provided the speckle is due to random alignments only. However, if there is medium range ordering, there will be special angles where the normalized variance increases. These will occur at scattering vectors that correspond to the underlying structural length scales. The speckle will be maximum when the width of the point spread function equals the characteristic length scale of the medium range order. In the image on the left, which is of amorphous germanium (23 nm thick), we can see that the speckliness is changing as a function of tilt angle. This is a clear signature of medium range order. The normalized variance can be plotted as a function of tilt angle (scattering vector) to reveal the peaks.

In the case of amorphous silicon and germanium, which are tetrahedral semiconductor materials, the medium range order is believed to be due to paracrystalline regions within the sample. The paracrystallites are believed to be topologically cubic, with characteristic diameter around ~1.5 nm, and are strained. The small size and strained nature of the paracrystallites renders them "diffraction amorphous" (meaning it is very hard to detect them by diffraction alone). A cartoon illustrating the difference between random alignments and paracrystalline regions is shown on the right.

A second, equivalent, method for conducting FEM experiments is to use the STEM mode. In this case, the objective aperture still defines the point spread function (resolution) of the image by controlling the width of the probe. At each probed point, a microdiffraction pattern is obtained. By scanning the sample on a point by point basis, a set of microdiffraction patterns is collected. The normalized variance of the microdiffraction patterns gives the equivalent information to that obtained by TEM.

Ideally, the full set of FEM data is a 4-dimensional set of data. Two dimensions for the x-y locations of the image point (probe location), and two dimensions for the qx, qy diffraction vectors of the dark field tilt angles (microdiffraction patterns). Thus, the first TEM method collects all the x, y position data (i.e. image intensities) one q-vector (beam tilt) at a time, whereas the second STEM method collects all the qx, qy data one sample point at a time.

Fluctuation microscopy is not restricted to electron microscopy. We (Dushyant Kumar, ASU, Ian McNulty, David Paterson and Murray Gibson, Argonne) are conducting experiments at the 2-ID-B soft x-ray beamline to probe MRO in self-assembled nanoscale materials at length scales of ~100 nm. These FXM experiments are conducted using the second approach, using probes that are generated either by pinholes or zone plates. Dushyant Kumar is building a Fluctuation Optical Microscope (FOM) to probe mesoscale materials. the FOM also provides a flexible testbed for developing the methodologies needed at the beamline, where beam time is at a premium.

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Last updated July 3rd, 2005.

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