Diffraction topography

Topography is exploited to a lesser extent with neutrons, and is the same concept as dark field imaging in an electron microscope.

In the 1950s and 1960s, topographic investigations played a role in detecting the nature of defects and improving crystal growth methods for germanium and (later) silicon as materials for semiconductor microelectronics.

A related field are investigations of materials and devices for X-ray optics, such as monochromator crystals made of Silicon, Germanium or Diamond, which need to be checked for defects prior to being used.

The basic working principle of diffraction topography is as follows: An incident, spatially extended beam (mostly of X-rays, or neutrons) impinges on a sample.

Theoretical calculations, and in particular numerical simulations by computer based on this theory, are thus a valuable tool for the interpretation of topographic images.

However, the exit angles of the respective diffracted beams will differ, leading to overlapping regions of enhanced intensity as well as to shadows in the image, thus again giving rise to contrast.

orientation contrast occurs on a macroscopic scale, it can also be generated more locally around defects, e.g. due to curved lattice planes around a dislocation core.

This is the reason why topography requires high-resolution X-ray films or CCD cameras with the smallest pixel sizes available today.

Thirdly, even with perfect detectors and ideal geometric conditions, the visibility of special contrast features, such as the images of single dislocations, can be additionally limited by diffraction effects.

Highly ordered, strongly diffracting materials – like minerals or semiconductors – are generally unproblematic, whereas e.g. protein crystals are particularly challenging for topographic imaging.

If the sample needs to be displaced, e.g. in order to scan its surface through the beam in several steps, additional translational degrees of freedom are required.

Since about the mid-1990s, CCD cameras have emerged as a practical alternative, offering many advantages such as fast online readout and the possibility to record entire image series in place.

X-ray sensitive CCD cameras, especially those with spatial resolution in the micrometer range, are now well established as electronic detectors for topography.

General criteria for judging the practical usefulness of detectors for topography applications include spatial resolution, sensitivity, dynamic range ("color depth", in black-white mode), readout speed, weight (important for mounting on diffractometer arms), and price.

Disadvantages include the high X-ray dose, possibly leading to radiation damage to the sample, and the necessity to carefully shield the experiment.

For a cylindrically bent crystal the Bragg planes in the crystal lattice will lie on Archimedean spirals (with the exception of those orientated tangentially and radially to the curvature of the bend, which are respectively cylindrical and planar), and the degree of curvature can be determined in a predictable way from the length of the spots and the geometry of the set-up.

Quantitative analysis can be performed with the help of image simulation by computer algorithms, usually based on the Takagi-Taupin equations.

Several of the properties of synchrotron radiation are advantageous also for topography applications: The high collimation (more precisely the small angular source size) allows to reach higher geometrical resolution in topographs, even at larger sample-to-detector distances.

Neutron topography can make use of contrast mechanisms that are partially different from the X-ray case, and thus serve e.g. to visualize magnetic structures.

Although considerable progress has been achieved, topography on protein crystals remains a difficult discipline: Due to large unit cells, small structure factors and high disorder, diffracted intensities are weak.

Based on white-beam topography, the new aspect consists in placing a fine-scaled metallic grid ("reticule") between sample and detector.

By recording reticulographic images at several sample-to-detector distances, and appropriate data processing, local distributions of misorientation across the sample surface can be derived.

CCDs achieve online readout in (almost) real-time, dispensing experimentalists of the need to develop films in a dark room.

A further, decisive advantage of digital topography is the possibility to record series of images without changing detector position, thanks to online readout.

This makes it possible, without complicated image registration procedures, to observe time-dependent phenomena, to perform kinetic studies, to investigate processes of device degradation and radiation damage, and to realize sequential topography (see below).

By following the diffracted intensity in one pixel across the entire sequence of images, local rocking curves from very small areas of sample surface can be reconstructed.

Although the required post-processing and numerical analysis is sometimes moderately demanding, the effort is often compensated by very comprehensive information on the sample's local properties.

In contrast to the Rocking Curve Imaging method, it is more appropriate for more highly disturbed (polycrystalline) materials with lower crystalline perfection.

These channels transmit intensity only in specific, parallel directions, and thus guarantee a one-to-one-relation between detector pixels and points on the sample surface, which would otherwise not be given in the case of materials with high strain and/or a strong mosaicity.

The spatial resolution of the method is limited by a combination of detector pixel size and channel plate periodicity, which in the ideal case are identical.