Crystallography
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Crystallography
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"In anticipation, it can be said that such a three-dimensional pattern acts as a diffraction grating to light having wavelengths of the same order of magnitude as the translation repeat period of the pattern." - Martin Julian Buerger (1903-1986)
Crystallography constitutes a fundamental science of condensed matter and is a critical tool for solving problems in polycrystalline thin film structures.
The periodic repetition of atomic positions in crystals determines their fundamental optical and electronic properties. Slight deviations in the lattice changes these properties according to well-established principles. For a single crystal, solid state theory and Hooke's law are combined to relate structural deviations to thermal, electrical and mechanical properties.
The Nye triangle, relating thermal, electrical and mechanical properties of a crystal, according to J. F. Nye (1957).
Polycrystalline thin films are assemblages of numerous single crystals (grains) separated by their surfaces, known as grain boundaries, the properties of which can critically affect the operation of electronic devices made from them. For example, thin film solar cells made from group II-VI and group I-III-VI compound semiconductor materials exhibit better performance than their single crystal counterparts; the converse is true for cells made from group III-V or group IV materials.
Lattice dimensions in single crystal and polycrystalline specimens can be measured using x-ray diffraction (XRD), in much the same way that a reflection grating is used to analyze visible light.
Diffraction by a space lattice according to Martin Buerger (1948).
Every crystalline material has a unique pattern of diffraction peaks which can be used to identify it.
Here is a wide angle pattern of a Cd0.6Zn0.4Te alloy thin film made by physical vapor deposition. The scan was taken using Cuka x-rays. The peak positions provide lattice information while the relative peak intensities provide information on the orientation of grains to the substrate.
Different incident and diffracted beam configurations can be used to learn different properties of films. For a symmetric XRD scan such as shown above, the peak positions indicate the lattice constants of the film, while the relative peak intensities provide information about the alignment, or orientation of grains with the substrate.
The shape of the diffraction peaks can reveal deviations in composition, strain, and grain size; the latter particularly as we approach the nano-scale. In practice, we can combine diffraction measurements with composition measurements to determine the properties of a statistically significant fraction of grains, grain boundaries, and exposed surface in polycrystalline thin films. In unstrained, chemically uniform films with grain size >50 nm, all grains have the same lattice constant and exhibit very sharp diffraction peaks. In many compound materials, chemical non-uniformities such as spatially varying alloy formation broadens the peaks:
This narrow angle XRD plot shows the time evolution of the (333) diffraction peak in a CdTe/CdS thin film structure before and after annealing.
The sharp blue peak is the CdTe (333) reflection for a film in a CdTe/CdS thin film stack, in the as-deposited condition. After thermal annealing at 400°C in a reactive ambient, the two films interdiffuse and the CdTe peak smears out towards higher Bragg angle, and lower lattice spacing. The time-progressive nature of the change (red peaks) indicates a diffusion process that terminates at the 400°C equilibrium alloy composition shown. For the intermediate time cases, the bimodal peak shape derives from the effects of grain boundary and bulk diffusion processes in a film having bimodal grain size distribution.
For films with composition gradients or residual strain through the film thickness, due to compressive or tensile forces acting on the grains, it is useful to measure diffraction from different depths through the film. This is accomplished by glancing (or grazing) incidence x-ray diffraction (GIXRD), in which the incident beam is fixed at very low angles to restrict the material volume contributing to diffraction signal. By making measurements at different incident beam angles we can obtain a depth profile of lattice spacing variations, with corresponding changes in peak shape:
Here are measured (left) and modeled (right) GIXRD patterns of a Cu(InGa)Se2 thin film having a through-film gradient in Ga/In composition.
This specimen was deposited onto a Mo-coated glass substrate and then peeled away to reveal the interface. The different curves in each box correspond to diffraction from different depths in the exposed film. The model used to represent the data consists of an exponential gradient in Ga composition, with the most Ga, indicated by the tailing signal at high Bragg angle, at the exposed film surface.
Analysis such as this allows researchers to refine experimental conditions to control film composition through its depth, which is important for controlling properties in thin film solar cell devices. |
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