Influence of asymmetrical angle on crystal lattice strain analysis using Voigt-function method

Abstract

The Voigt function provides a rapid and easy method of explaining the breadths of diffraction profiles, and it defines two main broadening types: the domain size and strain component. The latter is caused by lattice imperfection (dislocation and different defects). Thus, diffraction can be used to measure crystal strain with very high precision and accuracy. However, each of all the crystals used in the present study has asymmetrical angle due to the processes of cutting grinding and polishing. This deviation angle is the angle between the considered lattice plane and crystal surface. The crystal with asymmetrical angle also satisfies Bragg's law but with different incident angle and reflected one. In the following, we investigate the crystal strain as a function of asymmetrical angle to evaluate the lattice distortion in detail. The single crystal silicon samples with different asymmetrical angles (in a range from 0.008 to 5.306) are prepared in this experiment. The lattice plane is (111). After grinding and polishing, the surface and subsurface damage are almost wiped off to remove internal stress which comes from cracks and grain refinement. Only broadening from lattice strain depends on the nature of imperfection, and the shape of crystallite can be left. It is convenient to acquire the full width at half maximum (FWHM) and integral breadth of diffraction curve by high resolution X-ray diffraction technique. Using the Voigt function method, diffraction line is characterized by all three parameters of the half-width integral breadth and form factor. The crystal lattice strains are calculated by analyzing the experimental line profile composed of Cauchy and Gaussian parts. Simulation of coherence diffraction of asymmetric crystal silicon is achieved by ray tracing code SHADOW. Both the theoretical calculation and experimental results show that if asymmetrical angle reaches 0.749, the half-width and integral breadth of diffraction curve change obviously compared with the situation where asymmetrical angle reaches 0.008. This is why the calculation error of crystal strain will be beyond 5% by the Voigt function method no matter whether we use theoretical value or experimental data. It is shown that the precise crystal cut is extremely important for device application. And this conclusion will also be helpful in other crystal studies by using X-ray diffraction parameters.