Modeling the compositional dependence of electron diffraction in dilute GaAs- and GaP-based compound semiconductors

The change in the intensity of the (200) electron-beam reflection induced by the incorporation of isovalent impurities in GaAs and GaP is studied theoretically. Calculations are performed in the framework of the kinematical scattering theory. The structure factor of random alloys was obtained using atomic form factors calculated with the density-functional theory and an empirical-potential valence force-field model for the structure relaxation. The calculations include the effect of redistribution of the electron density on the electron-scattering amplitudes as well as the effect of the local lattice distortions associated with the impurity sites. We propose a way to calculate these distortions analytically and to introduce them in a simple form to the expression for the structure factor. This method is an alternative to the simulations, which invoke demanding computations for atomic relaxation, and enables quantitative prediction of the compositional variation of the structure factor for dilute alloys taking into account static atomic displacements. The implications of the results for quantification of composition fluctuations in heterostructures using dark-field transmission electron microscopy are discussed. The effect of nitrogen and boron incorporation on the intensity of the (200) reflection is found to be partly compensated by the static atomic displacements they cause. Neglecting this effect would lead to an underestimation of the impurity content by approximately a factor of two. The redistribution of the electron density is found to be less crucial for the evaluation of the chemical composition leading to a relative error in the (200) scattering amplitude of about 16%.