Effect of bonding and static atomic displacements on composition quantification inInxGa1−xNyAs1−y

Abstract

This study addresses the influence of static atomic displacements (SAD) and chemical bonding in (InGa)(NAs) alloys on structure factors for electron scattering and stresses their importance for compositional analysis. First, SAD are derived using valence force field (VFF) methods and their reliability is demonstrated by calculating residual atomic forces using density-functional theory (DFT). A systematic study of structure factors for low indium and nitrogen contents is given by means of full DFT calculations on the one hand and atomistic models on the other. We show that the consideration of SAD via VFF together with the inclusion of bonding via modified atomic scattering amplitudes is in best agreement with a full DFT calculation, providing the possibility to include bonding effects also if large cells containing ${10}^{6}$ atoms are considered. Second, a technique is presented, which allows the extraction of atomically resolved indium and nitrogen composition maps by evaluating strain and contrast in transmission electron microscopic two-beam images simultaneously. As the fringe contrast is compared with Bloch wave simulations, which in turn require accurate structure factors, we exemplify the influence of SAD and bonding on composition profiles regarding an ${\text{In}}_{0.08}{\text{Ga}}_{0.92}{\text{N}}_{0.03}{\text{As}}_{0.97}$ quantum well structure. In this respect, imaging conditions may be chosen for which SAD are of minor influence for conventional transmission electron microscopy, whereas relative errors larger than 25% can arise for the compositions if bonding is neglected.