The effect of the static atomic displacements on the structure factors of weak reflections in cubic semiconductor alloys

Abstract

We show that the static atomic displacements (SDs) from the average crystal sites, which exist in all III–V and II–VI semiconductor alloys where atoms having different covalent radii share a mixed sublattice, have a large effect on the structure factors (SFs) of the weak reflections (h + k + l = 4n + 2) of the cubic crystals of such alloys. Using atomistic simulations, this effect is studied quantitatively for 25 ternary alloys. Parameters describing the variations in the SFs with alloy composition for both electrons and X-rays are given. The sign of the difference between SFs calculated with and without SDs is the same for most alloys with a type-III or type-II mixed sublattice and reverses for a type-V mixed sublattice. Non-zero imaginary parts appear for reflections with all indices non-zero. We use a simple approximation to explain these results, to provide general rules for the effect of the SDs and to estimate its magnitude. We also study quantitatively the large effect of the SDs in quaternary Ga_{1− x} In _x As_{1− y} N _y alloys with y ≪ 1. Our calculations explain part of the difference between the experiments and the standardly calculated SFs of Ga _1−x In _x As alloys. They show that the SDs must be taken into account, particularly when such ‘quasiforbidden’ reflections are used to measure alloy composition by electron microscopy.

Acknowledgements

This work was supported by Région Ile de France, by SESAME project 1377 and by Conseil Général de l’Essonne. We also thank Andreas Rosenauer for fruitful discussions.