Anisotropy of defect introduction by electron irradiation in compound semiconductors

Abstract

Two possible interpretations of the anisotropy for production of defects by electron irradiation in semiconductors with zinc-blende or Wurtzite structures, shadowing effect, and secondary atomic interactions, are quantitatively examined. For an electron beam perfectly aligned with a [111] hybrid bond direction, it is possible to derive an expression for a shadowing cross section which in principle measures the probability that an atom A masks its nearest neighbor B in the forward beam direction, and therefore that atoms A prevent the incident beam from interacting with atoms B and displacing them. Although these shadowing cross sections are several orders of magnitude larger than the displacement cross sections, we show that, due to electronic scattering and lattice vibrations, they are still much too weak to explain the experimentally observed anisotropies. To investigate the secondary atomic interactions, a simple dynamic model has been developed, where interactions are taken into account in the nearest neighbors atomic shell only. Interactions are described by elastic collisions in which the primary knock-on atom A loses a fraction ΔTB of its initial kinetic energy T0. ΔTB is obtained from an exact integration of classical equations of motion. It is assumed that atom A is definitively displaced if T0−ΔTB is larger than a certain isotropic threshold energy Td, which allows an anisotropic displacement cross section to be deduced. It is shown that this dynamic model predicts with a reasonable quantitative agreement the experimental results obtained in GaAs after irradiations along opposite [111] directions, when using a hard core or Born–Mayer potential to describe the atomic interactions. In particular, the observed reversal of the anisotropy at higher irradiation energies is predicted for the correct order of magnitude of the crossover energy, equal to about twice the threshold energy, and is shown to be the direct consequence of the tetrahedral coordination of the crystal. The magnitude of the anisotropy for irradiation energies larger than the crossover is a sensitive function of the interaction potential range. In the case of a hard core potential the fit gives a hard core radius equal to about twice the Bohr radius which is exactly the expected value for interatomic collisions in the energy range considered here. The paper is concluded by a brief survey of experimental data available for other compound semiconductors. Although they do not allow such a precise comparison as for GaAs, we show that they are entirely consistent with the dynamic model presented here.