Parametrization of an anharmonic Kirkwood–Keating potential for AlxGa1−xAs alloys

Abstract

We introduce a simple semiempirical anharmonic Kirkwood-Keating potential to model A x B 1−x C-type semiconductors. The potential consists of the Morse strain energy and Coulomb interaction terms. The optical constants of pure components, AB and BC, were employed to fit the potential parameters such as bond-stretching and -bending force constants, dimensionless anharmonicity parameter, and charges. We applied the potential to finite temperature molecular-dynamics simulations on Al x Ga 1−x As for which there is no lattice mismatch. The results were compared with experimental data and those of harmonic Kirkwood-Keating model and of equation-of-motion molecular-dynamics technique. Since the Morse strain potential effectively describes finite temperature damping, we have been able to numerically reproduce experimentally obtained optical properties such as dielectric functions and reflectance. This potential model can be readily generalized for strained alloys.

Local Structure Invariant Potential for InxGa1-xAs Semiconductor Alloys

“…While potential parameters of alloys are determined based on the dispersion relation and reflectance of the binary parent alloys, the model is easy to implement to any atomic composition of semiconductor alloys. 16 In this article, we fit the potential parameters of anharmonic Kirkwood-Keating potential for In x Ga 1-x As for various atomic compositions and verify that MD simulations based on the fitted model reproduces experimentally observed optical properties of alloys. The article is organized as the followings: In section 2, the anharmonic Kirkwood-Keating model is briefly discussed as well as the compositional dependence of potential parameters.…”

“…The parameter βIn-As-In mainly controls the downshift of the TO phonon frequency within the Brillouin zone such that one can independently fit βIn-As-In using experimentally measured TO shift. 16 The linear dependence of TO shift for pure InAs crystals on β In-As-In is well described in Fig. 1.…”

“…Solid line is the least square regression fit of six data points. Table 1. potential with a Morse potential in order to introduce physical damping effect at finite temperature: 16 Index i runs over all atoms and j and k run over the four nearest neighbours of atom i in tetrahedral structure. rij is the distance between atoms i and j, while 0 ij r is the equilibrium distance.…”

“…On the other hand, the long-range Coulomb interaction was taken into account by means of the Ewald sum. 20,21 Since the parameters of pure GaAs crystals have been thoroughly examined and determined elsewhere, 16 we consider pure InAs crystals. The parameters α In-As and β In-As-In are fitted to reproduce experimentally measured elastic constants and phonon frequencies using a simple expression for the optical phonon frequency in the limit of long wavelength: 22 where µ is the reduced mass of InAs and h 0 ω is the low temperature limit of the phonon frequency.…”