Computational study of structural and elastic properties of random Al_xGa_yIn_{1 −x−y}N alloys

Abstract

In this work we present a detailed computational study of the structural and elastic properties of cubic Al(x)Ga(y)In(1 - x - y)N alloys in the framework of the Keating valence force field model, for which we perform an accurate parametrization based on state-of-the-art density functional theory calculations. When analysing structural properties, we focus on the concentration dependence of the lattice constant, as well as on the distribution of the nearest and the next nearest neighbour distances. Where possible, we compare our results with experiment and calculations performed within other computational schemes. We also present a detailed study of the elastic constants for Al(x)Ga(y)In(1 - x - y)N alloy over the whole concentration range. Moreover, we include the accurate quadratic parametrization for the dependence of the alloy elastic constants on the composition. Finally, we examine the sensitivity of the obtained results to computational procedures commonly employed in the Keating model for studies of alloys.

Fully analytic valence force field model for the elastic and inner elastic properties of diamond and zincblende crystals

“…Thus, unlike potentials for which a numerical fitting is required, and a new fitting is needed for each material, eqs. (17) to (20) ideally represent a VFF for any ZB or diamond structure material: once the elastic constants and the Kleinman parameter are known, so too are the force constants. Unlike the Keating potential which describes exactly only the elastic constants C 11 and C 12 , with significant errors often found for C 44 ζ, the above relations ensure that these properties are reproduced exactly.…”

“…For example, eqs. (14) and (17)(18)(19)(20) may be used to obtain expressions for the other elastic constants, C 0 44 , E 11 and D 14 . These expressions may then be used to predict quantities on which the model has not been parameterised to ascertain the suitability of the potential for the different materials.…”

“…The calculation of the strain and relaxed atomic positions of large supercells is of crucial importance to the semiconductor science community. 17,18 This is because the electronic and optical properties of heterostructures are strongly influenced by their strain state. 19 Furthermore, computationally cheaper continuum models are able to account for neither the atomic-scale variation of composition, nor the atomic-scale reduction in symmetry which have significant effects on electronic properties.…”

Inapplicability of Martin transformation to elastic constants of zinc-blende and wurtzite group-III nitride alloys

“…Recently, Łopuszy nski and Majewski have applied the Martin transformation to determine the composition dependence of the elastic constants in WZ InAlGaN quaternary alloys using the results obtained for the ZB phase by the valence force field (VFF) approach. 18,19 In the present work, we investigate the applicability of the Martin transformation to ternary group-III nitride alloys. To this end, we have performed DFT calculations of the elastic constants in WZ and ZB nitride alloys using special quasirandom structures (SQSs) to model random distribution of the group III elements in supercells.…”

Application of the bond valence method in the non-isovalent semiconductor alloy (GaN)1−x(ZnO)x

“…The ionic Zn-O bond is softer than the covalent Ga-N bond. For isovalent III-V semiconductor alloys, the widely used Keating valence force field (KVFF) model [45] yields generally good accuracy [46,47,48,49,50,51].…”