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

Abstract

The applicability of the Martin transformation [R. M. Martin, Phys. Rev. B 6, 4546 (1972)] to the elastic constants of wurtzite and zinc-blende group-III nitride alloys is examined using density functional theory calculations. The composition dependencies of the elastic constants in InGaN, AlGaN, and InAlN are determined by means of ab-initio calculations and compared with the results obtained from the Martin's method. A detailed analysis reveals that the Martin transformation can approximate reasonably well the dependence of the elastic constants on composition in wurtzite InGaN alloys, except for the case of C33 where it predicts too small bowing. However, it fails to reproduce correctly the composition dependencies of C13 and C33 in wurtzite InAlN and C13, C33, and C44 in wurtzite AlGaN. In order to identify the origin of the failure of the Martin transformation, the effective elastic constants of strained wurtzite alloys with the ideal value of the lattice axial ratio c/a have been investigated. It is shown that these effective elastic constants are significantly closer to the elastic constants predicted by the Martin's method which indicates that the breakdown of the Martin transformation in group III nitride alloys is partially caused by the deviation of the c/a axial ratio from the ideal value.