First- and second-order piezoelectricity in III-V semiconductors

Abstract

We present the results of first-principles plane-wave pseudopotential calculations of piezoelectric coefficients of first and second order for a total of nine III-V binary phases (AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb) of zinc-blende semiconductors. These coefficients are used to calculate the piezoelectric fields for [111]-oriented quantum wells (QWs) with different well-barrier combinations and various dimensions. We derive an approximate analytic expression for the strain tensor in the case of pseudomorphic growth along an arbitrary growth direction. Together with the piezoelectric coefficients, this allows a simple calculation of the piezoelectric field up to second order in strain for an arbitrary growth direction and any material combination within the nine III-Vs presented here. Nonlinear contributions to the polarization are shown to be of significant magnitude for all the materials presented. In some cases the field is increased by the second-order terms; in some cases it is decreased. We analyze the chemical trends of the obtained coefficients. We compare our results to available experiments and find good agreement in one-third of the cases, while for the remaining cases the calculated field is larger to significantly larger than in the measurements. We discuss the popular experimental techniques and highlight possible reasons for the discrepancies.