Nonlinear elasticity effect in group III-nitride quantum heterostructures:Ab initiocalculations

Abstract

We investigate the effect of the nonlinear elasticity in nitride quantum wells (QWs) and superlattices (SLs), manifesting itself in changes of the elastic constants caused by the intrinsic hydrostatic pressures, present in the heterostructures due to the lattice misfit between constituents. Since the intrinsic hydrostatic pressure in the tensile-strained layers is negative, we have performed ab initio calculations of the elastic constants for wurtzite GaN, InN, and AlN subjected to the hydrostatic dilatation. We have found that, for all considered nitrides, the elastic constants ${C}_{11}$, ${C}_{12}$, ${C}_{13}$, and ${C}_{33}$ significantly decrease with decreasing negative values of pressure. Particularly, the strong nonlinear dependences on negative values of pressures have been obtained for the ${C}_{11}$ and ${C}_{33}$ elastic constants. These findings reveal that the tensile stress modifies the elastic constants of the nitride semiconductors stronger than the compressive stress, and both stresses should be considered when one wants to take into account the nonlinear elasticity in the nitride heterostructures. Next, we study the effect of the nonlinear elasticity in $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{Ga}\mathrm{N}$ and $\mathrm{In}\mathrm{Ga}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$ SLs and QWs. We show that the influence of the effect of the nonlinear elasticity on the interband and intersubband transition energies in these structures depends crucially on the strain state of heterostructures. For the structures with compressively strained quantum wells, the usage of the nonlinear elasticity leads to decrease of the interband transition energies, originating from the decrease of the absolute values of the volumetric strain in the wells. For the structures with tensile-strained barriers, the effect of the nonlinear elasticity increases the energies of the interband transitions due to the decrease of the absolute values of the built-in electric fields. For the freestanding SLs, the effect of the nonlinear elasticity on the interband transition energies is relatively small, in comparison with the strained structures. The influence of the nonlinear elasticity on the intersubband transition energies in the nitride heterostructures is dominated by the changes in the built-in electric fields. We show that the nonlinear elasticity effect decreases considerably the energies of the intersubband transitions in the structures with tensile-strained barriers. Relatively small changes of the intersubband transition energies are obtained for the structures with compressively strained wells and for the freestanding structures.