Nonlinear elasticity in III-N compounds:Ab initiocalculations

Abstract

We have studied the nonlinear elasticity effects in zinc-blende and wurtzite crystallographic phases of III-N compounds. Particularly, we have determined the pressure dependences of elastic constants in InN, GaN, and AlN by performing ab initio calculations in the framework of plane-wave pseudopotential implementation of the density-functional theory. The calculations have been performed employing two exchange-correlation functionals, one within the local density approximation and the other within the generalized gradient approximation. We have found that ${\mathrm{C}}_{11}$, ${\mathrm{C}}_{12}$ in zinc-blende nitrides and ${\mathrm{C}}_{11}$, ${\mathrm{C}}_{12}$, ${\mathrm{C}}_{13}$, ${\mathrm{C}}_{33}$ in wurtzite nitrides depend significantly on hydrostatic pressure. Much weaker dependence on pressure has been observed for ${\mathrm{C}}_{44}$ elastic constant in both zinc-blende and wurtzite phases. Further, we have examined the influence of pressure dependence of elastic constants on the pressure coefficient of light emission, $d{E}_{E}∕dP$, in wurtzite $\mathrm{In}\mathrm{Ga}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$ and $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{Ga}\mathrm{N}$ quantum wells. We have shown that the pressure dependence of elastic constants leads to a significant reduction of $d{E}_{E}∕dP$ in nitride quantum wells. Finally, we have considered the influence of nonlinear elasticity of III-N compounds on the properties of hexagonal nitride quantum dots (QDs). For typical wurtzite $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}$ QDs, we have shown that taking into account pressure dependence of elastic constants results in the decrease of volumetric strain in the QD region by about 7%. Simultaneously, the average $z$ component of the piezoelectric polarization in the QDs increases by $0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MV}∕\mathrm{cm}$ compared to the case when linear elastic theory is used. Both effects, i.e., decrease of volumetric strain as well as increase of piezoelectric field, decrease the band-to-band transition energies in the QDs.