Nonlinear elasticity in III-N compounds:Ab initiocalculations

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 C₁₁, C₁₂ in zinc-blende nitrides and C₁₁, C₁₂, C₁₃, C₃₃ in wurtzite nitrides depend significantly on hydrostatic pressure. Much weaker dependence on pressure has been observed for C₄₄ 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, dE₄∕dP, in wurtzite InGaN∕GaN and GaN∕AlGaN quantum wells. We have shown that the pressure dependence of elastic constants leads to a significant reduction of dE₄∕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 GaN∕AlN 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. 10. 3em{0ex}MV∕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.