The electronic band structures of ${\text{In}}_x{\text{Ga}}_{1-x}\text{N}$, ${\text{In}}_x{\text{Al}}_{1-x}\text{N}$, and ${\text{In}}_x{\text{Ga}}_y{\text{Al}}_{1-x-y}\text{N}$ alloys are calculated by ab initio methods using a supercell geometry, and the effects of varying the composition and atomic arrangements are examined. Particular attention is paid to the magnitude of and trends in bowing of the band gaps. Indium composition fluctuation (clustering) is simulated by different distributions of In atoms and it is shown that it strongly influences the band gaps. The gaps are considerably smaller when the In atoms are clustered than when they are uniformly distributed. An explanation of this phenomenon is proposed on the basis of an analysis of the density of states and the bond lengths, performed in detail for ternary alloys. Results for the band gaps of ${\text{In}}_x{\text{Ga}}_y{\text{Al}}_{1-x-y}\text{N}$ quaternary alloys show a similar trend. It is suggested that the large variation in the band gaps determined on samples grown in different laboratories is caused by different degrees of In clustering.

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 $0.1\mathrm{MV}∕\mathrm{cm}$ 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.

The influence of hydrostatic pressure on the emission and absorption spectra measured for various types of InGaN structures (epilayers, quantum wells, and quantum dots) is studied. While the known pressure coefficients of the GaN and InN band gaps are about 40 and 25 meV/GPa, respectively, the observed pressure-induced shifts in light emission energy in the InGaN alloys differ significantly from concentration-interpolated values. With increasing In concentration, and thus decreasing emission energy, the observed pressure coefficients become very small, reaching zero for emission energies ∼2 eV (roughly the value of the InN band gap). On the other hand, the pressure coefficient derived from absorption experiments exhibit a much smaller decrease with decreasing energy when referred to the same scale as the emission data. First-principles calculations of InGaN band structures and their modification with pressure are performed. The results are not able to explain the huge effect observed in the emission experiments, but they are in good agreement with the optical absorption data. Significant bowings of the band gap and its pressure coefficients are found, and they are especially large for small In concentrations. This behavior is related to the changes in the upper valence band states due to In alloying. Some possible mechanisms are discussed which might be expected to account for the low pressure coefficients of the light emission energy and the difference between the sensitivity of the emission and absorption to pressure.

We have studied the influence of hydrostatic pressure on the light emission from a strained GaN/AlGaN multiquantum well system. We have found that the pressure coefficients of the photoluminescence peak energies are dramatically reduced with respect to that of GaN energy gap and this reduction is a function of the quantum well thickness. The decrease of the light emission pressure coefficient may be as large as 30% for a 32 monolayer (8 nm) thick quantum well. We explain this effect by the hydrostatic-pressure-induced increase of the piezoelectric field in quantum structures. Model calculations based on the $\mathrm{k\times p}$ method and linear elasticity theory reproduce the experimental results well, demonstrating that this increase may be explained by small anisotropy of the wurtzite lattice of GaN and a specific interplay of elastic constants and values of the piezoelectric tensor.

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.

Dependence of elastic constants on composition and atomic arrangement in wurtzite InxGa1-xN and InxAl1-xN alloys is studied by self-consistent ab initio calculations within a supercell model. It is found that a Vegard's-like law, i.e., linear dependence on the alloy content, x, can be accepted for C12, C13, and C44 in InxGa1-xN, and for C12, C13, and C33 in InxAl1-xN, whereas significant sublinear deviations are obtained for C11 and C33 in InxGa1-xN and for C11 and C44 in InxAl1-xN. The effect of In atoms clustering, modeled by grouping In atoms in a part of a supercell, leads to a decrease in C11, C12, and C44, and an increase in C33, in both InxGa1-xN and InxAl1-xN alloys. Therefore, in the alloys with clustered In atoms, C11, C12, and C44 show significant sublinear behavior on composition in both InxGa1-xN and InxAl1-xN, whereas the composition dependence of C33 is almost linear in InxGa1-xN and significantly superlinear in InxAl1-xN. The dependence of the bulk modulus on composition is slightly sublinear in InxGa1-xN and InxAl1-xN alloys and changes little due to the In clustering effect.