A comprehensive and detailed study of the composition dependence of lattice constants, band gaps and band offsets has been performed for bulk Ge _{1− x} Sn _x alloy in the full composition range using state-of-the-art density functional theory methods. A spectral weight approach to band unfolding has been applied as a means of distinguishing the indirect and direct band gaps from folded supercell band structures. In this way, four characteristic regions of the band gap character have been identified for Ge _{1− x} Sn _x alloy: an indirect band gap ( x < 6.5%), a direct band gap (6.5% < x < 25%) and an inverse band gap ( x > 25%) with inverse spin–orbit split-off for 45% < x < 85%. In general, it has been observed that the bowing parameters of band edges (Γ and L -point in conduction band (CB _Γ and CB _L ), valence band (VB), and spin–orbit (SO) band) are rather large ( b CB Γ = 2.43 ± 0.06 eV, b CB L = 0.64 ± 0.04 eV, b VB = −0.59 ± 0.04 eV, and b SO = −0.49 ± 0.05 eV). This indicates that Ge _{1− x} Sn _x behaves like a highly mismatched group IV alloy. The composition dependence of lattice constant shows negligible bowing ( b _a = −0.083 Å). Obtained results have been compared with available experimental data. The origin of band gap reduction and large bowing has been analyzed and conclusions have been drawn regarding the relationship between experimental and theoretical results. It is shown that due to the low DOS at the Γ-point, a significant filling of CB by electrons in the direct gap regime may easily take place. Therefore, the Burstein–Moss effect should be considered when comparing experimental data with theoretical predictions as has already been shown for other intrinsic n -type narrow gap semiconductors (e.g. InN).

A key material system for opto- and high-power electronics are III-nitrides. Their functionality can be expanded when bandgap engineering is extended beyond common materials such as AlN, GaN, and InN. Combining these three compounds with boron nitride and other III–V compounds (GaP, GaAs, GaSb, InP, etc.) is an intuitive method of expanding bandgap engineering in semiconductor devices. This may allow improvement of current devices for which performances are limited by the intrinsic properties of common III-nitride alloys, as well as the creation of novel devices. A comprehensive review of this activity is presented in this article, including an up-to-date compilation of material parameters for wurtzite boron nitride; its alloying with other III-nitrides, including structural and optical characterization; the band anticrossing model for III-nitrides diluted with group V atoms; their synthesis and structural and optical characterization; and examples of applications of III-nitrides containing boron and group V atoms in semiconductor devices. It is shown to be very beneficial for ultraviolet emitters to incorporate alloying of III-nitrides with BN, as these compounds have lattice constants much smaller than that of AlN, offering unique possibilities in strain engineering. It is shown that the incorporation of P, As, Sb, and Bi in GaN is low when the material is deposited at this temperature, which is optimal for the host. Lowering the growth temperature significantly enhances the incorporation of isovalent dopants, but deteriorates the optical quality of the material. The obtained changes in the electronic band structure can be beneficial in many applications, including water splitting or shifting emission toward longer wavelengths.

Formation of an intermediate band in ${\mathrm{GaN}}_x{\mathrm{P}}_{0.4}{\mathrm{As}}_{0.6-x}$ alloys due to the isovalent doping by nitrogen is studied by photoreflectance and absorption spectroscopy. The fundamental energy gap transition ($E_0$) observed for an N-free alloy is replaced by two optical transitions ($E_{-}$ and $E_{+}$) in GaNPAs layers. The $E_{-}$ and $E_{+}$ transitions are explained within the band anticrossing model, where the localized level of nitrogen interacts with the conduction band of the GaPAs host, splitting it into two subbands. The valence band (VB) is mostly unaffected by nitrogen incorporation as confirmed by the same spin-orbit splitting for N-free and N-containing alloys. The energy position of the $E_{-}$ subband and a strong optical absorption between the VB and the $E_{-}$ subband indicates the GaNPAs alloys have an electronic structure suitable for intermediate-band solar cells. Such an electronic structure is not observed for other III–V alloys like GaInAs, GaInAsP, etc., for which the virtual crystal approximation can be applied to describe the evolution of the electronic structure with the alloy content. Results obtained in this work clearly show that GaNPAs with a few percent of nitrogen is an unusual material system, for which the electronic structure properties differ very significantly from properties of well-known III–V alloys, and the application of virtual crystal approximation in this case is inappropriate or very limited.

The electronic band structure of MoS₂, MoSe₂, WS₂, and WSe₂, crystals has been studied at various hydrostatic pressures experimentally by photoreflectance (PR) spectroscopy and theoretically within the density functional theory (DFT). In the PR spectra direct optical transitions (A and B) have been clearly observed and pressure coefficients have been determined for these transitions to be: α_A = 2.0 ± 0.1 and α_B = 3.6 ± 0.1 meV/kbar for MoS₂, α_A = 2.3 ± 0.1 and α_B = 4.0 ± 0.1 meV/kbar for MoSe₂, α_A = 2.6 ± 0.1 and α_B = 4.1 ± 0.1 meV/kbar for WS₂, α_A = 3.4 ± 0.1 and α_B = 5.0 ± 0.5 meV/kbar for WSe₂. It has been found that these coefficients are in an excellent agreement with theoretical predictions. In addition, a comparative study of different computational DFT approaches has been performed and analyzed. For indirect gap the pressure coefficient have been determined theoretically to be −7.9, −5.51, −6.11, and −3.79, meV/kbar for MoS₂, MoSe₂, WS₂, and WSe₂, respectively. The negative values of this coefficients imply a narrowing of the fundamental band gap with the increase in hydrostatic pressure and a semiconductor to metal transition for MoS₂, MoSe₂, WS₂, and WSe₂, crystals at around 140, 180, 190, and 240 kbar, respectively.