Transition energies and direct-indirect band gap crossing in zinc-blende AlxGa1−xN

Abstract

The electronic and optical properties of zinc-blende (zb) Al x Ga 1−x N over the whole alloy composition range are presented in a joint theoretical and experimental study. Because zb-GaN is a direct ( v → c ) semiconductor and zb-AlN shows an indirect ( v → X c ) fundamental band gap, the ternary alloy exhibits a concentration-dependent direct-indirect band gap crossing point the position of which is highly controversial. The dielectric functions of zb-Al x Ga 1−x N alloys are measured employing synchrotron-based ellipsometry in an energy range between 1 and 20 eV. The experimentally determined fundamental energy transitions originating from the , X, and L points are identified by comparison to theoretical band-to-band transition energies. In order to determine the direct-indirect band gap crossing point, the measured transition energies at the X point have to be aligned by the calculated position of the highest valence state. Thereby density-functional theory (DFT) based approaches to the electronic structure, ranging from the standard (semi)local generalized gradient approximation (GGA), self-energy corrected local density approximation (LDA-1/2), and meta-GGA DFT (TB-mBJLDA) to hybrid functional DFT and many-body perturbation theory in the GW approximation, are applied to random and special quasirandom structure models of zb-Al x Ga 1−x N. This study provides interesting insights into the accuracy of the various numerical approaches and contains reliable ab initio data on the electronic structure and fundamental alloy band gaps of zb-Al x Ga 1−x N. Nonlocal Heyd-Scuseria-Ernzerhof-type hybrid-functional DFT calculations or, alternatively, GW quasiparticle calculations are required to reproduce prominent features of the electronic structure. The direct-indirect band gap crossing point of zb-Al x Ga 1−x N is found in the Al rich composition range at an Al content between x = 0.64 and 0.69 in hybrid functional DFT, which is in good agreement with x = 0.71 determined from the aligned experimental transition energies. Thus our study solves the long-standing debate on the nature of the fundamental zb-Al x Ga 1−x N alloy band gap.

Ordinary dielectric function of corundumlike α−Ga2O3 from 40 meV to 20 eV

“…Substitution of Ga for Al in the corundum sesquioxide is expected to decrease transition energies. Similar behavior is reported for β sesquioxides [20] or when comparing AlN and GaN, both in the zinc-blende [65] and in the wurtzite polytype [66]. Also the classical III-V zinc-blende semiconductors AlAs and GaAs show a similar behavior [67].…”

Photoelastic properties of zinc-blende AlxGa1−xN in the UV: Picosecond ultrasonic studies

“…We associate the peak position in the wavelength dependence of n with the onset for optical electron-hole transition and correspondingly with the band gap E g of the alloy (i.e., E g = E 0 ). As was shown in previous studies with c-GaN [24], c-AlN [25], and (AlGa)N alloys [8] this is a good approximation and the values of E g defined in such a way are presented in Table I. We do not see any experimental evidence of indirect band gap in (AlGa)N which could happen when x approaches the value of 0.7 [8].…”

“…Furthermore, because c-AlGaN can be grown by MBE on Si and GaAs substrates, the optoelectronic devices can be integrated with conventional Si-and GaAs-based electronic devices. However, the cubic phase of AlGaN is metastable and it is difficult to grow high-quality layers containing few stacking faults and a small hexagonal component, therefore there are only a few works where the optical properties of c-Al x Ga 1−x N have been studied [6][7][8]. In those experiments, the ellipsometry technique was used to measure the layer thickness as well as the refractive index and extinction coefficient.…”

Computationally predicted energies and properties of defects in GaN

“…A variety of approaches have been proposed, 22 including applications of Hubbard-U-like terms (LDA + U or GGA + U) to cation d states 40 or to multiple orbital channels, 41 the Slater-Janak transition model, 42,43 modified pseudopotentials, 44 Becke-Johnson type functionals, 45,46 combining DFT with quasiparticle calculations, 35,36 and hybrid functionals. [47][48][49][50][51][52][53][54][55][56] Hybrid functionals have emerged as the current method of choice, 22 applicable to a wide variety of systems including defects in Si, 47,48 GaAs, 51 diamond, 48 and oxides.…”