Accurate ab initio predictions of III–V direct-indirect band gap crossovers

Abstract

We report the compositional dependence of the electronic band structure for a range of III-V alloys. Density functional theory with the PBE functional is insufficient to mimic the electronic gap energies at different symmetry points of the Brillouin zone. The HSE hybrid functional with screened exchange accurately reproduces the experimental band gaps and, more importantly, the alloy concentration of the direct-indirect gap crossovers for the III-V alloys studied here: AlGaAs, InAlAs, AlInP, InGaP, and GaAsP.PACS numbers: 71.20. Nr, 71.55.Eq Knowing the alloy concentrations where the semiconductor is direct or indirect is essential for optoelectronic device design. Consequently a correct quantitative assessment of the electronic structure across different symmetry points of the Brillouin zone for the alloy is vital. Most studies focused on density functional theory (DFT) calculations using the local density approximation (LDA) or the generalized gradient approximation (GGA) which do poorly on excited states. Only recently have hybrid functionals been used in predicting accurate excited states in individual semiconducting alloys. 1,2The Heyd-Scuseria-Ernzerhof (HSE) hybrid functional 3-7 , which combines the screened exchange with the Perdew-Burke-Ernzerhof (PBE) GGA functional, 8 out performs previous DFT methods in reproducing bulk band gaps. 6,9,10 We report HSE reproduces not only the band gaps across the entire composition range of each alloy studied here but also the direct-indirect band gap crossovers seen experimentally.Figure 1(a) demonstrates this significant improvement of HSE over PBE in predicting the direct-indirect (Γ-X) crossover (denoted by vertical arrows) for the AlGaAs alloy compared with experiment. 11 HSE reproduces the direct-indirect crossover within 5% Al concentration from the most recent experimental value published by Yi et al. 12 The PBE functional which doesn't take into account screened exchange overestimates this crossover by 23% Al concentration.The disordered zinc-blende (cubic) alloys are best modeled by special quasirandom structures (SQS), 13 ordered structures designed to reproduce the most important pair-correlation functions of a random alloy. The best possible 32-atom SQS's we produce for concentrations of x = 0.25 and x = 0.50 match the pair-correlation functions of a random alloy up to 3rd and 7th nearest neighbors, respectively. 14 The SQS with concentration x = 0.25 can be used interchangeably with that of x = 0.75. Table I gives the lattice vectors for each SQS used to describe the optical transitions as seen in the zinc-blende primitive cell through folding relations in the Brillouin zone. The SQS with concentration x = 0.50 has a basecentered orthorhombic space group symmetry with the

Accurate electronic properties for (Hg,Cd)Te systems using hybrid density functional theory

“…5 The Heyd-Scuseria-Ernzerhof (HSE) hybrid functional, 6,7 which combines the screened exchange with the PerdewBurke-Ernzerhof (PBE) GGA functional, 8 has been seen to reproduce experimental electronic properties as well as band offsets for a range of III-V alloys. 9,10 This study extends upon those by reporting that HSE outperforms standard DFT on the electronic structure of the II-VI alloy Hg 1−x Cd x Te by reproducing the experimental crossover at x = 0.17 (Ref. 11 ) transitioning from a semimetallic alloy with band inversion to a gapped semiconducting alloy.…”

“…We use our previously published 32-atom SQSs with Cd concentrations of 25%, 50%, and 75% for this alloy calculation. 9 The 25% and 75% SQSs, differing only by swapping Hg atoms with Cd atoms, match the pair-correlation functions of a random alloy up to 3rd nearest neighbor and the 50% SQS matches up to 7th nearest neighbor. The lattice constants for the Hg 1−x Cd x Te alloy are linearly interpolated between the experimental parent compound lattice constants of HgTe (a = 6.46Å) and CdTe (a = 6.48 A).…”

Single GaInP nanowire p-i-n junctions near the direct to indirect bandgap crossover point

“…The non-intentionally doped NWs showed a low temperature PL signal in the range 1.95 to 2.3 eV, with many relatively sharp peaks, as well as room temperature macro-PL displaying one relatively broad peak centered at 2.14 eV. The average composition, x ¼ 0.77, is slightly above the predicted direct to indirect crossover, 11 and the highest PL signal at about 2.25 eV fits well with the predicted crossover bandgap at low temperature. The lowerenergy peaks at low temperature could be related to the observed stacking faults, 22 or possibly surface-related states.…”

“…7 GaInP shells grown on GaAs NW cores have been used for NW-based LEDs on silicon, 8 while others have investigated strained GaInP NW shells 9,34 and molecular beam epitaxy (MBE)-grown GaInP NWs. 10 Theoretically, GaInP can reach a direct band gap of up to about 2.2 eV at room temperature, 11 but at the corresponding composition there is no suitable substrate for thin-film growth. Axial NW heterostructures, however, can be grown with large lattice mismatch since the strain can be relaxed vertically, and here we demonstrate devices with a bandgap close to the theoretical limit.…”

“…This effect could be related to the indirect X and L bands, which both have minima of around 2.2-2.3 eV at this composition. 11 Absorption should be effective in these bands due to the high effective masses, where possibly carriers get trapped without contributing to the photocurrent. However, the saturation could also be an optical effect due to reduced coupling of short wavelength light into the NWs.…”