[Paper Review] All-electron study of InAs and GaAs wurtzite: structural and electronic properties

Zeila Zanolli, Ulf von Barth|arXiv (Cornell University)|Oct 3, 2006

Advanced Chemical Physics Studies3 references3 citations

TL;DR

This study presents the first all-electron density functional theory (DFT) investigation of InAs and GaAs in the wurtzite phase using the full-potential linearized augmented plane wave (LAPW) method within the local density approximation (LDA). It reveals that the wurtzite phase has a slightly larger c/a ratio and reduced u/c compared to ideal values, and while the all-electron approach predicts a lower equilibrium volume and higher binding energy for wurtzite InAs than zinc-blende, the energy difference is below the 30 meV numerical accuracy, preventing a definitive stability prediction.

ABSTRACT

The structural and electronic properties of the wurtzite phase of the InAs and GaAs compounds are, for the first time, studied within the framework of Density Functional Theory (DFT). We used the full-potential linearized augmented plane wave (LAPW) method and the local density approximation (LDA) for exchange and correlation and compared the results to the corresponding pseudopotential calculations. From the structural optimization of the wurtzite polymorph of InAs we found that the c/a ratio is somewhat greater than the ideal one and that the internal parameter u/c has a value slightly smaller than the ideal one. In the all-electron approach the wurtzite polymorph has a smaller equilibrium volume per InAs pair and a higher binding energy when compared to the zinc-blende phase whereas the situation is reversed in the pseudo treatment. The energy differences are, however, smaller than the accuracy of standard density-functional codes (~30 meV) and a theoretical prediction of the relative stability of the two phases cannot be made. In order to investigate the possibility of using an LDA calculation as a starting point for many-body calculations of excitations properties, we here also present the band-structures of these materials. The bands are calculated with and without relativistic effects. In InAs we find that the energy gaps of both polymorphs are positive when obtained from a non-relativistic calculation and negative otherwise. For both semiconductors, we determine the spin-orbit splittings for the zinc-blende and the wurtzite phases as well as the crystal-field splittings for the new wurtzite polymorphs.

Motivation & Objective

• To investigate the structural and electronic properties of wurtzite InAs and GaAs, which are metastable phases not previously studied experimentally.
• To resolve discrepancies in prior pseudopotential-based studies by employing all-electron calculations with full-potential LAPW method.
• To assess the reliability of LDA as a starting point for many-body GW calculations by benchmarking band structures.
• To compute spin-orbit and crystal-field splittings for the wurtzite phase, which are critical for interpreting optical and electronic measurements in nanowires.

Proposed method

• Employed all-electron full-potential linearized augmented plane wave (LAPW) method for accurate electronic structure calculations.
• Used the local density approximation (LDA) for exchange and correlation, with scalar relativistic treatment and spin-orbit coupling as corrections.
• Performed structural optimization for both zinc-blende and wurtzite phases of InAs, comparing equilibrium lattice parameters and binding energies.
• Calculated band structures using non-relativistic, scalar-relativistic, and spin-orbit-coupled approximations to assess relativistic effects.
• Used experimental lattice constants from TEM measurements for GaAs to improve comparison with experimental data.
• Computed energy gaps, spin-orbit splittings, and crystal-field splittings from the band structures for both polymorphs.

Experimental results

Research questions

• RQ1 What are the equilibrium structural parameters (c/a ratio, u/c) of wurtzite InAs and GaAs, and how do they deviate from ideal values?
• RQ2 Which phase—zinc-blende or wurtzite—is more stable for InAs, and can the energy difference be resolved within standard DFT accuracy?
• RQ3 How do relativistic effects, particularly spin-orbit coupling, influence the band structure and band gap in wurtzite InAs and GaAs?
• RQ4 To what extent does the LDA band structure serve as a reliable starting point for GW calculations of excited-state properties?
• RQ5 What are the spin-orbit and crystal-field splittings in the wurtzite phase, and how do they compare to experimental values?

Key findings

• The wurtzite InAs phase has a c/a ratio slightly larger than the ideal 8/3 and an internal parameter u/c slightly smaller than the ideal 0.375.
• The all-electron approach predicts a lower equilibrium volume and higher binding energy for wurtzite InAs compared to zinc-blende, but the energy difference is only ~3 meV, below the ~30 meV numerical accuracy of standard DFT codes.
• For InAs, the non-relativistic LDA calculation yields a positive band gap, but including spin-orbit coupling results in a negative gap, indicating a zero-gap semiconductor prediction.
• In GaAs, the scalar-relativistic LDA calculation correctly predicts a semiconducting gap (327 meV without S-O, 211 meV with S-O), though it remains significantly underestimated compared to experiment (1.629 eV).
• The spin-orbit splitting in GaAs is calculated as 339 meV (zinc-blende) and 340 meV (wurtzite), in good agreement with experimental values.
• The crystal-field splitting in wurtzite GaAs is calculated as 79 meV, a value that is significant for understanding the band structure in wurtzite nanowires.