Electron–phonon coupling in semiconductors within the GW approximation

Abstract

The magnitude of the renormalization of the band gaps due to zero-point motions of the lattice is calculated for 18 semiconductors, including diamond and silicon. This particular collection of semiconductors constitute a wide range of band gaps and atomic masses. The renormalized electronic structures are obtained using stochastic methods to sample the displacement related to the vibrations in the lattice. Specifically, a recently developed one-shot method is utilized where only a single calculation is needed to get similar results as the one obtained by standard Monte-Carlo sampling. In addition, a fast real-space GW method is employed and the effects of G 0 W 0 corrections on the renormalization are also investigated. We find that the band-gap renormalizations inversely depend on the mass of the constituting ions, and that for the majority of investigated compounds the G 0 W 0 corrections to the renormalization are very small and thus not significant.

Theory of the special displacement method for electronic structure calculations at finite temperature

“…Our calculated band gap narrowing due to zero-point effects is 57 meV. This value is in very good agreement with previous calculations based on non-perturbative adiabatic approaches, yielding 56-65 meV [15,19,23,25,26] as well as with experimental values, in the range of 62-64 meV [86,87]. Ref.…”

“…[95]. The slight underestimation of the experimental slope with temperature can be corrected by performing GW calculations instead of standard DFT/LDA [10,23], but overall the agreement between the present calculations and experiments is very good.…”

“…[10]. It is well established that GW quasiparticle corrections change these results by strengthening the electron-phonon coupling [10,23]: in order to incorporate this effect it will be sufficient to perform a GW calculation using the ZG displacement.…”

“…[46], [47] and [48] applied this method to the dielectric function of Zn 2 Mo 3 O 8 , metallic hydrogen, and BaSnO 3 , respectively; Ref. [23] used this technique to compute GW quasiparticle band gaps at finite temperature for diamond, BN, SiC, Si, AlP, ZnO, GaN, ZnS, GaP, AlAs, ZnSe, CdS, GaAs, Ge, AlSb, CdSe, ZnTe, and CdTe; Ref. [49] calculated exciton-phonon couplings in hexagonal boron nitride; and Refs.…”

Predominance of non-adiabatic effects in zero-point renormalization of the electronic band gap

“…As the adiabatic approximation is inherent in this approach, we denote it as ASC, for "adiabatic supercell". A recent publication by Karsai, Engel, Kresse and Flage-Larsen 34 , hereafter referred to as KEKF, presents ASC ZPR g based on DFT values, as well as based on G 0 W 0 values for 18 semiconductors, with experimental comparison for 9 of them. Both AHC and ASC methodologies have been recently reviewed 35 .…”