Accurate band gaps and dielectric properties from one-electron theories (abstract only)

Abstract

For semiconductor modeling, a major shortcoming of density functional theory is that thepredicted band gaps are usually significantly too small. It is generally argued that thisshortcoming is related to the fact that density functional theory is a ground state theory,and as a result, one is not allowed to associate the one-electron energies with the energies ofquasi-particles. Although this fundamental objection is certainly correct, the modeling ofthe positioning of donor and acceptor levels in semiconductors faces serious limitations withpresent density functionals.Several solutions to this problem have been suggested. A particular attractive and fairlysimple one is the inclusion of a small fraction of the non-local exchange in the Hamiltonian(hybrid functionals). This approach leads to sensible band gaps for most semiconductors,but fails for ionic solids. A more reliable approach is via many-electron Green’sfunction techniques, which have made tremendous advances in recent years. Here GW calculations in various flavors are presented for small gap and large gap systems,comprising typical semiconductors (Si, SiC, GaAs, GaN, ZnO, ZnS, CdS andAlP), small gap semiconductors (PbS, PbSe, PbTe), insulators (C, BN, MgO,LiF) and noble gas solids (Ar, Ne). The general finding is that single-shot G0W0 calculations based on wavefunctions obtained from conventionaldensity functional theory yield too small band gaps, whereas G0W0 calculations following hybrid functional calculations tend to overestimate the bandgaps by roughly the same amount. This is at first sight astonishing, since thehybrid functionals yield very good band gaps themselves. The contradiction isresolved by showing that the inclusion of the attractive electron–hole interactions(excitonic effects) is required to obtain good static and dynamic dielectricfunctions using hybrid functionals. The corrections are usually incorporated in GW calculations using ‘vertex corrections’, and in fact inclusion of these vertex correctionsrectifies the predicted band gaps.Finally, in order to remove the dependence on the initial wavefunctions, self-consistent GW calculations are presented, again including an approximate treatment of vertexcorrections. The results are in excellent agreement with experiment, with a few per centdeviation for all materials considered. We conclude that predictive band gapengineering is now possible with the theoretical description approaching experimentalaccuracy.