Relativistic and core-relaxation effects on the energy bands of gallium arsenide and germanium

Relativistic self-consistent band-structure calculations using either norm-conserving pseudopotentials or the linear-muffin-tin-orbital method (LMTO) demonstrate that relativistic effects on some conduction bands of gallium arsenide, if qualitatively not unexpected, are however, surprisingly large (the direct gap is reduced by one-half), despite the relatively light atoms. This is discussed in terms of a simple bonding-antibonding picture: Relativistic effects may either be depressed or amplified, with respect to free atoms, by the formation of bands and bonds. The gallium 3d core states are known to be shallow, i.e., not far enough from the 4s and 4p energies to allow them to be treated as completely frozen-core states. Therefore, in a new self-consistent LMTO calculation we treat them on the same footing as the other valence-band states. The most evident effects of the Ga 3d core-relaxation are a further, sizable shrinkage of the gaps, and a clear improved agreement of the valence bands with photoemission experiments. We stress the influence of relativistic and core-relaxation effects on the bands of GaAs, and also show, for the first time, that the intrinsic failure of the local-density approximation as far as gaps are concerned is much larger for third-row semiconductors than for, e.g., the better-known case of Si. This is emphasized by our calculation for the neighboring elemental semiconductor, germanium, where almost no gap is found, i.e., metallization has occurred one row too early. The calculated gaps are a necessary reference for the development of the density-functional theory of the energy gap.