Local-density-derived semiempirical nonlocal pseudopotentials for InP with applications to large quantum dots

In the same way that atomic calculations have been used previously to extract bare ionic pseudopotentials, self-consistent bulk calculations can be used to construct screened atomic pseudopotentials. We use such a method to construct screened nonlocal atomic pseudopotentials for InP. A series of bulk, local-density-approximation (LDA) calculations are performed on a few InP crystal structures, covering a range of unit-cell volumes, to produce bulk potentials {${\mathrm{V}}_{\mathrm{LDA}}$ (G)}. By solving a set of linear equations, we extract from these crystalline potentials the corresponding screened atomic 'spherical LDA' (SLDA) potentials ${\mathrm{v}}_{\mathrm{SLDA}}^{\mathrm{\alpha }>}$(|q|) for sites α=In or P. In combination with the nonlocal part of the usual LDA pseudopotentials, these SLDA potentials give band structures and wave functions that are virtually indistinguishable from the self-consistent LDA results for bulk InP. In the next step, we apply linear changes to the local SLDA potentials (while keeping the nonlocal potentials at their LDA values), to fit the band structures to experiment. Interestingly, this removal of LDA eigenvalue errors requires only small and subtle changes in the potential—mostly an upshift in the region near the cation core, with nearly no change at the bond center. Furthermore, the linear changes to the SLDA potentials result mostly in an upshift of the conduction bands with little effect on the valence bands. Because only small changes in the potential suffice to fit the bands to experimental results, the wave functions remain virtually unchanged relative to those in the original LDA calculation. Hence, we obtain semiempirical pseudopotentials which can produce ab initio LDA-quality wave functions with experimentally measured band structures, effective masses, and deformation potentials. The potentials obtained here were deposited on an FTP site and can be used by interested readers. Since the resulting pseudopotentials are 'soft' (with small high-momentum components), they can be applied within a plane-wave basis in combination with a Gaussian correction to large systems for which LDA calculations are prohibitively expensive. As an illustration, we apply our InP screened atomic pseudopotentials to calculate quantum size effects on the band gaps of InP dots with sizes up to 700 atoms. Good agreement is found between the theoretical and the experimental band gaps. Fitting the calculated band gaps ${\mathrm{E}}_{\mathrm{g}}$ (in unit of eV) versus the effective dot sizes D (in unit of Å) gives ${\mathrm{E}}_{\mathrm{g}}$ =1.45+37.295/${\mathrm{D}}^{1.16}$ . This prediction differs significantly from the quadratic size dependence ${\mathrm{D}}^{\mathrm{-}2.0}$ expected from simple effective-mass theory.