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

Abstract

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-densityapproximation ͑LDA͒ calculations are performed on a few InP crystal structures, covering a range of unit-cell volumes, to produce bulk potentials ͕V LDA ͑G͖͒. By solving a set of linear equations, we extract from these crystalline potentials the corresponding screened atomic ''spherical LDA'' ͑SLDA͒ potentials v SLDA ␣ ͉͑q͉͒ for sites ␣ϭIn 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 values͒, 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 components͒, 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 E g ͑in unit of eV͒ versus the effective dot sizes D ͑in unit of Å͒ gives E g ϭ1.45ϩ37.295/D 1.16. This prediction differs significantly from the quadratic size dependence D Ϫ2.0 expected from simple effective-mass theory. ͓S0163-1829͑97͒05203-X͔

Semiempirical pseudopotential approach for nitride-based nanostructures andab initiobased passivation of free surfaces

“…The defective band gap inherited from DFT is correct by a slight adjustment of the nonlocal channel of the potential which has only a very marginal effect on the wave functions, as shown previously. 3,5,41 The derived method should be applicable to other materials. Eventually, the method can be built on the basis of GW calculations.…”

“…We have followed the idea 3,5 to use the screened effective potential from a DFT bulk calculation to extract a spherically averaged atomic pseudopotential. We have derived the analytic connection between the screened DFT effective potential and the atomic quantities in the case of wurtzite bulk unit cells.…”

“…These semiemipirical pseudpotentials (SEPs) were derived for CdSe and InP and their accuracy demonstrated. 3,5 In this work, we follow a similar procedure for the derivation of nitride SEPs. Former treatment of nitrides was at the level of empirical pseudopotentials (as opposed to SEPs) which assume an empirical analytic functional dependence (a sum of Gaussians) instead of being obtained from DFT-LDA and include only a local component, while the SEPs are angularmomentum-dependent nonlocal (or semilocal) potentials.…”

“…The advantages of SEPs compared to the local empirical pseudopotentials have been discussed earlier, generally to zinc-blende semiconductors. [3][4][5] In this work, we have extended the SEP formulation to wurtzite semiconductors, and more specifically to GaN.…”

Electronic structure of strainedInP/Ga0.51InPryor1, Pistol2, Samuelson3 1997Phys. Rev. B21141300View full textAdd to dashboardCite

“…The pyramidal shape and presence of strain in the islands makes for a potentially rich electronic structure. Theoretical studies of strained islands have employed various degrees of approximation to the geometry, strain distribution, and electron dynamics, ranging from single band models of hydrostatically strained islands, to multiband models including realistic shapes and strain distributions [1][2][3][4].…”