Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set

We present ab initio quantum-mechanical molecular-dynamics simulations of the liquid-metal--amorphous-semiconductor transition in Ge. Our simulations are based on (a) finite-temperature density-functional theory of the one-electron states, (b) exact energy minimization and hence calculation of the exact Hellmann-Feynman forces after each molecular-dynamics step using preconditioned conjugate-gradient techniques, (c) accurate nonlocal pseudopotentials, and (d) Nos\'e dynamics for generating a canonical ensemble. This method gives perfect control of the adiabaticity of the electron-ion ensemble and allows us to perform simulations over more than 30 ps. The computer-generated ensemble describes the structural, dynamic, and electronic properties of liquid and amorphous Ge in very good agreement with experiment. The simulation allows us to study in detail the changes in the structure-property relationship through the metal-semiconductor transition. We report a detailed analysis of the local structural properties and their changes induced by an annealing process. The geometrical, bonding, and spectral properties of defects in the disordered tetrahedral network are investigated and compared with experiment.

Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium.

The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

Self-interaction correction to density-functional approximations for many-electron systems

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

The semiconductor ZnO has gained substantial interest in the research community in part because of its large exciton binding energy (60meV) which could lead to lasing action based on exciton recombination even above room temperature. Even though research focusing on ZnO goes back many decades, the renewed interest is fueled by availability of high-quality substrates and reports of p-type conduction and ferromagnetic behavior when doped with transitions metals, both of which remain controversial. It is this renewed interest in ZnO which forms the basis of this review. As mentioned already, ZnO is not new to the semiconductor field, with studies of its lattice parameter dating back to 1935 by Bunn [Proc. Phys. Soc. London 47, 836 (1935)], studies of its vibrational properties with Raman scattering in 1966 by Damen et al. [Phys. Rev. 142, 570 (1966)], detailed optical studies in 1954 by Mollwo [Z. Angew. Phys. 6, 257 (1954)], and its growth by chemical-vapor transport in 1970 by Galli and Coker [Appl. Phys. ...

/pdf/a-comprehensive-review-of-zno-materials-and-devices-21a3zjadem.pdf

A comprehensive review of zno materials and devices

It is shown how the introduction of volume-dependent elastic interactions into lattice models of order-disorder transformations, in addition to the familiar constant-volume interactions (analogous to Ising ''spin energies''), leads to qualitatively new features in a binary A/sub x/B/sub 1-x/ phase diagram.

Effect of chemical and elastic interactions on the phase diagrams of isostructural solids.

Free-standing InP quantum dots have previously been theoretically and experimentally shown to have a direct band gap across a large range of experimentally accessible sizes. We demonstrated that when these dots are embedded coherently within a GaP barrier material, the effects of quantum confinement in conjunction with coherent strain suggest there will be a critical diameter of dot ({approx}60 {Angstrom}), above which the dot is direct, type I, and below which it is indirect, type II. However, the strain in the system acts to produce another conduction state with an even lower energy, in which electrons are localized in small pockets at the interface between the InP dot and the GaP barrier. Since this conduction state is GaP X{sub 1c} derived and the highest occupied valence state is InP, {Gamma} derived, the fundamental transition is predicted to be indirect in both real and reciprocal space ({open_quotes}type II{close_quotes}) for all dot sizes. This effect is peculiar to the strained dot, and is absent in the freestanding dot. {copyright} {ital 1998} {ital The American Physical Society}

https://arxiv.org/pdf/cond-mat/9801191.pdf

Prediction of a strain-induced conduction-band minimum in embedded quantum dots

A model is proposed for discussing deep defect levels in covalent solids, based on the representation of the one−electron energies of the crystal by the eigenvalue spectrum of a small periodic cluster of atoms. Calculations of this model by semiempirical MO−LCAO methods for a vacancy problem in hexagonal boron nitride and graphite and substitutional boron impurity in graphite, yield satisfactory results when compared with experimental EPR, thermoluminescence, and thermally−stimulated−currents data.

Small periodic cluster calculation on point defect problems in hexagonal layered solids

The electronic structure of GaAsN alloys was previously described in terms of nitrogen “cluster states” (CS) that exist in the dilute alloy in the bandgap, and “perturbed host states” (PHS) inside the conduction band. As the nitrogen concentration increases, the PHS plunge down in energy overtaking the CS. We show theoretically that the CS respond to the application of pressure in two different ways: the highly localized deep CS emerge (or remain) in the gap, because their pressure coefficient is lower than that of the conduction band minimum. In contrast, the shallow CS (first to be overtaken) hybridize so strongly with the conduction band that their pressure coefficient becomes comparable to that of the conduction states. These states fail to emerge into the gap upon application of pressure because they move, with application of pressure, at a similar rate with conduction states.

/pdf/failure-of-nitrogen-cluster-states-to-emerge-into-the-3m84y07bq2.pdf

Failure of nitrogen cluster states to emerge into the bandgap of GaAsN with application of pressure

While $(\mathrm{InAs}{)}_{n}/(\mathrm{GaSb}{)}_{n}$ (001) superlattices are semiconducting for $nl{n}_{c}\ensuremath{\approx}28\mathrm{ML},$ for $ng{n}_{c}$ the InAs electron level ${e}_{\mathrm{InAs}}$ is below the GaSb hole level ${h}_{\mathrm{GaSb}},$ so the system is converted to a nominal semimetal. At nonzero in-plane wave vectors $({\mathbf{k}}_{\ensuremath{\Vert}}\ensuremath{\ne}0),$ however, the wave functions ${e}_{\mathrm{InAs}}$ and ${h}_{\mathrm{GaSb}}$ have the same symmetry, so they anticross. This opens up a ``hybridization gap'' at some ${\mathbf{k}}_{\ensuremath{\Vert}}={\mathbf{k}}_{\ensuremath{\Vert}}^{*}.$ Using a pseudopotential plane-wave approach as well as a (pseudopotential fit) eight-band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ approach, we predict the hybridization gap and its properties such as wave-function localization and out-of-plane dispersion. We find that recent model calculations underestimate this gap severely.

Alex Zunger

Papers

Effect of chemical and elastic interactions on the phase diagrams of isostructural solids.

Prediction of a strain-induced conduction-band minimum in embedded quantum dots

Small periodic cluster calculation on point defect problems in hexagonal layered solids

Failure of nitrogen cluster states to emerge into the bandgap of GaAsN with application of pressure

Anticrossing semiconducting band gap in nominally semimetallic InAs/GaSb superlattices