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

The bulk GaAs0.5P0.5 alloy with lattice constant a(0.5) has an indirect band gap. First‐principles self‐consistent pseudopotential band structure calculations show that the monolayer (GaAs)1 (GaP)1 superlattice (SL) in either the (001) or the (111) layer orientation G is also indirect if constrained epitaxially on a substrate whose lattice constant is a(0.5). However, if grown coherently on a GaAs substrate we predict that both of these SLs will have a direct band gap. This is explained in terms of the deformation potentials of the underlying materials. Predicted band offsets are given for both (001) and (111) GaP/GaAs.

Prediction of direct band gaps in monolayer (001) and (111) GaAs/GaP superlattices

Thermodynamic instability of Ag/Au and Cu/Pd metal superlattices

The electronic structure consequences of the perturbations caused by dilute nitrogen impurities in $\mathrm{GaP}$ are studied by means of supercell calculations using a fully atomistic empirical pseudopotential method. We find that numerous localized states are introduced by a single $\mathrm{N}$ atom and $\mathrm{N}$ clusters, not only close to the band edge but also throughout the $\mathrm{GaP}$ conduction band, up to $\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ above the conduction band edge. These localized states suggest an alternative interpretation for a previously puzzling observation of splitting of photoluminescence excitation intensity at the $\mathrm{GaP}$ ${\ensuremath{\Gamma}}_{1c}$ energy into two features, one blueshifting and the other staying pinned in energy with increasing $\mathrm{N}$ concentration.

Penetration of electronic perturbations of dilute nitrogen impurities deep into the conduction band ofGaP1−xNx

We investigate whether the electric field gradient (EFG) at an atomic site in the unit cell of a periodic solid can be modeled via the electrostatic field gradient set up by atomic point charges outside that site. To test this approach we contrast the EFG predicted by such point-ion models for long-range ordered GaInP2 alloys with the results obtained from self-consistent all-electron calculations in the local density approximation (LDA). We first tested our LDA approach for ZnAl2O4, for which experimental data exist, finding the quadrupole coupling constant Qcc(27Al)=3.94 MHz, compared with the measured value of |Q|=3.68 MHz. Applying next the LDA approach to perfectly ordered GaInP2 (for which experimental data do not exist), we find the LDA quadrupole coupling constant Qcc=−4.83, −2.84, and 13.08 MHz for 69Ga, 71Ga, and 115In, respectively. We further find that more than 95% of these EFGs originate from the anisotropic electron charge distribution within a small sphere of radius ∼0.2 A about the respec...

Point-ion versus density functional calculations of electric field gradients in ordered GaInP2

The energies of various steps on the As-terminated GaAs(001)-2 × 4 surface are evaluated using a novel, approximate method of “linear combination of structural motifs”. It is based on the observation that previous total energy minimizations of semiconductor surfaces produced invariably equilibrium structures made of the same recurring local structural motifs, e.g. tetrahedral fourfold Ga, pyramidal threefold As, etc. Furthermore, such surface structures were found to obey consistently the octet rules as applied to the local motifs. We thus express the total energy of a given semiconductor surface as a sum of (i) the energies eM of the local structural motifs appearing in the surface under consideration and (ii) an electrostatic term representing the Madelung energy of point charges resulting from application of the octet rule. The motif energies are derived from a set of pseudopotential total energy calculations for flat GaAs(001) surfaces and for point defects in bulk GaAs. This set of parameters suffices to reproduce the energies of other (001) surfaces, calculated using the same pseudopotential total energy approach. Application to GaAs(001)-2 × 4 surfaces with steps reveals the following. (i) “Primitive steps”, defined solely according to their geometries (i.e. step heights, widths and orientations) are often unstable. (ii) Additional, non-geometric factors beyond step geometries such as addition of surface adatoms, creation of vacancies and atomic rebonding at step edges are important to lower step energies. So is step-step interaction. (iii) The formation of steps is generally endothermic. (iv) The formation of steps with edges parallel to the direction of surface As dimers (A steps) is energetically favored over the formation of steps whose edges are perpendicular to the As dimers (B steps).

Alex Zunger

Papers

Prediction of direct band gaps in monolayer (001) and (111) GaAs/GaP superlattices

Thermodynamic instability of Ag/Au and Cu/Pd metal superlattices

Penetration of electronic perturbations of dilute nitrogen impurities deep into the conduction band ofGaP1−xNx

Point-ion versus density functional calculations of electric field gradients in ordered GaInP2

Structure and formation energy of steps on the GaAs(001)-2×4 surface