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. ...

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A comprehensive review of zno materials and devices

$3d$ transition impurities in wide-gap oxides may function as donor/acceptor defects to modify carrier concentrations, and as magnetic elements to induce collective magnetism. Previous first-principles calculations have been crippled by the LDA error, where the occupation of the $3d$-induced levels is incorrect due to spurious charge spilling into the misrepresented host conduction band, and have only considered magnetism and carrier doping separately. We employ a band-structure-corrected theory, and present simultaneously the chemical trends for electronic properties, carrier doping, and magnetism along the series of $3{d}^{1}--3{d}^{8}$ transition-metal impurities in the representative wide-gap oxide hosts ${\text{In}}_{2}{\text{O}}_{3}$ and ZnO. We find that most $3d$ impurities in ${\text{In}}_{2}{\text{O}}_{3}$ are amphoteric, whereas in ZnO, the early $3d$'s (Sc, Ti, and V) are shallow donors, and only the late $3d$'s (Co and Ni) have acceptor transitions. Long-range ferromagnetic interactions emerge due to partial filling of $3d$ resonances inside the conduction band and, in general, require electron doping from additional sources.

Electronic structure, donor and acceptor transitions, and magnetism of 3d impurities in In2O3 and ZnO

Recent refinement studies of a consolidated set of Si structure factors have produced information on the Si charge density with an unprecedented level of accuracy, unmatched by any other crystallographic study to date. In this work we examine the extent to which an accurate implementation of the local-density formalism can describe the charge distribution in silicon, as well as that of the experimentally less-refined data on diamond and germanium. Results of a refinement study of recent germanium and diamond measurements are presented and compared with the ab initio calculations. Our ab initio calculated structure factors for Si show a twofold to fivefold improvement in the R factor over previous local-density calculations

Electronic charge distribution in crystalline diamond, silicon, and germanium.

A new approach to the fully self-consistent solution of the one-particle equations in a periodic solid within the Hohenberg-Kohn-Sham local-density-functional formalism is presented. The method is based on systematic extensions of non-self-consistent real-space techniques of Ellis, Painter, and collaborators and the self-consistent reciprocal-space methodologies of Chaney, Lin, Lafon, and co-workers. Specifically, our approach combines a discrete variational treatment of all potential terms (Coulomb, exchange, and correlation) arising from the superposition of spherical atomiclike overlapping charge densities, with a rapidly convergent three-dimensional Fourier series representation of all the multicenter potential terms that are not expressible by a superposition model. The basis set consists of the exact numerical valence orbitals obtained from a direct solution of the local-density atomic one-particle equations and (for increased variational freedom) virtual numerical atomic orbitals, charge-transfer (ion-pair) orbitals, and "free" Slater one-site functions. The initial crystal potential consists of a non-muffin-tin superposition potential, including nongradient free-electron correlation terms calculated beyond the random-phase approximation. The usual multicenter integrations encountered in the linear-combination-of-atomic-orbitals tight-binding formalism are avoided by calculating all the Hamiltonian and other matrix elements between Bloch states by three-dimensional numerical Diophantine integration. In the first stage of self-consistency, the atomic superposition potential and the corresponding numerical basis orbitals are modified simultaneously and nonlinearly by varying (iteratively) the atomic occupation numbers (on the basis of computed Brillouin-zone averaged band populations) so as to minimize the deviation, $\ensuremath{\Delta}\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$, between the band charge density and the superposition charge density. This step produces the "best" atomic configuration within the superposition model for the crystal charge density and tends to remove all the sharp "localized" features in the function $\ensuremath{\Delta}\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ by allowing for intra-atomic charge redistribution to take place. In the second stage, the three-dimensional multicenter Poisson equation associated with $\ensuremath{\Delta}\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ through a Fourier series representation of $\ensuremath{\Delta}\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ is solved and solutions of the band problem are found using a self-consistent criterion on the Fourier coefficients of $\ensuremath{\Delta}\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$. The calculated observables include the total crystal ground-state energy, equilibrium lattice constants, electronic pressure, x-ray scattering factors, and directional Compton profile. The efficiency and reliability of the method is illustrated by means of results obtained for some ground-state properties of diamond; comparisons are made with the predictions of other methods.

Self-consistent numerical-basis-set linear-combination-of-atomic-orbitals model for the study of solids in the local density formalism

Spontaneous Atomic Ordering in Semiconductor Alloys: Causes, Carriers, and Consequences

Using a valence force field approach and ab initio pseudopotential calculations, we examine the role of subsurface strain in the ordering of Ga0.5In0.5P alloys. We show that depending on the orientation of the surface phosphorus dimers, these alloys can have (i) a CuPtA ordering for 1×2 or c(4×4) reconstruction; (ii) a CuPtB ordering for 2×1 or β2(2×4) reconstruction; and (iii) a triple period ordering for 2×3 or c(8×6) reconstruction. These results are in good agreement with recent experiments of Gomyo et al. [Phys. Rev. Lett. 72, 673 (1994); Jpn. J. Appl. Phys. 34, L469 (1995)].

Alex Zunger

Papers

Electronic structure, donor and acceptor transitions, and magnetism of 3d impurities in In2O3 and ZnO

Electronic charge distribution in crystalline diamond, silicon, and germanium.

Self-consistent numerical-basis-set linear-combination-of-atomic-orbitals model for the study of solids in the local density formalism

Spontaneous Atomic Ordering in Semiconductor Alloys: Causes, Carriers, and Consequences

Surface dimerization induced CuPtB versus CuPtA ordering of GaInP alloys