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

It has been previously shown by Politzer, Parr, and Boyd that the radius rm at which atomic radial charge densities 4rr2P(r) have their outer minimum constitutes a chemically meaningful quantum mechanical core radius It is shown here that {rm} correlates linearly with the position r(0)nd of the outer node in the l = 0 valence orbital and also with the l = 0 classical crossing point rl = 0 of the recently developed a priori density‐functional atomic pseudopotential The universality of these definitions of the quantum core size is indicated in view of these surprising correlations (AIP)

Pseudopotential and all‐electron atomic core size scales

Statistical Properties of Exciton Fine Structure Splittings and Polarization Angles in Quantum Dot Ensembles MING GONG, Department

Thermophotovoltaic (TPV) devices are intended to absorb photons from hot blackbody radiating objects, often requiring semiconductor absorbers with band gap of $\ensuremath{\simeq}0.6\text{ }\text{eV}$. The random ${\text{In}}_{x}{\text{Ga}}_{1\ensuremath{-}x}\text{As}$ alloy lattice matched $({x}_{\text{In}}=0.53)$ to a (001) InP substrate has a low-temperature band gap of 0.8 eV, about 0.2 eV too high for a TPV absorber. Bringing the band gap down by raising the In concentration induces strain with the substrate, leading to a two-dimensional $(2\text{D})\ensuremath{\rightarrow}\text{three}$-dimensional (3D) morphological transition occurring before band gaps suitable for TPV applications are achieved. We use the inverse band structure approach, based on a genetic algorithm and empirical pseudopotential calculations, to search for lattice-matched InAs/GaAs multiple-repeat unit structures with individual layer thicknesses lower than the critical thickness for a $2\text{D}\ensuremath{\rightarrow}3\text{D}$ transition. Despite the fact that quantum confinement usually increases band gaps, we find a quantum superlattice structure with the required reduced gap (and a significant optical transition) that matches all target requirements. This is explained by the predominance of (potential-energy) level anticrossing effects over (kinetic) quantum confinement effects.

Using superlattice ordering to reduce the band gap of random (In,Ga)As/InP alloys to a target value via the inverse band structure approach

Au 1 : 0.334408, 0.331184, 0.998269 Au 2 : 0.665592, 0.668816, 0.001731 Au 3 : 0.502058, 0.995884, 0.250000 Au 4 : 0.834174, 0.331652, 0.250000 Au 5 : 0.334408, 0.331184, 0.501731 Au 6 : 0.665592, 0.668816, 0.498269 Au 7 : 0.497942, 0.004116, 0.750000 Au 8 : 0.165826, 0.668348, 0.750000 Pd 1 : 0.000000, 0.000000, 0.000000 Pd 2 : 0.166849, 0.666302, 0.250000 Pd 3 : 0.000000, 0.000000, 0.500000 Pd 4 : 0.833151, 0.333698, 0.750000

Erratum: Global space-group optimization problem: Finding the stablest crystal structure without constraints [Phys. Rev. B 75, 104113 (2007)]

Electron-hole exchange interactions can lead to spin-forbidden ‘‘dark’’ excitons in direct-gap quantum dots. Here, we explore an alternative mechanism for creating optically forbidden excitons. In a large spherical quantum dot made of a diamond-structure semiconductor, the symmetry of the valence band maximum ~VBM! is t 2. The symmetry of the conduction band minimum ~CBM! in direct-gap material is a1, but for indirect-gap systems the symmetry could be ~depending on size! a1 , e ,o rt 2. In the latter cases, the resulting manifold of excitonic states contains several symmetries derived from the symmetries of the VBM and CBM ~e.g., t 2 3t 25A11E1T11T2 or t 23e5T11T2). Only the T2 exciton is optically active or ‘‘bright,’’ while the others A1 , E, and T1 are ‘‘dark.’’ The question is which is lower in energy, the dark or bright. Using pseudopotential calculations of the single-particle states of Si quantum dots and a direct evaluation of the screened electron-hole Coulomb interaction, we find that, when the CBM symmetry ist 2 , the direct electronhole Coulomb interaction lowers the energy of the dark excitons relative to the bright T2 exciton. Thus, the lowest energy exciton is forbidden, even without an electron-hole exchange interaction. We find that our dark-bright excitonic splitting agrees well with experimental data of Calcott et al., Kovalev et al., and Brongersma et al. Our excitonic transition energies agree well with the recent experiment of Wolkin et al. In addition, and contradicting simplified models, we find that Coulomb correlations are more important for small dots than for intermediate sized ones. We describe the full excitonic spectrum of Si quantum dots by using a many-body expansion that includes both Coulomb and exchange electron hole terms. We present the predicted excitonic spectra.

Alex Zunger

Papers

Pseudopotential and all‐electron atomic core size scales

Statistical Properties of Exciton Fine Structure Splittings and Polarization Angles in Quantum Dot Ensembles MING GONG, Department

Using superlattice ordering to reduce the band gap of random (In,Ga)As/InP alloys to a target value via the inverse band structure approach

Erratum: Global space-group optimization problem: Finding the stablest crystal structure without constraints [Phys. Rev. B 75, 104113 (2007)]

Dark excitons due to direct Coulomb interactions in silicon quantum dots