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

We present a general theory of compounds with partial long-range order. We derive a simple formula that determines the properties of a partially ordered compound from those of the perfectly random alloy and the fully ordered compound. The formula makes accurate predictions of both formulation energies and electronic band structures. We also use the formula to predict the band gaps of Al[sub 1[minus][ital x]]Ga[sub [ital x]]As/GaAs superlattices.

Evolution of alloy properties with long-range order.

Epitaxial strain energies of epitaxial films and bulk superlattices are studied via first-principles total-energy calculations using the local-density approximation. Anharmonic effects due to large lattice mismatch, beyond the reach of the harmonic elasticity theory, are found to be very important in Cu/Au (lattice mismatch 12%), Cu/Ag (12%), and Ni/Au (15%). We find that $〈001〉$ is the elastically soft direction for biaxial expansion of Cu and Ni, but it is $〈201〉$ for large biaxial compression of Cu, Ag, and Au. The stability of superlattices is discussed in terms of the coherency strain and interfacial energies. We find that in phase separating systems such as Cu-Ag the superlattice formation energies decrease with superlattice period, and the interfacial energy is positive. Superlattices are formed easiest on (001) and hardest on (111) substrates. For ordering systems, such as Cu-Au and Ag-Au, the formation energy of superlattices increases with period, and interfacial energies are negative. These superlattices are formed easiest on (001) or (110) and hardest on (111) substrates. For Ni-Au we find a hybrid behavior: superlattices along $〈111〉$ and $〈001〉$ behave like phase separating systems, while for $〈110〉$ they behave like ordering systems. Finally, recent experimental results on epitaxial stabilization of disordered Ni-Au and Cu-Ag alloys, immiscible in the bulk form, are explained in terms of destabilization of the phase separated state due to lattice mismatch between the substrate and constituents.

Effects of anharmonic strain on the phase stability of epitaxial films and superlattices: Applications to noble metals

Traditional sorting diagrams for ground states $(T=0$ stable atomic configurations) of bcc-based binary alloys predict simple crystal structures when simple parametric interactions (e.g., first few pairs) are assumed. However, the range and magnitude of interactions for real systems is not a priori known, and could lead to much greater structural complexity. We combine a density functional theory based, deterministic mixed-basis cluster expansion with an exhaustive enumeration scheme of $3\ifmmode\times\else\texttimes\fi{}{10}^{6}$ possible structures to determine the ground states of the bcc alloy Mo-Ta. The result is a rich ground-state line, changing one's outlook on bcc structural stability. We find Mo-rich (100) superlattices (including ${C11}_{\mathrm{b}}$ and $B2)$ coexisting with complex large-cell structures $({\mathrm{Mo}}_{4}{\mathrm{Ta}}_{9}$ and ${\mathrm{Mo}}_{4}{\mathrm{Ta}}_{12}).$ We demonstrate that a systematic cluster expansion construction scheme which includes both high-order pairs and many-body figures is a necessity to capture the ground states of Mo-Ta.

Structural complexity in binary bcc ground states: The case of bcc Mo-Ta

We present a cluster-based description of coherent binary or pseudobinary alloys and predict and contrast bulk and epitaxial composition-temperature phase diagrams and excess thermodynamic functions. This formalism addresses in a unified way phenomena characteristic of coherent epitaxial solids, including the following: for phase-separating alloys (whose constituents are insoluble in bulk below a miscibility-gap temperature), (i) epitaxial ordered phases not present in the bulk phase diagram and (ii) a stabilization of the disordered phase to far lower temperatures; and for all alloys, (iii) epitaxial changes of order-disorder transition temperatures and (iv) the pinning (``lattice latching'') of the composition near where an epitaxial alloy is lattice matched to a given substrate. We illustrate these effects for ${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Au}}_{\mathrm{x}}$, a typical ``ordering'' alloy (with stable ordered compounds in bulk) and for ${\mathrm{GaAs}}_{\mathrm{x}}$${\mathrm{Sb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$, a typical ``phase-separating'' alloy. Using a simple thermodynamic description of the reactions describing molecular-beam epitaxy growth of a coherent epitaxial isovalent semiconductor alloy, we demonstrate that composition pinning persists even in this growth method, and compare with available experiments.

Epitaxial effects on coherent phase diagrams of alloys.

Precise first-principles spin-polarized total-energy and band-structure calculations have been performed for the zinc-blende Mn chalcogenides with the use of the local-spin-density (LSD) approach. We find that the LSD is capable of identifying the correct magnetic-ground-state structure, but it overestimates the ordering temperature [ital T][sub [ital N]] and the valence-band exchange splitting [Delta][sub [ital x]][sup [ital p]]. The discrepancy is attributed to the overestimation by LSD of the [ital p]-[ital d] coupling. Adjusting this coupling by an external potential and fitting its parameters to the [ital s]- and [ital p]-band exchange splitting in MnTe alone, we find that [ital T][sub [ital N]]=73, 90, and 128 K, respectively, for MnTe, MnSe, and MnS, in good agreement with experiment. This shows that the failures of the LSD in reproducing [ital T][sub [ital N]] and [Delta][sub [ital x]][sup [ital p]] share a common physical origin, namely the overestimation of [ital p]-[ital d] coupling.

Alex Zunger

Papers

Evolution of alloy properties with long-range order.

Effects of anharmonic strain on the phase stability of epitaxial films and superlattices: Applications to noble metals

Structural complexity in binary bcc ground states: The case of bcc Mo-Ta

Epitaxial effects on coherent phase diagrams of alloys.

Electronic origins of the magnetic phase transitions in zinc-blende Mn chalcogenides.