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

Monte Carlo simulations of a chemically random Ga1-xInxP alloy are carried out. An interatomic potential has been parametrized to fit first-principle total-energy calculations of various ordered GaP/InP structures. Using this potential, good agreement between predicted and measured properties of the Ga1-xInxP alloy are obtained. This potential is then used to predict positions of atoms in Ga1-xInxP yielding for the phosphorous atomic-positions probability peaks at several distinct lattice locations which emerge from correlated atomic displacements. The evolution of these displaced positions with temperature is followed by molecular-dynamics calculations showing that the average thermal r.m.s. displacements Ū obey ŪIn > ŪP > ŪGa.

Correlated Atomic Displacements in the Chemically Random Ga1-xInxP Alloy

First-Principles Theory of Cation and Vacancy Ordering in LixCoO2

We present a theory of the evolution of the electronic structure of GaAsN alloys, from the dilute impurity limit to the fully formed alloy. Using large scale empirical pseudopotential calculations, we show how substitutional nitrogen forms Perturbed Host States (PHS) inside the conduction band whereas small nitrogen aggregates form localized Cluster States (CS) in the band gap. By following the evolution of these states with increasing nitrogen composition we develop a model that explains many of the experimentally observed phenomena, including high effective masses, Stokes shift in emission versus absorption, and anomalous pressure dependence.

Evolution of Electron States with Composition in GaAsN Alloys

We show that, contrary to the assertion of Alsina et al. in the preceding Comment, the theoretically calculated phonon sequence in ordered GaInP 2 does not violate the ‘‘alternation rule.’’ Analysis of the firstprinciples calculated phonon dispersion shows that CuPt-ordered GaInP 2 is a system where anisotropy of short-range forces is of the same magnitude as the electrostatic Coulomb interactions and the associated LO/TO splittings. We show how the phonon modes change with the degree of order, and demonstrate that our results, without revision, successfully account for the experimental infrared data.

Reply to ``Comment on `First-principles theory of the evolution of vibrational properties with long-range order in GaInP 2 ' ''

Interest in substitutional disordered alloys has recently reemerged with focus on the symmetry-sensitive properties in the alloy such as topological insulation and Rashba effect. A substitutional random alloy ${(AX)}_{x}{(BX)}_{1\ensuremath{-}x}$ of components $AX$ and $BX$ generally manifests a distribution of local environments, whereby each $X$ site, for example, can be locally decorated by different substitutional arrangements of {$A,B,X$} atoms, thus creating an inherently polymorphous network. Electrons will then respond to the existence of different local environments and site symmetries, creating local charge transfer and atomic displacements patterns observed in experiments. While the macroscopic average structure ${S}_{0}$, as seen by probes with long coherence length, may have the original high symmetry of the constituent compounds, many observable physical properties are sensitive to local symmetry, and are hence the average $\ensuremath{\langle}P({S}_{i})\ensuremath{\rangle}$ of the properties ${P({S}_{i});\phantom{\rule{0.28em}{0ex}}i=1,...,N}$ of the individual microscopic configurations ${{S}_{i};i=1,N}$ rather than the property $P(\ensuremath{\langle}{S}_{i}\ensuremath{\rangle})=P({S}_{0})$ of the macroscopically averaged high-symmetry (monomorphous) configuration ${S}_{0}$. The fundamental difference between the polymorphous representation $\ensuremath{\langle}P({S}_{i})\ensuremath{\rangle}$ versus the monomorphous $P({S}_{0})$ in modeling substitutionally disordered alloys led to the often diverging results between methods that ``see'' atomic details and those that see only the high symmetry of the constituents, while missing the atomic-scale resolution needed in many cases to discern local symmetry-related physics. A natural approach that captures the polymorphous aspect of random alloys is the well-known supercell approach where lattice sites are occupied by the alloyed elements with a particular form of disorder and solved via periodic electronic structure methods for sufficiently large supercells. However, such approaches tend to produce complex $E$ versus $\mathbit{k}$ dispersion relations (``spaghetti bands''), rendering the wave-vector $k$ information needed in theories of topology and Rashba physics and seen in angular resolved experiments, practically inaccessible. The results of such calculations have consequently been displayed as density of states. A solution that retains the polymorphous nature of the random alloy but reinstates the $E$ versus $\mathbit{k}$ relation in the base Brillouin zone is to unfold the supercell bands. This yields alloy ``effective band structure'' (EBS), providing a three-dimensional picture of the distribution of spectral density in the whole Brillouin zone. It consists of $E$- and $k$-dependent spectral weight with coherent and incoherent features, all created naturally by the specific nature of the chemical bonding underlying the polymorphous distribution of many local environments. We illustrate this EBS approach for CdTe-HgTe, PbSe-SnSe, and PbS-PbTe alloys, showing atomic-scale effects such as formation of a distribution of $A\text{\ensuremath{-}}X$ and $B\text{\ensuremath{-}}X$ bond lengths, local charge transfer, and the creation and destruction of valley degeneracies. In CdTe-HgTe, the disorder effect is so weak that the incoherent term is negligible, and the monomorphous approaches are still feasible in this alloy. In PbSe-SnSe, the stronger disorder effect introduces significant $(\ensuremath{\sim}150\phantom{\rule{0.16em}{0ex}}\mathrm{meV})$ band splitting of the topological band inversion, forming a sequential inversion of multiple bands which is important for the topological transition but absent in monomorphous methods. In PbS- PbTe, there is a strong disorder effect, revealing the emergence of ferroelectricity from the polymorphous network in this alloy.

https://link.aps.org/accepted/10.1103/PhysRevMaterials.3.044605

Alex Zunger

Papers

Correlated Atomic Displacements in the Chemically Random Ga1-xInxP Alloy

First-Principles Theory of Cation and Vacancy Ordering in LixCoO2

Evolution of Electron States with Composition in GaAsN Alloys

Reply to ``Comment on `First-principles theory of the evolution of vibrational properties with long-range order in GaInP 2 ' ''

Alloy theory with atomic resolution for Rashba or topological systems