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 ground-state configuration of a system of N electrons or holes (N = 1⋯8) in strongly confined InAs, InP, and Si quantum dots (diameter ~ 30 A) is calculated using pseudopotential single-particle energies and wave functions as input to the many-body expansion of the total energy The validity of generally accepted "rules of level occupation" (Hund's rule, Aufbau principle, and single spin-flip rule) is examined We find that while Hund's rule is generally obeyed, deviations from the Aufbau principle are common when single-particle energy levels are separated by a few meV We also find a few instances where the single spin-flip rule is violated, leading to "spin blockade" in linear conductance

https://iopscience.iop.org/article/10.1209/epl/i2000-00261-y/pdf

Hund's rule, spin blockade, and the Aufbau principle in strongly confined semiconductor quantum dots

Absence of redshift in the direct bandgap of silicon nanocrystals with reduced size

The electron?hole (e?h) exchange interaction leads to the splitting of the exciton into a pair of bright and a pair of dark states. This bright?dark?or singlet?triplet?exciton splitting was historically calculated as the sum of a long-range (LR) and a short-range (SR) component. Using a numerical atomistic approach, we are able to calculate the exchange integrals as a function of the e?h range of interaction S, revealing the 'internal' structure of the integrals. We apply this procedure to thickness-fluctuation GaAs/AlGaAs quantum dots (QDs), self-assembled InAs/GaAs QDs and colloidal InAs QDs. We find a heterogeneous situation, where the SR component contributes ~10, ~20?30 and ~20?50% to the total e?h exchange splitting, which is in the range of 10, 100 and 10?000 ?eV, for the three types of QDs, respectively. The balance between SR and LR is found to depend critically on the size, shape and type of structure. For all types of QDs we find, surprisingly, a range of interaction, close to the physical dimension of the structures, contributing to a reduction of the integral's magnitude. These results highlight the complexity of the exchange interaction, warning against simplified models, and establish the basic features of the nature and origin of dark?bright excitonic splitting in QDs.

https://iopscience.iop.org/article/10.1088/1367-2630/11/12/123024/pdf

Long- and short-range electron–hole exchange interaction in different types of quantum dots

The goal of ``band-gap engineering'' in substitutional lattices is to identify atomic configurations that would give rise to a desired value of the band gap. Yet, current theoretical approaches to the problems, based largely on compilations of band structures for various latice configurations, have not yielded simple rules relating structural motifs to band gaps. We show that the band gap of substitutional AlAs/GaAs lattices can be usefully expanded in terms of a hierarchy of contributions from real-space ``atomic figures'' (pairs, triplets, quadruplets) detemined from first-principles band-structure calculations. Pair figures (up to fourth neighbors) and three-body figures are dominant. In analogy with similar cluster expansions of the total energy, this permits a systematic search among all lattice configurations for those having ``special'' band gaps. This approach enables the design of substitutional systems with certain band-gap properties by assembling atomic figures. As an illustration, we predict that the [01\ifmmode\bar\else\textasciimacron\fi{}2]-oriented (AlAs${)}_{1}$/(GaAs${)}_{4}$/(AlAs${)}_{1}$/(GaAs${)}_{2}$ superlattice has the largest band gap among all ${\mathrm{Al}}_{0.25}$${\mathrm{Ga}}_{0.75}$As lattices with a maximum of ten cations per unit cell.

Alex Zunger

Papers

Hund's rule, spin blockade, and the Aufbau principle in strongly confined semiconductor quantum dots

Absence of redshift in the direct bandgap of silicon nanocrystals with reduced size

Long- and short-range electron–hole exchange interaction in different types of quantum dots

Real-space description of semiconducting band gaps in substitutional systems

Superlattice energetics and alloy thermodynamics of GaAs/Ge