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

Using the empirical pseudopotential method and large atomistically relaxed supercells, we have systematically studied the evolution of the electronic structure of ${\mathrm{GaP}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$ and ${\mathrm{GaAs}}_{1\ensuremath{-}x}{\mathrm{N}}_{x},$ from the dilute nitrogen impurity regime to the nascent nitride alloy. 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 and the ``perturbed host states'' with increasing nitrogen composition, we propose a new model for low-nitrogen-content ${\mathrm{GaAs}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$ and ${\mathrm{GaP}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$ alloys: As the nitrogen composition increases, the energy of the CS is pinned while the energy of the PHS plunges down as the nitrogen composition increases. The impurity limit (PHS above CS) is characterized by strongly localized wave functions, low pressure coefficients, and sharp emission lines from the CS. The amalgamation limit (PHS overtake the CS) is characterized by a coexistence of localized states (leading to high effective mass, exciton localization, Stokes shift in emission versus absorption) overlapping delocalized PHS (leading to asymmetrically broadened states, low temperature coefficeint, delocalized ${E}_{+}$ band at higher energies). The alloy limit (PHS well below CS) may not have been reached experimentally, but is predicted to be characterized by conventional extended states. Our theory shows that these alloy systems require a polymorphous description, permitting the coexistence of many different local environments, rather than an isomorphous model that focuses on few impurity-host motifs.

Theory of electronic structure evolution in GaAsN and GaPN alloys

Using the all-electron mixed-basis approach to the density-functional formalism for crystals, we calculate from first principles the electronic structure of zinc-blende ZnS, ZnSe, and ZnTe as well as that of their ordered pseudobinary alloys ${\mathrm{Zn}}_{2}$SSe, ${\mathrm{Zn}}_{2}$SeTe, and ${\mathrm{Zn}}_{2}$STe. For the latter we use as a model a CuAu I-like structure (space group $P\overline{4}m2$), and analyze the observed optical bowing in terms of three contributions: (i) a volume deformation of the band structure due to the replacement of the lattice constants of the binary constituents by that of the alloy, (ii) a chemical-electronegativity contribution due to charge exchange in the alloy relative to its constituent binary subsystems, and (iii) a structural contribution due to the relaxation of the anion-cation bond lengths in the alloy. The total bowing effect [the sum of (i)-(iii) above] agrees well with observations, yet the present analysis suggests a physical mechanism for optical bowing which differs profoundly from that offered by the popular virtual-crystal approach. The maximum contribution of disorder to the optical bowing is calculated for $\mathrm{Zn}{\mathrm{S}}_{x}{\mathrm{Te}}_{1\ensuremath{-}x}$ using a cluster-averaging method, resulting in a reduction in the bowing of the fundamental gap. We further discuss the band structures, x-ray scattering factors, charge distribution, and deformation potentials of the binary zinc chalcogenides and their ordered alloys.

Electronic structure of ZnS, ZnSe, ZnTe, and their pseudobinary alloys

The structure and implementation of a new general iterative method for diagonalising large matrices (the 'residual minimisation/direct inversion in the iterative subspace' method of Bendt and Zunger) are described and contrasted with other more commonly used iterative techniques. The method requires the direct diagonalisation of only a small submatrix, does not require the storage of the large matrix and provides eigensolutions to within a prescribed precision in a rapidly convergent iterative procedure. Numerical results for two rather different matrices (a real 50*50 non-diagonally dominant matrix and a complex Hermitian 181*181 matrix corresponding to the pseudopotential band structure of a semiconductor in a plane wave basis set) are used to compare the new method with the competing methods. the new method converges quickly and should be the most efficient for very large matrices in terms both of computation time and central storage requirements; it is quite insensitive to the properties of the matrices used. This technique makes possible efficient solution of a variety of quantum mechanical matrix problems where large basis set expansions are required.

https://iopscience.iop.org/article/10.1088/0305-4470/18/9/018/pdf

A new method for diagonalising large matrices

Chemists and material scientists have often focused on the properties of previously reported compounds, but neglect numerous unreported but chemically plausible compounds that could have interesting properties. For example, the 18-valence electron ABX family of compounds features examples of topological insulators, thermoelectrics and piezoelectrics, but only 83 out of 483 of these possible compounds have been made. Using first-principles thermodynamics we examined the theoretical stability of the 400 unreported members and predict that 54 should be stable. Of those previously unreported 'missing' materials now predicted to be stable, 15 were grown in this study; X-ray studies agreed with the predicted crystal structure in all 15 cases. Among the predicted and characterized properties of the missing compounds are potential transparent conductors, thermoelectric materials and topological semimetals. This integrated process-prediction of functionality in unreported compounds followed by laboratory synthesis and characterization-could be a route to the systematic discovery of hitherto missing, realizable functional materials.

Prediction and accelerated laboratory discovery of previously unknown 18-electron ABX compounds

We found theoretically that Na has three effects on CuInSe2: (1) If available in stoichiometric quantities, Na will replace Cu, forming a more stable NaInSe2 compound having a larger band gap (higher open-circuit voltage) and a (112)tetra morphology. The ensuing alloy NaxCu1−xInSe2 has, however, a positive mixing enthalpy, so NaInSe2 will phase separate, forming precipitates. (2) When available in small quantities, Na will form defect on Cu site and In site. Na on Cu site does not create electric levels in the band gap, while Na on In site creates acceptor levels that are shallower than CuIn. The formation energy of Na(InCu) is very exothermic, therefore, the major effect of Na is the elimination of the InCu defects and the resulting increase of the effective hole densities. The quenching of InCu as well as VCu by Na reduces the stability of the (2VCu−+InCu2+), thus suppressing the formation of the “Ordered Defect Compounds.” (3) Na on the surface of CuInSe2 is known to catalyze the dissociation of O2 int...

Alex Zunger

Papers

Theory of electronic structure evolution in GaAsN and GaPN alloys

Electronic structure of ZnS, ZnSe, ZnTe, and their pseudobinary alloys

A new method for diagonalising large matrices

Prediction and accelerated laboratory discovery of previously unknown 18-electron ABX compounds

Effects of Na on the electrical and structural properties of CuInSe2