Alex Zunger

Bio: Alex Zunger is an academic researcher from University of Colorado Boulder. The author has contributed to research in topics: Band gap & Quantum dot. The author has an hindex of 128, co-authored 826 publications receiving 78798 citations. Previous affiliations of Alex Zunger include Tel Aviv University & University of Wisconsin-Madison.

Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAs

Abstract: Contemporary theories of defects and impurities in semiconductors rely to a large extent on supercell calculations within density-functional theory using the approximate local-density approximation (LDA) or generalized gradient approximation (GGA) functionals. Such calculations are, however, affected by considerable uncertainties associated with: (i) the ``band-gap problem,'' which occurs not only in the Kohn-Sham single-particle energies but also in the quasiparticle gap (LDA or GGA) calculated from total-energy differences, and (ii) supercell finite-size effects. In the case of the oxygen vacancy in ZnO, uncertainties (i) and (ii) have led to a large spread in the theoretical predictions, with some calculations suggesting negligible vacancy concentrations, even under Zn-rich conditions, and others predicting high concentrations. Here, we critically assess (i) the different methodologies to correct the band-gap problem. We discuss approaches based on the extrapolation of perturbations which open the band gap, and the self-consistent band-gap correction employing the $\text{LDA}+U$ method for $d$ and $s$ states simultaneously. From the comparison of the results of different gap-correction, including also recent results from other literature, we conclude that to date there is no universal scheme for band gap correction in general defect systems. Therefore, we turn instead to classification of different types of defect behavior to provide guidelines on how the physically correct situation in an LDA defect calculation can be recovered. (ii) Supercell finite-size effects: We performed test calculations in large supercells of up to 1728 atoms, resolving a long-standing debate pertaining to image charge corrections for charged defects. We show that once finite-size effects not related to electrostatic interactions are eliminated, the analytic form of the image charge correction as proposed by Makov and Payne leads to size-independent defect formation energies, thus allowing the calculation of well-converged energies in fairly small supercells. We find that the delocalized contribution to the defect charge (i.e., the defect-induced change of the charge distribution) is dominated by the dielectric screening response of the host, which leads to an unexpected effective $1/L$ scaling of the image charge energy, despite the nominal $1/{L}^{3}$ scaling of the third-order term. Based on this analysis, we suggest that a simple scaling of the first order term by a constant factor (approximately 2/3) yields a simple but accurate image-charge correction for common supercell geometries. Finally, we discuss the theoretical controversy pertaining to the formation energy of the O vacancy in ZnO in light of the assessment of different methodologies in the present work, and we review the present experimental situation on the topic.

Zinc-blende-wurtzite polytypism in semiconductors.

Abstract: The zinc-blende (ZB) and wurtzite (W) structures are the most common crystal forms of binary octet semiconductors. In this work we have developed a simple scaling that systematizes the T=0 energy difference \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}$ between W and ZB for all simple binary semiconductors. We have first calculated the energy difference \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}^{\mathrm{LDF}}$(AB) for AlN, GaN, InN, AlP, AlAs, GaP, GaAs, ZnS, ZnSe, ZnTe, CdS, C, and Si using a numerically precise implementation of the first-principles local-density formalism (LDF), including structural relaxations. We then find a linear scaling between \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}^{\mathrm{LDF}}$(AB) and an atomistic orbital-radii coordinate R\ifmmode \tilde{}\else \~{}\fi{}(A,B) that depends only on the properties of the free atoms A and B making up the binary compound AB. Unlike classical structural coordinates (electronegativity, atomic sizes, electron count), R\ifmmode \tilde{}\else \~{}\fi{} is an orbital-dependent quantity; it is calculated from atomic pseudopotentials. The good linear fit found between \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}$ and R\ifmmode \tilde{}\else \~{}\fi{} (rms error of \ensuremath{\sim}3 meV/atom) permits predictions of the W-ZB energy difference for many more AB compounds than the 13 used in establishing this fit. We use this model to identify chemical trends in \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}$ in the IV-IV, III-V, II-VI, and I-VII octet compounds as either the anion or the cation are varied. We further find that the ground state of MgTe is the NiAs structure and that CdSe and HgSe are stable in the ZB form. These compounds were previously thought to be stable in the W structures.

Theory of the band-gap anomaly in AB C 2 chalcopyrite semiconductors

Abstract: Using self-consistent band-structure methods, we analyze the remarkable anomalies (g50%) in the energy-band gaps of the ternary $\mathrm{I}B\ensuremath{-}\mathrm{I}\mathrm{I}\mathrm{I}A\ensuremath{-}\mathrm{V}\mathrm{I}{A}_{2}$ chalcopyrite semiconductors (e.g., CuGa${\mathrm{S}}_{2}$) relative to their binary zinc-blende analogs $\mathrm{II}B\ensuremath{-}\mathrm{V}\mathrm{I}A$ (e.g., ZnS), in terms of a chemical factor $\ensuremath{\Delta}{E}_{g}^{\mathrm{chem}}$ and a structural factor $\ensuremath{\Delta}{E}_{g}^{S}$. We show that $\ensuremath{\Delta}{E}_{g}^{\mathrm{chem}}$ is controlled by a $p\ensuremath{-}d$ hybridization effect $\ensuremath{\Delta}{E}_{g}^{d}$ and by a cation electronegativity effect $D{E}_{g}^{\mathrm{CE}}$, whereas the structural contribution to the anomaly is controlled by the existence of bond alternation (${R}_{\mathrm{AC}}\ensuremath{ e}{R}_{\mathrm{BC}}$) in the ternary system, manifested by nonideal anion displacements $u\ensuremath{-}\frac{1}{4}\ensuremath{ e}0$. All contributions are calculated self-consistently from band-structure theory, and are in good agreement with experiment. We further show how the nonideal anion displacement and the cubic lattice constants of all ternary chalcopyrites can be obtained from elemental coordinates (atomic radii) without using ternary-compound experimental data. This establishes a relationship between the electronic anomalies and the atomic sizes in these systems.

Origins of coexistence of conductivity and transparency in SnO(2).

Abstract: SnO2 is a prototype "transparent conductor," exhibiting the contradictory properties of high metallic conductivity due to massive structural nonstoichiometry with nearly complete, insulator-like transparency in the visible range. We found, via first-principles calculations, that the tin interstitial and oxygen vacancy have surprisingly low formation energies and strong mutual attraction, explaining the natural nonstoichiometry of this system. The stability of these intrinsic defects is traced back to the multivalence of tin. These defects donate electrons to the conduction band without increasing optical interband absorption, explaining coexistence of conductivity with transparency.

Momentum-space formalism for the total energy of solids

Abstract: A momentum-space formalism for calculating the total energy of solids is derived. This formalism is designed particularly for application with the self-consistent pseudo- potential method. In the present formalism, the total energy is obtained through band- structure calculations without involving additional integrations. The Hellman-Feynman theorem is derived, as is a modified virial relation for the pseiidopotential Hamiltonian which provides an alternative way of calculating forces and total energies. The calculation of the total energy of solids and related derivatives with respect to structural degrees of freedom has been an ongoing problem since the early days of solid state physics (Wigner and Seitz 1933, 1934, Fuchs 1935). Quantum-mechanical calcu- lations on molecules suggest that correlation effects might sometimes be responsible for most of their binding energy (Schaefer 1972). The solid state approaches have concentrated on efforts to include most of these effects through an effective potential I/corr(p(r, Y')) (Hohenberg and Kohn 1964, Kohn and Sham 1965), rather than by complicated wave- function-related configuration interactions or many-electron perturbation techniques. Besides the problem of considering correlation effects, the self-consistent solution of the Schrodinger equation within a desired accuracy is quite difficult ; typically, the experi- mental binding energy of elemental solids is 10-4-10-5 times the total energy. These difficulties have inspired a large set of total-energy calculations that circumvents the complete solution of the Schrodinger equation (Harrison 1966, Heine and Weaire 1970). It is based on various approximations to the nearly-free-electron representation and may include the effect of more localised electrons (e.g. d states in transition metals) through specific interaction models (Moriarty 1974, 1977). As the variational self-consistent charge density remains unspecified in this approach, various forms of linear dielectric screening of the basic Coulomb interactions are introduced (Harrison 1966, Heine and Weaire 1970). Another set oftotal-energy calculations is based on direct solutions ofthe Schrodinger equation within a given interaction model : for example, Hartree-Fock (Harris and Monkhorst 1971, Wepfer et al 1974), density-functional (Ching and Callaway 1974,

Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium.

Abstract: 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.

Self-interaction correction to density-functional approximations for many-electron systems

Abstract: 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.

A comprehensive review of zno materials and devices

Abstract: 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. ...