Single-particle Electronic Structure Research Articles

Surface and thin-film photoemission spectrum of nickel metal: A many-body solution to a two-dimensionally periodic cluster.

An exact solution of a four-site crystal model with periodic boundary conditions, a {001} thin film with face-centered-cubic crystal structure, is presented for the nickel density of electron states, as would be measured in surface-sensitive valence-band photoemission. The object is to study modifications of the many-body electronic structure in the presence of surfaces. The model consists of (a) five d orbitals per site per spin, with nearest-neighbor hopping, (b) a one-electron occupation energy for each orbital, and (c) Coulomb repulsions between electrons on the same site. A realistic local-density-approximation one-electron structure and intrasite electron-electron interactions most generally allowed by atomic symmetry are used. Crystal-field effects and single-particle electronic structure in the nickel-film structure are discussed. The photoemission spectrum is calculated and compared with bulk results. Physical conclusions for the true nickel surface many-body states are drawn.

Tight-binding Green's-function approach to off-center defects: Nitrogen and oxygen in silicon.

We describe a new tight-binding Green's-function approach to defects in semiconductors which is expected to be particularly appropriate for off-center and aggregate systems. The universal two-center-integral expressions used in the tight-binding parametrization provide the mechanism for producing the appropriate Green's-function input for any impurity position. The method is tested here for off-center substitutional nitrogen and oxygen in silicon where we produce single-particle electronic structures and localizations. We discuss these computational results, strengths, and shortcomings of the method, and potential improvements.

Electronic structures of third-period interstitials in silicon

The single-particle electronic structures of the third-period interstitials in silicon, Mg, Al, Si, and S, are calculated by the self-consistent-field scattered-wave $X\ensuremath{\alpha} (\mathrm{SW}X\ensuremath{\alpha})$ cluster method. The impurity $X$ and its environment are simulated by the cluster $X{\mathrm{Si}}_{10}{\mathrm{H}}_{16}$, which has been used successfully in an earlier treatment of the transition-metal interstitials in silicon. We find that the ${a}_{1}$ and ${t}_{2}$ states which pass through the band gap for this series of impurities can be understood on the basis of a ligand-field model where the impurity $3s$ and $3p$ states are taken to interact with host states having large $s$ or $p$ characters, respectively, at the interstitial site. The gap states (deep levels) which result from these calculations are in agreement with those produced by recent tight-binding and self-consistent Green's-function calculations.

Theory of off-center impurities in silicon: Substitutional nitrogen and oxygen

The single-particle electronic structures and atomic displacements of substitutional nitrogen and oxygen in silicon are treated theoretically in a cluster representation using both the scattered-wave $X\ensuremath{\alpha}$ ($\mathrm{S}\mathrm{W}\ensuremath{-}X\ensuremath{\alpha}$) and modified neglect of diatomic overlap (MNDO) electronic-structure methods. Substitutional carbon and sulfur are treated to a lesser degree for the purpose of comparison. The impurity $X$ and its environment are simulated by the clusters $X{\mathrm{Si}}_{4}{\mathrm{H}}_{12}$ ($\mathrm{S}\mathrm{W}\ensuremath{-}X\ensuremath{\alpha}$ and MNDO) and $X{\mathrm{Si}}_{16}{\mathrm{H}}_{36}$ (MNDO only). In all cases, we find a localized occupied ${a}_{1}$ state in the gap with a localized unoccupied ${t}_{2}$ state above it when the impurity atoms are center. Using computed MNDO total energies for $X{\mathrm{Si}}_{4}{H}_{12}$ as a function of impurity displacement, we find spontaneous displacement directions correctly predicted for neutral carbon, nitrogen, oxygen, and sulfur, and for negative oxygen. By monitoring the single-particle energies and eigenvectors, we identify the driving force for the spontaneous asymmetric displacements as a pseudo\char22{}Jahn-Teller effect. We further explore the total energy with respect to simultaneous impurity and near-neighbor-silicon displacements, where the effect of the host outside the cluster is simulated by external connected to the four silicon atoms of the cluster. We find that it is necessary to use effective springs that are quite different from those which follow from a valence-force treatment in order to reproduce the observed spontaneous displacements of the substitutional nitrogen and oxygen impurities. This failure of the simple valence-force treatment is discussed. Our results also suggest a model for the thermal donor in silicon, whereby a substitutional oxygen is pushed on center by the strain field due to surrounding oxygen interstitials.

Theory defects in silicon: Recent calculations using finite molecular clusters

Deep-level impurities in semiconductors are characterized by perturbations of the host potential which are relatively localized to the vicinity of the impurity atom. This localization suggests that the impurity and its environment may be adequately simulated by a finite cluster of atoms, where surface effects are handled by some suitable termination. We illustrate this technique for two classes of silicon impurities: (i) interstitial iron-group transition-metal atoms, and (ii) substitutional oxygen and nitrogen. The single particle electronic structures are generated by the ab-initio scattered-wave Xα method and by the semi-empirical modified neglect of diatomic overlap method (MNDO) where appropriate. We also go beyond the conventional single-particle picture by considering the following extensions: (i) electronic relaxation accompanying electronic transitions, (ii) many-electron effects, and (iii) spontaneous impurity displacement.

Level positions of interstitial transition-metal impurities in silicon

The single-donor and single-acceptor level positions associated with defect- to band-state excitations are calculated for the interstitial transition-metal impurities V, Cr, Mn, Fe, Co, and Ni in silicon. Electronic relaxation and many-electron corrections are included. The single-particle electronic structures have been calculated by us previously according to the self-consistent-field scattered-wave $X\ensuremath{\alpha}$ cluster method, and reported in earlier papers. The effects of electronic relaxation are here estimated by the Slater transition-state procedure. Many-electron corrections are considered in two approximations: A spin-unrestricted approach which includes only spin-induced correlation between electrons, and an approach suggested by Hemstreet and Dimmock which includes both space- and spin-induced correlations between electrons, but in an approximate way. The level positions computed using the latter approximation scheme are in good agreement with experiment with the possible exceptions of the Fe single-acceptor level and the V single-donor level. It is found that the many-electron corrections to the computed level positions are relatively small (\ensuremath{\sim}0.1 eV) provided that the effect is properly included in both the initial and final states. Electronic relaxation is found to separate single-donor and single-acceptor levels by \ensuremath{\sim}0.3 eV.

Many-electron effects for interstitial transition-metal impurities in silicon

The interstitial iron-group transition-metal impurities are investigated by the self-consistent-field scattered-wave $X\ensuremath{\alpha}$ cluster method. The cluster ${\mathrm{Si}}_{10}$${\mathrm{H}}_{16}$ centered at the interstitial position represents the environment of each of the impurities V, Cr, Mn, Fe, Co, and Ni located at the origin. The single-particle electronic structure calculations reported in our previous publication are extended here to include many-electron effects in two different approximations. First, a spin-unrestricted calculation is performed with the hydrogen terminators moved in so that convergence is achieved. Second, a calculation based on a procedure introduced by Hemstreet and Dimmock is carried out. The first method includes spin-induced correlation between electrons; the latter includes space- and spin-induced correlation between electrons which are simultaneously in the transition-metal region. The results of both approaches indicate Hund's-rule ground states in all cases, consistent with the electron paramagnetic resonance studies of Ludwig and Woodbury. Term structures generated for V, Cr, Mn, and Fe provide optical transition energies and the corresponding symmetry selection rules for internal transitions.