Harold P. Hjalmarson

A Semi-empirical tight-binding theory of the electronic structure of semiconductors†☆

Abstract A nearest-neighbor semi-empirical tight-binding theory of energy bands in zincblende and diamond structure materials is developed and applied to the following sp3-bonded semiconductors: C, Si, Ge, Sn, SiC, GaP, GaAs, GaSb, InP, InAs, InSb, AlP, AlAs, AlSb, ZnSe, and ZnTe. For each of these materials the theory uses only thirteen parameters to reproduce the major features of conduction and valence bands. The matrix elements exhibit chemical trends: the differences in diagonal matrix elements are proportional to differences in free-atom orbital energies and the off-diagonal matrix elements obey the d−2 rule of Harrison et al. The lowest energy conduction bands are well described as a result of the introduction of an excited s state, s∗. on each atom. Examination of the chemical trends in this sp3s∗ model yields a crude but “universal” sp3s∗ model whose parameters do not depend explicitly on band gaps, but rather are functions of atomic energies and bond lengths alone. The “universal” model, although cruder than the sp3s∗ model for any single semiconductor, can be employed to study relationships between the band structures of different semiconductors; we use it to predict band edge discontinuities of heterojunctions.

Surface electronic states in GaAs1−xPx

The intrinsic electronic surface states of (110) GaAs1−xPx> are predicted as functions of alloy composition x. For x >xc ≈ 0.05, intrinsic states are found within the fundamental gap. The minimum energy of the surface band is primarily determined by the bulk electronic structure, not by the atomic relaxation at the surface.

Band structure of impurity-sheet-doped superlattice alloys

The band structure and density of states for large superlattices of (100) Ga‐site Ge and As‐site N impurity sheets in GaAs have been calculated by a semiempirical tight‐binding technique. Both of these two‐dimensional conduction‐band derived bands with a J‐point indirect minimum which is deep in energy (∠0.5 eV) relative to the bulk conduction band edge. The calculation, which was performed on a single impurity sheet, demonstrates that, in general, a planar defect localizes or binds one or more states. It is suggested that the large binding energies of these sheets will confine electric‐field‐accelerated carriers and thus such superlattices will be highly conductive parallel to the impurity sheets.

Theory of deep substitutional sp3‐bonded impurity levels and core excitons at semiconductor interfaces

A theory of the major chemical trends in the binding energies of deep substitutional sp3‐bonded impurity levels and Frenkel core excitons at interfaces is presented and applied to a GaAs/AlAs (110) interface.

Bound and resonant surface states at the (110) surfaces of AlSb, AlAs, and AlP

The dispersion curves E(?) have been calculated for bound and resonant (110) surface states of AlSb, AlAs, and AlP. AlSb is predicted to have no surface states within the bulk fundamental band gap, but AlAs and AlP are predicted to have surface state band minima which are very near the conduction band edge, and could lie either within the gap or immediately above the edge.

Effects of the environment on point‐defect energy levels in semiconductors

Deep impurity energy levels within the band gap of a semiconductor can be altered and manipulated by changing the environment of the impurity. The effects of a second impurity, an interface, and a surface have been evaluated for substitutional deep levels in a variety of semiconductor hosts.

Core excitons in Ga-V compound semiconductors

Abstract The major chemical trends in the energies of Ga 3d core excitons in GaP, GaAs, and GaSb are accounted for by a theory which treats only the central-cell part of the electron-hole interaction.

Single‐reflection layer‐scattering theory of low energy electron diffraction spectra

A simple general method for computing medium and low energy electron diffraction (LEED) spectra of layered materials has been developed for application to transition metal dichalcogenides. Electron transmission and reflection coefficients for each individual sheet of atoms are computed; the separate sheets are grouped into sandwiches which are stacked upon one another to form the crystal; the intersheet scattering is treated with the single‐reflection approximation. For an unrelaxed lattice whose sandwiches are separated by the distance b and whose intrasandwich layers are separated by a, the scattered electron intensity is ‖ f (a)  ‖ 2 S (b), where f (a) is the single‐sandwich form factor for the outermost sandwich. Lattice relaxation of the surface sandwich slightly modifies this result. The static structure factor S (b), which is a spiked function of energy and contains mainly bulk structural information, produces the principal peaks in the intensity versus energy spectrum, but the surface sandwich ref...