Publisher Summary This chapter discusses statistical exchange-correlation in the self-consistent field. There are two sides to a self-consistent field calculation: the determination of the potential and the solution of Schrodinger's equation for the one-electron problem. The solution of Schrodinger's equation has fortunately advanced far enough through the application of the electronic digital computer so that it can be regarded for most purposes as being a standardized technique. The main point of the method of Gaspar, Kohn, and Sham is that they derive the approximate exchange correction from an approximate Hamiltonian for the system by varying the spin-orbitals to minimize the average value of this Hamiltonian for the ground state. The approximate Hamiltonian has many important and valuable features that are described in the chapter.

Statistical Exchange-Correlation in the Self-Consistent Field

Several hundred thousands of tons of ZnO are used by per year, e.g. as an additive to concrete or to rubber. In the field of optoelectronics, ZnO holds promises as a material for a blue/UV optoelectronics, alternatively to GaN, as a cheap, transparent, conducting oxide, as a material for electronic circuits, which are transparent in the visible or for semiconductor spintronics. The main problem is presently, however, a high, reproducible and stable p-doping. We review in this contribution partly critically the material growth, fundamental properties of ZnO and of ZnO-based nanostructures, doping as well as present and future applications, with emphasis on the electronic and optical properties including stimulated emission. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

ZnO : From basics towards applications

ZnO is presently experiencing a research boom with more than 2000 ZnO-related publications in 2005. This phenomenon is triggered, for example, by hope to use ZnO as a material for blue/UV optoelectronics as an alternative to GaN, as a cheap, transparent, conducting oxide, as a material for electronic circuits that are transparent in the visible or for semiconductor spintronics. Currently, however, the main problem is to achieve high, reproducible and stable p-doping. Herein, we critically review aspects of the material growth, fundamental properties of ZnO and ZnO-based nanostructures and doping as well as present and future applications with emphasis on the electronic and optical properties including stimulated emission.

ZnO: Material, Physics and Applications

A review is presented of the various theoretical methods that have thus far been developed for the study of states introduced by impurities and other point defects in semiconductors. The main body of the paper is prefaced with brief sections on the role of impurities and defects in semiconductors and on the general aspects of experimental techniques, as an appropriate setting for the theoretical discourse. Theoretical methods, including those of the effective-mass type, and a wide range of methods appropriate to deep levels are then presented. Applications of these methods are discussed critically. Finally, the relative merits of the various approaches are compared and the prospects for future work are assessed.

The electronic structure of impurities and other point defects in semiconductors

When radiation is Compton-scattered the emerging beam is Doppler broadened because of the motion of the target electrons. An analysis of this broadened lineshape the Crompton profile, provides detailed information about the electron momentum distribution in the scatter. The technique is particularly sensitive to the behaviour of the slower moving outer electrons involved in bonding in condensed matter and can be used to test their quantum-mechanical description. The review begins with a brief survey of the historical development of the subject to within a decade of the present. The behaviour of quantum systems from a momentum viewpoint, is explained and the conditions under which the scattering experiment can be interpreted directly in terms of electron momentum density are discussed. The experimental techniques with gamma -rays, X-rays and electron beams are compared. Finally, recent results on insulators and conductors are surveyed and the extent to which they challenge conventional assumptions of band theory is critically reviewed.

https://iopscience.iop.org/article/10.1088/0034-4885/48/4/001/pdf

Compton scattering and electron momentum determination

The spin-orbit couplings in the valence bands of the zincblende and wurtzite structures such as cuprous halides and ZnO are investivigated in the tight-binding approximation. It is shown that the d-orbital of the cation contributes a negative term to the spin-orbit coupling in the valence band at k =0 in these compounds and, as a result of it, the spin-orbit splittings in the valence bands of CuCl and ZnO are inverted.

Spin-Orbit Coupling in Ionic Crystals with Zincblende and Wurtzite Structures

The Green's function method developed by Mahan for excitons is extended to the case that the interaction is not instantaneous. Energy corrections to the exciton due to recoil effects, retardation effects, renormalization constants and vertex parts arising from the interactions of an electron and a hole forming an exciton with longitudinal optical (LO) phonons, which were treated by Haken in another simplified manner, are explicitly calculated by using the extended method to first order in electron-phonon coupling constant α and in (\(E/\hbar\omega_{l}\)), where E is the binding energy of the exciton and ω l is the LO phonon frequency. It is shown that in these corrections, the recoil effect and the retardation effect cancel out each other and the renormalization effect and the vertex effect cancel out each other, and a resultant effective interaction between the electron and hole is reduced to Haken's result for large electron-hole separations.

Effective Electron-Hole Interaction in Shallow Excitons

The validity of the multivalley effective mass equation which has been conventionally used by many authors is examined. It is shown that the equation will not describe the intervalley mixing properly. An alternative equation which replaces the conventional equation is derived and discussed. Essential features of the new equation are: the lack of the intervalley mixing via kinetic energy, and the modification of impurity potential by the product of the periodic parts of the Bloch functions at the conduction band minima. Importance of the effect of anisotropy of the effective mass is discussed.

The Effective Mass Equation for the Multi-Valley Semiconductors

Reliable absorption line shape of the several higher members of the yellow exciton series in Cu 2 O has been measured by the photoelectric method using a monochromator with a large dispersion at 1.8 K, and has been analyzed on the basis of Toyozawa's formula. The origin of the half width is considered to come from the interband scattering of the exciton from the p state to the 1 s state by the two modes of L0 phonons. The estimated ratio in the line width of the n -th member to the second member of the exciton series is in agreement with the experimental one.

Exciton-L0 Phonon Scattering in Cu 2 O

Pseudopotential calculation for the anisotropies of the Compton-profiles of Si and Ge has been performed by using an inversion technique, based on the Fourier transform, and the special point method of Chadi and Cohen. No qualitative difference is found between the calculated anisotropies of the Compton-profiles of Si and those of Ge. It is concluded that, for semiconductors such as Si and Ge, the anisotropies of the Compton-profiles are insensitive to the change of the potential used in the band calculation and to a quality of the wave functions for the valence electrons.

Koichi Shindo

Papers

Spin-Orbit Coupling in Ionic Crystals with Zincblende and Wurtzite Structures

Effective Electron-Hole Interaction in Shallow Excitons

The Effective Mass Equation for the Multi-Valley Semiconductors

Exciton-L0 Phonon Scattering in Cu 2 O

Pseudopotential Approach to Anisotropies of Compton-Profiles of Si and Ge