Calculations of ground-state and excited-state properties of materials have been one of the major goals of condensed matter physics. Ground-state properties of solids have been extensively investigated for several decades within the standard density functional theory. Excited-state properties, on the other hand, were relatively unexplored in ab initio calculations until a decade ago. The most suitable approach up to now for studying excited-state properties of extended systems is the Green function method. To calculate the Green function one requires the self-energy operator which is non-local and energy dependent. In this article we describe the GW approximation which has turned out to be a fruitful approximation to the self-energy. The Green function theory, numerical methods for carrying out the self-energy calculations, simplified schemes, and applications to various systems are described. Self-consistency issue and new developments beyond the GW approximation are also discussed as well as the success and shortcomings of the GW approximation.

https://iopscience.iop.org/article/10.1088/0034-4885/61/3/002/pdf

The GW method

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

The problems dealt with concern the production of electron‐hole pairs in a semiconductor exposed to high‐energy radiation. The goal is to develop a simple phenomenological model capable of describing the present experimental situation from the standpoint of yield, variance, and bandgap dependence. We proceed on the premise that e, the average amount of radiation energy consumed per pair, can be accounted for by a sum of three contributions: the intrinsic bandgap (EG), optical phonon losses r(ℏωR), and the residual kinetic energy (9/5) EG. The approach differs from prior treatments in the sense that the residual kinetic energy relates to a threshold for impact ionization taken to be 32EG in accordance with indications stemming from studies of avalanching in p‐n junctions. This model is subjected to three quantitative tests: (a) Fano‐factor variations are found to reflect the relative weight of phonon losses [K=r(ℏωR)/EG], but residual energy fluctuations govern the statistical behavior for K2 ≲0.3. An appl...

Bandgap Dependence and Related Features of Radiation Ionization Energies in Semiconductors

Single-Crystal Elastic Moduli and the hcp → bcc Transformation in Ti, Zr, and Hf

This paper provides a historical review of the literature on the effects of radiation-induced displacement damage in semiconductor materials and devices. Emphasis is placed on effects in technologically important bulk silicon and silicon devices. The primary goals are to provide a guide to displacement damage literature, to offer critical comments regarding that literature in an attempt to identify key findings, to describe how the understanding of displacement damage mechanisms and effects has evolved, and to note current trends. Selected tutorial elements are included as an aid to presenting the review information more clearly and to provide a frame of reference for the terminology used. The primary approach employed is to present information qualitatively while leaving quantitative details to the cited references. A bibliography of key displacement-damage information sources is also provided.

Review of displacement damage effects in silicon devices

Electronic specific heat of Pd is deduced from the experimental data. Using the density of electronic states of Pd which has been determined from the low temperature specific heat data of Pd–Ag and Pd–Rh alloys and Ru metal by assuming the rigid band model, the electronic specific heat and the spin paramagnetic susceptibility of Pd are calculated at arbitrary temperatures. The calculated result for the temperature dependence of the electronic specific heat of Pd satisfactorily agrees with the experimental result, whereas the calculated values for spin paramagnetic susceptibility are considerably smaller than the observed values. The main difference will be attributable to the effect of the molecular field. The maximum in observed magnetic susceptibility at about 80°K can be explained by considering a peculiar band shape. Similar calculations to those for Pd metal are performed for Pd–Ag and Pd–Rh alloys.

Magnetic Susceptibility and Electronic Specific Heat of Transition Metals and Alloys II. Pd Metal and Pd-Ag and Pd-Rh Alloys

Electronic specific heats for various transition metals at higher temperature are deduced from experimental results. It is pointed out that the transition metals with small values of paramagnetic susceptibility and coefficient of low temperature specific heat, γ 0 , have larger values of the electronic specific heat than the extrapolation of γ 0 T , and the metals with large values of these have smaller values of the electronic specific heat than the extrapolation of γ 0 T , at higher temperatures. With use of electronic state density determined from the data of γ 0 , for Cr-Fe and Cr-V alloys, the temperature variations of electronic specific heat and spin susceptibility of Cr are calculated at arbitrary temperatures. The calculated electronic specific heats satisfactorily agree with the experimental results, whereas the calculated spin susceptibilities are smaller than the experimental results. It is pointed out that the main difference is attributable to the orbital paramagnetic susceptibility.

Calculations of Electronic Specific Heat and Paramagnetic Susceptibility of Chromium

The approximation method developed by Singwi et al. for classical distribution function is applied to the Wigner distribution function in a quantum system. In this way a quantum mechanical expression is derived for dielectric function of an interacting electron gas. Self-consistent numerical calculations of structure factor and dielectric function are carried out for an electron gas at metallic density of electrons. Pair distribution function, compressibility, correlation energy and dispersion relation of plasmons are numerically calculated from the calculated structure factor. The calculated results of the pair distribution function are found to be positive for the entire range of real metallic density of electrons.

Electron Correlations at Metallic Densities, II. Quantum Mechanical Expression of Dielectric Function with Wigner Distribution Function

Magnetic properties of Pd metal and Pd-Rh and Pd-Ag alloys with the addition of Co and Fe atoms are analyzed by the itinerant model of 4d-electrons. It is assumed that dissolved atoms have localized magnetic moments and are distributed at random. Spin quantum number of the localized moment of the dissolved atom and a molecular field coefficient between 4d-electron and dissolved atom are estimated from the comparison between our theory and experiments. The values of spin quantum number for localized magnetic moments are estimated as 1 and 3/2 for Co and Fe atoms in these alloys. Making use of these values and the value of molecular field coefficient among 4d-electrons and the density of states curve, which were obtained before for Pd metal, the composition dependences of the magnetic moment and the Curie temperature and the temperature dependences of paramagnetic susceptibility for these alloys are numerically calculated. The obtained results can explain almost all experiments satisfactorily.

Masao Shimizu

Papers

Magnetic Susceptibility and Electronic Specific Heat of Transition Metals and Alloys II. Pd Metal and Pd-Ag and Pd-Rh Alloys

Calculations of Electronic Specific Heat and Paramagnetic Susceptibility of Chromium

Electron Correlations at Metallic Densities, II. Quantum Mechanical Expression of Dielectric Function with Wigner Distribution Function

Magnetic Properties of Pd Metal and Pd-Rh and Pd-Ag Alloys Containing Co and Fe Atoms

Ferromagnetism and invar effect of FCC 3d-alloys