Ionization Interaction between Impurities in Semiconductors and Insulators

Abstract

and the vacancy mechanism being equivalent to the two "chemical reactions" A + V~&~A~+ V and B + V~~B~+V . The reaction rates in these models are derived in terms of the fundamental parameters of atom movements, and are themselves order-dependent.(6) The vacancy-interchange model has been applied to the case of Cu3Au, which has been studied experimentally by Burns and Quimby. A Bsymmetry was assumed, an activation energy and a pre-exponential factor were taken from the measurements of self-diffusion in pure copper and pure gold, and the remaining parameter of the theory was adjusted to produce agreement with the known critical temperature for ordering in this system. The theory then gives reasonably good agreement with relaxation times observed by Burns and Quimby over the temperature range of the experiments, 338'C to 388'C. (7) The developments outlined above have been concerned with homogeneous systems. The basic apparatus of multiparticle distribution functions and their equations of motion is equally applicable to inhomogeneous systems, including cases of domains of order in a disordered matrix, domains of antiphase order, and diffusion in alloys. 9. ACKNOWLEDGMENTS The writer is indebted to G. J. Dienes for numerous discussions and some important suggestions in the course of this work, and to S. L. Quimby for supplying information about his Cu3Au experiments.It is known that the free energy of an imperfect semiconductor or insulator crystal contains terms which arise from the ionizability of these imperfections and which represent chemical interactions between imperfections of the same and different kinds. We show that these ionization terms, which involve the Fermi level and the parameters of the energy band model, explain the systematic differences between eand p-type semiconductors in lattice vacancy concentration, in substitutional atom diffusion coe%cients, and in amphoteric impurity behavior. The ionization terms also explain the variation of solid-liquid impurity distribution coefficients with the crystal growth rate of certain semiconductors, and also the well-known "charge balance" effect in insulators.

An Analysis of Diffusion in Semiconductors

“…Let D N , D», De, and Ds; be the diffusion coefficients for donors, acceptors, electrons, and holes, respectively. Then, Eqs, (6), (8) and (10) yield where I N , II', I. and h are the respective diffusion currents of donors, acceptors, electrons, and holes, and -F is the average electrical force acting on a positively charged particle. The cross terms Dij(op,/ox) of equation ( 6) where i =oft j are assumed to be negligible.…”

“…His equations are: (6) where fLi is the chemical potential of the j-th component, t. the average resultant force due to any electrical or other fields acting on a particle of the i-th species, and nii are mobility terms obeying the reciprocity relation: (7) The term n u is proportional to the concentration n, of the particles of the i-th species and inversely proportional to the frictional forces opposing the displacement of these particles. Where these frictional forces are approximately invariant this can be written:…”

Photoluminescence evaluation of the quality of Cd0.9Zn0.1Te detectors doped with different indium concentrations

“…In heavy-doped semiconductor crystals (concentration value equal to $10 18 -10 19 cm À3 ) interactions such as vacancy-atom and vacancyion can play a large role. This proposition is conditioned by substantially increasing the acceptor-type vacancy concentration during crystal doping [11]. Thus, the number of equilibrium vacancies can rise 10-fold [12].…”

Self- and zinc diffusion in gallium antimonide

“…Longini and Greene were the first to incorporate the effect of charge states into diffusion theory [Longini, (1956)]. As discussed in Section 1.2, charged defects can be favored or suppressed depending on the Fermi level position in a semiconductor.…”