CRITICAL CONCENTRATION FOR THE METAL-NON METAL TRANSITION IN n-TYPE GERMANIUM AND SILICON

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The metal-non metal transition in n-type Ge and Si is considered by means of a model that has features in common with recent work on electron-hole droplets. The critical concentration is determined by comparing the energy of the metallic phase with the energy of an electron bound to a donor ion. Agreement with experiments is satisfactory and chemical shifts are reproduced. Pre- vious estimates of the critical concentration are reviewed. 1. Introduction. - In some non-crystalline systems in which atomic configurations are disordered in some way or another, metal-non metal (MNM) transitions are observed when appropriate physical parameters such as densities, impurity concentrations, electric fields, and temperatures are changed. Doped semi- conductors, like Ge : P and Si : P which we shall discuss here, are one of the best examples of such transitions. Hence they have been the subject of a large number of experimental and theoretical studies. Other examples are metal-ammonia solutions, metal- rare gas mixtures, supercritical metallic fluids, and excitons of high densities (I). At low concentrations and temperatures the conduc- tion in doped semiconductors is due to the hopping between impurity centers. With increasing concentra- tion, however, a rapid (but not sharp) increase in the conductivity occurs at a critical concentration, n,. For concentrations larger than n, the system has metallic characteristics. So far, two major theoretical schemes have been put forward to explain the observed tran- sition and the related electronic properties, i. e. the Mott-Hubbard-Anderson (I-31 scheme and the perco- lation theory for inhomogenous regions (4, 51. At this conference we find it appropriate to summa- rize previous estimates of n,. The classical explanation of the MNM transition was given by Mott (I), who predicted that it would occur when