Reviews of Modern Physics at 90

Abstract

VOLUME 40, NUMBER 4 0 CTOB ER 1968 ;V. ;oc.e..):or t. ie ', V. ;eta. .-'. 4'onmeta.. '.. 'ransition in '. .mpure Seniiconc. uctors NOBUO MIKOSHIBA E/ectrotechnical Laboratory, Tanushi, Tokyo, Japan It is convenient to classify the impurity states in semiconductors into three groups: low, intermediate, and high. Even at high concentrations anomalous (i.e. , nonmetallic) properties are observed. A simple "inhomogeneity" model is proposed in which the impurity states are regarded as spatial mixtures of metallic and nonmetallic regions. The model provides an explanation of the anomalous properties, at least qualitatively. I. IHTRODUCTION As is well known, it is convenient to classify the impurity states in impure semiconductors into three groups: the low, intermediate, and high concentrations of impurities. In the low-concentration range at low temperatures, the dc Hall effect cannot be observed and the electrons localized in the impurity site can carry the current only via a hopping motion. In the intermediate-concentration range, the Hall eQ'ect is observed, but the carrier concentration estimated is lower than the concentration of impurities. The re-sistivity in this range shows an activation energy ~2 which is strongly dependent on the concentration of impurities, N, and the overlap of impurity wave functions. In the high-concentration range, the Hall effect becomes nearly equal to that at room temperature. The resistivity is nearly independent of temperature, so that the electronic state can be regarded as a degenerate Fermi gas. The metal-nonmetal transition seems to occur at the concentration between the intermediate and high concentration ranges. According to the NMR experiment' in P-doped Si, the high-concentration range can be classiled into two regions, i.e. , the transition and metallic regions. In the transition region the Knight shift of "Si is observed, but does not obey the Korringa relation. The Korringa relation holds in the metallic region, where the so-called impurity band seems to merge into the conduction band. The numerical values of various concentration ranges and some characteristic properties are given in Table I for Sb-doped Ge and P-doped Si. Recent experiments have disclosed the following anomalous electric and magnetic properties in impure semiconductors: (i) The negative magnetoresistance' and the logarithmic temperature dependence of resistivity are observed in the high-concentration ranges. 20, 2293 (1965). (ii) The spin susceptibility obtained from ESRs shows no abrupt change at the metal-nonmetal transition. (jjj) The spin susceptibi1ity obtained from ESR4 in the high-concentration range is not proportional to S'" and has a temperature dependence below T=4. 2'K. (iv) The static susceptibility in the transition re-gion' shows a temperature-independent diamagnetism, but does not obey the Landau-Peierls-Pauli formula for the degenerate Fermi gas. In order to explain the activation energy e& in the intermediate-concentration range, the D band model has been discussed by some authors. However, if we take into account the overlap integral of the D wave functions, the bottom of the D band is not so lowered that the model cannot explain the properties of 62. On the other hand, the localized spin model 0 has been proposed for explaining the anomalous properties , (i), mentioned above. This model is based. on an analogy with the localized magnetic moment in dilute alloys. The model is not convincing, however, because the correlation effect which leads to the localized moment is not taken into account at the beginning in constructing the impurity band. In this paper we propose a simple "inhomogeneity" model, in which the impurity states are regarded as spacial mixtures of the metallic and nonmetallic regions. The relative numbers of impurities and the relative volumes of metallic and nonmetallic regions are estimated by using the Poisson distribution of impurities and the critical distance between impurities in the Mott transition. " It is shown that all anomalous properties mentioned above can be explained at least qualitatively by this simple model. 4 S. Maekawa, J. Phys. Soc. Japan Suppl. 21, 574 (1966).