Effect of potential fluctuations on the transport properties and the photoconductivity of compensated semiconductors. Application to semi-insulating GaAs. I. Semiconductor under equilibrium conditions

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Abstract
In highly compensated semiconductors, the potential fluctuations due to inhomogeneous distribution of impurities lead to fluctuations in the density of carriers and ionized deep levels (donor or acceptor). The result is that the local neutrality condition is no longer obeyed and only averaged quantities over a sample are experimentally attainable. We describe a statistical model of long range fluctuations, writing down an averaged neutrality equation. The Fermi energy, the dc free carrier density, and its activation energy, are very much dependent on the magnitude of the fluctuations and on the degree of compensation of the deep level. These variations are shown in the case of semi-insulating GaAs. A method of quantitative evaluation of the fluctuations and of the degree of compensation is given. It is applied to explain the data on non-Cr-doped semi-insulating GaAs samples.