Hall effect in finite specimens of arbitrary lifetime and trap content

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Abstract
This paper presents a linearized Hall-effect theory, applicable to specimens of arbitrary size, carrier concentration, lifetime, dielectric relaxation time, concentration of (single level) recombination centers, and surface properties. Along the lines of Van Roosbroeck and Casey, the distinction is made between the behavior of lifetime and relaxation semiconductors. By analogy with Popescu and Henisch, who dealt with injection, the Hall effect also involves "lifetime regimes" and "relaxation regime," depending on whether carriers are augmented or depleted in certain regions. The present analysis, which avoids the a priori assumption of space-charge neutrality, is one-dimensional and limited to small magnetic fields. The boundary conditions at the Hall electrodes are assumed to depend on effective surface recombination velocities for electrons and holes of arbitrary value. The results show that the corrective terms involving surface properties and sample size can be of either sign and of magnitude comparable to the value, of the Hall voltage calculated by conventional method. As expected, this is most important when the specimen dimensions in the direction of the Hall field are of the same order as the ambipolar diffusion length. The typical examples calculated include high-lifetime germanium.