Diffusion Currents in the Semiconductor Hall Effect

The usual Hall effect equation for semiconductors applies if the concentration of carriers is undisturbed. In a magnetic field, however, holes and electrons are swept to the same side of the conductor. A gradient of carrier concentrations is thereby established, giving rise to diffusion currents across the sample. The magnitude of the diffusion currents depends on the recombination velocity at the surface and on the lifetime of excess carriers in the interior.Partial differential equations governing the electric field and the variation of the carrier concentrations across the transverse cross section of the Hall sample are obtained. These are applied to rectangular and circular transverse cross sections. Equations for the Hall voltage as a function of both bulk lifetime and surface recombination velocity are derived and discussed. The analysis considers only disturbances which are linear in the applied magnetic field.