Galvanomagnetic Effects in Semiconductors at High Electric Fields

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Abstract
A treatment of magnetoconductivity is developed for high electric fields and general energy-band structure using a partial solution of the Boltzmann equation in a form similar to that set up by McClure for low electric fields. The present treatment is valid when the scattering processes are such that the distribution function varies but a small amount over an entire constant-energy surface, or, in the case of the many-valley band structure, over the part of a constant-energy surface within each valley. In the latter case, different distribution functions must be used for the different valleys. The elements of the magnetoconductivity matrix that results are expressed in terms of carrier concentration, total or within each valley, and averages over the carriers of a quantity involving the momentum relaxation time and the S tensor defined by McClure. This tensor, which depends on the shape of the constant-energy surfaces and on the magnetic-field strength, is evaluated for the individual valleys in a nondegenerate many-valley semiconductor. The magnetoconductivity matrix is then in a form convenient for calculation of conductivity and galvomagnetic effects for either low or high electric fields. It is used to obtain expressions for anisotropy voltage and Hall coefficient in high electric fields involving the number of carriers in each valley, orientation of the valleys, and valley averages over quantities involving relaxation time and energy.

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