Galvanomagnetic Effects in Semiconductors at High Electric Fields
Abstract
A treatment of magnetoconductivity is developed for high electric fields and general energyband 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 constantenergy surface, or, in the case of the manyvalley band structure, over the part of a constantenergy 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 constantenergy surfaces and on the magneticfield strength, is evaluated for the individual valleys in a nondegenerate manyvalley 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.
 Publication:

Physical Review
 Pub Date:
 July 1961
 DOI:
 10.1103/PhysRev.123.454
 Bibcode:
 1961PhRv..123..454C