Solution of the Boltzmann equation in ellipsoidal valleys with application to the valleys of GaAs and gaP

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Abstract
A method of calculation previously used in spherically symmetric valleys is extended to ellipsoidal valleys by expanding the perturbed distribution function as a series of spherical harmonics. Calculated results are presented for drift and Hall mobility and Hall number in n-GaAs and for drift mobility in n-GaP. For GaP the mobilities calculated at 300 K and 150 K are 300 and 1400 cm2V-1s-1 which are respectively 1.25 and 2.4 times the observed values. The agreement is considerably improved by including space charge scattering with a total effective area per unit volume of 4.3*107 m-1. For GaAs the mobilities calculated at 300 K and 100 K are 300 and 1600 cm2V-1s-1 which are respectively 1.09 and 0.66 times the values observed in very pure samples. The agreement with data for less pure GaAs samples is considerably improved by including space charge scattering with a total effective area per unit volume in the order of 3*107m-1.