Abstract
AbstractUsing the contraction mapping principle, we show how iterated solutions of the classical Boltzmann equation with Fermi statistics are obtained. The mathematical formalism allows manipulation of the Boltzmann equation separately from considerations of particular electron scattering mechanisms and proves existence, uniqueness, and convergence properties of the solutions. This technique potentially applies to a broad range of electronic transport problems, but in particular, Hall effects and magnetoresistance are considered in group [V, III‐V, and II‐VI semiconductors and semimetals. These results show the corrections between Hall mobility, magnetoresistance mobility, and drift mobility, e.g. Hall mobility differs from drift mobility by less than 30% for all the crystals considered. In addition, measurements of the Hall factor (rH) in GaAs from 0.1 to 90 kG are compared with theory and agreement is found to 4%.
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