Transverse Impact Ionization in Semiconductors

The electron distribution function in the presence of crossed electric and magnetic fields is calculated for an $n$-type semiconductor, with isotropic electron scattering by acoustical and optical phonons. The results are applied to a semiconductor rod, subject to a longitudinally applied electric field and a transverse magnetic field. It is found, in agreement with measurements by Toda and Glicksman, that the ionization rate can increase with increasing magnetic field, as a result of the generated Hall electric field. The effect is closely related to a magnetic trapping of electrons in the low-energy high-mobility region.