Impact Ionization in Crossed Fields in Semiconductors

Starting from the motion of the free electron, a model is developed for the impact ionization of electron-hole pairs in the presence of a strong transverse magnetic field. The ionization rate was found to depend only on the quotient of the effective electric field strength divided by the magnetic field $\frac{E_{\mathrm{eff}}}{B}$. For $n-\mathrm{I}\mathrm{n}\mathrm{S}\mathrm{b}$ the ionization rate was calculated in dependence of $\frac{E_{\mathrm{eff}}}{B}$ for different values of the mean free path for optical-phonon scattering. Impact ionization begins at $\frac{E_{\mathrm{eff}}}{B}=2.7\mathrm{}\times {10}^5$ m ${\sec }^{-1\mathrm{}}$.