Two-level model and the dynamic Hall effect in nonlinear semiconductors

Nonlinear transport properties of a semiconductor with an S-shaped negative differential conductivity is usually described by the well-established two-impurity-level model. However, previous attempts in using the two-impurity-level model to explain the observed dynamic Hall effect in nonlinear semiconductors failed, at least in the spatially homogeneous case. The model predicts a stable state when the transverse magnetic field B is zero, and as B increases to exceed a critical value, the system undergoes limit cycle oscillations, but no further bifurcation no matter how large B is. Experimentally it was observed that n-GaAs with shallow impurities at 4.2 K exhibits limit cycle oscillations when the static electric field E-0 exceeds a critical value with B = 0. When the applied transverse magnetic field B increases from 0 to about 100 mT, the system undergoes several bifurcation routes to chaos as E-0 increases. in this paper we establish a two-impurity-level model, with the assumption of spatial homogeneity, to explain the observed dynamic Hall effect in n-GaAs at 4.2 K. The dynamic behavior of our model has the main features of the experimental observations described in the above.