Periodic Generation and Propagation of Traveling Fronts in DC Voltage Biased Semiconductor Superlattices

The continuum limit of a recently-proposed model for charge transport in resonanttunneling semiconductor superlattices is analyzed. It is described by a nonlinear hyperbolic integrodifferential equation on a one-dimensional spatial support, supplemented by shock and entropy conditions. For appropriate parameter values, a time-periodic solution is found in numerical simulations of the model. An asymptotic theory shows that the time-periodic solution is due to recycling and motion of shock waves representing domain walls connecting regions of the superlattice where the electric field is almost uniform.