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The continuum limit of a recently proposed model for charge transport in resonant-tunneling semiconductor superlattices (SLs) 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 SL where the electric field is almost uniform.

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