Modulated Bloch Waves in Semiconductor Superlattices

We show that in a semiconductor superlattice with long scattering times, damping of Bloch oscillations due to scattering is so small that nonlinearities may compensate it and Bloch oscillations persist even in the hydrodynamic regime. In order to demonstrate this, we propose a Boltzmann-Poisson transport model of miniband superlattices with inelastic collisions and we derive by singular perturbation methods hydrodynamic equations for electron density, electric field, and the complex amplitude of the Bloch oscillations. Numerical solutions of these equations show stable Bloch oscillations with spatially inhomogeneous field, charge, current density, and energy density profiles. These Bloch oscillations disappear as scattering times become sufficiently short. For sufficiently low lattice temperatures (70 K), Bloch and Gunn type oscillations mediated by electric field, current, and energy domains coexist for a range of voltages. For larger lattice temperatures (300 K), there are only Bloch oscillations with stationary amplitude and electric field profiles.