Spatially Confined Bloch Oscillations in Semiconductor Superlattices

Abstract

Bloch oscillations are coherent oscillations of the position of electrons (and therefore also of the electric current) inside energy bands of a crystal under an applied constant electric field. Their frequency is proportional to the lattice constant and to the field and therefore can be tuned by an applied voltage. Damped Bloch oscillations have been observed by optical means in undoped semiconductor superlattices which are artificial crystal structures formed by growing a succession of equal periods comprising layers of at least two different semiconductors. We model Bloch oscillations in a doped superlattice by using Boltzmann‐Poisson equations and derive hydrodynamic equations for the electron, current and energy densities. For a superlattice with long scattering times, we show that the damping of Bloch oscillations is so small that nonlinearities may compensate it and provide stable oscillations of the current and energy densities. In this case, numerical solutions show that there are stable Bloch oscillations spatially confined to part of the superlattice, thereby having inhomogeneous field, charge, current density and energy density profiles. These Bloch oscillations disappear as scattering times become sufficiently short.