Stability analysis of steady state in strongly coupled semiconductor superlattice

We analytically study stability of a steady state mode of charge transport in a model of strongly coupled semiconductor superlattice (SL), described in the framework of semiclassical approximation. Using a set of small perturbations of the steady state we found the value of the voltage applied to the SL, for which one of the perturbations starts to demonstrate a positive increment of growth, thus manifesting the loss of the steady state stability. We expand our analysis for the case when the steady state is already unstable and the current oscillations take place. It is shown, that despite the appearance of new unstable perturbations, the frequency of current oscillations remained close to the first perturbation frequency.