A stochastic model for diffusion in a semiconductor layer under the effect of an external potential and non-uniform temperature

We study a stochastic model for the dynamics of charge carriers hopping from a lattice site to a neighboring one, in a one-dimensional (1D) semiconductor layer. Charge carriers are forced to migrate toward the central region by an external, harmonic potential. We also apply a non-uniform temperature, which is a linear combination of the temperature profiles generated by two heat sources. The first one is hot at the two ends of the semiconductor layer and pushes the charge carriers to stay around the center. The second one is hot around the center and produces the opposite effect. The composition of the two temperature profiles across the semiconductor layer generates two symmetric minima with respect to the central region. We show that this model is a bistable system, and by using both analytical and numerical methods we analyze the effect of different controlling parameters on the diffusion of charge carriers. We also study the crossing rate of charge carriers through the thermally activated barrier, and the stochastic resonance (SR) arising in the presence of a time-varying signal. Our results show that the application of an external potential provides a strong spectral amplification peak η, which occurs at a even lower temperature than the one we reported recently in Aragie (2020).