Theory of charge fluctuations and domain relocation times in semiconductor superlattices

Shot noise affects differently the nonlinear electron transport in semiconductor superlattices depending on the strength of the coupling among the superlattice quantum wells. Strongly coupled superlattices can be described by a miniband Boltzmann–Langevin equation from which a stochastic drift-diffusion equation is derived by means of a consistent Chapman–Enskog method. Similarly, shot noise in weakly coupled, highly doped semiconductor superlattices is described by a stochastic discrete drift-diffusion model. The current–voltage characteristics of the corresponding deterministic model consist of a number of stable branches corresponding to electric field profiles displaying two domains separated by a domain wall. If the initial state corresponds to a voltage on the middle of a stable branch and is suddenly switched to a final voltage corresponding to the next branch, the domains relocate after a certain delay time, called relocation time. The possible scalings of this mean relocation time are discussed using bifurcation theory and the classical results for escape of a Brownian particle from a potential well.