  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.
