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A stochastic discrete drift-diffusion model is proposed to account for theeffects of shot noise in weakly coupled, highly doped semiconductorsuperlattices. Their current-voltage characteristics consist of a number stablemultistable branches corresponding to electric field profiles displaying twodomains separated by a domain wall. If the initial state corresponds to avoltage on the middle of a stable branch and a sudden voltage is switched sothat the final voltage corresponds to the next branch, the domains relocateafter a certain delay time. Shot noise causes the distribution of delay timesto change from a Gaussian to a first passage time distribution as the finalvoltage approaches that of the end of the first current branch. These resultsagree qualitatively with experiments by Rogozia {\it et al} (Phys. Rev. B {\bf64}, 041308(R) (2001)).Comment: 9 pages, 12 figures, 2 column forma

Nonlinear stochastic discrete drift-diffusion theory of charge fluctuations and domain relocation times in semiconductor superlattices