  In weakly coupled, current biased, doped semiconductor superlattices, domain
walls may move upstream against the flow of electrons. For appropriate doping
values, a domain wall separating two electric field domains moves downstream
below a first critical current, it remains stationary between this value and a
second critical current, and it moves upstream above. These conclusions are
reached by using a comparison principle to analyze a discrete drift-diffusion
model, and validated by numerical simulations. Possible experimental
realizations are suggested.
