  We study theoretically the dynamical rectification of a terahertz AC electric
field, ie. the DC current and voltage response to the incident radiation, in
strongly coupled semiconductor superlattices. We address the problem of
stability against electric field domains: A spontaneous DC voltage is known to
appear exactly for parameters for which a spatially homogeneous electron
distribution is unstable. We show that by applying a weak direct current bias
the rectifier can be switched from a zero DC voltage state to one with a finite
voltage in full absence of domains. The switching occurs near the conditions of
dynamical symmetry breaking of an unbiased semiconductor superlattice.
Therefore our scheme allows for the generation of DC voltages that would
otherwise be unreachable due to domain instabilities. Furthermore, for
realistic, highly doped wide miniband superlattices at room temperature the
generated DC field can be nearly quantized, that is, be approximately
proportional to an integer multiple of h\omega/2\pi ea where a is the
superlattice period and \omega\ is the AC field frequency.
