  We theoretically show that conditions for THz gain and conditions for
formation of destructive electric domains in semiconductor superlattices are
fairly different in the case of parametric generation and amplification. Action
of an unbiased high-frequency electric field on a superlattice causes a
periodic variation of energy and effective mass of miniband electrons. This
parametric effect can result in a significant gain at some even harmonic of the
pump frequency without formation of electric domains and corruption from pump
harmonics.
