We show that space-charge instabilities (electric field domains) in semiconductor superlattices are the attribute of absolute negative conductance induced by small constant and large alternating electric fields. We propose the efficient method for suppression of this destructive phenomenon in order to obtain a generation at microwave and THz frequencies in devices operating at room temperature. We theoretically proved that an unbiased superlattice with a moderate doping subjected to a microwave pump field provides a strong gain at third, fifth, seventh, etc. harmonics of the pump frequency in the conditions of suppressed domains.
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