Abstract
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 an efficient method for the suppression of this destructive phenomenon in order to obtain the 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 the third, seventh, etc. harmonics of the pump frequency under conditions of suppressed domains.