Over the past 15 yr or more, researchers have been trying to achieve gain for electromagnetic fields in the terahertz frequency region using biased semiconductor superlattices, but with little success. In this work, we employ our model of the excitonic states in biased GaAs/Al0.3Ga0.7As semiconductor superlattices to find the optimal structures for amplification of terahertz radiation. In particular, we determine the optimum well width, barrier width, and bias field for terahertz fields with frequencies ranging from 1 to 4 terahertz. We find that gain coefficients on the order of 40 cm−1 should be achievable over most of this frequency range.

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