The characteristics of second‐harmonic generation (SHG) of microwaves in a semiconductor at low lattice temperatures are investigated theoretically over a wide range of the dc bias field, beginning from a weakly heated carrier ensemble up to the onset of impurity breakdown giving due consideration to the effect of recombination of the nonequilibrium carriers in the presence of deep repulsive traps. The calculations are carried out for a parabolic law of dispersion and a scalar effective mass. In comparison to what can be obtained under the condition where the nonequilibrium carriers are captured by attractive traps or in the absence of recombination effects, the results of the quantum trapping of the nonequilibrium carriers by the repulsive traps bring in interestingly both qualitative and quantitative changes in the characteristics throughout the entire range of the bias field. The curves for the efficiency of SHG versus the bias field show a number of optimum fields for which the generation would be most efficient. The inadequacies of the present theory are pointed out and the scope for refinement of the same is discussed.
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