We have measured and theoretically analyzed the doping density, N(D), dependence of the intersubband absorption coefficient alpha, the quantum efficiency eta, the optical gain g, the dark current I(D), and the detectivity D*. We discuss the optimum doping and show that D* depends only weakly on both N(D) and also the bias voltage, V(b). In particular, we find that the dark current can be reduced by three orders of magnitude, without significantly reducing the detectivity. This would substantially alleviate the undesirable filling of imaging array multiplexer storage capacitors, thereby allowing longer integration times and thus higher sensitivity.