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The dark current is a fundamental figure of merit to characterize the performance of high-sensitivity, low-noise mid- and far-infrared barrier photodetectors. In the context of HgCdTe barrier photodetectors, the trend is to use very low doping concentrations, in an attempt to minimize recombination processes. In the present work, through TCAD simulations, we delve deeper into the design of low-dark-current <inline-formula><tex-math notation="LaTeX">$p{\mathrm{B}}n$</tex-math></inline-formula> detectors, showing the possible existence of an optimum doping. This occurrence is investigated and interpreted also by means of closed-form expressions for the lifetimes, emphasizing the role of the interplay between Auger and Shockley-Read-Hall generation processes.