Unipolar nBn photodetector structures have recently emerged as a viable alternative to the traditional p-n junction infrared photodiode approach. However, realization of a unipolar nBn detector technology using the mercury-cadmium-telluride (HgCdTe) alloy system is a challenging task because of the lack of a barrier material with a favorable valence band offset. In this paper, advanced quantum mechanical calculations, based on the nonequilibrium Green's function (NEGF) formalism, are used to demonstrate that it is possible to achieve diffusion-limited dark current performance in HgCdTe nBn detectors by incorporating a type-III HgTe/CdTe superlattice (SL) barrier layer. Optimal design parameters for CdTe layer thickness, HgTe layer thickness, and total number of periods are presented in order to achieve maximum hole current transmission through the barrier layer, and therefore diffusion-limited dark current performance. The NEGF simulation framework herein presented allows greater insight into effects associated with electron and hole wave function propagation in the SL barrier layer as well as the calculation of individual carrier current components. The presented results form a good basis for the fabrication of high-performance SL barrier HgCdTe nBn detectors.