Dark currents in medium-wave nBn structures based on HgCdTe grown with the aid of molecular beam epitaxy on the (013) GaAs substrates are studied. The passivation of the surface of the side walls of the mesastructures is performed using Al2 O3 films formed by plasma atomic layer deposition. It is shown that the volume component of the dark current dominates in the nBn structures with a composition in the barrier layer of 0.84. The activation energy of the current is close to the band gap of the absorbing layer. Comparison of the experimental results with the results of the Rule07 empirical model shows that the diffusion limitation of the dark current takes place in the fabricated structures in a temperature interval of 180–300 K. The results indicate that the molecular beam epitaxy of HgCdTe on alternative substrates is a promising method for fabrication of unipolar barrier detectors for a spectral interval of 3–5 μm.