In recent years, type-II superlattice-based devices have completed the offer of the electronic industry in many areas of applications. Photodetection is one of them, especially in the mid-infrared wavelength range. It is due to the unique feature of a superlattice material, which is a tuneable bandgap. It is also believed that the dark current of superlattice-based photodetectors is strongly suppressed due to the suppression of the band-to-band tunnelling current in a superlattice material. This argument relies, however, on a semi-classical approach that treats superlattice as a bulk material with effective parameters extracted from the kp analysis. In the paper, a superlattice device is analysed on a quantum level: the non-equilibrium Green’s function method is applied to the two-band Hamiltonian of the InAs/GaSb superlattice p-i-n diode. The analysis concentrates on the band-to-band tunnelling with the aim to validate the correctness of a semi-classical description of the phenomenon. The results of calculations reveal that in a superlattice diode, the inter-band tunnelling occurs only for certain values of energy and in-plane momentum, for which electronic and hole sub-bands cross. The transitions occurring for vanishing in-plane momentum produce resonances in the current-voltage characteristics – the feature which was reported in a few experimental observations. This scenario is quite different from that occurring in bulk materials, where there is a range of energy-momentum pairs for which the band-to-band tunnelling takes place, and so current-voltage characteristics are free from any resonances. However, simulations show that, while not justified for a detailed analysis, the semi-classical description can be applied to superlattice-based devices for an ‘order of magnitude’ estimation of the band-to-band tunnelling current.