Diode detectors (DDs) are widely used in electronic information and communication systems. In this study, a numerical modeling of the electric potential distribution and current passing in contacts of niobium nitride (NbN) with a bismuth-antimony (Bi-Sb) semiconductor alloy was performed. Earlier, we have studied the case in which the surface states were in thermodynamic equilibrium with a semiconductor. In this article, an opposite situation is studied, when the surface states are in thermodynamic equilibrium with a superconductor. The possibility to design diode detectors based on these contacts that operate at temperatures (T) of liquid helium 4.2 K and 1 K is explored. The dependences of current responsivity (CR), voltage responsivity (VR), and noise equivalent power (NEP) on signal frequency (f) are analyzed. The obtained results are compared with literature data. DDs operating at the temperature of liquid nitrogen (T = 77.4 K) and liquid helium are considered. A comparison with the available literature data shows that the proposed DDs can be 10÷100 times better. The physical reasons of these advantages are discussed. It is shown that unique properties of Bi-Sb alloys and especially of Bi0.88Sb0.12 alloy make these alloys very promising materials for cryoelectronics.