Diode detectors (DDs) are widely used in electronic information and communication systems. In this paper, the numerical modeling of the electrical potential distribution and current passing in the contacts of a normal metal or a superconductor with a bismuth–antimony (Bi–Sb) semiconductor alloy has been conducted. The possibilities of designing DDs based on these contacts to operate at a temperature (T) of liquid helium of 4.2 K and 1 K have been explored. The dependences of current responsivity (CR), voltage responsivity (VR) and noise equivalent power (NEP) on the free electron concentration have been analyzed. The physical causes of these dependences have been examined. The effect the signal frequency (f) on the detecting parameters has been shown. The obtained results have been compared with the literature data. Comparison with the currently available literature data has shown that proposed DDs can be 1–2 orders better. The physical reasons for these advantages have been discussed. It has been shown that the unique properties of Bi–Sb alloys, particulalrly the Bi0.88Sb0.12 alloy, make these alloys promising materials for cryoelectronics.