A simple analytical model for the current - voltage behaviour of silicon resistor at liquid helium temperature (LHeT) is presented. It is derived from a more sophisticated analysis, taking account of impurity breakdown by impact ionization and of barrier-limited (BL) and space-charge-limited (SCL) current flow. As will be shown, the turn-on/turn-off hysteresis can be understood by considering the slow, 'forced' build-up of a depletion region at the injecting contact. Both material-(technology-)related parameters and measurement history determine the injection threshold of the device. This breakdown/hysteresis behaviour is also seen in the characteristics of more 'complicated' devices at LHeT and enhances parasitic phenomena in cryogenic circuitry.