Abstract: A device of the form metal1|semiconductor|metal2 is discussed, in which the semiconductor is assumed to be p-type, donors are not present, yet electron hopping in the impurity band is possible due to partial occupancy. The two electrodes (metal1 and metal2) are assumed to be asymmetric (contact potentials wise) one leading to depletion and the other one with zero contact potential. The defect distribution and I–V relations are solved numerically assuming steady state. The effects of sample thickness, ionization–recombination reaction constant, recombination rate and hopping mobility are discussed. Different thicknesses, from nano to macro, are considered. The results are compared with a classical model in which the acceptors are fully ionized and no hopping is possible. The classical model is equivalent to a device with a Schottky junction on one side. The question of the existence of regions with local neutrality (l.n.) is discussed, and the concentration profile there is solved for the cases of strict l.n. and quasi-local neutrality. It is found that the sample thickness and ionization–recombination reaction constant have significant effects on the I–V relations of this device, whereas the hopping mobility and recombination time have a lesser effect. A comparison with the classical model shows that though the addition of the hopping conduction mechanism may have a significant effect on the defect distribution, the effects on the I–V relations are usually quantitative only, and not qualitative, as long as the ionization–recombination reaction constant is not too high. Hence, investigating the I–V relations is not sufficient to decide if hopping occurs in a sample. To distinguish between the classical model and the present model, one needs further experimental knowledge about the sample in question.