The gradual freezing-out of conduction electrons with decreasing temperature eventually leads to a situation in which the main contribution to the electrical conductivity comes from electrons hopping directly between impurities without any excursion to the conduction band. This is called hopping conductivity. Electrons jump from occupied donors to empty ones, and therefore the presence of empty positions on donors is a necessary condition. At low temperatures this condition can be fulfilled only by compensation.
The hopping mechanism of conduction corresponds to a very low mobility, since the electron jumps are associated with a weak overlap of wave-function tails from neighboring donors. Nevertheless, it wins in the competition with band conduction, because only an exponentially small number of free carriers can participate in the latter.
