Space-charge limited current in the single-electron regime

The current injected into a semiconducting thin film is space-charge limited when the total number of electrons crossing per transit time is on the order of $CV/e.$ With nanoscale fabrication techniques it is possible, however, to make the capacitance so small that $CV/e$ is on the order of 1. In this paper we determine the properties of space-charge limited current in such a single-electron regime for a model of a molecular semiconductor for which charge transport takes place by hopping. We discuss the similarities with Coulomb blockade effects for a linear array of tunnel junctions between metal islands.