Charge transport in metal/semiconductor/metal devices based on organic semiconductors with an exponential density of states

In amorphous organic semiconductors in which electron or hole transport is due to hopping in an exponential density of states (DOS), the mobility is proportional to n(b), where n is the carrier density and where b increases with increasing width of the DOS. Exact analytical expressions are given for the steady-state and frequency-dependent current density in single-carrier metal/semiconductor/metal devices, based on such materials. For b > 1, the cross over frequency between a conductive and capacitive ac response is shown to be much larger than the inverse steady-state carrier transit time. The relevance to the analysis of the ac small-signal response in small-molecule and polymer layers, such as are used in organic light-emitting devices, is discussed.