Variable-range hopping charge transport in organic thin-film transistors

The charge transport in organic thin-film transistors (OTFTs) is assessed in terms of variable range hopping (VRH), by numerical simulations, analytical analyses and comparisons to published experimental results. A numerical simulator, built on the fundamental relations for VRH, provides a simple key dependence that the sum of hopping energy and energy bending under bias is equal to the hopping energy in the bulk material, the latter a bias-independent function of the absolute temperature. This relation binds electrostatics and VRH in OTFTs, at various assumptions for density of states (exponential, double-exponential and normal distributions). It generates and confirms many analytical expressions accumulated over the years for mobility, conductance, potential profiles in the depth of the organic semiconducting film and their relation to bias, film-thickness, also explaining the performance of OTFTs at elevated temperatures. The relations between charges, mobility and bias in OTFTs adhere from the above key dependence. We provide a method to obtain the distribution of the hopping time, which establishes explanations to non-stationary effects in OTFTs, such as dispersive transport, non-reciprocal transitions between on and off-states of the OTFT (usually attributed to gate bias stress and charge build-up), and low-frequency noise in the OTFT channel current.