Transition from bulk transport to surface transport in organic field effect transistors

We propose a theory of trap-filling transitions in organic thin films in a planar field effect transistor geometry containing an exponential trap distribution. We find that the thickness of the accumulation layer produced by the gate voltage in those devices depends strongly on the degree of energetical disorder in the active layer. As a consequence, the charge-carrier transport in systems with a high degree of energetical disorder can have two regimes: (i) a bulklike regime (BL), where the charge-carrier mobility decreases with the thickness of the semiconductor film and (ii) a surface transport (ST) regime, where the charge-carrier mobility saturates and does not depend on the thickness of the film. We derive approximate analytical expressions for the current-voltage characteristics, the saturation current as a function of the gate voltage (saturation transfer curve), and the field-effect mobility for each regime of charge-carrier transport. We show that the BL/ST transition is characterized by a variation of 2 in the power-law exponent followed by the mobility as a function of the gate voltage after a critical value. By means of our simple model, we discuss the conditions for the observation of the BL/ST transition in thin-film organic field effect transistors. We show that the mobility can have a maximum with increasing deposition of semiconductor material, depending on the nature of the percolative transport in the submonolayer and monolayer scales and on the degree of energetic disorder in the film. Finally we test our model using experimental data measured in alpha, omega-dihexylquaterthiophene devices reported in the literature.