Master equation model for Gaussian disordered organic field-effect transistors

We model organic field-effect transistors with Gaussian disordered energy distribution by a coupled three-dimensional steady-sate master equation and two-dimensional Poisson equation. By numerically solving these equations, we find that under moderate gate voltages the carrier distribution in the direction perpendicular to the semiconductor/insulator is broader and there is a non-negligible part of carrier residing outside of the first layer. In addition, our computation explicitly shows that the field-effect mobility is closer to the local mobility near the interface instead of the bulk mobility.