Analytical Surface Potential Calculation for Organic Thin-film Transistors

In this work, we present a tenably accurate and computationally efficient analytical calculation of the surface potential in organic thin-film transistors (OTFTs). Double exponential density of states is used to model deep and tail trap states for carrier electrostatics. We employ the Lambert-W function to obtain the analytical surface potential expression. The validity of the obtained expressions is ascertained through a comparison between the numerical and explicit expressions. Furthermore, we also build on a model that was based on Lagrange Reversion theorem and test its validity for different biasing conditions. The proposed model, by virtue of its explicit analytical nature, while preserving the underlying physics, is suitable for the development of surface-potential-based compact models for OTFTs, which can be used for circuit design.