Analytic model for organic field-effect transistors based on Vissenberg-Matters mobility model

Abstract

The fundamental I–V formula of an organic field effect transistor (OFET) is reformulated as double integral of mobility function by using the Poisson’s equation. The reformulated I–V formula overcome the divergence of the integrand in original I–V formula and is convenient not only for further analytic derivations but also for numerical calculations. An analytic binomial expansion for arbitrary power is proposed to analytically derive the OFET model based on Vissenberg-Matters (VM) mobility model being able to consider all terms deduced from the completed VM model. The numerical calculations for six OFET made of four kinds of materials show that the matching degree between theoretical I–V curves and the experimental data is satisfactory for completed model, but evident deviations for I_D–V_D curves exhibited in usual treatment that only considering first term deduced from the VM model. It is important to consider all terms in modelling OFET to ensure accuracy and reliability for extraction of parameters. These are useful for practical applications and device simulations.