Abstract Analytical expressions have been developed for the analysis of static and dynamic behaviour of hydrogenated-amorphous-silicon based field-effect transistors. The current/voltage, capacitances and transcapacitances/voltage characteristics are related to the material parameters. The characteristic temperature, T c , of the exponential band-tail states distribution is shown to influence strongly their shape and magnitude. An exact integration of the potential in the structure has allowed us to give expressions for the source and drain resistances. Finally, we present an equivalent circuit of a-Si:H TFT which can be employed in circuit simulation for the optimisation of integrated circuits.