We report on a device model for thin-film transistors (TFTs) in the framework of Mott's trap-and-release transport theory for disordered semiconductors. The model features a so-called Mott function that is demonstrated to be powerful for analytically deriving the terminal characteristics and other critical parameters of TFTs, including threshold voltage, subthreshold swing, and field-effect mobility. The model is validated by way of application to an amorphous InGaZnO (IGZO)-based TFT, for which good agreement between the analytical and experimental data are obtained. This study offers a simple yet powerful formalism for effective parameter characterization and extraction for oxide and other related TFTs, including those from the organic materials family.