In this work we present analytical models for the drain current and threshold voltage of Zinc oxynitride thin film transistors. A surface potential based modeling approach has been adopted and the exact closed form solutions for the potential profile, drain current and threshold voltage have been obtained. In order to account for the effects of both free and localized charges in the semiconductor, an effective charge density method has been used. The models were validated against experimental data from literature. The models show good agreement with the data.