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A physical-based analytical direct current model is developed for undoped polycrystalline silicon thin-film transistors including both subthreshold and above-threshold regimes by assuming an exponential density of trap states. Based on the charge sheet method, diffusion and drift currents are calculated in the subthreshold regime. The parameter is introduced to describe the increase in trapped charge with increasing gate voltage in the above-threshold regime, and a new simple drain current expression is presented. The proposed model is compared with the Pao-Sah model and verified with the experimental data. A good agreement is obtained.