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In this paper, an analytical a-Si:H thin-film transistor (TFT) model based on surface potential is presented. Firstly, an explicit approximation for the surface potential as a function of terminal voltages is proposed. In the new analytical solution, simultaneously, the effects of localized trapped charges and free carriers are considered. Moreover, the complex iterative computation is eliminated in the solution. Comparing with the numerical results, the proposed solution shows a high accuracy for predicting the surface potential under various biases. Secondly, a charge sheet model is then developed for the analysis of DC characteristics of a-Si:H TFT. The improved model can describes all operation regions via an unique formula and it is verified by a reasonable agreement between the simulated results and the experimental data.