Accounting for the deep Gaussian and tail exponential distribution of the density of states, a physical approximation for potentials of amorphous silicon thin-film transistors using a symmetric dual gate(s DG a-Si:H TFT) has been presented. The proposed scheme provides a complete solution of the potentials at the surface and center of the layer without solving any transcendental equations. A channel current model incorporating features of gate voltage-dependent mobility and coupling factor is derived. We show the parameters required for accurately describing the current–voltage(I–V) characteristics of DG a-Si:H TFT and just how sensitively these parameters affect TFT current. Particularly, the parameters’ dependence on the I–V characteristics with respect to the density of deep state and channel thickness has been investigated in detail. The resulting scheme and model are successively verified through comparison with numerical simulations as well as the available experimental data. Accounting for the deep Gaussian and tail exponential distribution of the density of states, a physical approximation for potentials of amorphous silicon thin-film transistors using a symmetric dual gate (s DG a-Si: H TFT) has been presented. a complete solution of the potentials at the surface and center of the layer without solving any transcendental equations. A channel current model incorporating features of gate voltage-dependent mobility and coupling factor is derived. We show the parameters required for accurately describing the current-voltage Particularly, the parameters’ dependence on the I-V characteristics with respect to the density of deep state and channel thickness has been investigated. (I-V) characteristics of DG a-Si: H TFT and just how sensitive in detail. The resulting scheme and model are sequential verified through comparison with numerical simulations as well as the available experimental dat a.