Taking deep Gaussian and tail exponential distribution of the density of states into account, a novel scheme for potentials of amorphous silicon thin film transistor using symmetric dual gate has been present. The proposed scheme, valid from below to above threshold regimes, provides a completed solution of the potentials at the surface and mid of the layer without solving any transcendental equation. Validity of the work has been verified by extensive comparison to the rigorous numerical simulations. The calculation efficiency has finally been demonstrated. A significant promotion is obtained. (C) 2014 Elsevier Ltd. All rights reserved.