A physical-based explicit calculation to the height of grain boundary barrier has been derived based on the quasi-two-dimensional approach at discrete grain boundaries. The analytical solution is obtained by using the Lambert W function, combining both the uniform distributed deep states and the exponential tail states. The proposed scheme is demonstrated as an accurate and computationally efficient solution in a closed form, which can serve as a basis for the discrete-grain-based models of mobility and drain current in polysilicon thin film transistors. It is verified successfully by comparisons with both numerical simulation and experimental data. (c) 2013 Elsevier Ltd. All rights reserved.