In this work, a two-dimensional potential distribution formulation is presented for multi-material gate poly-crystalline silicon thin film transistors. The developed formulation incorporates the effects due to traps and grain-boundaries. In short-channel devices, short-channel effects and drain-induced barrier lowering (DIBL) effect exists, and are accounted for in the analysis. The work aims at the reduction of DIBL effect and grain-boundary effects i.e. to reduce the potential barriers generated in the channel by employing gate-engineered structures. A study of work-functions and electrode lengths of multi-material gate electrode is done to suppress the potential barriers, hot electron effect and to improve the carrier transport efficiency. Green's function approach is adopted for the two-dimensional potential solution. The results obtained show a good agreement with simulated results, thus, demonstrating the validity of our model. (C) 2007 Elsevier B.V. All rights reserved.