A dual material gate (DMG) amorphous indium gallium zinc oxide(a-IGZO) thin-film transistor (TFT) is proposed, which has a gate structure of lateral-contact-metals with two working functions. In view of multiple gate materials and localized/delocalized states, the potential calculations using Poisson’s equation are complicated and without analytical solution, which complicates the gate controllability analysis and future compact modeling methodology. Therefore, we have developed an analytical 2-D potential model, that shows a great agreement with the numerical solution, taking into account asymmetry effects and scaling behavior. It can be used to tune potential or electric-field profiles by dual material gate engineering, increase the average channel electric field, reduce the electric-field at the Drain side, and thus improve the performance of short-channel a-IGZO TFT with immunity to Drain-Induced-Barrier-Lowing and hot carrier effect.