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We propose a new two-dimensional (2-D) analytical model of a dual material gate MOSFET (DMG-MOSFET) for reduced drain-induced barrier lowering (DIBL) effect, merging two metal gates of different materials, laterally into one. The arrangement is such that the work function of the gate metal near the source is higher than the one near the drain. The model so developed predicts a step-function in the potential along the channel, which ensures screening of the drain potential variation by the gate near the drain. The small difference of voltage due to different gate material keeps a uniform electric field along the channel, which in turn improves the carrier transport efficiency. The ratio of two metal gate lengths can be optimized along with the metal work functions and oxide thickness for reducing the hot electron effect. The model is verified by comparison to the simulated results using a 2-D device simulator ATLAS over a wide range of device parameters and bias conditions.