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In this paper, we propose the application of a dual material gate (DMG) in a tunnel field-effect transistor (TFET) to simultaneously optimize the on-current, the off-current, and the threshold voltage and also improve the average subthreshold slope, the nature of the output characteristics, and immunity against the drain-induced barrier lowering effects. We demonstrate that, if appropriate work functions are chosen for the gate materials on the source side and the drain side, the TFET shows a significantly improved performance. We apply the technique of DMG in a strained double-gate TFET with a high-k gate dielectric to show an overall improvement in the characteristics of the device, along with achieving a good on-current and an excellent average subthreshold slope. The results show that the DMG technique can be applied to TFETs with different channel materials, channel lengths, gate-oxide materials, gate-oxide thicknesses, and power supply levels to achieve significant gains in the overall device characteristics.