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We investigate the gate controlled direct band-to-band tunneling (BTBT) current in monolayer transition-metal dichalcogenide (MX₂) channel-based tunnel field effect transistor (TFET). Five MX₂ materials (MoS₂,MoSe₂,MoTe₂,WS₂,WSe₂) in their 2-D sheet forms are considered for this purpose. We first study the real and imaginary band structure of those MX₂ materials by density-functional theory (DFT), which is then used to evaluate the gate-controlled current under the Wentzel-Kramers-Brillouin (WKB) approximation. It is shown that all five MX₂ support direct BTBT in their monolayer sheet forms and offer an average ON current and subthreshold slope of 150 μA/μm (at V_d=0.1 V) and 4 mV/dec, respectively. Furthermore, we also demonstrate the strain effect on the complex band structures and the performances of MX₂ based TFETs. It is observed that a certain tensile strain becomes favorable for the improvement of ON-current performances.