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A bilayer graphene-based electrostatically doped tunnel field-effect transistor (BED-TFET) is proposed. Unlike graphene nanoribbon TFETs in which the edge states deteriorate the OFF-state performance, BED-TFETs operate based on bandgaps induced by vertical electric fields in the source, channel, and drain regions without any chemical doping. The performance of the transistor is evaluated by self-consistent quantum transport simulations. This device has several advantages: 1) ultra-low power (V_DD=0.1 V); 2) high performance (I_ON/I_OFF >10⁴); 3) steep subthreshold swing (SS<;10mv/dec); and 4) electrically configurable between N-TFET and P-TFET post fabrication. The operation principle of the BED-TFET and its performance sensitivity to the device design parameters are presented.