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Band-to-band tunneling field-effect transistors (BTBT FETs) are expected to exhibit a subthreshold swing (SS) better than the 60-mV/dec limit of conventional metal-oxide-semiconductor FETs at room temperature. Through atomistic modeling of a suite of realistically extended InAs p-i-n single-gate (SG) and dual-gate (DG) ultrathin-body (UTB) and gate-all-around nanowire (GAA NW) devices with a gate length of 20 nm, we demonstrate that such a reduced SS can only be achieved if the electrostatic potential under the gate contact is very well controlled. We find that GAA NWs keep an SS less than 60 mV/dec for diameters larger than 10 nm, while the bodies in DG and SG UTBs must be scaled down to 7 and 4 nm, respectively. Still, all the considered devices are characterized by an on current smaller than the ITRS requirements.