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Three different carbon nanotube (CN) field-effect transistor (CNFET) designs are compared by simulation and experiment. While a C-CNFET with a doping profile similar to a "conventional" (referred to as C-CNFET in the following) p-or n-MOSFET in principle exhibits superior device characteristics when compared with a Schottky barrier CNFET, we find that aggressively scaled C-CNFET devices suffer from "charge pile-up" in the channel. This effect which is also known to occur in floating body silicon transistors deteriorates the C-CNFET off-state substantially and ultimately limits the achievable on/off-current ratio. In order to overcome this obstacle we explore the possibility of using CNs as gate-controlled tunneling devices (T-CNFETs). The T-CNFET benefits from a steep inverse subthreshold slope and a well controlled off-state while at the same time delivering high performance on-state characteristics. According to our simulation, the T-CNFET is the ideal transistor design for an ultrathin body three-terminal device like the CNFET.