Single-walled carbon nanotubes have been integrated into silicon for use in vertical carbon nanotube field-effect transistors (CNTFETs). A unique feature of these devices is that a silicon substrate and a metal contact are used as the source and drain for the vertical transistors, respectively. These CNTFETs show very different characteristics from those fabricated with two metal contacts. Surprisingly, the transfer characteristics of the vertical CNTFETs can be either ambipolar or unipolar (p-type or n-type) depending on the sign of the drain voltage. Furthermore, the p-type/n-type character of the devices is defined by the doping type of the silicon substrate used in the fabrication process. A semiclassical model is used to simulate the performance of these CNTFETs by taking the conductance change of the Si contact under the gate voltage into consideration. The calculation results are consistent with the experimental observations.