The goal of the present work is to explore the concept of nanotechnology, carbon nanotubes and its function in Carbon Nanotube Field Effect Transistor (CNFET) and develop an analytical theory for nanometer-size field-effect transistor. This thesis research models and characterizes the future opportunities of CNFETs within digital designs.  The energy band of CNFETs has been modeled at equilibrium. For equilibrium condition, the carrier concentration is found by allowing the local electrostatic potential to rigidly shift the carbon nanotube density of states. The effect of contacts characteristics leading to the potential spikes in the tube at the source and drain of height determined by both work functions of source and drain and V gs have been explored.  By approximating the potential barrier shape and using Landauer-Büttiker expression it can be seen that CNFET have noteworthy IV characteristics. The current characteristics are similar to MOSFETs, having the operation being controlled by the electric field from the gate and source/drain voltage which can lead to strong band bending allowing carriers to tunnel through the interface barrier