The intrinsic velocity is shown to be the ultimate limit to the saturation velocity in a very high electric field. The unidirectional intrinsic velocity arises from the fact that randomly oriented velocity vectors in zero electric field are streamlined and become unidirectional giving the ultimate drift velocity that is limited by the collision-free (ballistic) intrinsic velocity. In the nondegenerate regime, the intrinsic velocity is the thermal velocity that is a function of temperature and does not sensitively depend on the carrier concentration. In the degenerate regime, the intrinsic velocity is the Fermi velocity that is a function of carrier concentration and independent of temperature. The presence of a quantum emission lowers the saturation velocity. The drain carrier velocity is revealed to be smaller than the saturation velocity due to the presence of the finite electric field at the drain of a MOSFET. The popular channel pinchoff assumption is revealed not to be valid for either a long or short channel. Channel conduction beyond pinchoff enhances due to increase in the drain velocity as a result of enhanced drain electric field as drain voltage is increased, giving a realistic description of the channel length modulation without using any artificial parameters. The velocity so obtained is considered in modeling the current voltage characteristics of a MOSFET channel in the inversion regime and excellent agreement is obtained with experimental results on an 80-nm channel.
