The effective potential and its use in simulation

Quantum effects are known to occur in the channel of MOSFETs, where the confinement is in the direction normal to the oxide interface. For quite some time, there has been a desire to categorize this quantization and determine the role it plays in semiconductor devices. The questions that must be addressed in simulation are difficult. Pushing to dimensional sizes, such as sub-50 nm gate lengths, will probe the transition from classical to quantum transport, and there is no present approach to this regime that has proved effective. Contrary to the classical case in which electrons are negligibly small, the finite extent of the momentum space available to the electron sets size limitations on the minimum wave packet - this is of the order of a few nanometers - and leads to the effective potential. The use of the effective potential for analyzing the effect of quantization on semiconductor devices is discussed.