Effective potentials and the onset of quantization in ultrasmall MOSFETs

The connection between the minimum size of an electron wavepacket, and the introduction of an effective potential is discussed. The effective potential approach has a long history of use in trying to transition the gap between classical mechanics and quantum mechanics. An effective potential is one in which the quasi-classical regime is approximated through a density which arises from the effective potential W(x) through exp[-βW(x)]. The generation of the effective potential W(x) gives the effects of the onset of quantization in the system. In this paper, we study the use of the effective potential in a triangular well formed between the oxide and the depletion field of the semiconductor. We determine the quantization energy of the carriers in the potential well and their mean set-back from the interface. Finally, we show the connection between the effective potential and the Bohm-derived quantum potentials that have become of interest in simulations.