Inversion Charge Linearization in MOSFET Modeling and a Rigorous Derivation of the EKV Compact Model

In this paper, the implications of inversion charge linearization in compact MOS transistor modeling are discussed. The charge-sheet model provides the basic relation among inversion charge and applied potentials, via the implicit surface potential. A rigorous derivation of simpler relations among inversion charge and applied external potentials is provided, using the technique of inversion charge linearization versus surface potential. The new concept of the pinch-off surface potential and a new definition of the inversion charge linearization factor are introduced. In particular, we show that the EKV charge-based model can be considered as an approximation to the more general approach presented here. An improvement to the EKV charge-based model is proposed in the form of a more accurate charge-voltage relationship. This model is analyzed in detail and shows an excellent agreement with the charge sheet model. The normalization of voltages, current and charges, as motivated by the inversion charge linearization, results in a major simplification in compact modeling in static as well as non-quasi-static derivations.