On the form of 1-D nonlinear Poisson's equation and the concept of neutralization voltage for non-uniformly doped MOSFETs

Various types of doped 1-D nonlinear Poisson's equations existing in conventional and junctionless multi-gate MOSFET modeling literature are extensively examined. It is found that their reference levels used to define the potential in Poisson's equation are different, and some of them are not compatible with the potential definition in the commonly used formula of oxide-interface boundary condition. Those correct equations are identified by showing their compatibility with the oxide-interface boundary condition and verified by TCAD simulations. Moreover, the necessity to introduce the concept of neutralization voltage to replace the flat-band voltage for non-uniformly doped MOSFETs is discussed.