A novel analytical threshold voltage model of MOSFETs with implanted channels

A novel analytical model for the threshold voltage of long-channel MOSFETs with implanted channels is presented. The model is simple from a computational point of view and yields accurate values of the threshold voltage, if the implant profile is gaussian. The analytical difficulty posed by the gaussian function to solve Poisson's equation has been removed by the use of a new integrable function that closely fits with the gaussian and a doping transformation based on a piecewise averaging approximation. The use of this function opens the way to a new technique of modelling semiconductor devices with gaussian doping. The threshold voltage and the profiles of potential and electric field inside the channel are calculated from their closed-form expressions for different doping and biasing conditions. The accuracy of the model is established by comparison with the results of the numerical solution for a gaussian doped channel and some experimental results. The possibilities of extending the model to short-channel MOSFETs and handling practical non-gaussian implant profiles are discussed.