An analytical model for the internal electric field in submicrometer MOSFETs

A pseudo-two-dimensional analytical MOSFET model is presented. The channel is divided into source, drain, and junction regions. The source region includes an expression for the carrier-velocity saturation based on the Scharfetter-Gummel formula. The drain region includes an expression for the spread of the lateral field into the bulk. The bulk field in the drain region is described by the radial field from a semicircular drain junction. The junction region describes the voltage drop across a diffused doping profile given an exponential approximation at the junction. The saturation condition is evaluated for both the validity of the gradual channel approximation (GCA) in the source region and carrier-velocity saturation in the drain region. The model elucidates the dependence of the surface field on substrate bias, drain junction depth, and diffusion profile. The model is compared to MINIMOS calculations and found to correlate within 10% for all bias and device combinations of interest for modeling EPROM devices. The computation time of the model is two to three orders of magnitude shorter than full two-dimensional MINIMOS simulations