A physical compact MOSFET mobility model including accurate calculation of saturation surface potential

We describe a vertical field electron mobility model that has been implemented in a SOI MOSFET surface potential based compact model. The main scattering mechanisms-surface roughness, phonon, and Coulomb scattering-are included. All scattering terms have been retained when calculating the drain saturation surface potential psi(sLsat). This yields a quartic expression in psi(sLsat). Taking the exact quartic solution results in numerical instabilities in psi(sLsat) at under some conditions, which cannot be corrected using numerical limiting. Instead, a method has been devised in which the quartic is approximated by a stable quadratic expression. The accuracy of the approximate solution is very high, with deviations from the exact solution of no more than a few mV.