Derivation of a nonlinear variance equation and its application to SOI technology

An analytic nonlinear equation for variance was derived along with a method based on response surface mapping techniques to calculate the variance using the proposed equation. The technique was applied to the threshold voltage of a 0.1-/spl mu/m silicon-on-insulator MOS device, and the variance value obtained was verified using Monte Carlo simulation. The threshold voltage dependence upon active-layer thickness was found to be highly nonlinear due to the device's going from the fully depleted to the partially depleted regime. Analysis of the variance showed that the effect of the nonlinear terms (18.7%) is more important than the effect of the mixed term (-0.7%) and almost as important as the contribution of the second most dominant input-process parameter (23.6%). This illustrates the importance of the proposed nonlinear equation.