Three-Dimensional Closed-Form Model for Potential Barrier in Undoped FinFETs Resulting in Analytical Equations for VT and Subthreshold Slope

An analytical approach for modeling the electrostatic potential in nanoscale undoped FinFETs is derived. This method uses a 2-D solution for this potential within a double-gate FET and takes into account the top gate electrode as the third dimension by applying the conformal mapping technique. Herewith, an analytical closed-form model for the height of the potential barrier below threshold is defined which includes 3-D effects. From that, models for subthreshold slope and threshold voltage of nanoscale triple-gate FETs are derived. The results are in good agreement with numerical device simulation results and measurements for channel lengths down to 20 nm.