Three-Dimensional Closed-Form Model for Potential Barrier in Undoped FinFETs Resulting in Analytical Equations for $V_{T}$ 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.