Closed-form physics-based models for threshold voltage and subthreshold slope in FinFETs including 3D effects

Electrical device parameters such as leakage current below threshold, subthreshold current and threshold voltage are dominated by the height of the potential barrier which the carriers have to surmount to enter the drift region of the channel. This barrier is located at the minimum of the electrostatic potential along the direction from source to drain. Furthermore, the most leaky path in the channel cross-section will be at the position with highest electron concentration, and hence where the maximum potential is located. In this paper we present an analytical, structure-oriented model for the potential barrier in FinFETs, which inherently includes short-channel effects. In our approach, we focus on solving the 3D Laplace equation in a cross-section of the channel which is located at the position of the potential barrier. We assume the substrate oxide to be thick enough that field lines going from the channel into the substrate can be neglected. We consider a FinFET device with undoped channel region, and hence in subthreshold operation the depletion charge can be neglected. Herewith 3D Poisson´s equation is reduced to a 3D Laplace equation.