Closed-form 2D modeling of sub-100 nm MOSFETs in the subthreshold regime

Closed-form 2D modeling of deep-submicron and sub-100 nm MOSFETs is explored using a conformal mapping technique where the 2D Poisson equation in the depletion regions is separated into a 1D long-channel case and a 2D Laplace equation. The 1D solution defines the boundary potential values for the Laplacian, which in turn provides a 2D correction of the channel potential. The model has been tested for classical MOSFETs with gate lengths in the range 200-250 nm, and for a super-steep retrograde MOSFET with a gate length of 70 nm. With a minimal parameter set, the present modeling reproduces both qualitatively and quantitatively the experimental data obtained for such devices.