Analytic modeling of potential and threshold voltage for short-channel thin-body fully depleted silicon-on-insulator MOSFETs with a vertical Gaussian doping profile

We verify that one-dimensional (1D) Gaussian expression is an appropriate approximation of the vertical doping profile, which is obtained by combining perpendicular ion implantation and rapid thermal annealing (RTA), for short-channel thin-body (20-30nm) fully depleted (FD) silicon-oninsulator (SOI) MOSFETs. The two-dimensional (2D) potential distribution of the silicon film is derived by adopting the evanescent mode analysis method, in which the potential function is broken into 1D long-channel and 2D short-channel potentials. The threshold voltage model is represented by the minimum front-and back-surface potentials of the silicon film. The application of the threshold voltage model can be extended to a 12 nm channel length. The results obtained using the models match well with the 2D numerical simulation results obtained using the Synopsys Sentaurus Device. They provide a feasible way of developing new 2D models for nonuniform nanoscale thin-body FD-SOI devices.