| An analytical three-dimensional model for small-geometry Metal Oxide Semiconductor Field Effect Transistors (MOSFET's) has been developed for the fully recessed oxide isolation scheme based on the charge sheet approximation. This model simultaneously solves the three-dimensional Poisson's equation and the one-dimensional current continuity equation using the Fourier analysis method making it much faster than numerical models. The analytical solution is carried out for the case of a uniformly doped substrate and a constant mobility. Realistic boundary conditions are used at the source and drain ends of the channel, which makes the formulation more accurate. Conformal mapping is used to derive the boundary conditions at the gate oxide-silicon interface and at the sidewalls. Hence, no fitting parameters are required.;Using this analytical technique, a closed form three-dimensional drain current expression is obtained for the first time. The expression for the drain current is a function of process and device parameters such as device length and width, gate oxide thickness, field oxide thickness, substrate doping concentration, source and drain junction depths and substrate bias. The software implementation of the analytical model is compared with the three-dimensional numerical device simulator Atlas using similar physical assumptions. Good agreement is achieved under all bias conditions for devices with channel widths down to 0.2 mum and channel lengths down to 0.1 mum. Potential profiles and electric field profiles can also be generated from the solutions predicted by the three-dimensional model. The accuracy, speed, absence of fitting parameters and feasibility of the model make it remarkably useful for Computer Aided Design (CAD) applications. Discussion of future models with nonuniform substrate doping concentration and nonconstant mobility is provided. |
