Modeling of threshold voltage of a quadruple gate transistor

In this paper, a three dimensional analytical solution of electrostatic potential is presented for undoped (or lightly doped) quadruple gate MOSFET by solving 3-D Poisson's equation. It is shown that the threshold voltage predicted by the analytical solution is in close agreement with TCAD 3-D numerical simulation results. For numerical simulation, self-consistent Schrodinger-Poisson equations, calibrated by 2D non equilibrium green function simulation, are used. This analytical model not only provides useful physics insight of effects of gate length and body width on the threshold voltage, but also serves as a basis for compact modeling of quadruple gate MOSFETs.