Exact analytical solution of channel surface potential as an explicit function of gate voltage in undoped-body MOSFETs using the Lambert W function and a threshold voltage definition therefrom

Two useful applications of the Lambert W function to undoped-body MOSFET modeling are presented. Firstly, it is applied to the problem of inverting the gate voltage versus channel surface potential equation. The result is an exact analytical solution of the channel surface potential as an explicit function of the gate voltage for either n or p channel operation. Additionally an approximate but highly accurate analytical solution is presented which is continuously valid for all regions of operation. Secondly, we propose a new unambiguous analytical definition for the threshold voltage of these undoped-body devices. This definition overcomes the impossibility of using the traditional definition based on the bulk Fermi potential, and the ambiguities introduced by other definitions. The threshold voltage is mathematically described also using the Lambert W function at the transition point from subthreshold to superthreshold behavior. An approximation for the -1 branch of the Lambert W function is proposed to express the threshold voltage approximately using elementary logarithmic functions. These new descriptions are then verified against two-dimensional numerical device simulations. (C) 2003 Elsevier Ltd. All rights reserved.