The shifted-rectangle approximation for simplifying the analysis of ion-implanted MOSFETs and MESFETs

Abstract

The ability to express the depletion layer voltage drop V d in terms of a quadratic function of the gate controlled depletion charge Q d is shown to be a key to the success of analytical modelling of ion-implanted MOSFETs and MESFETs. It is shown that such a quadratic function for the V d- Q d characteristics of implanted FETs can be obtained by approximating the implanted doping profile by a “shifted-rectangle” profile whose parameters can be derived directly from implantation parameters. It is also shown that the shifted-rectangle approximation (SRA) is not just an artifice for simplicity but accurately conserves the actual Q d, V d and depletion width conditions of both shallow and deep implanted Gaussian shaped doping profiles. The SRA simplifies the analysis of multiple-implanted devices and can be considered to be a basic approximation to be used along with the depletion and gradual channel approximations for a simple and accurate analysis of the non-uniformly doped FETs.