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

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Abstract

The ability to express the depletion layer voltage drop Vd in terms of a quadratic function of the gate controlled depletion charge Qd 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 Vd-Qd 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 Qd, Vd 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.

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