Analytical modeling of the channel-charge in ion-implanted MOSFETs and MESFETs

摘要

Analytical modelling of implanted Buried Channel (BC) and Surface Channel (SC) MOSFETs and MESFETs is difficult since the highly non-uniform channel doping profile cannot be integrated analytically to obtain the charge-voltage characteristics of the channel depletion layer. The present paper derives a general approximation to the non-uniform profile which gives simple and accurate closed form expressions directly in terms of device parameters for the various characteristics of all the FETs under all implant and bias conditions (the implant may be shallow, deep or multiple, and it may be partially or fully depleted depending upon the bias conditions). The derivation does not make any a-priori assumptions about the shape of the approximate profile. Instead, the shape emerges from a new formulation of the analytical modelling problem. It is shown that the necessary condition for analytical modelling of all the three FETs is the same, namely, expressing the depletion layer voltage drop V$-d$/ as a polynomial of the depletion charge Q$-d$/, where the degree of the polynomial can not exceed two. Next it is demonstrated that such a polynomial for the V$-d$/ -Q$-d$/ characteristics of implanted FETs can be obtained by approximating the doping profile by a 'shifted-rectangle' profile whose parameters can be derived directly from implantation parameters.