Equivalent doping profile transformation: a semi-empirical, analytical method for predicting breakdown characteristics of an approximate single-diffused parallel-plane junction

In this paper, a semi-empirical analytical method called the equivalent doping profile transformation method (EDPTM) has been proposed for the first time to predict the breakdown characteristics of an approximate single-diffused parallel-plane pn-junction that has a doping profile of the combination of a diffused side linear gradient constant and a constant substrate doping concentration, which considers the influence of the diffusion gradient level on the space charge region of the substrate side. Through the equivalent doping profile transformation, this approximate pn-junction turns into a double-sided asymmetric linear-graded junction (Jin et al., 1999). As a result, the breakdown voltage, critical peak electrical field, and the maximum depletion layer width can be carefully evaluated at different doping substrate concentration and gradient constant combinations. Compared with previous approximations such as abrupt and classical symmetrical linear-graded junctions, this method can give exact breakdown characteristics of a single-diffused pn-junction. The results are in excellent agreement with the numerical analysis, which proves the validity of this new method.