The $R_{\mathrm{\scriptscriptstyle ON},\mathrm {min}}$ of Balanced Symmetric Vertical Super Junction Based on R-Well Model

Abstract

The global optimization of the balanced symmetric vertical superjunction (VSJ) device is proposed based on the R-well model for the first time to realize the unique minimum specific on-resistance R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON,min</sub> . The R-well model, which is originated from our previous VSJ mode theory, shows the relationship between R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON</sub> and the doping concentration N under the given pillar width W and breakdown voltage V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> . The global R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON</sub> optimization is realized to obtain the design formulas of N and the pillar length Ld. The calculated results are in good agreement with the simulations. It is demonstrated from the comparisons with the simulations and the existing experiments that the optimization in this paper realizes the unique R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on,min</sub> with a relationship of R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON</sub> ∝ V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.03</sup> . The R-well model is also universal for other R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</sub> optimizations.