Abstract
The optimum doping profile of a lightly doped layer that introduces the minimum series resistance and sustains a given junction breakdown voltage is derived. The theory applies to a one-dimensional Schottky diode and qualitatively to the collector or drain doping profiles of transistors. The minimum series resistance is found to be about 3.7 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-9</sup> <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V\min{B}\max{2.6}</tex> Ω.cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> for an n silicon layer. The optimum doping profile can be closely approximated by a conventional uniformly doped n-n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> structure.
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