Optimum doping profile for minimum ohmic resistance and high-breakdown voltage

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
^-9
V\min{B}\max{2.6}
Ω.cm
²
for an n silicon layer. The optimum doping profile can be closely approximated by a conventional uniformly doped n-n
⁺
structure.