Ideal FET doping profile

Using variational calculus it is possible to show, for each MOSFET voltage and device topology, that there exists an ideal drain region doping profile which yields the optimum resistance versus breakdown voltage tradeoff. Because of the inclusion, in the resistance, of the effects of spreading resistance this profile tends to have a higher doping concentration (lower resistivity) at the blocking junction, this point being at or near the point of maximum spreading resistance, a minimum in doping partway into the drain and then asymptotically approach a
(1 - X/W)^{-1/2}
form as derived by Hu [1] at the edge of the depletion layer. The theory and calculations in this paper compare the Hu profile, a constant profile and our optimum profile for various practical geometries over a range of breakdown voltages. It is shown that the higher the device voltage and the less important the spreading resistance effects, the closer the ideal profile approaches that of Hu. The ideal profile concept applies equally well to other FET or majority carrier (resistive) devices.