Automated design of random dopant fluctuation resistant MOSFETs

An optimization technique is presented for the design of fluctuation resistant MOSFETs. This technique allows the computation of the doping profiles that minimize the standard deviation of fluctuations of transistor parameters induced by random dopant fluctuations (RDF). Constraints are taken into consideration by using the Lagrange multipliers technique. It is shown that by carefully designing the doping profiles, the random dopant-induced fluctuations of threshold voltage can be suppressed up to 50% in MOSFETs with channel lengths of 25 nm. Analytical equations are presented for the optimum doping profiles that minimize the random dopant-induced fluctuations of the threshold voltage in long-channel MOSFETs. It is shown that, in both long-channel and short-channel devices, the size of the undoped region should be at least ¿ of the width of the depletion region in order to suppress efficiently the random dopant-induced fluctuations.