Stochastic response surface method and tolerance analysis in microelectronics

Tolerance analysis is a very important tool for chip design in the microelectronics industry. The usual method for tolerance analysis is Monte Carlo simulation, which, however, is extremely CPU intensive, because in order to yield statistically significant results, it needs to generate a large sample of function values. Here we report on another method, recently introduced in several fields, caged stochastic response surface method, which might be a viable alternative to Monte Carlo simulation for some classes of problems. The application considered here is on the tolerance analysis of the current of a submicrometer n(+)-n-n(+) diode as a function of the channel length and the channel doping. The numerical simulator for calculating the current is based on the energy transport hydrodynamical model introduced by Stratton, which is one of the most widely used in this field.