Robust parameter design for integrated circuit fabrication procedure with respect to categorical characteristic

We consider a robust parameter design of the process for forming contact windows in complementary metal-oxide semiconductor circuits. Robust design is often used to find the optimal levels of process conditions which would provide the output of consistent quality as close to a target value. In this paper, we analyze the results of the fractional factorial design of nine factors: mask dimension, viscosity, bake temperature, spin speed, bake time, aperture, exposure time, developing time, etch time, where the outcome of the experiment is measured in terms of a categorized window size with five categories. Random effect analysis is employed to model both the mean and variance of categorized window size as functions of some controllable factors as well as random errors. Empirical Bayes' procedures are then utilized to fit both the models, and to eventually find the robust design of CMOS circuit process by means of a Bootstrap resampling approach.