Run-to-run control of inductively coupled C₂F₆ plasma etching of SiO₂: Multivariable controller design and numerical application

A model-based run-to-run control method has been devised for an inductively coupled plasma etcher and applied to a numerical process for etching SiO ₂ film with C₂F₆ plasmas. The controller was designed to minimize a quadratic cost of control error for the oxide etch rate and etch uniformity by run-wise integral action of the RF power, chamber pressure and RF bias voltage. Through numerical simulation, it was shown that the controller can truly minimize the cost even when the set point is given not to be reached by the process.