Abstract

This work considers the modeling and control of positive optical photoresist development. The control effort is applied to this final process step in order to compensate for deviations in previous irreversible steps. A new approach to line-width control is studied. State estimation, combining interferometric development measurements with a process model, is used to calculate the time at which developer breakthrough to the substrate occurs. Parameter identification is used to determine any sample-to-sample changes in the process model. The optimal control policy is shown to be bang-bang with switching at the final time. A model describing development after breakthrough is derived and used to calculate the final developer shutoff time, based upon an on-line identified development process parameter. The policy is tested experimentally on different batches of the same resist type. Results indicate that accurate control is achieved, despite changes in environmental conditions and unexpected transient disturbances.

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