Simultaneous optimal bottom linewidth and side-wall curvature control of wet etching



Etching is one of the critical steps in the fabrication of microelectronics devices. A time-optimal control problem with a dual-term terminal cost including both bottom linewidth and side-wall curvature is formulated to implement an optimal open-width design principle. A singular-arc solution does not exist and the control action is bangbang. The optimal switching time is analytically calculated. The feasibility and effectiveness of this technique are illustrated by simulation studies. This design and control philosophy can easily be applied to other microelectronics manufacturing processes.