Obtaining uniform surface finish across large length scales is extremely important in Chemical Mechanical Planarization (CMP). Existing control strategies use results from model simulations to propose open-loop control strategies to reduce the step height on surfaces being polished. In the present work, we propose a strategy to control the surface profile of substrate during CMP process. The evolution of the surface profile is predicted using the state space model of the polishing process. The resulting state space equation is solved and a closed form solution of the surface profile is obtained as a function of time. Based on the solution, we provide a fundamental limitation for the machining process in terms of the extent of planarization that can be achieved for a given material budget.

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