Actuator optimization for flatness correction of deformed surfaces

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By 2030, the global semiconductor industry is projected to hit the valuation of becoming a trillion dollar industry. Advancements in electronic devices have gave rise to tougher requirements thereby requiring the manufacturers to push the limits of consistency. This has lead to a need to enhance the accuracy of the chip manufacturing process. Wafer flatness is one of the primary prerequisites for attaining high accuracy in integrated circuit manufacturing. The high accuracy is achieved by incorporating optical lithography in the development of circuits with small feature sizes. The current lithography machine requires precise estimation of wafer flatness on a sub-nanometer scale for the elimination of deviations between the exposed region and the plane of focus. In this thesis, the point of focus is on the short stroke positioning system of a lithography machine. The critical aspect of flatness is interpreted by performing scanning operations on a wafer table surface. These operations provide an estimation of the types of deformations the wafer is subjected to. The wafer table acts as a wafer carrier, which undergoes lithography operations. Therefore, it becomes very critical to examine the nature of the wafer table. After performing scans for surface deformations, an optimization problem is formulated which involves placing piezoelectric actuators under the wafer table. The role of the piezoelectric actuators is to correct the wafer table thereby enhancing its flatness property. Through this research, the optimization yields to give a better estimation of flatness by placement of actuators. The problem formulation and the solution proposed are able to correct the flatness by approximately 95% of the initial deformation value. The work done in this research can be extended from an application point of view and can be utilized in estimating and correcting the deformations of any given structure. Since this research involved working in a 2-dimensional domain, the further implications of this research involves extending the proposed flatness correction technique to a 3-dimensional domain.