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.

The absolute and relative stability are critical aspects of designing Controlled Motion Systems (CMS). The maximum attainable CMS performance depends highly on the design of the structural part and the actuator and sensor configuration, as mechanical vibrations can endanger stability. This thesis presents a method for designing CMS's using optimal design. The set of vibration modes that violates the stability criterion might change during the optimization process, which is undesired from an optimization point of view. An aspect of this method is to ensure stability by imposing a constraint regarding the stability of each vibration mode individually. The stability constraint proposed in this thesis aids in well-performing optimization that converges to feasible designs. This thesis presents a new way of modeling the open-loop response. It uses a standard PID controller often used in industry, and the structural model is a function of the poles and zeros of the system instead of the conventional modal parameters. Only three parameters are required to evaluate the robustness of a single mode. A robustness response surface was obtained via simulations and modeled using NURBS. The robustness response surface is used to evaluate the proposed robustness constraint. The surface model is suited for gradient-based optimization methods. The proposed method was tested on a relatively simple model of a motion system. The optimizer converged to unconventional solutions that outperformed designs obtained using engineering principles.