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.

High performance machines such as those used in the semiconductor industry, robotics or racing engines have lots of fast moving parts. The dynamic properties of these moving parts are crucial to the performance of the machine. Therefore these moving parts have to be carefully designed which is often a very time consuming iterative process. In this thesis a general method to optimize the dynamic properties of a structure utilizing topology optimization is investigated. More specifically, the method will be focused on the optimization of eigenfrequencies whilst achieving specific ratios between eigenfrequencies, as dynamic performance requirements are often linked to such criteria. We refer to this class of topology optimization problems as problems involving constrained eigenfrequencies. A particular case of interest is the desired multiplicity of two or more eigenfrequencies, that is a ratio of 1. Several crucial aspects of the topology optimization of eigenfrequencies are investigated, these are the material interpolation methods, mode tracking techniques, multiplicity problems and obtaining a discrete design. By comparing different material interpolation methods, a clear view on the effects of different methods is obtained, leading to solid arguments for selecting a linear material interpolation method for topology optimization of eigenfrequencies. A simple yet effective method of tracking the eigenmodes during the optimization process combined with a solution for the multiplicity problems is presented and verified to show similar results as a more complex analytical approach. A new method of obtaining a discrete design without applying penalization or modification of the eigenvalue problem has been developed using a modified objective function. This method shows promising results and is a good candidate for replacing the material interpolation penalization method. By combining these results, a general and capable framework for the topology optimization of constrained eigenfrequencies is obtained. Using the presented framework, a practical application of the method is given by the design of a cantilever used in an atomic force microscope. Feasible and well-performing designs have been generated, both from a functional and manufacturing point of view.

Topology optimization has seen increased interest with the development of additive manufacturing (AM) as a manufacturing method, because of its ability to utilize the geometric complexity that AM offers. However AM still imposes some restrictions on the design, most notably on its minimum feature size, overhang, and enclosed voids. Enclosed voids are problematic because for most AM methods it is impossible to remove supports from them, additionally for powder-based AM these enclosed voids trap unmelted powder adding parasitic mass. In this thesis, two new methods have been investigated to alleviate this issue, the eigenfrequency method and the flood fill method. The eigenfrequency method utilizes the eigenfrequency of an inverted density field, which changes enclosed voids to floating masses. These floating masses have rigid body modes, which can then be prevented by applying a minimum eigenfrequency constraint. The eigenfrequency method encountered a large problem in the form of intermediate densities, which were used to satisfy the eigenfrequency constraint instead of the elimination of enclosed voids. The flood fill method utilizes a modified flood fill algorithm, which is a filter with a resulting density field where every enclosed void element is changed to solid. The flood fill method did successfully eliminate enclosed voids in both 2D and 3D problems, at the cost of very little additional computational effort. It also allows for direct control over the location, amount, and size of the void elimination features by varying boundary elements, running additional flood fills, and morphologic operators, respectively.

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.

In a high-precision system that performs measurements or tooling on a workpiece, alignment of the tool and workpiece is of prime importance. To prevent misalignment, which leads to a loss in accuracy and precision, unwanted vibrations in structures must be attenuated. Topology Optimization (TO) is evolving as a mature design tool that provides innovative designs beyond human creativity. This thesis focuses on developing and investigating TO methods for the limitation of response peaks on a flat surface for suspended structures. When optimizing for multiple excitation frequencies at multiple output points, the complexity of the problem increases, and the number of required constraints grows manifold. Thus, for a compact formulation, there is a need for aggregation of peaks in both dimensions, space, and frequency. Furthermore, the application requires the top surface of the suspended structure to remain flat during operation. In such a scenario, where a structure is excited harmonically, the dynamic deformations on the surface become key to quantifying surface flatness. The incorporation of dynamic flatness measures in TO framework is studied and implemented, and the results show that the proposed methods look promising.