A deformable wafer table for semiconductor lithography
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For the past decades, the semiconductor industry has mainly focused on decreasing the feature size on inte-grated circuits. The number of transistors that can be fitted on an integrated circuit doubles roughly every 18-24 months, referred to as Moore's law. By using state-of-the-art extreme ultraviolet (EUV) photolithog-raphy machines, the achievable critical dimension (e.g., gate length or linewidth) on integrated circuits is currently approximately 10-20nm. As the demand for efficient computing power is expected to continue to grow, and further 2D miniaturization becoming increasingly challenging, the semiconductor industry is now looking to vertical integration: effectively stacking more functional layers to build up a 3D integrated circuit. This places new requirements on photolithography machines. In these systems, thin silicon substrates, called wafers, are exposed with ultraviolet light to create the features that make up an integrated circuit. The deposition and processing of preceding layers cumulatively introduce stress into the wafer. The resulting deformations can accumulate to over a millimeter of out-of-plane warpage of the wafer. When clamping a warped wafer on a wafer table, these out-of-plane deformations lead to in-plane deformations, due to fric-tion and slip between the wafer and wafer table, as well as the resulting wear of the wafer table. This leads to misalignment between consecutive layers, known as overlay errors. To address these issues, a conceptual design for a piezoelectric deformable wafer table is presented. Two applications are identified. First, to mitigate the effects of clamping a highly warped wafer onto a flat wafer table, the concept of conformal wafer loading is introduced. To minimize slip between the wafer and wafer table during wafer load, the wafer table is actuated conformal to the wafer, prior to clamping the wafer. By actuating the wafer table along the neutral bending plane of the wafer, the wafer can be flattened without introducing relative motion between the wafer and wafer table. Secondly, overlay and focus errors can be reduced using intra-field corrections. During exposure, the wafer can be locally deformed to match the aerial image projected by the optical system, which compensates for both remaining deformations in the wafer, as well as optical aberrations. A design for a deformable wafer table is presented based on a multilayered piezoelectric actuator, on top of which a glass-ceramic wafer clamp is placed. For both conformal wafer loading and intra-field corrections, it is necessary to independently actuate in-plane strain across two orthogonal axes, in-plane shear strain, cur-vature across two orthogonal axes, and finally a twisting curvature. This is accomplished by stacking six pie-zoelectric layers, each of which can generate piezoelectric strain in a specific in-plane direction. Two embod-iments are analyzed: first, a design based on monolithically sintering ceramic lead-zirconate-titanate (PZT), to which an in-plane electric field can be applied using embedded interdigitated electrodes (IDEs); secondly, a design based on stacked monocrystalline lithium niobate (LN) wafers with planar electrodes, where the in-plane strain is obtained through a favorable crystal orientation. Key aspects of this design such as the layer thickness, electrode dimensions, and material orientation are optimized using a lightweight mathematical plate model. By combining this model with a finite element unit cell simulation, the microscopic deformations around the interdigitated electrodes could be scaled to the macroscopic deformation of the deformable wafer table. Using this method, the PZT and LN concepts were compared, and found to yield similar performance. While PZT has a higher piezoelectric coefficient, the ma-terial away from the IDEs does not efficiently contribute to generating strain. The low piezoelectric coeffi-cient of LN is largely compensated by the much higher coercive field, and all material between the planar electrodes is efficiently used. By splitting the wafer table actuator into segments, actuation at higher spatial frequencies is facilitated. This will increase both the conformal wafer loading performance, by reducing the mismatch between wafer and wafer table shape, as well as the intra-field correction performance by enabling higher-order corrections. The actuator influence functions of the segments are calculated using a finite element model, leveraging shell elements for computational efficiency. To characterize the different segmentations, two methods are pre-sented. The first is based on using an intermediate orthogonal decomposition of the solution space, and evaluating how well the actuator system can approximate the most relevant modes from this decomposi-tion. For this method, Zernike and Legendre polynomials are used for evaluating conformal wafer loading and intra-field corrections respectively. The second method is based on taking the singular value decomposi-tion of the reachable actuator space, and optionally combining the associated singular values into a perfor-mance measure. For the requirements set in this thesis, a 61-element hexagonal segmentation resulted in a good balance between performance and complexity. For both the PZT- and the LN-based design, a prototype was developed. For the PZT concept, multiple itera-tions were produced, based on tape casting PZT sheets and screen printing the interdigitated electrodes, followed by binder burnout, sintering and poling. However, the binder burnout proved difficult to control, resulting in repeated failures. It is hypothesized that a better process control of the tape casting and screen printing could improve the probability of success. Next, an LN-based prototype was produced using com-mercially available off-the-shelf LN wafers, with sputtered electrodes connected through brass foil spacers. This prototype demonstrated the feasibility of independently actuating curvature and in-plane strain, as well as achieving large deformations using the presented actuator concept. In conclusion, a design for a deformable wafer table was presented, which enables both conformal wafer loading and intra-field corrections. By stacking six piezoelectric layers, three in-plane strain and three curva-ture components can be independently actuated. Two types of piezoelectric layers were investigated, and their dimensions optimized for maximum curvature. First, ceramic lead-zirconate-titanate (PZT) can be sin-tered with embedded interdigitated electrodes which are used for both poling and actuating the layers. Sec-ondly, monocrystalline lithium niobate (LN) wafers can be stacked, separated by planar electrodes to actuate the layers. Although PZT has a high piezoelectric coefficient, the material is utilized less efficiently with the interdigitated electrodes, and manufacturing a prototype proved very difficult. In contrast, the crystal orien-tation of LN can be tuned for maximal performance, and the actuator concept was proven with a prototype made from commercially available LN wafers. To increase the spatial resolution of the deformable wafer table, a segmented design was analyzed, with a hexagonal 61-element segmentation providing an optimal balance between complexity and performance.
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