Kinodynamic Generation of Wafer Scanners Trajectories Used in Semiconductor Manufacturing

The operation time of an ideal reliable wafer scanner model is defined at the die level where the actual exposure process takes place as the time unit per die, or at the wafer substrate level as the time unit per wafer substrate. Therefore, the machine throughput is given as the reciprocal of the operation time. The involved motion profiles of a machine, namely the step-and-scan trajectories, function as the heartbeats that drive its multidisciplinary elements, which suggests that a multidisciplinary design optimization should be involved when such profiles are selected or designed. This is also true when considering the traverse motion profiles among rows and columns within the wafer substrate. The step-and-scan trajectories affect the machine throughput, performance, and die yield. The effects of tracking such profiles appear as structural vibration, tracking errors, and thermal loading at various machine elements such as the actuators, the reticle, the wafer, and the projection elements specifically when the exposure high-energy duration and frequency are not taken into consideration while designing the reference motion. From the dynamics perspective, having a reference motion with nonzero and bounded higher-order derivatives is recommended since it enhances the tracking performance of the machine, however, its ability to increase the operation time is usually overlooked. In an attempt to understand such effects, we present a case study that outlines the aforementioned aspects using three step-and-scan profiles of mainly $3^{rd}$ -order. Taking the dynamics of the driven stage into consideration through input shaping, both the step-and-scan and traverse motion profiles are analyzed. We provide analytical expressions that can be used to generate both types of motion profiles on the fly without additional optimization. A simulation example of a simplified wafer scanner machine shows the usefulness of the proposed framework. Note to Practitioners - Choosing the most suitable operating conditions of a lithography machine is challenging. These conditions affect machine productivity, profit margin, and maintenance. In this paper, we reveal the relation between the selection of operating conditions based on several decision variables- and the kinodynamic step-and-scan trajectory generation based on specific machine parameters and clients' requirements. Being chart-based, the selection process of an operating point can be less practical at some points. However, using appropriate curve fitting tools, the information provided in the optimal operating charts can be put into suboptimal closed-form expressions that facilitate the selection process. Therefore, the designed trajectories parameters can be easily saved in lookup tables for ease of evaluation and future use. This helps in accommodating changes in the operation plans and flexible manufacturing systems. Also, starting with a given set of machine parameters, it is possible to calculate the optimal machine operating point when the input shaping technique is used, as illustrated in this paper.</p

Retrospective-Cost Adaptive Control of Uncertain Hammerstein-Wiener Systems with Memoryless and Hysteretic Nonlinearities

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97108/1/AIAA2012-4449.pd

On characterization of a generic lithography machine in a multi-directional space

In this paper, we present a dynamics modeling approach for lithographic machines. These machines consist of N-open chains with multiple stages in each chain. A stage can suppress or exert motion in specific directions. The stages affect each other through the structural connections available within a chain or various chains. We want to capture the energy transfer in the machine to better realize the design requirements. A specific application will be the optical lithography wafer-scanner machine. In such machines, step-and-scan motion profiles demand synchronization between the chains end-effectors. The rapid production rates requirements are projected onto the design space as high-acceleration profiles that will cause vibration based on the energy paths available. Various positioning errors will take place during the production of one complete substrate. Characterizing the machine dynamics due to jointly motion and vibration helps in providing better ways to synthesis the controllers for each stage. To minimize the positioning errors, we also propose replacements of specific stages where actively controlled fine positioning stages are used. The presented machine characterization provides a means to design and optimize such stages as will be illustrated through simulation examples

On Synchronization of Generic Lithography Machine Open-chains using a Novel Fine-Positioning Stage System

In this paper, we present an extension of our work on the characterization of lithography machines. So far, the machine was approximated using three open chains, reticle, optics and wafer chains, all sharing one common root. In general, the performance of the machine is assessed under partial or full synchronization among the chains being involved. The previously developed fine-positioning stage, or smart-material board, is utilized here to realize two types of synchronization, a partial one dealing with the synchronization error between the reticle and the wafer chains, specifically, and a modified synchronization which factors in all the chains motions. This stage provides additional degrees of freedom that can be used to regulate the tracking errors in a chain and to achieve partial or full synchronization as proposed herein without affecting the stability of the remaining stages. Therefore, in case an update is needed, the fine-positioning stage controller can be tuned either online or while the machine is at standstill. This feature of the fine-positioning stage makes it suitable as an add-on to exiting machines whose controllers' settings are preferred to be held constant with the possibility of increasing their performance. These advantages will be illustrated by a simulation example

A suppress-excite approach for online trajectory generation of uncertain motion systems

We present a framework that allows designing point-to-point closed-form trajectories and identifying flexible modes, jointly. The impulse response of a k-cascaded second-order notch filter is altered by composing it with a polynomial function of even degree in the time domain. The filter impulse response parameters are designed based on the available prior knowledge about the lightly-damped uncertain modes of the driven stage. The resulting chirps signals suppress the response of these oscillatory modes within selected suppression bands in the frequency domain. To check for unknown flexible modes within any desired frequency intervals of interest, the complement of the suppression bands is excited using excitation chirps signals. Using transmissibility, then the frequencies associated with the unknown flexible modes are identified, and the k-cascaded notch filter is updated accordingly. This update process may involve optimizing the parameters of the original filter, or the new filter when the order k changes. Also, real-time trajectory extrapolation is guaranteed under the proposed framework by the simple calculations required. The effectiveness of the proposed framework is illustrated through a numeric simulation example where the integration of both kinematic and dynamic constraints gives rise to the notion of kinodynamical trajectories