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

Feasibility of hydraulic separation in a novel anaerobic-anoxic upflow reactor for biological nutrient removal

ABSTRACT : This contribution deals with a novel anaerobic-anoxic reactor for biological nutrient removal (BNR) from wastewater, termed AnoxAn. In the AnoxAn reactor, the anaerobic and anoxic zones for phosphate removal and denitrification are integrated in a single continuous upflow sludge blanket reactor, aiming at high compactness and efficiency. Its application is envisaged in those cases where retrofitting of existing wastewater treatment plants for BNR, or the construction of new ones, is limited by the available surface area. The environmental conditions are vertically divided up inside the reactor with the anaerobic zone at the bottom and the anoxic zone above. The capability of the AnoxAn configuration to establish two hydraulically separated zones inside the single reactor was assessed by means of hydraulic characterization experiments and model simulations. Residence time distribution (RTD) experiments in clean water were performed in a bench-scale (48.4 L) AnoxAn prototype. The required hydraulic separation between the anaerobic and anoxic zones, as well as adequate mixing in the individual zones, was obtained through selected mixing devices. The observed behaviour was described by a hydraulic model consisting of continuous stirred tank reactors and plug-flow reactors. The impact of the denitrification process in the anoxic zone on the hydraulic separation was subsequently evaluated through model simulations. The desired hydraulic behaviour proved feasible, involving little mixing between the anaerobic and anoxic zones (mixing flowrate 40.2% of influent flowrate) and negligible nitrate concentration in the anaerobic zone (less than 0.1 mgN L-1) when denitrification was considered

Green Pathways for the Enzymatic Synthesis of Furan-Based Polyesters and Polyamides

The attention towards the utilization of sustainable feedstocks for polymer synthesis has grown exponentially in recent years. One of the spotlighted monomers derived from renewable resources is 2,5-furandicarboxylic acid (FDCA), one of the most promising bio-based monomers, due to its resemblance to petroleum-based terephthalic acid. Very interesting synthetic routes using this monomer have been reported in the last two decades. Combining the use of bio-based monomers and non-toxic chemicals via enzymatic polymerizations can lead to a robust and favorable approach towards a greener technology of bio-based polymer production. In this chapter, a brief introduction to FDCA-based monomers and enzymatic polymerizations is given, particularly focusing on furan-based polymers and their polymerization. In addition, an outline of the recent developments in the field of enzymatic polymerizations is discussed. </p

Nonlinear control of optical storage drives with improved shock performance

An experimental demonstration is given of a nonlinear dynamic filter applied to an optical playback device (CD-drive) forautomotive applications. The filter is based on a static input–output nonlinearity that transforms the standard linear control designinto a shock-dependent control design. To relax the sufficient condition imposing stability, a dynamic filter is introduced. Thecombination of dynamic filter and static input–output nonlinearity forms a nonlinear dynamic filter that enables a large amount ofloop gain increase. With this filter, the controlled lens dynamics in radial (tracking) direction are studied both experimentally andnumerically in terms of shock suppression, and show a significant improvement in shock performance

Extended Projected Dynamical Systems with Applications to Hybrid Integrator-Gain Systems

The class of projected dynamical systems (PDS) has proven to be a powerful framework for modeling dynamical systems of which the trajectories are constrained to a set by means of projection. However, PDS fall short in modeling systems in which the constraint set does not satisfy certain regularity conditions and only part of the dynamics can be projected. This poses limitations in terms of the phenomena that can be described in this framework especially in the context of systems and control. Motivated by hybrid integrator-gain systems (HIGS), which are recently proposed control elements in the literature that aim at overcoming fundamental limitations of linear time-invariant feedback control, a new class of discontinuous dynamical systems referred to as extended projected dynamical systems (ePDS) is introduced in this paper. Extended projected dynamical systems include PDS as a special case and are well-defined for a wider variety of constraint sets as well as partial projections of the dynamics. In this paper, the ePDS framework is connected to the classical PDS literature and is subsequently used to provide a formal mathematical description of a HIGS-controlled system, which was lacking in the literature so far. Based on the latter result, HIGS-controlled systems are shown to be well-posed, in the sense of global existence of solutions

Iterative Pole–Zero model updating: A combined sensitivity approach

A crucial step in the control of a weakly damped high precision motion system is having an accurate dynamic model of the system from actuators to sensors and to the unmeasured performance variables. A (reduced) Finite Element (FE) model may be a good candidate apart from the fact that it often does not sufficiently match with the real system especially when it comes to machine-to-machine variation. To improve the dynamic properties of the FE model toward the dynamic properties of a specific machine, an Iterative Pole–Zero (IPZ) model updating procedure is used that updates numerical poles and zeros of Frequency Response Functions (FRFs) toward measured poles and zeros, which can be extracted from the measured FRFs. It is assumed that in a practical situation, the model (physical) parameters that cause discrepancy with the real structure are unknown. Therefore, the updating parameters will be the eigenvalues of the stiffness and/or damping (sub)matrix. In this paper, an IPZ model updating is introduced which combines the sensitivity functions of both poles and zeros (with respect to the corresponding updating parameters) together with the cross sensitivity functions between poles and zeros. The procedure is verified first using simulated experiments of a pinned-sliding beam structure and then using non-collocated FRF measurement results from a cantilever beam setup

Oblique Projected Dynamical Systems and Incremental Stability Under State Constraints

Projected dynamical systems (PDS) are discontinuous dynamical systems obtained by projecting a vector field on the tangent cone of a given constraint set. As such, PDS provide a convenient formalism to model constrained dynamical systems. When dealing with vector fields, which satisfy certain monotonicity properties, but not necessarily with respect to usual Euclidean norm, the resulting PDS does not necessarily inherit this monotonicity, as we will show. However, we demonstrate that if the projection is carried out with respect to a well-chosen norm, then the resulting 'oblique PDS' preserves the monotonicity of the unconstrained dynamics. This feature is especially desirable as monotonicity allows to guarantee important (incremental) stability properties and stability of periodic solutions (under periodic excitation). These properties can now be guaranteed based on the unconstrained dynamics using 'smart' projection instead of having to carry out a difficult a posteriori analysis on a constrained discontinuous dynamical system. To illustrate this, an application in the context of observer re-design is presented, which guarantees that the state estimate lies in the same state set as the observed state trajectory

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