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

Stability and performance of variable gain controllers with application to a dvd storage drive

This paper deals with the control design for optical storage drives. A nonlinear design is suggested to overcome the tradeoff between disturbance rejection, in the sense of tracking error reduction during low-frequency shock and vibration, and playability, in the sense of sensor noise tracking during high-frequency disc surface defects. Based on a variable gain control design, it is shown that improvements in disturbance rejection can be obtained without unnecessarily affecting playability. With this design, additional control is applied beyond a pre-defined error level. Accordingly, it is shown that large vibrations induce additional control effort giving improved disturbance rejection while, at the same time, small vibrations hardly induce any additional control effort thus leaving the playability properties unaffected. The variable gain strategy is studied regarding closed-loop stability and regarding performance. Closed-loop stability is derived on the basis of absolute stability theory. Performance is quantified using a measure derived from the linear sensitivity function. Based on the amplitude of the linear sensitivity function, the maximum absolute values of the periodic nonlinear response subjected to harmonic excitation are computed within a frequency range of interest. Experiments are performed on an industrial setup to validate the numerical results, and to illustrate the applicability of the nonlinear control design in a dvd application

Stability and performance of variable gain controllers with application to a dvd storage drive

This paper deals with the control design for optical storage drives. A nonlinear design is suggested to overcome the tradeoff between disturbance rejection, in the sense of tracking error reduction during low-frequency shock and vibration, and playability, in the sense of sensor noise tracking during high-frequency disc surface defects. Based on a variable gain control design, it is shown that improvements in disturbance rejection can be obtained without unnecessarily affecting playability. With this design, additional control is applied beyond a pre-defined error level. Accordingly, it is shown that large vibrations induce additional control effort giving improved disturbance rejection while, at the same time, small vibrations hardly induce any additional control effort thus leaving the playability properties unaffected. The variable gain strategy is studied regarding closed-loop stability and regarding performance. Closed-loop stability is derived on the basis of absolute stability theory. Performance is quantified using a measure derived from the linear sensitivity function. Based on the amplitude of the linear sensitivity function, the maximum absolute values of the periodic nonlinear response subjected to harmonic excitation are computed within a frequency range of interest. Experiments are performed on an industrial setup to validate the numerical results, and to illustrate the applicability of the nonlinear control design in a dvd application

MIMO feed-forward design in wafer scanners using a gradient approximation-based algorithm

An experimental demonstration is given of a data-based multi-input multi-output (MIMO) feed-forward control design applied to the motion systems of a wafer scanner. Atop a nominal single-input single-output (SISO) feed-forward controller, a MIMO controller is designed having a finite impulse response (FIR) filter structure. The coefficients in this structure are obtained from a gradient approximation-based algorithm. The aid of the FIR filter structure is mostly through its efficient (and limited) set of perturbed-parameter experiments needed to obtain the FIR coefficients. The effectiveness of the optimized feed-forward design in achieving improved servo tracking performances is demonstrated on a high-speed and nano-accurate MIMO wafer stage of an industrial wafer scanner

Robust data-driven control for the stage synchronization problem

The aim of this paper is to extend iterative feedback tuning (IFT), which is a databased approach for controller tuning, with robustness constraints. Hereto a constrained IFT problem is formulated that is solved by introducing a penalty function. Essentially, the gradient estimates decompose into (a) the well-known IFT gradients and (b) the gradients with respect to this penalty function. Experimental results obtained from the motion control systems of an industrial wafer scanner confirm enhanced performance with guaranteed robustness properties