CLEANROOM TECHNOLOGIES

Analyzing, correcting stepper system vibration: A case study

Kenneth Medearis, Kenneth Medearis Associates

When an advanced technology tool such as those used in semiconductor fabs is not performing properly, it is often assumed that the problem can be traced to vibratory motions of the supporting floor system. This assumption may or may not be correct. As seen in Figure 1, the floor is only one component of the total system that must be considered when evaluating structural dynamics.¹ Also included are the tool's support pedestal, the floor support columns and lateral bracing, the building's foundation, and the soil below. In addition, the tool itself is of major importance but has frequently been ignored when troubleshooting problems. One of the reasons for this neglect is the acceptance by some of unsubstantiated generic criteria for the categorization of tools wherein velocity component levels are stipulated. However, for such velocity component levels to have any real credibility, it would be necessary to evaluate each tool's internal dynamic system, which, so far, has not been done.

Figure 1: Components for evaluating the dynamic motions of a stepper and the responses of the supporting floor system. The total system must be modeled in three dimensions, i.e., x, y, and z responses computed and evaluated.

Indeed, most tool manufacturers have concentrated their R&D efforts in the areas of tool optics and electronics, not vibrational dynamics. They have incorporated rubber isolation mounts and granite inertia blocks as part of their tools' internal dynamic systems, but those components have generally not been chosen based on comprehensive theoretical or experimental analyses. The result is that a tool's internal dynamic system can be a contributor to, or even the root cause of, operational difficulties. Figure 2 depicts vibration trace segments for a not untypical situation. The two parts of the figure clearly reveal that the motions recorded at the microscope level were on the order of 10—12 times those of the floor system. In this example, the internal dynamic system was amplifying vibrations rather than isolating the tool from them. To further illustrate the importance of considering the overall vibration scenario, this paper describes a situation in which a stepper experiencing a vibration-related production problem was found to be a prime, but not the only, contributor to that problem.

Figure 2: Vibration trace segments showing the lateral motions of (a) a supporting floor and (b) an aligner microscope. The dominant frequencies were ~20 and ~15 Hz, respectively (g=386.4 in./sec²).

Analyzing the Situation

Upon installation, it was found that a stepper was experiencing unacceptable vibratory motions, such that it could not pass the manufacturer's acceptance test. The tool manufacturer therefore took a number of on-site vibration measurements, an example of which is given in Figure 3. Unfortunately, the measurement values obtained were acceleration spectra, which can distort the vibratory scenario. As explained in detail elsewhere by the author, displacement is the most rational means of defining vibratory motions, partially because it is frequency independent.^1—3 To elaborate, it is known that, for harmonic motions, velocity is a function of displacement times frequency, and acceleration is a function of displacement times frequency-squared. Thus, a significant acceleration value may result when even a small displacement value is multiplied by a large frequency squared.

Figure 3: On-site vibration measurement spectra of the stepper (g=386.4 in./sec²).

That is precisely what happened when the tool manufacturer interpreted its vibration measurements. Although it correctly concluded the floor motions were relatively small and acceptable, it focused on the frequency-distorted acceleration magnitudes, identifying frequencies > 200 Hz as prime culprits (as indicated on Figure 3). However, structural dynamacists would recognize that those frequencies are far too high to be associated with either the floor or the steel pedestal that supported the stepper. When called in to consult on the problem, the author also took acceleration measurements for purposes of comparison as well as determining displacement measurement values (see Figure 4). The latter showed that the floor motions did not exceed 20 µin. peak to peak, and the associated displacement at >200 Hz was less than 1/2 µin. peak to peak.

Figure 4: Floor-motion recording trace segments for (a) floor vertical motion, (b) floor E­W motion, and (C) N­S motion (g=386.4 in./sec2).

The stepper manufacturer had also noted the motions of the steel support pedestal were somewhat high and concluded, erroneously, that the transmission of motions at frequencies >200 Hz was increasing the stage-settling time, which was, in turn, causing operational errors. A pertinent unanswered question, however, was, what was the source of the excitations? Because the manufacturer's attention was focused on the frequency-distorted acceleration data, the question of how a 1/2-µin. motion could cause such major problems had not been raised.

To answer this question required consideration of the total system, including the stepper itself. As seen in Figure 1, a stepper's operating stage is located on top of a granite block, which rests on rubber supports. Both of these components should result in the generation of low-frequency (1—10 Hz) motion that should be detectable in the tool's acceleration spectra. Reexamining Figure 3, a relevant peak at about 4.5 Hz is easily seen, which indicates that the stepper was a significant participant in the vibration problem, not just a victim of motion generated elsewhere. When displacement values for the stepper components were measured, they were found to be in the 1000—2000-µin. peak-to-peak range at the top of the granite block during stepper operation, and in the 200—500-µin. peak-to-peak range at the top of the steel pedestal. Both of these motion levels are deemed unacceptable, exceeding the 100 µin. peak-to-peak that has been recommended for high-tech facilities (see Figure 5).¹

Figure 5: Impulse excitation-structural dynamics response criteria based on theoretical and field measurements for some 100 facilities.1

Determining the Problem's Root Cause

At that point it was clear that the stepper's internal dynamic system was implicated in the excessive-motion situation. To correct a problem, however, one must determine its root cause, which had not yet been accomplished. The granite block was included in the stepper system to control forces generated by stage movements, and the rubber mounts were intended as an isolation mechanism, but was either functioning as intended? The fact is that neither component was effective in the pertinent system dynamics for this situation. The force required to cause the measured motions is only about 10 lb, which can easily be generated by stage movements, especially when there is a heavy granite block on soft rubber supports to be excited. It was thus concluded that the stepper system was contributing to the generation of the vibration problem.

Figure 6: Vibration trace segments showing the lateral motion of (a) the granite block excited by manual pushing and (b) the steel support pedestal excited by stepper operation.

The next step in the dynamic analysis was to prove the premise that the problem's root cause was indeed the motion of the massive granite block, which was, in turn, the result of the stepper stage movements. The means by which this step was accomplished are illustrated in Figure 6. First, the approximate fundamental frequency of the granite block rubber mount system was evaluated using a simple hand-impulse excitation. In the resulting time history shown in Figure 6a, it is easily seen that the first-mode frequency was 4.5 Hz. Next, the forced motions of the steel pedestal during stepper operation were recorded, and, as the typical segment given in Figure 6b indicates, the dominant frequency of those motions was also about 4.5 Hz. Because stage motion—generated forces primarily excite the granite block/rubber mount system fundamental mode, the correspondence of the two frequencies proves that the stepper's dynamic system was indeed generating the dominant excitations, while the dynamic response of the low-stiffness steel support pedestal was exacerbating the situation.

Correcting the Problem

As the above analyses revealed, the dynamic design of a stepper system, with its granite block and rubber mounts, is far from optimal. Unfortunately, however, that design cannot be easily modified. Thus, in this situation, it was necessary to design a new steel pedestal that would have better dynamic response characteristics. Based on further structural dynamics studies, that was successfully accomplished, and the desired stepper performance has been achieved. The comparative trace segments given in Figure 7 clearly attest to the success of the effort.

Figure 7: Typical vibration trace segments obtained during stepper operation for (a) the original steel pedestal and (b) the redesigned pedestal (g=386.4 in/sec²).

Conclusion

The case study presented here illustrates the importance of considering total dynamic systems when troubleshooting vibration-related equipment problems. All system components are potentially major contributors to an unacceptable vibratory situation. In this case, the stepper was a major player; the supporting floor was not. The often-neglected low-stiffness support pedestal was also deemed to be deficient (which indicates that the proposed option of supporting steppers on isolation tables that have even less stiffness should be given careful thought). The bottom line is that installation retrofits are always undesirable and costly. Appropriate structural dynamics studies should be conducted prior to installation if operational problems are to be avoided.

References

1.Medearis K, "Rational Vibration and Structural Dynamics Evaluations for Advanced Technology Facilities," Journal of the Institute of Environmental Sciences, 38(5):35—44, 1995.

2. Medearis K, "Rational Damage Criteria for Low-Rise Structures Subjected to Blasting Vibrations," Journal of the Institute of Civil Engineers, pp 611—621, September 1978.

3.Medearis K, "A Rational Method for Predicting Damage to Historical Structures Subjected to Blasting Vibrations," in Proceedings of International Society of Explosives Engineers, pp 301—218, March 1993.

Kenneth Medearis, PhD, is the founder and technical director of Kenneth Medearis Associates, Fort Collins, CO. Before organizing the consulting firm in 1969, he served as a professor of engineering and mathematics at Colorado State University, where he set up and directed the computer center. A registered professional engineer in several states and a member of the International Standards Organization committees on vibration and dynamics, Medearis has written a number of scientific publications and a book entitled Numerical-Computer Methods for Engineers and Physical Scientists. In 1995, he received the Institute of Environmental Sciences' Maurice Simpson Award for a technical paper on vibration and structural dynamics evaluations of advanced-technology facilities. Medearis received BS and MS degrees in civil engineering and structural engineering, respectively, from the University of Illinois and his PhD in structural dynamics from Stanford University.

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