Technical Viewpoint

Formulating scientifically based specifications to control floor and tool vibration in IC fabs

Kenneth Medearis

Vibration. The word is almost a mantra that sometimes is used to scare facility owners into justifying additional funding to "fix" or "prevent" vibration-related issues in any project, be it a tool installation, a fab retrofit, or the construction of a new facility. Few people in the construction field are actually trained in the science of the structural response to vibration, and fewer still have the necessary experience to effectively deal with the effects and mitigation of vibration-related problems.

The traditional approach to vibration-related problems is to assume that architects, facility engineers, or tool suppliers will deal with them. Many simply defer to specifications proposed by such organizations as IEST or SEMI in the hope that simply incorporating such specifications into their designs will solve the problem. This approach has not proven to be effective and can be costly if it is implemented during a production ramp-up. Many specifications and methods of measuring, responding to, and correcting for vibration do not necessarily reflect the most optimal practices or follow well-established scientific principles. Nor do they often solve the problem.

This article provides theoretically and experimentally verified recommendations for dealing with vibration issues in the semiconductor fab. These recommendations are cost-effective and increase the performance of a fab's dynamic system, including its structure, flooring, walls, infrastructure, and tools. Based on established scientific practices and experience derived from nonsemiconductor industries, the article challenges many current methods for dealing with vibration.—Bruce Huling, Motorola

Although modern concepts of vibration and structural dynamics for addressing lithographic tool installations have been known for several years, the semiconductor industry has been willing to accept demonstrably incorrect, poorly defined theories and criteria for fab floor designs.¹ As noted in the literature, the industry's failure to apply correct vibration theories to fab installations has resulted in ill-advised structures, such as minuscule 10 x 10-ft structural bays, and led to astronomical construction costs.^1,2 The IC industry has begun to change, but it may still take years for it to fully appreciate a modern approach to vibration control.

Equipment manufacturers have also been slow to address their floor vibration needs in easily understandable, scientifically grounded terms. Moreover, excitation sources are almost never defined and certainly not well understood. Contrary to widespread belief, properly constructed, reasonably balanced rotating machinery installations are rarely the major source of excitation. For example, after 29 large fan towers were direct-mounted to the supporting floor immediately adjacent to a large fab, their excitations were found to be almost undetectable on the fab floor. Regardless, the view prevails that such fan towers must be supported on ineffective "isolation" systems, although that is not the case for residential fans. Low-stiffness isolation systems often tend to cause balancing problems and the premature demise of the fans.

In fact, primary fab floor excitations are typically associated with cart and personnel movements (footfall), tool and associated equipment operation, and the motion of suspended ducting and pipes. The validity of this view has been confirmed by an unpublished study by a major computer chip manufacturer. Since some fabs' vibration specifications make no mention of tool operation or cart and personnel movements, such specifications pertain only to an empty building and are therefore clearly of no value. Such specifications have apparently been generated to minimize responsibility and liability rather than to address floor system vibratory performance.

Equally unfortunate is the little-known fact that most manufacturer-provided floor-vibration criteria are actually not based on scientific studies. Typical examples are given in Figure 1, which shows stepper floor-vibration specifications. Although it is reasonable to assume that the steppers in the illustration would have similar floor-vibration specifications, they do not. Indeed, some of the specified motions are unrealistic on nonempty, operational fab floors, where there are people and tools. For example, the maximum displacement specification for stepper 1(a) of ~5 µin. at a frequency of 40 Hz is simply unachievable.

 

Figure 1: Floor-vibration specifications, peak-to-peak displacement components, for four different steppers.

It should be recognized, however, that it is difficult for toolmakers to provide valid floor-vibration specifications for structural systems they have not designed, and virtually impossible using a frequency component­type specification for which the excitation is not even defined.

In contrast, a "total vibratory system" is comprehensive because it includes information on the supporting soil, columns, floor system, tool pedestal, and tool components.¹ Based on the premise that the source of the vibration can be isolated, this comprehensive view has often been ignored. Consequently, tool manufacturers, in some cases, have simply incorporated erroneous fab floor-vibration criteria (which have been generated by others) into their specification information.

Vibration consultants often formulate incorrect vibration-control specifications because they have not received adequate scientific training. The field of structural dynamics—the study of the dynamics of structures, such as fab floor and tool-framing systems—is typically a graduate engineering curriculum requiring an undergraduate background in structures, structural design, and vibration. However, undergraduate courses in vibration, acoustics, and electrical or mechanical engineering do not provide any background in structural engineering. At the same time, a structural engineering curriculum almost never includes courses in elementary vibration or even mechanical engineering, much less structural dynamics. Consequently, the most accurate recommendations for fab and tool-pedestal structural systems are made by those who have not merely received on-the-job training in the field of vibration control but who have an academic background in the science of structural dynamics.

It is unlikely that an elementary vibration consultant without a background in structural design and engineering can team up with a structural engineer without a background in vibration to achieve efficient, effective solutions. Because it is likely that neither expert will really understand what the other is talking about, except in the most general terms, the requisite checks and balances will be lacking.

Another significant source of inaccurate specifications is the vibration measurement taker, that person or company that takes measurements with a vibration instrument but which has little or no knowledge, beyond the basics, of how to run the instrument as explained in the operating manual.

Inaccurate specifications may be supported by the warranty statement accompanying a tool purchase: "The customer must supply verification of compliance with the vibration specification upon request. Failure to do so will void the warranty." But what if the specification is invalid? How is a fab supposed to comply with it? In fact, toolmakers' floor-vibration specifications are rarely satisfied, leading most toolmakers to accept precise floor-vibration specifications arrived at on the basis of scientific criteria.

Generating Faulty Specifications Based on Frequency-Related Criteria

If vibration specifications for sensitive tools have no scientific basis, they should not be included in tool information packages. Intensely promoted but demonstrably incorrect, frequency-related component motion concepts are a major part of the problem. These concepts result in such inappropriate specification terms as one-third-octave acoustic band, fast Fourier transform (FFT), power spectral density (PSD), velocity or acceleration, and frequency-related components. This practice can be partially attributed to the output provided by some, but not all, commercially available measurement instruments. Such representations are often completely confusing to those who must use them, such as equipment engineers and even tool manufacturers' own personnel.

These specifications ignore the following considerations:

• Frequency-related component motion criteria have not been accepted by qualified structural dynamicists.
• Although toolmakers claim that such criteria are applicable to floor structural systems, no structural or structural dynamics textbook mentions them. While Fourier analysis is briefly addressed in elementary textbooks on vibration, one-third-octave acoustic bands are not. Even if a floor-system vibratory situation were truly random and broadband, which it is not, frequency-related motion components must still be appropriately evaluated for their dynamic responses, although not by means of the methods that have been presented to the semiconductor industry.^3,4
• System frequencies are often not of major importance. Dynamic-response evaluations are frequently made without even computing frequencies, even though such frequencies can be easily determined if necessary.¹
• Equipment and structural engineers preparing static designs for advanced-technology facilities typically have no understanding of such concepts as one-third-octave acoustic band, FFT, or power spectral density and do not know how to use them for preliminary designs. Such representations are thus of little or no practical value. Moreover, structural dynamicists do not generally use these methods. All engineers, however, can understand and measure total floor displacement.
• The sole use of components-of-motion criteria for evaluating vibratory response situations was proven to be inadequate many years ago in several structural dynamics studies at major universities. It was shown that summations of mathematically valid response spectra components, much less FFT representations, do not provide precise solutions.⁴
• Typical operational-fab excitations caused by such factors as moving carts and personnel cannot achieve the minuscule, ~1 µin., displacements associated with component criteria based on 100-µin./sec velocity. This is easily proven by considering a typical fab floor having a fundamental frequency of 30 Hz. The displacement for a 100-µin./sec velocity is 100/(2 x x 30) = 0.53 µin., or approximately 1.1 µin. peak to peak. This value cannot be achieved even by a well-constructed slab-on-grade floor system.⁵ Excessively large structural systems are the end result of attempting to achieve the unachievable—a suspended fab floor structural system with the stiffness of granite.¹

Achieving Floor Stability and Vibration Resistance

The stability and vibration resistance of the supporting floor system must be addressed in some fashion by toolmakers as well as structural and equipment engineers. There are certainly limber floors and large bay sizes that are not satisfactory for supporting vibration-sensitive tools. The criteria for these floor systems, however, must be easily understood and usable by all parties. Unfortunately, very few understand the frequency-related motion component criteria that have often been advanced to deal with this problem.

Using floor-vibration criteria based on a broad range of motion-component frequencies, such as 0­100 Hz, completely ignores the fundamentals of structural dynamics response and frequency pertaining to floor systems as well as the fundamentals of higher mathematics.^1,3,4 For example, such component measurements do not accurately reflect floor vibrations caused by footfall or cart excitations.

Most frequencies within the 0­100-Hz range are irrelevant to fab floor-system vibrations. Structural dynamicists know that floor systems act as "response filters"—that is, floors only respond significantly to excitations that correspond to their fundamental frequencies, filtering out most of the excitations that might exist in the 0­100-Hz range.³ Figure 2 illustrates this fact in its depiction of the actual vertical-response amplitudes of a fab floor subject to harmonic unbalance excitations from 0­100 Hz. As is almost always the case, the maximum response is concentrated at the floor fundamental vertical frequency of ~31 Hz, which means that a broadband, frequency-related component criterion has little or no value.

 

Figure 2: Floor-vibration response "filtering": peak-to-peak displacement for various harmonic excitation frequencies. The maximum magnification factor is only 4, even at the floor fundamental vertical frequency of 31 Hz.

Floor time-history responses (and frequencies) can be accurately computed using modern finite element theory.¹ In contrast to the types of broadband random-vibration concepts that proponents seek to apply to the semiconductor industry, random-vibration structural dynamics theories have been used to analyze multicomponent rocket structural systems.^3,4 A case in point is a rocket structural system with a thin-skin panel with a fundamental frequency of 100 Hz. Pertinent 100-Hz excitations can be transmitted to the skin via the broadband frequencies associated with motor detonation. However, although a tool may have a 100-Hz mechanical component, the supporting fab floor system with a fundamental frequency of 20­40 Hz will filter out any potentially detrimental 100-Hz excitations. This scenario presupposes a rational floor (not tool) vibration specification. If the floor does not transmit the excitation to the tool, the tool's components will not be affected. Tool vibration and structural dynamics are another matter. These factors must be addressed by multicomponent studies that are merited, but rarely performed, for very expensive tools.

The means for specifying allowable floor vibrations are summarized in Figure 3.¹ For vibration-sensitive tools, the total vertical displacement motion at the center of the bay induced by footfall should not exceed 100 µin. peak to peak. The associated bay center static stiffness must be at least 1000 kip/in. Structural engineers should be able to easily calculate the latter for preliminary static designs. For tools that are ultrasensitive to vibration, the more-stringent total motion response of 50 µin. peak to peak and a stiffness value of 4000 kip/in. should be used. These values do not represent structural overkill but correspond to a well-constructed slab-on-grade floor system.⁵ Horizontal motions and stiffness rates should be based on the same values. The horizontal motions of the floor, even with a minimal shear-wall system, are typically less than vertical motions, but they still merit careful consideration. Final theoretical response analyses and evaluations should always be made by a qualified structural dynamicist.

 

Figure 3: Graph used for specifying allowable floor vibrations to determine the recommended fab floor structural system. Response to foot impulse excitation versus stiffness points are used to generate the solid line.

The displacement-based criteria provided in this article, unlike frequency-related criteria, are easy to use. They have a sound theoretical basis, have been verified by hundreds of on-site measurements, and have been used at several hundred tool installations. Equipment manufacturers have approved of these installations. Furthermore, several manufacturers of sophisticated tools have provided their own floor-system stiffness recommendations. Finally, no vibration-related difficulties have been reported at any of the tool installations whose specifications are based on displacement criteria.

Conclusion

The generation of rational, easy-to-use, floor vibration specifications is long overdue. In some 25 years of dynamic studies for the semiconductor industry, the author has rarely encountered anyone who knows how to use any of the vast menagerie of cumbersome floor vibration specifications provided by tool manufacturers and acoustics consultants. Most of these specifications do not even define the excitation and thus have little scientific value.

This article has presented simple, easy-to-use, floor vibration specifications that are understandable to all engineers and have been successfully implemented in many tool installations. As an internationally acclaimed engineer once stated, "If a solution is not both theoretically sound and easy to use, it is not the best solution."

References

1. K Medearis, "Rational Vibration and Structural Dynamics Evaluations for Advanced Technology Facilities," Journal of the Institute of Environmental Sciences 38, no. 5 (1995): 35­44.
2. PB Ross, "Moore's Second Law," Forbes Magazine (March 1995).
3. SH Crandall, Random Vibrations (Cambridge, MA: MIT Press, 1963).
4. R Clough, "Earthquake Analysis by Response Spectrum Superposition," Bulletin of the Seismological Society of America (1962).
5. K Medearis, "Fan Foundation Systems—Analysis and Design Guidelines" (Palo Alto, CA: The Electric Power Research Institute [EPRI], 1986).  

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 in Fort Collins, 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's Maurice Simpson Award for a technical paper on vibration and structural dynamics evaluations of advanced-technology facilities. Medearis r eceived a BS in civil engineering and an MS in structural engineering from the University of Illinois in Champaign-Urbana and a PhD in structural dynamics from Stanford University in Palo Alto, CA. (Medearis can be reached at 970/484-3553 or kma@kenmedearis.com.)

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