1.1 Overview of design methodology

 Effective and efficient design of vibration sensitive optical (and electron microscope based) equipment strongly depends on the design strategy and methodology.  The old approach of developing a design with only minor consideration of vibration issues often results in a lengthy and expensive process involving numerous design and prototype iterations.  However, if appropriate attention is focused on the vibration issues the design process requires fewer iterations, resulting in significant advantages in cost and time.

 An effective design methodology usually includes the following design steps:

1.     Identification of vibration performance requirements

2.     Determination of internal vibration sources and strategies to minimize their adverse impacts

3.     Optimization of structural design by use of finite element modeling

4.     Modal analysis testing of the prototype

5.     Vibration performance testing under operational conditions

6.     Development of design modifications if needed (repeat steps 3 to 5)

7.     Determination of the specification of maximum acceptable levels of facility floor vibration

 

1.2. Identification of vibration performance requirements

 The identification of vibration performance requirements usually results from the development of the overall error budget.  For example when developing an inspection system that will have an overall accuracy of 0.1 micron, the allowable vibration error would be typically 0.01 to 0.02 micron (10% to 20% of the total error budget).

 The term vibration error refers to the amplitude of the imaging error caused during the imaging (or exposure) interval by the differential motion between the optics and the target being imaged.  This is usually quite different from the amplitude of vibration on either the optics or the imaging target.  For example, at many frequencies the entire system can exhibit nearly rigid body motion which results in small amplitudes of differential motion even with large absolute motion.  At other frequencies, the system has resonances in which the optics and the imaging target move differently (sometimes in the opposite direction) resulting in differential motions which are greater than the motion of either the optics or the imaging target.

 In most optical systems, the most vibration sensitive time is not the time of maximum vibration.  For example, many optical systems utilize X-Y stages to move the imaging target in a process sequence of move, stop, wait, image, and repeat.  The largest vibration in this cycle is typically associated with stage starting and stopping transients.  However, the vibration amplitude has usually decayed significantly before the critical imaging takes place.  Thus, it is important to determine how much settling time the system is allowed between the stopping of the stage motion and the beginning of the critical imaging.

 It is also necessary to define how much environmental vibration the system must be able to properly function in. The criteria for maximum acceptable floor vibration is often based on published generic criteria appropriate for the type of facility into which the system will be eventually installed.  Examples of such criteria are given in Section 5 of this paper.

 A typical statement of vibration performance requirements might be as follows:  "The vibration error of this system will be less than 0.02 micron during critical imaging. Critical imaging will begin 0.2 seconds after the stage has stopped.  The system will be capable of performing in an environment which does not exceed the FHA level B criteria (as defined in Section 5)."

 

1.3. Determination of internal vibration sources and strategies to minimize their adverse impacts

 Any successful optic system must be able to perform well in the presence of both internal and external sources of vibration.  It is therefore imperative to determine at the outset the nature of the internal sources of vibration, and to develop strategies to minimize negative effects.

 The greatest source of vibration in critical optical systems is often the motion of the stage system.  Thus it is valuable to estimate the parameters of the stage system which will dictate the vibration input forces to the system.  These parameters include the approximate weight and geometry of the stage system, as well the motion parameters such as the maximum stage velocities and accelerations (and acceleration versus time profiles).  These parameters will be necessary to develop estimates of forcing functions which are utilized in the finite element process.

 Other important vibration sources include fans and other rotating equipment and other attached moving systems such as wafer handler robotics.

 The resulting dynamic forces of significant sources should be estimated based on force equals mass times acceleration type calculations.  The frequency content of these forces can be estimated by the acceleration versus time profiles of stages, and from the rpm of rotating components.

 Strategies for minimizing the adverse impacts of these internal sources should be considered.  For example, stages may be designed with high stiffness and low mass, stage acceleration versus time profiles may be adjustable to keep

energy away from the system's structural resonant frequencies, rotating equipment may be precisely balanced and/or mounted on soft isolators, etc.

 

1.4. Optimization of structural design by use of finite element modeling

 Once the design develops to the point were system geometries have been roughly determined, a finite element model of the system should be developed.   The graphical output from finite element analysis often provides the designer valuable insight into the nature of various vibration issues that can not be acquired any other way.

 This modeling will also greatly assist in making important design decisions such as the sizing of structural members, the selection between different structural design alternatives, the calculation of vibration amplitudes resulting from internal and external sources, and the determination of desired characteristics of the vibration isolation system.

 When selecting components for the vibration isolation system it is useful to analyze not only the vibration isolation effectiveness of the isolators, but also the sag errors that result when the optical system's structure is tilted in the presence of gravity.  Some very soft isolation system's will exhibit significant tilt (and the resulting deformation errors) in the presence of low frequency vibration which is occasionally present in facilities.

 The process of finite element modelling consists of the approximation of a real continuous structural system as a set of discrete points which are connected by elements each with defined geometries and material properties.  The designer

therefore enters the coordinates associated with each point (some modelling programs can develop the coordinates based on a CAD file), as well as definitions of each element geometry and material type, and specifies boundary conditions applied to specific points.

 Once the model has been built the designer can easily use the software to calculate resonant frequencies and mode shapes of the structure as well as the response amplitudes from internal and external sources of vibration.  If the calculated responses are not acceptable then the structural model can be modified and reanalyzed until the calculated responses are acceptable.   This iterative process is done quickly and inexpensively compared to the process of iterating with actual prototypes.

 

1.5. Modal analysis testing of the prototype

 Once the first prototype structure of the system is built it is often valuable to perform modal analysis testing on it to determine the actual resonant frequencies, dampings, and mode shapes associated with each of the system's structural resonances.  These measured modal parameters may be significantly different from those calculated by finite element analysis (especially with inexperienced analysts) due to errors in the model.

 The results of the modal analysis testing can be used to improve the finite element model until their agreement is good.  At this point the finite element model will more accurately predict the effects of various changes to the system's structure.

 Modal testing involves the measurement and analysis of input forces and resulting response vibrations that result from dynamic excitation provided by a shaker or instrumented hammer.  A modal analysis testing system usually consists of a spectrum analyzer to perform the necessary measurements, and a computer with appropriate software to analyze the data, as well as the appropriate force and response measurement transducers and an exciter.

 To conduct the testing an input force is applied to the structure at one location and the vibration response is measured sequentially at an array of locations distributed over the entire structure.  For each measurement the transfer function is measured between the applied force and the response motion.

 This transfer function defines the ratio between response and force as a function of frequency.  The transfer functions are complex frequency spectra with a magnitude and phase value at every frequency.  Analysis of the test data involves curve-fitting the measured transfer functions in order to obtain the resonant frequencies, dampings, and mode shapes.

 The location of the measurement points are carefully chosen in order to be able to accurately identify the modes of the structure over the frequency range of interest.  Prior to testing, the coordinates of the measurement points and the

input force location are entered into the modal analysis testing system computer.  Other pertinent information such as gain and sensitivity of transducers, transducer serial numbers, location and date are also recorded.

 

1.6. Vibration performance testing under operational conditions

 Once the prototype system is physically operational (i.e., stages are functioning, etc.) it is beneficial to perform measurements to document the vibration performance of the system.

 These measurements usually involve direct measurement of differential vibration between the optics and the imaging target.  Sometimes these measurements utilize standard vibration sensors.   Other times the signal from the imaging system can be directly utilized to provide the necessary vibration information.

 It is prudent to measure vibration during all modes of operation.  For example, the vibration resulting from stage motion transients is often a function of the distance of the stage movements as well as the X and Y locations of the stage system.

 

1.7. Development of design modifications if needed

 If the measured vibration performance is not acceptable it becomes necessary to develop design modifications to improve the vibration performance of the system.  These modifications may involve changes in the structural stiffness, mass, anddamping.

 In most situations there are several possible alternative modifications that are worth considering.  Often designers consider mainly mass and stiffness of the structures and overlook relatively simple but effective modifications that

involve increasing the system's damping.  In other situations, many of the damping options are limited by the application - such as within a vacuum chamber where the outgasssing associated with most damping materials is unacceptable.

 Once again, finite element modelling is a valuable tool to estimate the effects of specific modifications to the system's structure, and to develop the best modification alternative.

 

1.8. Determination of the specification of maximum acceptable levels of facility floor vibration

 The most accurate method of developing an initial specification of maximum acceptable levels of facility floor vibration involves low level shake table testing of the optical system.  However, this is also the most time consuming and expensive approach.  As a result, low level shake table testing of optical systems is rarely performed.

 A wide range of alternative and approximate methods of development of the specification have evolved.  On one extreme many vendors effectively pull their specification out of thin air without any measurement.  In other instances

vendors copy or make slight modifications to previous specifications which exist for earlier model products or adopt a competitors specifications without any measurement of actual vibration sensitivity.

 In many other instances a more serious attempt is made to develop a specification.  Sometimes a shaker is brought in to shake the floor in the facility where the system was developed.   When the facility has a stiff slab-on-grade floor it is often not practical to generate sufficient vibration to disturb the optical system.

 Care must also be exercised when using an electromagnetic shaker to test electron microscope based systems to make sure that the observed disturbances are due to the vibration and not the magnetic fields generated by the shaker.

 Regardless of which technique is used to develop an initial specification it is valuable to keep track of the actual vibration levels at the installation sites of the optical systems.  This information can be used to refine the specification or to resolve specific questions, should the need arise.

 On many systems the errors which result from a given amplitude of differential motion between the imaging target and the optics is a function of the frequency.  This frequency dependence is due to the effective duration of the optical measurement.  It is necessary to account for any such frequency dependence when using this technique to estimate floor vibration sensitivity.

 Once the floor vibration sensitivity has been determined it is often desired to simplify the complex sensitivity curve by breaking into a set of discrete values for different frequency ranges.

 It is important to note that an unrealistically restrictive specification may discourage potential customers from purchasing the optical system.   On the other hand, a specification which allows too much vibration may result in a system failing acceptance testing due to vibration problems.