Patent Publication Number: US-8976336-B2

Title: Shear-layer chuck for lithographic apparatus

Description:
BACKGROUND 
     1. Field of the Invention 
     The present invention relates to a lithographic apparatus and method of securely holding an object in the lithographic apparatus. 
     2. Related Art 
     A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g., comprising part of, one, or several dies) on a substrate (e.g., a silicon wafer). Transfer of the pattern is typically via imaging the pattern using a UV radiation beam onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning” direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate. 
     Conventionally, a clamping device is used to securely hold an object, such as, a reticle or a substrate, to a supporting base structure, referred to as a “stage.” The “stage” is alternatively referred to as a “table,” a “frame,” or a “force frame.” The clamp can be referred to as a “chuck.” A stage may be coupled to a chuck by a variety of means, including kinematic supports at three points. A chuck may also be constructed integral to the stage. During movement of the stage, or during an exposure operation, the object is typically securingly coupled to the chuck using a normal force (i.e., a force acting perpendicular to the chuck) generated by electrostatic attraction or a partial vacuum between the object and the chuck. The normal force and a normal stiffness of the chuck serve to secure the object in a normal direction during the movement or exposure. In a tangential direction, i.e., in a plane of the chuck, the object is prevented from moving relative to the chuck during movement or exposure through friction between the chuck and the object. 
     When acceleration is imparted to the stage during exposure or pre-exposure alignment, a stress is transferred from the stage to the chuck, and this stress may cause the chuck as well as the object to deform. Typically the transfer of acceleration-induced stress from the stage to the chuck (as well as from the chuck to the object) is not uniform. This gives rise to a potential for slip between the chuck and the object, especially in cases where the chuck deformation is large. Chuck deformation may also be caused by temperature differences between the stage, the chuck, and/or the object, resulting in slippage of the object relative to the chuck. 
     A conventional approach to limit the transfer of stress between the chuck and the stage is to use precision-machined kinematic or semi-kinematic mounts to isolate the chuck from the stage. However, kinematic mounts at a number of discrete locations may not uniformly distribute the transfer of stress. An alternative approach to distribute the transfer of stress more uniformly is to use a chuck comprising a plurality of burls that make local contacts with the supported object. 
       FIG. 2A  depicts a conventional chuck  200  comprising a plurality of burls  225 . A stage  230  holds an object  210 , e.g., by electrostatic force applied through a planar electrode  220  in a normal direction. Object  210  has a top surface  212  and a bottom surface  214 , which is opposite top surface  212 . Burls  225  support object  210 . Each of the burls  225  acts like a spring, shown symbolically as spring  205 , providing a predetermined amount of shear compliance. 
       FIG. 2B  is a bottom view showing bottom surface  214  of object  210 . Top ends of burls  225  form local contacts  227  at bottom surface  214  of object  210 . 
     Dimension and arrangement of burls  225  may be tailored to some extent to provide shear compliance. However, materials used in burls  225  have many additional requirements, including but not limited to, hardness, machineability, coefficient of thermal expansion, etc. Thus, it may be difficult to tailor burls  225  for a desired shear compliance in all directions of interest. For example, while it is desirable to have a high shear compliance at an interface of object  210  and burls  225 , it is also desirable to have a low normal compliance at the interface. Burls  225  that directly contact object  210  typically have high compliance in normal direction as well, making it harder to optimize the overall shear compliance of the system. Moreover, burls  225  with the desired shear compliance are typically long and slender, and their shape makes electrostatic clamping of the object quite challenging. Additionally, planarity of object  210  may be compromised due to non-uniform stress distribution in burls  225 . 
     SUMMARY 
     It is desirable to design a chuck that provides a desired shear compliance to minimize slippage of a supported object under a condition of stress, but does not suffer from the limitations described above. 
     According to a first embodiment of the present invention, a system comprises a chuck and an array of elongated elements having first and second respective ends, such that the first ends contact the chuck and the second ends contact a stage. Through using the array of elongated elements, a transfer of stress between the stage and the chuck is rendered substantially uniform, resulting in minimization of slippage of an object relative to the first surface of the chuck during a movement of the chuck relative to the stage. 
     According to another embodiment, a method comprises coupling an array of elongated elements between a chuck and a stage, such that longitudinal axes of the elongated elements are normal to the chuck and the stage, and first ends of the elongated elements contact a second surface of the chuck, and second ends of the elongated elements contact the stage. Under a condition of stress, a transfer of the stress between the stage and the chuck is rendered substantially uniform through using the array of elongated elements. The method further comprises supporting an object on a first surface of the chuck, the first surface being opposite the second surface. The method also comprises subjecting the chuck and the stage to the condition of stress, and measuring deformations of the chuck and the stage under the condition of stress to correlate the measured deformations with slippage of the object relative to the first surface of the chuck. 
     According to a further embodiment, a lithographic apparatus comprises an illumination system configured to produce a beam of radiation, a patterning device configured to pattern the beam of radiation, a projection system configured to project the patterned beam of radiation onto a substrate, and a support system. The support system comprises a chuck having a first surface and a second surface, and an array of elongated elements having first and second respective ends and having longitudinal axes, the longitudinal axes being normal to the second surface of the chuck, such that the first ends contact the second surface of the chuck and the second ends contact a stage. Through using the array of elongated elements, a transfer of stress between the stage and the chuck is substantially uniform, resulting in minimization of slippage of an object relative to the first surface of the chuck during a deformation of the chuck due to the stress. The pattering device or the substrate is configured to be the object mounted on the chuck. 
     According to yet another embodiment, a system supporting an object comprises a chuck having a first surface that supports the object; a stage that supports the chuck in one or more directions of translation or rotation; and an interface layer between the chuck and the stage with a relatively low stiffness in at least one direction of translation or rotation with respect to the other directions of translation or rotation, resulting in minimization of slippage of the object relative to the first surface of the chuck during deformation of the chuck due to a stress between the stage and the chuck. 
     According to yet another embodiment, a system comprises a chuck having a first surface and a second surface, which is located opposite the first surface, wherein the chuck is configured to hold an object; and an array of elongated elements having first and second respective ends and having longitudinal axes normal to the second surface of the chuck, wherein the first ends contact the second surface of the chuck and the second ends contact a stage to isolate the chuck from the stage by rigidly coupling the chuck to the stage such that the array of elongated elements uniformly distribute stress therebetween. 
     Further embodiments, features, and advantages of the present inventions, as well as the structure and operation of the various embodiments of the present invention, are described in detail below with reference to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated herein and form a part of the specification, illustrate one or more embodiments of the present invention and, together with the description, further serve to explain the principles of the invention and to enable a person skilled in the pertinent art to make and use the invention. 
         FIG. 1  schematically depicts a reticle-based lithographic apparatus, according to an embodiment of the present invention. 
         FIGS. 2A and 2B  schematically depict a chuck in a lithographic apparatus comprising a plurality of burls supporting an object. 
         FIG. 3  schematically depicts a support structure with a chuck coupled to a stage through a shear layer comprising elongated elements, according to an embodiment of the present invention. 
         FIGS. 4A and 4B  schematically show details of the support structure shown in  FIG. 3 , according to an embodiment of the present invention. 
         FIGS. 4C and 4D  schematically show top and side views of detailed pin layouts of an example chuck with a shear layer, according to an embodiment of the present invention. 
         FIG. 5  schematically depicts a deformation of the chuck, the elongated elements, and the stage of  FIG. 3 , when an acceleration force is imparted on the stage, according to an embodiment of the present invention. 
         FIG. 6  schematically depicts an isometric view of a section of a support structure, according to an embodiment of the present invention, showing effects of thermal stress. 
         FIG. 7  schematically depicts deformations of the chuck, the supported object, and the elongated elements of the shear layer shown in  FIG. 6 , when there is no temperature gradient in the stage, according to an embodiment of the present invention. 
         FIG. 8  schematically depicts deformations of the chuck, the supported object, the stage, and the elongated elements of the shear layer shown in  FIG. 6 , when there is an example temperature gradient in the stage, according to an embodiment of the present invention. 
         FIGS. 9A and 9B  schematically show two different configurations of the elongated elements of the shear layer of  FIG. 3 , according to two embodiments of the present invention. 
         FIGS. 10A-10C  schematically show different views of an embodiment of the present invention where an interface membrane layer is used in between the chuck and the stage. 
         FIGS. 11 and 12  schematically show flowcharts describing example processes, according to various embodiments of the present invention. 
     
    
    
     One or more embodiments of the present invention will now be described with reference to the accompanying drawings. In the drawings, like reference numbers can indicate identical or functionally similar elements. Additionally, the left-most digit(s) of a reference number can identify the drawing in which the reference number first appears. 
     DETAILED DESCRIPTION 
     This specification discloses one or more embodiments that incorporate the features of this invention. The disclosed embodiment(s) merely exemplify the invention. The scope of the invention is not limited to the disclosed embodiment(s). The invention is defined by the claims appended hereto. 
     The embodiment(s) described, and references in the specification to “one embodiment”, “an embodiment”, “an example embodiment”, etc., indicate that the embodiment(s) described can include a particular feature, structure, or characteristic, but every embodiment cannot necessarily include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is understood that it is within the knowledge of one skilled in the art to effect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described. Additionally, terms indicating physical orientation, such as “top”, “bottom”, “side” etc. are used for illustrative purposes only, and do not limit the invention to any particular orientation. 
     Embodiments of the invention can be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the invention can also be implemented as instructions stored on a machine-readable medium, which can be read and executed by one or more processors. A machine-readable medium can include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium can include read only memory (ROM); random access memory (RAM); magnetic disk storage media; optical storage media; flash memory devices; electrical, optical, acoustical or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.), and others. Further, firmware, software, routines, instructions can be described herein as performing certain actions. However, it should be appreciated that such descriptions are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc. 
     Lithographic Apparatus 
       FIG. 1  schematically depicts an embodiment of lithographic apparatus  100  suitable for use with one or more embodiments of the present invention. The apparatus comprises an illumination system (illuminator) IL configured to condition a radiation beam B (e.g., UV radiation or DUV radiation); a support structure (e.g., a mask table) MT constructed to support a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to accurately position the patterning device in accordance with certain parameters; a substrate table (e.g., a wafer table) WT constructed to hold a substrate (e.g., a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate in accordance with certain parameters; and a projection system (e.g., a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W. 
     The illumination system IL may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of optical components, or any combination thereof, for directing, shaping, or controlling radiation. 
     The support structure MT supports, i.e., bears the weight of, the patterning device MA. It holds the patterning device MA in a manner that depends on the orientation of the patterning device MA, the design of the lithographic apparatus  100 , and other conditions, such as for example whether or not the patterning device MA is held in a vacuum environment. The support structure MT can use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device MA. The support structure MT may be a frame or a table, for example, which may be fixed or movable as required. The support structure may ensure that the patterning device MA is at a desired position, for example with respect to the projection system PS. Any use of the terms “reticle” or “mask” herein may be considered synonymous with the more general term “patterning device.” 
     The term “patterning device” used herein should be broadly interpreted as referring to any device that can be used to impart a radiation beam with a pattern in its cross-section such as to create a pattern in a target portion of the substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate, for example if the pattern includes phase-shifting features or so called assist features. Generally, the pattern imparted to the radiation beam will correspond to a particular functional layer in a device being created in the target portion, such as an integrated circuit. 
     The patterning device may be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography, and include mask types such as binary, alternating phase-shift, and attenuated phase-shift, as well as various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted so as to reflect an incoming radiation beam in different directions. The tilted mirrors impart a pattern in a radiation beam which is reflected by the mirror matrix. 
     The term “projection system” used herein should be broadly interpreted as encompassing any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term “projection lens” herein may be considered as synonymous with the more general term “projection system.” 
     As here depicted, the apparatus is of a transmissive type (e.g., employing a transmissive mask). Alternatively, the apparatus may be of a reflective type (e.g., employing a programmable mirror array of a type as referred to above, or employing a reflective mask). 
     The lithographic apparatus  100  may be of a type having two (dual stage) or more substrate tables (and/or two or more mask tables). In such “multiple stage” machines the additional tables may be used in parallel, or preparatory steps may be carried out on one or more tables while one or more other tables are being used for exposure. 
     Referring to  FIG. 1 , the illuminator IL receives a radiation beam from a radiation source SO. The source SO and the lithographic apparatus  100  may be separate entities, for example when the source SO is an excimer laser. In such cases, the source SO is not considered to form part of the lithographic apparatus  100  and the radiation beam B is passed from the source SO to the illuminator IL with the aid of a beam delivery system BD comprising, for example, suitable directing mirrors and/or a beam expander. In other cases, the source SO may be an integral part of the lithographic apparatus  100 , for example when the source is a mercury lamp. The source SO and the illuminator IL, together with the beam delivery system BD if required, may be referred to as a radiation system. 
     The illuminator IL may comprise an adjuster AD for adjusting the angular intensity distribution of the radiation beam. Generally, at least the outer and/or inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illuminator IL can be adjusted. In addition, the illuminator IL may comprise various other components, such as an integrator IN and a condenser CO. The illuminator IL may be used to condition the radiation beam B, to have a desired uniformity and intensity distribution in its cross-section. 
     The radiation beam B is incident on the patterning device (e.g., mask MA), which is held on the support structure (e.g., mask table MT), and is patterned by the patterning device. Having traversed the mask MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and position sensor IF (e.g., an interferometric device, linear encoder or capacitive sensor), the substrate table WT can be moved accurately, e.g. so as to position different target portions C in the path of the radiation beam B. Similarly, the first positioner PM and another position sensor (which is not explicitly depicted in  FIG. 1 ) can be used to accurately position the mask MA with respect to the path of the radiation beam B, e.g., after mechanical retrieval from a mask library, or during a scan. In general, movement of the mask table MT may be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which form part of the first positioner PM. Similarly, movement of the substrate table WT may be realized using a long-stroke module and a short-stroke module, which form part of the second positioner PW. In the case of a stepper (as opposed to a scanner) the mask table MT may be connected to a short-stroke actuator only, or may be fixed. Mask MA and substrate W may be aligned using mask alignment marks M 1 , M 2  and substrate alignment marks P 1 , P 2 . Although the substrate alignment marks as illustrated occupy dedicated target portions, they may be located in spaces between target portions (these are known as scribe-lane alignment marks). Similarly, in situations in which more than one die is provided on the mask MA, the mask alignment marks may be located between the dies. 
     The depicted apparatus could be used in at least one of the following modes: 
     1. In step mode, the mask table MT and the substrate table WT are kept essentially stationary, while an entire pattern imparted to the radiation beam is projected onto a target portion C at one time (i.e., a single static exposure). The substrate table WT is then shifted in the X and/or Y direction so that a different target portion C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C imaged in a single static exposure. 
     2. In scan mode, the mask table MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e., a single dynamic exposure). The velocity and direction of the substrate table WT relative to the mask table MT may be determined by the (de-) magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width (in the non-scanning direction) of the target portion in a single dynamic exposure, whereas the length of the scanning motion determines the height (in the scanning direction) of the target portion. 
     3. In another mode, the mask table MT is kept essentially stationary holding a programmable patterning device, and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, generally a pulsed radiation source is employed and the programmable patterning device is updated as required after each movement of the substrate table WT or in between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography that utilizes programmable patterning device, such as a programmable mirror array of a type as referred to above. 
     Combinations and/or variations on the above described modes of use or entirely different modes of use may also be employed. 
     Although specific reference may be made in this text to the use of lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described herein may have other applications, such as the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat-panel displays, liquid-crystal displays (LCDs), thin-film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “wafer” or “die” herein may be considered as synonymous with the more general terms “substrate” or “target portion,” respectively. The substrate referred to herein may be processed, before or after exposure, in for example a track (a tool that typically applies a layer of resist to a substrate and develops the exposed resist), a metrology tool and/or an inspection tool. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. Further, the substrate may be processed more than once, for example in order to create a multi-layer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers. 
     The terms “radiation” and “beam” used herein encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of or about 365, 248, 193, 157 or 126 nm) or extreme ultraviolet radiation (5 nm or above). 
     The term “lens,” where the context allows, may refer to any one or combination of various types of optical components, including refractive and reflective optical components. 
     Example Embodiment of Object Support Structure 
       FIG. 3  shows an example support structure  300  for an object  210 , according to an embodiment of the present invention. Support structure  300  comprises an interface layer referred to as a shear-compliant stress layer  320  (also referred to as the “shear-layer”) coupling a chuck  321  and a stage  230 . Object  210  is mounted on a first surface  322  of chuck  321 . As mentioned above, object  210  may be a patterning device or a substrate. 
     In various examples, stage  230  may be made of a variety of materials, including, but not limited to, silicon-silicon carbide (SiSiC), Invar, stainless steel, aluminum oxide, Zerodur® (a glass-ceramic composite by Schott Glass Technologies), etc. In one example, stage  230  may be kinematically supported by a plurality of kinemetic mounts (not shown). A similar configuration may also be used when various bearing arrangements, e.g., an air bearing, are used for supporting of stage  230 . In the example embodiment shown in  FIG. 3 , stage  230  is driven magnetically in the XY plane. In this example, a yoke  365  is housed within stage  230 . Yoke  365  may be comprise or any other suitable material. In this example, z-direction magnetic actuators  370  are used to magnetically levitate stage  230 , so that stage  230  can be driven in the XY plane. 
     In one example, chuck  321  is designed with high flatness, so that object  210  is mounted with requisite flatness on first surface  322  of chuck  321 . For example, chuck  321  may be made from a material with a relatively low coefficient of thermal expansion, such as Zerodur®. However, the present invention is not limited to a Zerodur® chuck, and other materials may be used. Desirable properties of the chuck material include chemical stability, structural homogeneity, good machineability, etc. 
     In one example, shear-layer  320  may comprise an array of elongated elements  325  (also referred to as “pins”), whose first ends are coupled to a second surface  323  of chuck  321 , second surface  323  being opposite first surface  322  on which object  210  is mounted. Elongated elements  325  may be evenly spaced. Elongated elements  325  may not make direct contact with object  210 , i.e., an interface between elongated elements  325  and chuck  321  is some distance away from the interface between chuck  321  and object  210 . In this configuration, it is easier to tailor the shear-compliance of the elongated elements  325 , because the normal compliance of elongated elements  325  becomes less of a design issue. Incorporation of shear-layer  320  enables achieving a relatively low stiffness in at least one direction of translation or rotation with respect to the other directions of translation or rotation of chuck  321 . Elongated elements  325  may comprise materials including, but not limited to, Invar, SiSiC, stainless steel, etc, depending on the desired functionalities of shear-layer  320 . In one example, a primary functionality of shear-layer  320  may be to distribute stress uniformly. Dimension and spatial arrangement of elongated elements  325  may be chosen so that under a condition of stress, a transfer of stress between stage  230  and chuck  321  is uniform. This may be done, for example, because a uniform transfer of stress minimizes the possibility of slippage of object  210  during deformation of chuck  321 . 
     In one example, support structure  300  allows for combining disparate materials in a single construction that is easy to manufacture, but provides for a flexible design. The structure may allow for simultaneous reduction of mass and improvement of stiffness in the normal direction. One example embodiment using disparate materials comprises using Zerodur® for chuck  321 , Invar for pins  325 , and SiSiC for stage  230 . Another example embodiment eliminates using Invar for pins  325 , and comprises using form-compliant pins or elongated burls integrated with stage  230  made of SiSiC or other materials, as appropriate. Yet another embodiment comprises chuck  321 , stage  230 , and shear-layer  320  being made of a same material, e.g. Invar, Zerodur®, etc. 
     Additionally, or alternatively, one or more additional objects  350  and/or  360  may be supported by chuck  321 . For example, object  350  and/or  360  may be positional sensors, that are used for determining a desired position and/or alignment of object  210 . Positional sensors  350  and/or  360  may measure displacement or slippage of object  210  in the xy plane under a condition of stress with respect to a reference position. The reference position may be denoted by fixed coordinates or the initial position of object  210  prior to the condition of stress. Additional objects  350  and/or  360  may also be fiducial marks that facilitate initial positioning and/or alignment of object  210 . They may also assist in measuring a relative displacement of object  210 , and adjusting the position and alignment of object  210 . 
       FIG. 4A  shows an upside-down view of support structure  300 , showing z-direction magnetic actuators  370  coupled to a bottom surface  372  of stage  230 . 
       FIG. 4B  shows a cut-out view of the inner structure of stage  230 , according to one embodiment of the present invention. In this embodiment, stage  230  may not be constructed as a solid block in order to reduce mass and accommodate other structures. A central region  423  of stage  230  may comprise intersecting baffles  434  and  432  that cross each other in x and y directions, respectively. This type of structure provides adequate structural strength and stiffness for stage  230 , while keeping the overall mass low. 
       FIG. 4C  illustrates an example arrangement of elongated elements  325  (i.e., an example pin layout) on a bottom surface  323  of the chuck  321 . Contact areas of the elongated elements  325  on the bottom surface  323  of the chuck  321  are denoted as  425 . The chuck  321  has a central region  424  that is aligned and coupled to the central region  423  (shown in  FIG. 4B ) of the stage  230  through the elongated elements  325 . Although not specifically shown in  FIG. 4C , object  210  may be mounted above central region  424 . Extension regions  422  and  427  outside central region  424  may also comprise contact areas  425 . 
       FIG. 4D  illustrates a side view of chuck  321  coupled to stage  230 , and corresponds to the top view shown in  FIG. 4C . In an example embodiment, a height ‘h’ of the elongated elements  325  may be about 6 mm, and a pitch ‘p’ of elongated elements  325  may be about 20 mm. Each elongated element may have about a 2 mm diameter. Other dimensional values may be used in alternative designs, as the invention is not limited to any particular dimensional values, or any particular arrangement of elongated elements  325 . 
     Acceleration-Induced and Thermally-Induced Stress Simulation 
       FIGS. 5-8  illustrate results of computer simulations that have been performed to predict expected deformation of chuck  321 , stage  230 , and elongated elements  325  (shown in  FIG. 3 ) under expected conditions of stress. In one example, Computer Aided Design (CAD) software, e.g., Solidworks (by Solidworks Corp. of Concord, Mass.) can be used to construct the schematic geometric figures to perform simulations. To perform the actual simulations under conditions of stress, a design analysis software, e.g., ANSYS® (by ANSYS, Inc. of Canonsburg, Pa.) may be used. 
     In particular,  FIG. 5  depicts deformations of components of support structure  300  when an acceleration force  505  is imparted to stage  230 . In  FIG. 5 , a scale of the deformation is magnified to more easily illustrate the nature of deformation of different components of support structure  300 . According to an example simulation, deformation of chuck  321  beneath object  210  is as low as about 1.5 nm when an acceleration force of about 10 g is imparted to stage  230 , deforming stage  230  by about 10-20 nm. An exemplary shear stiffness value of about 30 N/um is exhibited by elongated elements  325 , which are assumed to be about 6 mm tall and about 2 mm in diameter. In this example, chuck  321  is deformed in a range of about 1-2 nm for acceleration as high as about 100 m/sec 2 . Compared to that, a conventional baseline support structure construction may experience chuck deformation values as high as 27 nm under similar acceleration. 
       FIG. 6  depicts an isometric view of a section  600  of a support structure  300  (e.g., a quarter of the entire structure), according to an embodiment of the present invention. In the following  FIGS. 7 and 8 , deformations (greatly exaggerated) produced due to temperature differences between object  210 , chuck  321 , and/or stage  230  are shown. The structure shown in  FIG. 6  is similar to the structure  300  shown in  FIG. 3 . The additional objects  350  and  360  are not shown in  FIG. 6 . However, a cross section view of optional cooling channels  615  are shown through both chuck  321  and stage  230 . Cooling channels  615  help in maintaining a target temperature in portions of the support structure. Baffles  434  and  432  running along x and y directions, respectively, are also shown in  FIG. 6 . 
       FIG. 7-8  show the deformations (exaggerated for illustrative purposes) of object  210 , chuck  321 , and elongated elements  325 , when support structure  300  of  FIG. 6  is under a thermal stress due to relative temperature differences. In this example, stage  230  may comprise SiSiC.  FIG. 7  shows a condition where there is no thermal gradient in stage  230 . This simulation shows a thermal overlay of about 1.7 nm. 
       FIG. 8  shows the deformations (exaggerated for illustrative purposes) of object  210 , chuck  321 , and elongated elements  325  when a thermal gradient of about 0.05 K is assumed in the SiSiC stage  230 . Stage  230  itself is deformed in this situation. Thermal overlay is slightly improved in this situation. 
     Shear-Layer Pin Configurations 
       FIGS. 9A and 9B  show two different configurations of elongated elements  325 , e.g.,  325 A and  325 B, respectively, of a shear layer, according to various embodiments of the present invention. In both the embodiments, an epoxy layer  980  is used to couple chuck  321  with stage  230  through elongated elements  325 . In  FIG. 9A , a pin configuration  325 A is shown, which has a flat first end  990  coupled to chuck  321 , and a second end  985  coupled to stage  230 , for example in a close-fit hole  986  of stage  230  that may be filled with epoxy. In  FIG. 9B , a pin configuration  325 B is shown, which has a first end  992  coupled to chuck  321  in a loose-fit hole  993  of chuck  321 , which may be filled with epoxy, and a second end  985  coupled to stage  230  in a close-fit hole  986  of stage  230 , which also may filled with epoxy. 
     As will be appreciated by persons skilled in the art, various other configurations of the pins or elongated elements  325  may be used too without departing from the scope of the invention. For example, brazing the pins to the chuck and/or the stage, using fasteners (e.g., threaded joints), machining the pins or other shaped structures directly into the chuck and/or the stage, etc. are all viable alternative embodiments of the present invention. 
     Alternative Embodiment of Object Support Structure with Interface Membrane 
       FIGS. 10A-10C  show an alternative embodiment  1000  of the support structure  300 , employing a shear-layer  1020 , wherein an interface membrane layer  1035  (see  FIG. 10B ) is disposed between a chuck  321  and a stage  230 .  FIG. 10A  shows an isometric view of support structure  1000 , a portion of which (enclosed within the bounding square A) is shown with greater magnification in  FIG. 10B . In  FIG. 10B , interface membrane layer  1035  is clearly seen. Interface membrane layer  1035  may have pin patterns machined into it, through which elongated elements  325  pass. Interface membrane layer  1035  and elongated elements  325  may be made integral to each other out of the same material, e.g., Invar, SiSiC etc. Thickness of interface membrane layer  1035  is designed so that shear-layer  1020  can provide a desired shear compliance.  FIG. 10C  shows a further magnified side view of a portion of support structure  1000  in square A in  FIG. 10A , showing details of shear-layer  1020 . 
     Methods for Measuring Object Slippage under Stress 
       FIGS. 11 and 12  schematically illustrate flowcharts of methods  1100  and  1200 , respectively, according to embodiments of the present invention. Method  1100  relates to acceleration-induced stress in the support structure, and method  1200  relates to thermal stress in the support structure. In one example, methods  1100  and  1200  can be practiced by one or more of the systems discussed above. 
     In block  1110 , a chuck and a stage are coupled through a shear layer including elongated elements. 
     In block  1115 , a patterning device or a substrate is supported on the chuck. 
     In block  1120 , an acceleration is imparted to the stage. As a result, the stage, the elongated elements and the chuck are deformed. 
     In block  1125 , deformations of the chuck are measured. 
     In block  1130 , measured deformations of the chuck is correlated with a slippage of the patterning device or the substrate on the chuck. 
     In  FIG. 12 , blocks  1210 ,  1215 ,  1225 , and  1230  of method  1200  are substantially identical to blocks  1110 ,  1115 ,  1125 , and  1130 , respectively, of method  1100 . However, in block  1220 , thermal stress is induced in the support structure due to temperature difference between the stage, the chuck, and the patterning device or substrate. 
     Additionally, or alternatively, in other embodiments a method may be used when a stress is produced by a combination of acceleration and temperature difference. 
     CONCLUSION 
     While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not limitation. It will be apparent to persons skilled in the relevant art that various changes in form and detail can be made therein without departing from the spirit and scope of the invention. Thus, the breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents. 
     It is to be appreciated that the Detailed Description section, and not the Summary and Abstract sections, is intended to be used to interpret the claims. The Summary and Abstract sections can set forth one or more, but not all exemplary embodiments of the present invention as contemplated by the inventor(s), and thus, are not intended to limit the present invention and the appended claims in any way.