FIELD OF THE INVENTION 
       [0001]    The present invention describes a pin used to support a thin substrate, such as a silicon wafer, during stress measurements. 
       BACKGROUND 
       [0002]    Flat substrates, such as semiconductor wafers, are stressed during certain processing steps, e.g., depositing or etching thin films. Stress in deposited layers can warp the substrate, which can adversely affect subsequent process steps, device performance, reliability and line-width control. Thus, it is desirable to measure the radius of curvature of a substrate as well as measure the stress on a substrate that is associated with a processing step. The measurement of stress is executed many times during processing and is used to help ensure that the substrate has been properly processed and that the completed devices will perform as expected. 
         [0003]    In general, the basic procedure for measuring stress is to measure the shape of the substrate, process the substrate, measure the shape of the substrate again and then calculate the change in shape of the substrate that is associated with that particular process step. The change in shape is correlated to the stress on the substrate. Processing steps that are generally monitored include an etch process, a thermal process or a thin film deposition process (the process most commonly monitored). Typically, a diameter scan of the substrate is made and the Stoney equation is utilized to calculate the stress: 
         [0000]    
       
         
           
             
               
                 
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                        
                       
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         [0000]    where σ is stress, E is Young&#39;s modulus, 1) is Poisson&#39;s ratio, t s  is the substrate thickness, t f  is the film thickness, and r is the difference in the radius of curvature that is measured during the pre-processing diameter scan curve and the post-processing diameter scan curve. The Stoney equation (eq. 1) is used for round substrates. It should be understood that rectangular or square substrates may also be measured for stress using a different equation or other computational techniques. 
         [0004]    For a thermal process where no film is added or removed, the calculated change in the radius of curvature of the substrate may be used to gauge process control since the Stoney equation of eq. 1 is not valid when the film thickness t f  is zero. 
         [0005]    Another parameter that can be used to quantify the stress measurement is bow. Bow is the difference in height between the chord and the arc of the substrate for the curve that is generated from the difference between the before and after processing scans. Bow is sometimes reported instead of stress and is used for process control, particularly for substrates that are not round. For purposes of the present disclosure, stress and bow are interchangeable and are therefore collectively referred to herein as stress. 
         [0006]    During most processing and metrology steps, the substrate is held to a chuck on a stage using vacuum. The employed vacuum will easily overcome the stress induced deformation of the substrate and will hold the substrate flat against the chuck. Accordingly, a conventional vacuum chuck cannot be used to hold a substrate for stress measurements. To make a stress measurement, the substrate is supported at a limited number of locations so that the stress can freely deform the substrate. 
         [0007]    Generally, the substrate is supported at three locations on pins so that the substrate is supported at the identical locations for both the pre and post measurement. If four or more pins were used, the substrate might be supported at different locations for the pre and post measurements due to the change in shape of the substrate after processing compromising the quality of the stress measurement. 
         [0008]    A stress measurement generally requires the collection of a multitude of points along a diameter of the substrate when the Stoney equation (eq. 1) is employed. In conventional stress metrology tools, the measurement hardware is held stationary and the substrate is moved to the desired measurement locations using some form of a stage. For example, a stage may move the substrate in X,Y and Z coordinates or to reduce the stage footprint, in R, θ and Z coordinates. Alternatively, the measurement hardware may move relative to the substrate, or both may move. In general, holding the substrate stationary and moving the measurement hardware is less desirable for most of the commonly employed measurement techniques, particularly when prealignment and loading of the substrate is considered. 
         [0009]    Of course, it is important that the substrate does not move relative to the support pins when the stage moves the substrate to a new measurement location. To prevent movement of the substrate relative to the pins, the acceleration of the stage may have to be reduced compared to its value when the substrate is being held by vacuum so as to not disturb the substrate&#39;s position with respect to the pins. Other techniques that are sometimes used to prevent the substrate from moving relative to the pins are vacuum gripping the substrate before stage motion or a contact edge gripper. These techniques, however, complicate the hardware and degrades the throughput, as well as potentially creating particulate problems. 
         [0010]    Another consideration for supporting the substrate during the stress measurements is gravity. For very small stress values, the substrate deflection due to gravity may overwhelm the deflection due to stress. Gravity, substrate orientation, measurement precision and other factors limit the smallest stress values that can practically be measured. To minimize the gravitational contribution to substrate deflection, the three support locations are typically chosen to be on a circle that has a radius that is ⅔ of the radius of the substrate. If the support locations were on a smaller radius, the outer part of the substrate would sag down while the center would bulge upward. If the support locations were on a larger radius, the outer part of the substrate would be relatively flat, but the center of the substrate would sag down. Generally, the chosen support locations should minimize the total height range of a flat substrate due to gravity. 
         [0011]    In a stress metrology tool, it is desirable to have the highest throughput possible while maintaining the best precision. Thus, improvements of support pins used to support a substrate during stress measurements are desired. 
       SUMMARY 
       [0012]    A chuck, which may hold a substrate during stress measurements, includes a number of pins that support the substrate. In accordance with one embodiment, each support pin has a dome shaped upper surface that contacts a bottom surface of a substrate when supporting the substrate. The dome shaped upper surface minimizes contact with the substrate as well as assists in maintaining the same contact location with the substrate regardless of substrate shape. The dome shaped upper surface may be formed of a layer of soft material having a high coefficient of static friction to hold the substrate stationary with respect to the pins when the chuck is accelerated by a stage during stress measurements. Additionally, the layer of soft material may be a thin layer that covers a hard internal dome to reduce creep. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]      FIG. 1  shows a perspective view of a chuck with a plurality of support pins, in accordance with an embodiment of the present invention. 
           [0014]      FIG. 2  shows a perspective view of one support pin with a dome shaped upper surface. 
           [0015]      FIG. 3  shows a cross-sectional view of one support pin with a layer of material that covers an internal dome to form the dome shaped upper surface. 
           [0016]      FIGS. 4A and 4B  illustrate side views of a conventional flat topped pin in contact with a portion of a substrate that has a convex and concave curvature, respectively. 
           [0017]      FIGS. 5A and 5B  illustrate side views of a support pin with a dome shaped upper surface in contact with a portion of a substrate that has a convex and concave curvature, respectively. 
       
    
    
     DETAILED DESCRIPTION 
       [0018]      FIG. 1  shows a perspective view of a chuck  100  with a plurality of pins  110  in accordance with an embodiment of the present invention. The pins  110  can move up and down from the chuck. Vacuum, air pressure or motors can be the energy source for the movement of the pins  110 . The pins  110  may be used to contact and hold a substrate (illustrated by broken lines  102 ) during stress measurements.  FIG. 2  shows a perspective view and  FIG. 3  shows a cross-sectional view of one of the pins  110 . As can be seen in  FIGS. 2 and 3 , pin  110  includes a dome shaped upper surface  112 , which contacts the back of the substrate  102  ( FIG. 1 ). In one embodiment, the dome shaped upper surface  112  of the pin  110  is formed with a layer  114  of relatively soft material that covers a hard internal dome  116 . 
         [0019]    The convex dome shape of the upper surface  112  reduces the contact area of the pin  110  relative to a conventional flat topped pin. A reduced contact area reduces the potential for particulate contamination. Moreover, because the contact area of the pin  110  is relatively small compared to the diameter  110   d  of the pin  110 , the location of the contact between the pin  110  and the substrate  102  is relatively insensitive to changes in the shape (i.e., convex or concave flexing) of the substrate  102  and therefore increases precision in the stress measurement relative to conventional flat topped pins. 
         [0020]    To obtain the best precision during stress measurements, the substrate  102  must be supported at identical locations for both the pre and post measurements. If the contact area between the pin and a substrate is large, a potential placement problem can occur. A large contact area of a support pin can cause the contact location on a substrate to change when the shape of the substrate changes.  FIGS. 4A ,  4 B and  FIGS. 5A ,  5 B illustrate a conventional flat topped pin  200  and the pin  110 , respectively, supporting a substrate  102  and illustrate the sensitivity of the contact locations to changes in the substrate shape.  FIGS. 4A and 4B  illustrate side views of a conventional flat topped pin  200  in contact with a portion of a substrate  102  that has a convex curvature in  FIG. 4A  and a concave curvature in  FIG. 4B . It should be understood that in practice, the shape of the substrate is typically complex and is not a simple concave or convex curvature. Nevertheless, the illustrated curvatures are useful to illustrate the sensitivity of the contact position due to the substrate shape. 
         [0021]      FIGS. 4A and 4B  illustrate the center of the substrate  102  with center lines  102 c and ⅔ of the radius of the substrate  102 , i.e., the desired support location, is illustrated with support lines  102   s.  As can be seen, in  FIG. 4A , when the substrate  102  has a concave curvature, the flat topped pin  200  contacts the substrate  102  as a location  202  that is less than ⅔ of the radius of the substrate, i.e., between the center line  102   c  and the support line  102   s.  When the substrate  102  has a convex curvature, as illustrated in  FIG. 4B , however, the flat topped pin  200  contacts the substrate  102  at a location  204  that is greater than ⅔ of the radius of the substrate, i.e., past the support line  102   s.  The difference between the desired contact location, i.e., at support line  102 s and the actual support location  202  or  204  in this case is approximately the radius of the flat topped pin  200 . Variation in the location that the substrate  102  is supported changes the gravitational contribution to the substrate shape and thus, can add an error to the Stoney equation (eq. 1) calculation of stress. For example, assume that  FIG. 4A  illustrates the substrate during a pre measurement and  FIG. 4B  illustrates the substrate during a post measurement and that three flat topped pins with diameters of  8 mm are located on a circle with a diameter of 200 mm and 120° apart (for a 300 mm wafer). The average diameter of the circle of contact will be 192 mm for the pre measurement and 208 mm for the post measurement. This 4% change in contact location will modify the gravitational contribution to the shape a measurable amount and add an error to the stress calculated by the Stoney equation (eq. 1). 
         [0022]      FIGS. 5A and 5B  are similar to  FIGS. 4A and 4B , but illustrate the substrate  102  supported by a pin  110  with a dome shaped upper surface  112 . As can be seen in  FIGS. 5A and 5B , when the pin  110  supports a substrate  102  with a concave or convex curvature, the actual support locations  122  and  124 , respectively, is at approximately the desired support line  102   s.  Thus, relative to conventional flat topped pin  200 , the location of contact between the pin  110  and the substrate  102  is relatively insensitive to changes in the shape (i.e., convex or concave flexing) of the substrate  102 . 
         [0023]    The radius of curvature  112 R (shown in  FIG. 3 ) of the dome shaped upper surface  112  of the pin  110  effects the sensitivity of the contact location to changes in the shape of the substrate. A small radius of curvature  112 R results in a decrease of the sensitivity of the contact location to the shape of the substrate, but also a reduction in the friction that holds the substrate  102  stationary relative to the pins  110  during movement of the chuck. With a radius that is too small, there will not be enough friction to hold the substrate  102  stationary relative to the pins  110 . While a small radius of curvature reduces the contact area, it also increases the stress on the layer  114  that forms the dome shaped upper surface  112 . The increased stress on the layer  114  may cause increased deformation of the layer  114 , and thus, the contact area may not decrease as much as expected. Further, increased stress on the layer  114  may cause the layer  114  to separate from the pin  110  resulting in reliability problems. On the other hand, a large radius of curvature  112 R results in an increase in the sensitivity of the contact location to the shape of the substrate, but produces a large contact area thereby decreasing the probability of substrate movement. Thus, a compromise between a large and small radius of curvature  112 R is used. For example, for a dome shaped upper surface  112  that has a diameter  112   d  of 0.25 inches, a radius of curvature  112 R between 0.125 inches to 0.5 inches, and in particular 0.168 inches has been found to be adequate. 
         [0024]    As can be seen in  FIGS. 2 and 3 , a layer  114  of material covers the pin  110  to form the upper surface  112 . The layer  114  is formed from a material that possesses a high coefficient of static friction that prevents movement of the substrate  102  relative to the pins  110 , even when the substrate  102  is subjected to acceleration. By way of example, the coefficient of static friction may be greater than approximately  3 . Accordingly, once the substrate  102  is properly placed on the pins  110 , a stage  104  may move the chuck  100  and substrate  102 , as indicated by arrows  106  in  FIG. 1 , to measure multiple locations of the substrate  102  and the substrate  102  will not move relative to the pins  110 . If desired, a smaller coefficient of static friction may be used with a reduced acceleration and, thus, reduced throughput. Additionally, the layer  114  is soft enough to avoid scratching the back of the substrate  102 , which could generate particles. 
         [0025]    The hardness of the layer  114  that forms the dome shaped upper surface  112  is another consideration. If the layer  114  used to form the dome shaped upper surface  112  is too soft, the stress from the weight of the substrate  102  may increase the contact area too much. However, a layer  114  that is hard may have a lower coefficient of static friction. Using silicone or another similar material, with a hardness of 20 shore A to 50 shore A has been found to be adequate. 
         [0026]    As illustrated in the cross-sectional view of  FIG. 3 , the pin  110  may be produced with a hard internal dome  116 . The internal dome  116  is on the top of the body  118  of the pin  110 , e.g., on a top surface  117  of the body  118 , and in one embodiment is integrally formed with the body  118  of the pin  110 . In some embodiments, the body  118  may have no top surface  117  but has a rounded top surface to form the internal dome  116 . The internal dome  116  may be, e.g., aluminum or other appropriate material. Alternatively, the internal dome  116  may be separately manufactured and mounted to the top surface  117  of the body  118  of the pin  110  mechanically, e.g., by screwing the internal dome into the pin  110 , or through a chemical fastener, such as epoxy. The internal dome  116  is covered with a thin layer of the layer  114  to form the upper surface  112 . Using an internal dome  116  with a large surface area and an adhesion promoter between the internal dome  116  and the layer  114  will minimize the potential for damage to the upper dome surface  112  of the pin  110  from improper handling or any type of shear force. For example, sandblasting the surface of the internal dome  116  followed by thorough cleaning can improve adhesion significantly. Alternatively or additionally, machining small features such as grooves or dovetails into the internal dome  116  during the manufacturing process will also be an effective adhesion promoting procedure. Moreover, Dow Corning produces primers that are designed to improve the adhesion of silicone compounds to a range of materials including aluminum or anodized aluminum surfaces, which may be used to promote adhesion between the layer  114  and the internal dome  116 . For example, Dow Corning P5200 clear adhesion promoter may be used to improve the adhesion of a range of silicone compounds to anodized aluminum. 
         [0027]    The use of a hard internal dome  116  with a thin layer  114 , which has a high coefficient of static friction, has been found to significantly reduce creep (compared to the use of a thick layer  114 ). Creep is the deformation of the layer  114  due to an applied stress over time. Creep can add a significant error to a stress measurement as it can cause the substrate to move in the Z direction over the time that it takes to collect data for a diameter scan of the substrate  102 . For example, it has been observed that if the dome  112  is made entirely of a relatively soft dome material, i.e., without an internal dome  116 , the material can creep significantly, e.g.,  20  microns over 10-15 minutes after not having a substrate on the pins for the previous 60 minutes. Creep can add a non-linear shape to the measured substrate shape which will modify the calculated radius of curvature and add an error to the stress calculation. 
         [0028]    With the use of an internal dome  116  with the layer  114 , creep is significantly reduced. It has been found that creep is reduced in proportion to the reduction in the thickness of the layer  114 . For example, creep was reduced from 20 microns in 15 minutes for a cast silicone dome (approximately 6 mm at its thickest) to 2 microns in 15 minutes when a 0.5 mm thick coating of the same silicone material was applied to an internal dome  116 . Such a reduction in creep is particularly significant when measuring a change in shape of the substrate as small as  10  microns. Thus, it is believed that a layer  114  with a thickness between 0.25 mm to 2 mm, and specifically, 0.5 mm, is adequate. 
         [0029]    Although the present invention is illustrated in connection with specific embodiments for instructional purposes, the present invention is not limited thereto. Various adaptations and modifications may be made without departing from the scope of the invention. Therefore, the spirit and scope of the appended claims should not be limited to the foregoing description.
A chuck, which may hold a substrate during stress measurements, includes a number of pins that support the substrate. Each support pin has a dome shaped upper surface that contacts a bottom surface of a substrate when supporting the substrate. The dome shaped upper surface minimizes contact with the substrate as well as assists in maintaining the same contact location with the substrate regardless of substrate shape. The dome shaped upper surface may be formed of a layer of soft material having a high coefficient of static friction to hold the substrate stationary with respect to the pins when the chuck is accelerated moved during or between stress measurements. Additionally, the layer of soft material may be a thin layer that covers a hard internal dome to reduce creep.