Abstract:
Apparatus for use in preparing heterostructures having a reduced concentration of defects including apparatus for stressing semiconductor substrates to allow them to conform to a crystal having a different crystal lattice constant.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present application claims the benefit of U.S. Provisional Application No. 61/747,613, filed Dec. 31, 2012; of U.S. Provisional Application No. 61/793,999, filed Mar. 15, 2013; of U.S. Provisional Application No. 61/790,445, filed Mar. 15, 2013 and of U.S. Provisional Application No. 61/788,744 filed Mar. 15, 2013, each of which is incorporated herein by reference. 
     
    
     FIELD OF THE DISCLOSURE 
       [0002]    The present disclosure relates generally to apparatus to stress a semiconductor substrate. 
       BACKGROUND 
       [0003]    A continuing need exists for apparatus that may be used to stress a semiconductor structure. 
       SUMMARY 
       [0004]    One aspect of the present disclosure is directed to an apparatus for bending a semiconductor substrate. The substrate has a generally planar position and a bent position. The apparatus includes a chamber and a heater for heating the chamber. A substrate holder is mounted in the chamber. The holder includes a plurality of spaced-apart elongate pins. Each pin has a support surface for contacting the substrate. The support surfaces are disposed for contacting the substrate in the bent position. 
         [0005]    In another aspect, an apparatus for bending a semiconductor substrate includes a chamber, a heater for heating the chamber, a pressure modulator for causing a pressure differential across the substrate sufficient to exert stress on the substrate and a substrate holder mounted in the chamber. The substrate has a front surface, a back surface and a peripheral edge. The substrate holder includes a front ring and a back ring. Each ring includes an annular support for contacting the substrate adjacent a peripheral edge of the substrate. The front ring is adapted to contact the front surface and the back ring is adapted to contact the back surface of the substrate. 
         [0006]    In yet a further aspect of the apparatus for stressing a semiconductor substrate, the apparatus includes a chamber, a heater for heating the chamber and a substrate holder mounted in the chamber. The substrate has a front surface, a back surface and a peripheral edge. The substrate holder has a front ring, a back ring and a clamp for holding the front ring and back ring. Each ring includes an annular support for contacting the substrate adjacent a peripheral edge of the substrate. The front ring is adapted to contact the front surface and the back ring adapted to contact the back surface of the substrate. 
         [0007]    In another aspect of the present disclosure is directed to an apparatus for stressing a generally circular semiconductor substrate. The substrate has a central axis, a front surface and a back surface which are generally perpendicular to the central axis, a peripheral edge extending from the front surface to the back surface and a circumferential groove in the back surface adjacent the peripheral edge. The apparatus includes a chamber, a heater for heating the chamber and a substrate holder mounted in the chamber. The holder includes a generally planar back support having an annular boss sized to be received in the groove in the back surface of the substrate. The boss is movable to exert stress on the substrate. 
         [0008]    In a further aspect, an apparatus for stressing a generally circular semiconductor substrate comprises a chamber, a heater and a substrate holder mounted in the chamber. The substrate has a central axis, a front surface and a back surface which are generally perpendicular to the central axis. A peripheral edge extends from the front surface to the back surface. The substrate includes a ring bonded to the back surface adjacent the peripheral edge. The substrate holder includes a generally planar back support having a flange adapted to engage the ring on the back surface of the substrate. The support is movable to exert stress on the substrate. 
         [0009]    A further aspect of an apparatus for bending a semiconductor substrate includes a chamber, a heater for heating the chamber, a pressure modulator for causing a pressure differential across the substrate sufficient to exert stress on the substrate and a substrate holder mounted in the chamber. The substrate has a front surface, a back surface and a peripheral edge. The substrate is movable between a generally planar position and a bent position. The substrate holder includes a concave-shaped support having a plurality of holes therethrough. The pressure modulator is adapted to pull a vacuum through the holes to thereby pull the substrate into the concave-shaped support. 
         [0010]    Yet a further aspect of the present disclosure is directed to an apparatus for stressing a semiconductor substrate. The substrate has a central axis, a front surface and a back surface which are generally perpendicular to the central axis. A peripheral edge extends from the front surface to the back surface. The apparatus includes a chamber, a heater for heating the chamber and a substrate holder mounted in the chamber. The holder includes a generally planar back support and a press for receiving and compressing the substrate. The press is adapted to generally uniformly compress the substrate radially inward at its peripheral edge toward its central axis. 
         [0011]    Various refinements exist of the features noted in relation to the above-mentioned aspects of the present disclosure. Further features may also be incorporated in the above-mentioned aspects of the present disclosure as well. These refinements and additional features may exist individually or in any combination. For instance, various features discussed below in relation to any of the illustrated embodiments of the present disclosure may be incorporated into any of the above-described aspects of the present disclosure, alone or in any combination. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0012]      FIG. 1  is a perspective view of an apparatus for processing a semiconductor substrate according to one embodiment of the present disclosure; 
           [0013]      FIG. 2  is a perspective view of the apparatus of  FIG. 1  with a portion of a chamber removed for clarity; 
           [0014]      FIG. 3  is a cross-section view of a substrate holder of one embodiment of the present disclosure; 
           [0015]      FIG. 4  is a perspective view of the substrate holder of  FIG. 3 ; 
           [0016]      FIG. 5  is a cross-section view of a substrate holder of a second embodiment of the present disclosure; 
           [0017]      FIG. 6  is a perspective view of a tubular pin used in the substrate holder of  FIG. 5 ; 
           [0018]      FIG. 7  is a cross-section view of a second embodiment of an apparatus for stressing a semiconductor substrate; 
           [0019]      FIG. 8  is a partial cross-section view of the substrate holder of the apparatus shown in  FIG. 7 ; 
           [0020]      FIG. 9  is a partial cross-section view of the substrate holder showing a coating on the peripheral edge of the substrate; 
           [0021]      FIG. 10  is a cross-section view of a third embodiment of an apparatus for stressing a semiconductor substrate; 
           [0022]      FIG. 11  is a partial cross-section view of the substrate holder of the apparatus shown in  FIG. 10 ; 
           [0023]      FIG. 12  is a partial cross-section view of the substrate holder illustrating movement of the substrate and top ring upon application of the holder by arrows; 
           [0024]      FIG. 13  is a partial cross-section view of a fourth embodiment of an apparatus for stressing a semiconductor substrate; 
           [0025]      FIG. 14  is a cross-section view of a fifth embodiment of an apparatus for stressing a semiconductor substrate; 
           [0026]      FIG. 15  is a cross-section view of a sixth embodiment of an apparatus for stressing a semiconductor substrate; 
           [0027]      FIG. 16  is a cross-section view of the substrate holder of the apparatus shown in  FIG. 15 ; 
           [0028]      FIG. 17  is a cross-section view of the apparatus; 
           [0029]      FIG. 18  is a cross-section view of the substrate holder of  FIG. 18  indicating stretching of the substrate by an arrow; 
           [0030]      FIG. 19  is a partial cross-section view of a third embodiment of a substrate holder; 
           [0031]      FIG. 20  is a partial cross-section view of an apparatus with the substrate support of  FIG. 19 ; 
           [0032]      FIG. 21  is a partial cross-section view of the substrate holder of  FIG. 19 ; 
           [0033]      FIG. 22  is a partial cross-section view of a fourth embodiment of a substrate holder; 
           [0034]      FIG. 23  is a partial cross-section view of an apparatus with the substrate support of  FIG. 22 ; 
           [0035]      FIG. 24  is a cross-section view of the substrate holder of  FIG. 23  illustrating the direction of application of the front and back support by arrows; 
           [0036]      FIG. 25  is a cross-section view of another a fifth of a substrate holder; 
           [0037]      FIG. 26  is a cross-section view of a sixth embodiment of a substrate holder; 
           [0038]      FIG. 27  is a cross-section view of a seventh embodiment of a substrate holder; 
           [0039]      FIG. 28  is a cross-section view of a seventh embodiment of an apparatus for stressing a semiconductor substrate; 
           [0040]      FIG. 29  is a cross-section view of an eighth embodiment of a substrate holder; 
           [0041]      FIG. 30  is a bottom view of a substrate holder of a tenth embodiment of a substrate holder; 
           [0042]      FIG. 31  is a cross-section view of the substrate holder of  FIG. 31 ; 
           [0043]      FIG. 32  is a cross-section view of the substrate holder mounted to a mounting block support; 
           [0044]      FIG. 33  is a cross-section view of the substrate holder and mounting block support with a substrate loaded thereon; and 
           [0045]      FIG. 34  is a cross-section view of the substrate holder and mounting block support with a substrate in a stressed position. 
       
    
    
       [0046]    Corresponding reference characters indicate corresponding parts throughout the drawings. 
       DETAILED DESCRIPTION 
       [0047]    Aspects of the present disclosure include apparatus for applying a stress to a semiconductor substrate such as a silicon substrate (e.g., a wafer). Referring now to  FIGS. 1-2 , the apparatus  11  may include a chamber  31  and a substrate holder  20  having a substrate support  47  for supporting a semiconductor substrate  49 . The illustrated apparatus  11  is a single substrate processing apparatus; however, the apparatus and methods disclosed herein are suitable for use in other apparatus including, for example, multiple substrate processing apparatus. 
         [0048]    The apparatus may also include a “stressor” for stressing the substrate. For instance, the stressor or stressor assembly may include one or more heaters  15  or a pressure modulator  27 . The heater  15  may stress the substrate by causing the substrate to expand at a rate different than the substrate holder (or a portion of the holder) as described below. Alternatively or in addition, the stressor may be pressure modulator  27  that imparts a differential pressure across the substrate. These are merely some examples of possible stressors and others are contemplated within the scope of this disclosure. 
         [0049]    The apparatus  11  includes a chamber  31  having an interior space defined in part by walls  33 . A perspective of the chamber  31  is shown in  FIG. 2  with portions of the chamber walls removed to better illustrate the apparatus  11 . Within the interior space of the chamber  31  is a substrate holder  20  to support a semiconductor substrate  49 . The holder  20  illustrated in  FIGS. 1-2  is a susceptor  47  but other holder arrangements (e.g., tubes, rings, clamps and the like) are contemplated, some of which are more fully described below. The substrate holder is designated as  20  in  FIGS. 1-2  and as  20  plus a multiple of  100  ( 120 ,  220 ,  320  etc.) in  FIG. 3-34 ). 
         [0050]    The chamber  31  may rest on a shaft  9  or other suitable support. The apparatus  11 , such as the shaft  9 , may include devices for causing the holder to grasp and/or release the substrate  49 , such as suitable control valves and/or hydraulic or pneumatic lines or tensioning cables and the like. The chamber  31  may include other arrangements than those shown herein without departing from the scope of the present disclosure. 
         [0051]    The substrate holder or portions of the holder may be generally opaque to absorb radiant heating light produced by heaters  15  such as high intensity radiant heating lamps that may be located above and below the chamber  31 . The holder may be constructed of opaque graphite coated with silicon carbide. The walls of the chamber  31  may be made of a transparent material to allow radiant heating light to pass into the chamber. For example, the walls of the chamber  31  may be made of transparent quartz. Quartz is generally transparent to infrared and visible light and is chemically stable under typical processing temperatures. 
         [0052]    Heaters  15  other than high intensity lamps may be used to provide heat to the chamber  31  such as, for example, resistance heaters and inductive heaters. In addition or alternatively, the heaters  15  may be included within the interior space of the chamber  31  or may be integral with the chamber walls without departing from the scope of the present disclosure. In other words, the heater or heaters may be of any suitable type, size and shape, and may be disposed inside or outside the chamber. An infrared temperature sensor (not shown) such as a pyrometer may be mounted on the chamber  31  to monitor the temperature of the holder  20  or substrate  49  by receiving infrared radiation emitted by the holder or substrate. A system controller  5  ( FIG. 1 ) may be used to control various operating parameters associated with the chamber  31  including, for example, stressor control, gas flow rates and chamber temperature and pressure. It should be understood that apparatus and chamber designs other than that shown in  FIGS. 1-2  may be utilized without departing from the scope of the present disclosure. 
         [0053]    In certain embodiments, the apparatus  11  may be configured for and/or include structure suitable for applying a stress to a semiconductor substrate and, optionally, for depositing a semiconductor material such as an epitaxial layer on the substrate. In such embodiments, a process gas that includes the semiconductor material may flow into the apparatus  11  from a source of process gas, such as a gas cylinder, to a gas manifold (not shown) and into the chamber  31 . Gas may be introduced to the chamber  31  before, throughout or after processing. The gas may be heated prior to contacting the substrate  49 . The process for depositing an epitaxial layer on a surface of the semiconductor substrate may include methods known in the art and as, for example, as described in U.S. Pat. Nos. 5,789,309; 5,904,769 and 5,769,942. Typically, growth of the epitaxial layer is achieved by chemical vapor deposition. Generally speaking, chemical vapor deposition involves the introduction of volatile reactants with a carrier gas (usually hydrogen) into the chamber  31 . 
         [0054]    Various embodiments of the substrate holder for use in applying a stress to a semiconductor substrate will now be described. Some alternative embodiments of substrate holders and stressors (e.g., heater, pressure modulators and the like) for stressing a semiconductor substrate are illustrated below, but other holders and stressors are contemplated within the scope of this disclosure. It should be understood that the holders and stressors may be utilized as a part of the apparatus  11  and chamber  31  described above and may be used in combination with a heater for heating the chamber. 
         [0055]    Referring now to  FIGS. 3-4 , a substrate holder  20  may include a number of spaced-apart elongate pins  22  that support the semiconductor substrate  49 . The pins  22  are attached to a mounting block  25 . A force may be applied to the substrate  49  to cause the substrate to move (e.g., bend) and contact the pins. The pins  22 , or the upper portions thereof, may collectively define a support surface that is disposed for contacting the substrate  49  in the bent (i.e., stressed) position. 
         [0056]    The pins  22 , or the upper portions thereof, may be arranged in a concave pattern such that upon application of a sufficient force, the substrate  22  deforms or bends from its substantially planar shape to conform to the concave arrangement of the pins. By deforming in this manner, the substrate  22  is stressed. 
         [0057]    In certain other embodiments, the apparatus includes a pressure modulator as shown in  FIG. 1  (and  FIG. 7  below) to create a pressure differential across the substrate that is sufficient to exert stress on the substrate. Other stressors may be used in these embodiments. 
         [0058]    As shown in  FIGS. 5-6 , pins  22 ′ may be tubular, thereby defining a lumen for fluid flow. In some embodiments, the pins  22 ′ are fluidly connected to a pressure modulator  27  such as a pump for pulling a vacuum. The vacuum applied to the substrate  49  may pull the substrate toward the pins by a pulling force. For example, variation in distance between the pins and substrate via a concave pattern of the pins may cause different amounts of pulling force to be applied to portions of the substrate. These differential forces cause stress to be applied to the semiconductor substrate  49 . 
         [0059]    The pins  22 ,  22 ′ generally support the substrate in the vertical direction but may be configured so that they do not restrict movement of the substrate in horizontal or radial directions. Allowing radial movement of the substrate during heating allows the substrate to expand radially without causing slip and dislocations. The pins may extend through (rather than from) a mounting block and be connected through a series of conduits as described below and shown in  FIGS. 31-35 . 
         [0060]    Referring now to  FIGS. 7-12 , in one embodiment of an apparatus for bending a semiconductor substrate, the apparatus includes a substrate holder  120  having a front ring  131  and a back ring  132 . The front ring  131  includes an annular front support  134  and the back ring  132  includes an annular back support  136  for contacting and supporting the substrate  49 . Note the front and back rings may have an L-shaped cross-section as shown in  FIG. 8 . The front ring  131  is generally adapted to contact the front surface of the substrate  49  at a discrete radial position and the back ring  132  is generally adapted to contact the back surface of the substrate  49  at a discrete radial position. The radial position is slightly inward from the substrate edge. The radial position at which the front annular support  134  and back annular support  136  contact the substrate  49  may be the same as illustrated in  FIG. 8  or may be different without departing from the scope of the present disclosure. 
         [0061]    Referring to  FIG. 10 , the apparatus for bending the substrate  49  (e.g., stressor) may include a pressure modulator  27  such as a pump to cause a differential pressure across the substrate. In other words, pressure is higher on one side of the wafer than the other. This differential pressure stresses the substrate and may bend the substrate. In such embodiments, the front ring  131  and back ring  132  act as a seal such that the differential pressure across the substrate  49  may be maintained. The pressure modulator  27  may be in fluid communication with a vent  3  that extends through the wall of the chamber  31  to a sealed cavity  4  within the chamber. The differential pressure applied across the substrate  49  may cause the substrate to bend in the direction of lower pressure. 
         [0062]    Bending of the substrate  49  may cause surfaces of the substrate to move between the front and back rings  131 ,  132 . Further, thermal expansion of the substrate  49  (i.e., a thermal expansion greater than the thermal expansion of the rings  131 ,  132 ) may cause the surfaces to move between the rings  131 ,  132 . In one embodiment and as shown in  FIG. 9 , a protective coating  137  covers a portion of the substrate  49  and, in particular, covers the peripheral edges of the substrate. The coating  137  may generally be any protective material that protects the wafer from damage (such as slip and dislocations) while the substrate is held between the rings  131 ,  132 . 
         [0063]    Referring now to  FIG. 13 , a front ring  131 ′ and back ring  132 ′ of the holder  120 ′ may be arranged such that the rings contact the substrate  49  near but not at the peripheral edge of the substrate as with the rings  130 ,  131  of apparatus  120  ( FIG. 8 ). The rings  131 ′,  132 ′ may be integral with the lid and/or bottom of the chamber  31 ′. Vents  3 ′ may extend through the rings  131 ′,  132 ′ of the chamber  31 ′. The vents  3 ′ may be located near the center of the substrate  49  and may limit the deflection of the substrate upon activation of the pressure modulator  27 . 
         [0064]    The holder  120 ′ may also include a planar support  126  that supports the substrate  49  such as before application of the rings  131 ′,  132 ′. In certain embodiments, the substrate  49  is attached to the planar support  126 . The planar support may be made of a material that has a different thermal expansion coefficient than the substrate (i.e., the rings thermally expand at a different rate than the substrate) to cause the substrate to compress or stretch when the support and substrate are heated or cooled. 
         [0065]    Referring to  FIG. 14 , in some embodiments of the apparatus, the apparatus exerts stress on the substrate  49  by use of the thermal expansion of the substrate. The substrate holder  220  may include a clamp  240  including a front ring  231  and a back ring  232  that exerts a holding force on the substrate  49 . The front ring  231  includes an annular front support  234  and the back ring  232  includes an annular back support  236 . The supports  234 ,  236  contact the substrate  49  at the peripheral edge of the substrate and are adapted to contact the front and back of the substrate respectively. For example, the substrate holder  220  illustrated in  FIG. 14  may be used without a pressure modulator. In should be noted that the rings, supports, bosses, clamps and the like of the various holders described herein may also be moved radially by any mechanical method including use of pneumatics, hydraulics, motors and the like. 
         [0066]    The rings  231 ,  232  may be constructed of a material that has a different thermal expansion coefficient than the substrate (i.e., the rings thermally expand at a different rate than the substrate). The holding force of the clamp  240  in combination with the differential expansion rates of the rings  231 ,  232  upon heating or cooling causes stress in the substrate  49 . In embodiments where the rings  231 ,  232  have a larger expansion coefficient than the substrate  49 , the rings cause the substrate to stretch radially. In embodiments where the rings  231 ,  232  have a smaller expansion coefficient than the substrate  49 , the substrate exerts an inward force on the substrate (i.e., compression of the substrate) which results in bending of the substrate. 
         [0067]    Referring now to  FIGS. 15-18 , in another embodiment, a substrate holder  320  includes a generally planar back support  346  that includes an annular boss  347  that is sized and shaped to be received in a groove  348  in the back of the substrate  49 . The boss  347  is movable such that it exerts stress on the substrate  49 . For instance, the back support  346  may be made of a material that expands at a lesser rate than that of the substrate  49  upon heating causing compression of the substrate. Alternatively, the back support  346  may be made of a material that expands at a greater rate than that of the substrate  49  upon heating causing stretching of the substrate. 
         [0068]    The substrate holder  320  may also include a front ring and back ring (not shown) with annular supports similar to the front ring  131  and back ring  132  shown in  FIG. 8  for sealing of the substrate and allowing a pressure modulator to create a pressure differential across the substrate to stress the substrate. The chamber  31  that contains the holder  320  may include a vent  3  and sealed cavity  4  for application of a vacuum or pressure ( FIG. 17 ). The back ring may be interior to the back support  346  and the front ring may be aligned with the back ring or may be sized and shaped to be closer to the peripheral edge of the substrate than the back ring. The substrate may include a coating as shown in  FIG. 9 . 
         [0069]    In some embodiments and as shown in  FIGS. 19-21 , the substrate holder  320  also includes a front support  350  having an annular ring  352  that extends from the front support. The ring  352  exerts a downward force on the substrate  49  to prevent the substrate from dislodging from the boss  347  during compression or expansion of the substrate during heating. Other structures for accomplishing this function are contemplated within the scope of this disclosure. 
         [0070]    In other embodiments and as shown in  FIGS. 22-24 , the substrate holder  420  includes a back support  446  and boss  447  similar or identical to that shown in  FIGS. 15-21 . The substrate holder  420  also includes a front support  451  and a front boss  455  that is sized and shaped to be received in a groove  457  in the front surface of the substrate  49 . The front support  451  may also be made of a material that expands at a lesser rate than that of the substrate  49  upon heating causing compression of the substrate or may be made of a material that expands at a greater rate than that of the substrate  49  upon heating causing stretching of the substrate. 
         [0071]    Referring to  FIGS. 25-27 , stressing apparatus  520  of this embodiment includes a planar back support  561  for supporting the substrate  49  and a generally circular press  560  with a circular opening for receiving and compressing the substrate. The planar support may extend only partially toward the center of the substrate as in  FIGS. 26-28  or may extend continuously beneath the substrate  49 . The press  560  may continuously encircle the substrate or, as shown in  FIG. 27 , may include a plurality of arc-shaped segments  563  that form the opening for receiving the substrate  49 . The press  560  and/or segments  563  may be movable inward relative to the substrate  49  to compress the substrate. For instance, the press  560  may be moved as a result of being composed of a material that expands at a lesser rate than that of the substrate  49  such that the press will compress the substrate upon application of heat. The substrate holder  520  may also include front and/or back rings (not shown) to form a seal upon use of a pressure modulator for creating a pressure differential across the substrate as described above. 
         [0072]    Referring now to  FIG. 28 , the substrate holder  620  includes a first concave-shaped support  670  and a second concave-shaped support  675  opposite the first concave-shaped support. The first concave-shaped support  670  includes a plurality of holes  671  formed therein for pulling a vacuum through the holes and for pulling the substrate  49  toward the first concave-shaped support. An upper portion  677  of the first support  670  contacts a portion of the substrate  49  in its unbent position. A lower portion  678  that is generally larger than the upper portion and which contains the holes  671  for pulling a vacuum contacts the substrate when it is in its bent position. A vent  679  is formed in the second support  675  and the support forms a cavity  672  to allow a vacuum to be pulled through the vent and cavity to stress the substrate. The annular support  675  generally only contacts the substrate  49  near or at the peripheral edge of the substrate. 
         [0073]    Referring to  FIG. 29 , a substrate holder  720  includes a generally planar back support  781  and a flange  783 . The substrate  49  includes a ring  780  attached to the back surface of the substrate near the peripheral edge of the substrate. The flange  783  is adapted to engage the ring  780 . The support  781  and flange  783  are movable relative to the substrate to compress the substrate. For instance, the support  781  and/or flange  783  may be moved as a result of being composed of a material that expands at a greater rate than that of the substrate  49  such that the flange  783  will stretch the substrate upon application of heat. In embodiments where the ring  780  of the substrate is interior to the flange  783  (not shown), the support  781  and/or flange  783  may be moved as a result of being composed of a material that expands at a lesser rate than that of the substrate  49  such that the flange  783  will compress the substrate upon application of heat. 
         [0074]      FIG. 30  illustrates the bottom of a mounting block  991  of a substrate holder  920 . A series of tubes  989  extend through the mounting block  991  to a concave-shaped support  992  ( FIG. 32 ). The tubes  989  are connected via a series of conduits  990 . The mounting block  991  may include a handling groove  993  for inserting and removing the mounting block from the processing chamber  31  ( FIG. 1 ). As shown in  FIG. 32 , the mounting block  991  may be supported on a mounting block support  994  within the chamber. A vacuum tube  996  extends through the mounting block support  994  and is in fluid communication with the conduits  990  and tubes  989  upon insertion of the mounting block into the chamber  31  ( FIG. 1 ). A substrate  49  is placed on the mounting block  991  ( FIG. 33 ). Upon application of vacuum, the substrate  49  bends toward the concave-shaped support  992  causing stress in the substrate ( FIG. 34 ). 
         [0075]    Generally, the stress on the substrate may be directed perpendicular to the axis of the substrate, either by compressing or stretching by use of the embodiments of the apparatus shown in, for example,  FIGS. 14-27  and  29 . Alternatively the stress may be directed along or parallel to the axis of the substrate, such as by use of the embodiments of the apparatus shown in, for example,  FIGS. 5 ,  7 - 13 ,  28  and  30 - 34 . 
         [0076]    When introducing elements of the present disclosure or the preferred embodiment(s) thereof, the articles “a”, “an”, “the” and “said” are intended to mean that there are one or more of the elements. The terms “comprising”, “including” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. 
         [0077]    As various changes could be made in the above apparatus and methods without departing from the scope of the disclosure, it is intended that all matter contained in the above description and shown in the accompanying figures shall be interpreted as illustrative and not in a limiting sense.