Patent Document

BACKGROUND OF THE INVENTION  
         [0001]    1. Technical Field  
           [0002]    The present invention relates to an electronic structure, and associated method of fabrication, for coupling a heat spreader above a chip to a chip carrier below the chip.  
           [0003]    2. Related Art  
           [0004]    A chip on a chip carrier may have a heat spreader on a top surface of the chip, such that the heat spreader is directly coupled to the chip carrier by an adhesive material that encapsulates the chip. If the heat spreader and the chip carrier have about a same coefficient of thermal expansion (CTE), then the adhesive material helps keep the chip carrier-chip-heat spreader structure approximately flat during thermal cycling. Nonetheless, cracking resulting from thermal cycling has been observed to occur at the surface of the chip carrier where a bounding surface of the adhesive material contacts the chip carrier. The cracking can propagate into the chip carrier and damage circuit lines within the chip carrier.  
           [0005]    A method and structure is needed for preventing said damage to said circuit lines within the chip carrier.  
         SUMMARY OF THE INVENTION  
         [0006]    The present invention provides a method for forming an electronic structure, comprising the steps of:  
           [0007]    providing a substrate, a chip on a surface of the substrate and coupled to the substrate, and a thermally conductive member;  
           [0008]    forming a fillet of at least one adhesive material on the chip and around a periphery of the chip and placing the thermally conductive member on a portion of the fillet and over a top surface of the chip, wherein the at least one adhesive material is uncured, wherein the fillet couples the thermally conductive member to the substrate, and wherein an outer surface of the fillet meets the surface of the substrate at a contact curve and makes an average contact angle θ 1AVE  with the surface of the substrate; and  
           [0009]    curing the at least one adhesive material after which the outer surface of the fillet makes an average contact angle θ 2AVE  with the surface of the substrate such that θ 2AVE  does not exceed about 25 degrees.  
           [0010]    The present invention provides an electronic structure, comprising:  
           [0011]    a substrate;  
           [0012]    a chip on a surface of the substrate and coupled to the substrate;  
           [0013]    a fillet of at least one adhesive material on the chip and around a periphery of the chip, wherein an outer surface of the fillet meets the surface of the substrate at a contact curve and makes an average contact angle θ AVE  with the surface of the substrate, and wherein θ AVE  does not exceed about 25 degrees; and  
           [0014]    a thermally conductive member on a portion of the fillet and over a top surface of the chip, wherein the fillet couples the thermally conductive member to the substrate.  
           [0015]    The present invention method and structure for coupling a heat spreader above a chip to a chip carrier below the chip in a manner that prevents damage to circuit lines within the chip carrier during thermal cycling operations.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0016]    [0016]FIG. 1 depicts a front cross-sectional view of an electronic structure having a chip on a surface of a substrate, in accordance with embodiments of the present invention.  
         [0017]    [0017]FIG. 2 depicts FIG. 1 after a dam of a first adhesive material has been dispensed on a peripheral portion of the substrate.  
         [0018]    [0018]FIG. 3 depicts FIG. 2 after an inner bead of a second adhesive material has been dispensed on a top surface of the chip and around a periphery of the chip, and after a thermally conductive member has been placed on the second adhesive material and over the top surface of the chip, resulting in a first gap disposed between the inner bead and the dam.  
         [0019]    [0019]FIG. 4 depicts FIG. 3 after a force has been applied to the thermally conductive member, resulting in a redistribution of the second adhesive material such that a second gap replaces the first gap.  
         [0020]    [0020]FIG. 5 depicts FIG. 4 after the second gap has been filled with a third adhesive material.  
         [0021]    [0021]FIG. 6 depicts FIG. 1 after an adhesive material has been dispensed on a top surface of the chip and around a periphery of the chip, and after a thermally conductive member has been placed on the adhesive material and over the top surface of the chip.  
         [0022]    [0022]FIG. 7 depicts FIG. 6 after a force has been applied to the thermally conductive member in a direction toward the top surface of the chip resulting in a redistribution of the adhesive material.  
         [0023]    [0023]FIG. 8 depicts FIG. 7 after the adhesive material has been cured at an elevated temperature.  
         [0024]    [0024]FIG. 9 depicts FIG. 1 after an adhesive material has been dispensed on a top surface of the chip and around a periphery of the chip and extending to a peripheral portion of the substrate, and after a thermally conductive member has been placed on the adhesive material and over the top surface of the chip.  
         [0025]    [0025]FIG. 10 depicts FIG. 9 after a force has been applied to the thermally conductive member in a direction toward the top surface of the chip resulting in a redistribution of the adhesive material.  
         [0026]    [0026]FIG. 11 depicts a top view of the electronic structure of FIG. 5.  
         [0027]    [0027]FIG. 12 depicts a top view of the electronic structure of FIG. 6.  
         [0028]    [0028]FIG. 13 depicts a top view of the electronic structure of FIG. 9.  
         [0029]    [0029]FIG. 14 presents test results which show a reduction in contact angle that the dam of FIG. 5 makes with the substrate after the second gap has been filled with the third adhesive material. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0030]    [0030]FIG. 1 illustrates a front cross-sectional view of an electronic structure  10  having a chip  14  over a substrate  12 , in accordance with embodiments of the present invention. An underfill  16  is disposed between the chip  14  and the substrate  12 , and the underfill  16  encapsulates a peripheral portion of the chip  14 . The underfill  16  accommodates strain induced during thermal cycling due to a differential coefficient of thermal expansion (CTE) between the chip  14  and substrate  12 . The substrate  12 , which may comprise a chip carrier, includes a top surface  13 , a peripheral surface  15 , and a peripheral edge  17 . See FIGS. 11, 12, and  13 , each described infra, for top views depicting the chip  14 , the underfill  16 , and the peripheral edge  17 . Note the FIGS. 11, 12, and  13  show the portion of the underfill  16  which encapsulates the peripheral portion of the chip  14 , but does not show a portion  56  of the underfill  16  that is directly under the chip  14  .  
         [0031]    The following discussion presents three embodiment classes of the present invention. The first embodiment class is illustrated by FIGS.  1 - 5  and  11 . The second embodiment class is illustrated by FIGS.  1 ,  6 - 8 , and  12 . The third embodiment class is illustrated by FIGS.  1 ,  9 - 10 , and  13 .  
         [0032]    FIGS.  1 - 5  and  11  illustrate a first embodiment class of the present invention. FIG. 2 illustrates FIG. 1 after a dam  20  of a first adhesive material that has been dispensed on the surface  13  of the substrate  12 . As dispensed, the first adhesive material is uncured. The first adhesive material may comprise, inter alia, a first epoxy material that includes a first thixotrope at a thixotropic concentration such that the first adhesive material remains in place upon being dispensed. The dam  20  has an outer surface  21  that meets the substrate  12  in a planar area bounded by an inner contact curve  18  and an outer contact curve  19 . See FIG. 11, described infra, for a top view depicting the dam  20 , the inner contact curve  18 , and the outer contact curve  19 . Although the dam  20  may be dispensed at any desired location on the surface  13  of the substrate  12 , it may be advantageous to place the dam  20  beyond any electrical circuitry or other valuable structure in the substrate  12  in order to minimize potential damage to electrical circuitry or other valuable structure in the substrate  12 , as will be discussed infra. The dam  20  will constitute a dam portion of a fillet  27  that is depicted infra in FIG. 5.  
         [0033]    Returning to FIG. 2, the outer surface  21  of the dam  20  makes a contact angle θ 1  with the outer contact curve  19 . θ 1  is approximately constant along the outer contact curve  19  and θ 1AVE  denotes an average value of value of θ 1 ; i.e., an average contact angle along the outer contact curve  19 . Test results, which will be discussed infra, show small standard deviations in the contact angle of 5% to 7% of the average contact angle, which supports the preceding statement that θ 1  is approximately constant along the outer contact curve  19 .  
         [0034]    [0034]FIG. 3 illustrates FIG. 2 after an inner bead  22  of a second adhesive material has been dispensed on top surface  11  of the chip  14  and around a periphery of the chip, resulting in a gap  28  disposed between the inner bead  22  and the dam  20 . As dispensed, the second adhesive material is uncured. The second adhesive material may comprise, inter alia, a second epoxy material that includes a second thixotrope at a thixotropic concentration such that the second adhesive material remains in place upon being dispensed. The second adhesive material may be chosen to be the same as, or to differ from, the first adhesive material. The second adhesive material may differ from the first adhesive material with respect to one or more of: the epoxy material, the thixotrope, and the thixotropic concentration. The inner bead  22  will constitute an inner bead portion of the fillet  27  that is depicted infra in FIG. 5. Note that the second adhesive material of the inner bead  22  may be dispensed either before or after the first adhesive material of the dam  20  has been dispensed.  
         [0035]    [0035]FIG. 3 also illustrates a thermally conductive member  24  (e.g., a heat spreader) placed on the inner bead  22  and above the top surface  11  of the chip  14 . See FIG. 11, described infra, for a top view depicting the inner bead  22  and the thermally conductive member  24 . Note the FIG. 11 does not show a portion  52  of the inner bead  22  that is directly above the chip  14 , and disposed between the chip  14  and the thermally conductive member  24 .  
         [0036]    Returning to FIG. 3, a force  23  is applied to the thermally conductive member  24  in a direction  8  toward the chip  14 . The force  23  causes the second adhesive material of the inner bead  22  to be redistributed. FIG. 4 illustrates FIG. 3 after the force  23  has been applied to the thermally conductive member  24 , resulting in a second gap  29  that replaces the first gap  28 .  
         [0037]    [0037]FIG. 5 illustrates FIG. 4 after the second gap  29  has been filled with a third adhesive material  26 . See FIG. 11 for a top view of the electronic structure  10  of FIG. 5, including the third adhesive material  26 . As dispensed, the third adhesive material  26  is uncured. The third adhesive material  26  may comprise, inter alia, a third epoxy material that includes a third thixotrope at a thixotropic concentration such that the third adhesive material  26  flows upon being dispensed into the second gap  29 . The third adhesive material  26  differs from both the first adhesive material and the second adhesive material with respect to one or more of: the epoxy material, the thixotrope, and the thixotropic concentration. If the third adhesive material  26  includes the same epoxy material and thixotrope as the first adhesive material and/or the second adhesive material, then the third adhesive material  26  must have a lower thixotropic concentration than the thixotropic concentration of the first adhesive material and/or the second adhesive material. Allowable ranges of thixotropic concentration are case dependent and vary with the epoxy material and the thixotrope used. For a variety of epoxy materials and thixotropes, a representative thixotropic concentration of the third adhesive material  26  is less than about 1.5% by weight, and a representative thixotropic concentration of the first and/or second adhesive material  26  is greater than about 1.5% by weight.  
         [0038]    While the discussion supra associated with FIGS.  3 - 5  disclosed applying the force  23  (see FIG. 3) to the thermally conductive member  24  prior to filling the second gap  29  with the third adhesive material  26  (see FIGS.  4 - 5 ), the preceding steps could be reversed as follows. The first gap  28  (see FIG. 3) could first be filled with the third adhesive material  26 , followed by applying the force  23  to the thermally conductive member  24  which would redistribute the second adhesive material of the inner bead  22 . Regardless of whether the force  23  is applied to the thermally conductive member  24  before or after filling the second gap  29  (or the first gap  28 ) with the third adhesive material  26 , the structure in FIG. 5 relating to the third adhesive material  26  will result.  
         [0039]    After being dispensed, the third adhesive material  26 , flows and takes a shape that conforms to boundaries imposed by the inner bead  22  and the dam  20 . The third adhesive material  26  constitutes an extended fillet portion of the fillet  27 . Thus, the fillet  27  includes the inner bead portion (i.e., the inner bead  22 ), the extended fillet portion (i.e., the third adhesive material  26 ), and the dam portion (i.e., the dam  20 ). After being dispensed, the third adhesive material  26  interacts with the first adhesive material of the dam  20  in a manner that reduces the contact angle with the outer contact curve  19  to a lower value θ 2  in comparison with θ 1  (see FIG. 2). If θ 2AVE  denotes an average value of θ 2  around the outer contact curve  19  (see FIG. 11), then θ 2 &lt;θ 1  and thus θ 2AVE &lt;θ 1AVE .  
         [0040]    [0040]FIG. 14 presents test results which show the contact angle (as exemplified by θ 1  of FIG. 2 and θ 2  of FIG. 5) as a function of time for four data points  1 ,  2 ,  3 , and  4 . The indicated standard deviation (STD) corresponds to averaging over four contact angles at each of the data points  1 ,  2 ,  3 , and  4 . The four angles for averaging purposes correspond to four spatial points on the outer contact curve  19  of FIG. 1. The data point  1  represents an initial condition at ambient room temperature (i.e., about 21° C.) at which the inner bead  22  and the dam  20 , but not the third adhesive material  26  of FIG. 5, are on the substrate  12 . An initial contact angle θ 1  is 41±3 degrees (i.e, the average contact angle θ 1AVE  is 41 degrees subject to a standard deviation of 3 degrees). After the initial condition, the third adhesive material  26  is dispensed. The data point  2  occurs at ambient room temperature and 15 minutes after the third adhesive material  26  has been dispensed during which the contact angle has been reduced to 29±3 degrees. The data point  3  occurs at ambient room temperature and 30 minutes after the third adhesive material  26  has been dispensed during which time the contact angle has been reduced to 25±1 degrees. At about 60 minutes after the third adhesive material  26  had been dispensed, the electronic structure  10  was placed in a heated chamber at 130° C. for curing and was removed for final measurement of the contact angle θ 2  at about 30 minutes after being placed in the heated chamber. Accordingly, the data point  4  occurs after a total exposure of 60 minutes to the ambient room temperature and an additional exposure of 30 minutes to a temperature of 130° C. The final measured contact angle θ 2  associated with the data point  4  is 20±1 degrees. Thus, an unknown portion of the final 5 degree contact angle reduction from the data point  3  to the data point  4  occurs at ambient room temperature, and a remaining unknown portion of the final 5 degree contact angle reduction occurs at 130° C. Note that the standard deviation for the data points  1 ,  2 ,  3 , and  4  is only 5% to 7% of the average contact angle, which shows that the contact angle is approximately constant on the outer contact curve  19  of FIG. 11.  
         [0041]    The aforementioned test results show a total reduction in average contact angle of a factor of about 2 (i.e., from 41 degrees to 20 degrees), and a reduction in average contact angle of at least 1.6 (i.e., from 41 degrees to 25 degrees) during temperature exposure to only ambient room temperature. The reduction of the contact angle to 25 degrees or less (which is a satisfactory low contact angle) during temperature exposure to only ambient room temperature allows for pre-cure inspection of the contact angle, which enables parts having unacceptable contact angles to be discarded or reworked without incurring the cost and time of curing.  
         [0042]    Returning to FIG. 5, the contact angle reduction from θ 1  to θ 2  is caused by surface tension between the third adhesive material  26  and the first adhesive material of the dam  20 . In particular, the aforementioned surface tension generates a force which pulls the first adhesive material at the surface  21  of the dam  20  toward the third adhesive material  26  in a direction  9  which results in the contact angle reduction from θ 1  to θ 2 .  
         [0043]    After the third adhesive material  26  has been dispensed, the first adhesive material, the second adhesive material, and the third adhesive material  26  are cured at an elevated temperature. The elevated temperature is application dependent and is a function of the first adhesive material, the second adhesive material, and the third adhesive material  26 . The time for substantial completion of curing is a decreasing function of the cure temperature. A representative cure temperature and cure time is 130° C. for 4 hours. A cure temperature and associated cure time suitable for the intended application may be determined empirically without undue experimentation by one of ordinary skill in the art. As shown supra in the test results of FIG. 14, the contact angle reduction to 25 degrees or less takes place before curing.  
         [0044]    The aforementioned contact angle reduction to about 20-25 degrees or less for θ 2  and θ 2AVE  substantially prevents cracks from forming during thermal cycling on the surface  13  of the substrate  12  in a vicinity of the planar area bounded by the inner contact curve  18  and the outer contact curve  19  (see FIG. 11). The following table summarizes test results showing a percentage of parts that have developed one or more cracks as a function of the average contact angle that an outer surface of a fillet makes with a substrate surface.  
                                                     Average Contact   Parts With Cracks (%)            Angle (Degrees)   At 310 Cycles   At 675 Cycles   At 1053 Cycles               48   19    50   75       38   6   50   63       29   6   31   69       26   6   25   25       18   0    0   13                  
 
         [0045]    In the above table,  16  parts were tested at each contact angle in a wet thermal shock test having a temperature range of −55° C. to 125° C. in each cycle. The test results indicate that 63-75% of parts had crack formation during 1053 thermal cycles if the average contact angle θ 2  was 29 degrees or more. In contrast, only 13-25% of parts had crack formation during 1053 thermal cycles if the average contact angle was 26 degrees or less.  
         [0046]    Returning to FIG. 5, for thermal stress on the surface  13  induced during thermal cycling, crack formation is caused by a geometric stress concentration. The stress concentration at the outer contact curve  19  is a monotonically increasing function of the contact angle θ 2 , because as θ 2  increases, the height in the direction  7  of the third adhesive material  26  at the outer contact curve  19  increases, resulting in a corresponding increase in stiffness imposed on the substrate at the outer contact curve  19 . In the limit of θ 2  approaching zero degrees, the discontinuity in stress concentration across the outer contact curve  19  from inside the dam  20  to outside the dam  20  vanishes. Thus below a threshold contact angle θ 2 , the stress concentration is sufficiently low to render crack formation unlikely. Based on the test data presented supra, the threshold contact angle θ 2  is about 25 degrees.  
         [0047]    The actual values of θ 2  which may be obtained with the embodiment of the present invention, as described by FIGS.  1 - 5  and  11 , are case dependent and depend on the geometry of the third adhesive material  26  in relation to the geometry of the inner bead  22  and the dam  20 . For example, in order to effectuate a low contact angle, such as θ 2 , less than about 25 degrees, an exposed surface  30  of the third adhesive material  26  must be concave upward; i.e., concave in a direction  7 . Whether the exposed surface  30  is concave upward depends on the relative heights (in the direction  7 ) of the third adhesive material  26 , the inner bead  22 , and the dam  20 . Accordingly, θ 2  may be controlled or influenced by adjusting the volume of the third adhesive material  26  for a given size of the gap  29  (see FIG. 4) in consideration of the heights of the inner bead  22  and the dam  20 . Whether the exposed surface  30  is concave upward also depends on the width (in the direction  9 ) of the third adhesive material  26 , which may be adjusted by where the dam  20  is placed on the surface  13  of the substrate  12 . In consideration of the preceding variables in relation to the aforementioned case-dependent determination of θ 2 , one skilled in the art may determine, without undue experimentation, how to use the present invention to obtain desired contact angles θ 2 .  
         [0048]    The present invention, as embodied in FIGS.  1 - 5  and  11  may protect electrical circuitry or other valuable structure in the substrate  12  in either or both of two ways. A first way of accomplishing said protecting is by locating the dam  20  at specific locations on the surface  13  above or near electrical circuitry or other valuable structure in the substrate  12  needing protection, such that the contact angle θ 2  at the dam  20  is less than about 25 degrees at said specific locations. As stated supra, a contact angle θ 2  of less than about 25 degrees protects the surface  13  against cracking. A second way of accomplishing said protecting is by locating the dam  20  at specific locations on the surface  13  not above or near electrical circuitry or other valuable structure in the substrate  12  needing protection, so that even if cracking at the outer contact curve  19  at the dam  20  should occur, there would be no nearby electrical circuitry or other valuable structure to be damaged. Depending on how electrical circuitry or other valuable structure within the substrate  12  is distributed, the second way of accomplishing said protecting may include, inter alia, positioning the dam  20  such that the outer contact curve  19  is at a distance no greater than a specified distance from the peripheral edge  17  of the substrate  12 .  
         [0049]    FIGS.  1 ,  6 - 8 , and  12  illustrate a second embodiment class of the present invention. FIG. 6 illustrates FIG. 1 after a bead  32  of an adhesive material has been dispensed on a top surface of the chip  14  and around a periphery of the chip  14 , and after a thermally conductive member  24  has been placed on the bead  32  and over the top surface of the chip  14 . As dispensed, the adhesive material of the bead  32  is uncured. The adhesive material of the bead  32  may comprise an epoxy material that includes a thixotrope at a low thixotropic concentration (e.g., at a thixotropic concentration of less than about 1.5% by weight for many thixotrope-epoxy combinations) such that the viscosity of the adhesive material of the bead  32  initially decreases upon being heated. The bead  32  has an outer surface  33  that meets the substrate  12  in a planar area bounded by an outer contact curve  35 . See FIG. 12 for a top view of the electronic structure  10  of FIG. 6 depicting the bead  32 , the thermally conductive member  24 , and the outer contact curve  35 . Note the FIG. 12 does not show a portion  53  of the bead  32  that is directly above the chip  14 , and disposed between the chip  14  and the thermally conductive member  24 .  
         [0050]    Returning to FIG. 6, a force  63  is applied to the thermally conductive member  24  in the direction  8  toward the chip  14 . The force  63  causes the adhesive material of the bead  32  to be redistributed. FIG. 7 illustrates FIG. 6 after the force  63  has been applied to the thermally conductive member  24 . FIG. 7 shows the outer surface  33  of the bead  32  making a contact angle θ 3  with the surface  13  of the substrate  12 . The outer contact curve  35  of the bead  32  may be sufficiently close to the chip  14  so that the contact angle θ 3  is rather steep such as about 45° or more. θ 3  is approximately constant along the outer contact curve  35 . Noting that θ 3  may have minor variations along the contact curve  35 , θ 3AVE  denotes an average value of value of θ 3 ; i.e., an average contact angle along the outer contact curve  35 .  
         [0051]    Next, the adhesive material of the bead  32  is thermally cured at an elevated temperature. The elevated temperature is application dependent and is a function of the adhesive material of the bead  32 . The time for substantial completion of curing is a decreasing function of the cure temperature. A cure temperature and associated cure time suitable for the intended application. may be determined empirically without undue experimentation by one of ordinary skill in the art. At the onset of curing (i.e., during an initial time interval at the cure temperature), the viscosity of the adhesive initially decreases before the curing later increases the viscosity of the adhesive. The initial viscosity decrease reduces the contact angle to a value θ 4  that is less than about 25 degrees. Thus, the reduction of the contact angle from θ 3  to θ 4  occurs substantially during the aforementioned curing step. The low value of θ 4  (i.e., less than about 25 degrees) prevents cracks from forming during thermal cycling on the surface  13  of the substrate  12  in a vicinity of the planar area bounded by the outer contact curve  35 , as explained supra in conjunction with the analogous contact angle θ 2  of FIG. 5.  
         [0052]    FIGS.  1 ,  9 - 10 , and  13  illustrate a third embodiment class of the present invention. FIG. 9 illustrates FIG. 1 after a bead  42  of a high-thixotropic adhesive material (e.g., at a thixotropic concentration of at least about 1.5% by weight for many thixotrope-epoxy combinations) has been dispensed on a top surface of the chip  14  and around a periphery of the chip  14 , and after a thermally conductive member  24  has been placed on the bead  42  and over the top surface of the chip  14 . As dispensed, the adhesive material of the bead  42  is uncured. The high-thixotropic adhesive material of the bead  42  may comprise the high-thixotropic adhesive material such that the adhesive material remains in place upon being dispensed. The bead  42  has an outer surface  43  that meets the substrate  12  in a planar area bounded by an outer contact curve  45 . See FIG. 13 for a top view of the electronic structure  10  of FIG. 9 depicting the bead  42 , the thermally conductive member  24 , and the outer contact curve  45 . Note the FIG. 13 does not show a portion  54  of the bead  42  that is directly above the chip  14 , and disposed between the chip  14  and the thermally conductive member  24 .  
         [0053]    Returning to FIG. 9, a force  73  is applied to the thermally conductive member  24  in the direction  8  toward the chip  14 . The force  73  causes the adhesive material of the bead  42  to be redistributed. FIG. 10 illustrates FIG. 9 after the force  73  has been applied to the thermally conductive member  24 , after which an outer surface  43  of the bead  42  makes a contact angle θ 5  with the surface  13  of the substrate  12 .  
         [0054]    The bead  42  is positioned on the surface  13  of the substrate  12  in a manner that results in the contact angle θ 5  having a value of about 25 degrees or less. Such positioning of the bead  42  requires that a height H of a surface  38  of the thermally conductive member  24  above the surface  13  of the substrate  12  be sufficiently small in relation to a lateral distance D between the the thermally conductive member  24  and the outer contact curve  45 . An exact relation between H and D to keep the contact angle θ 5  to about 25 degrees or less is application dependent and depends on the high-thixotropic adhesive material of the bead  42 . For a given lateral distance D of about 100 mils, a representative height H is about 42 mils. A suitable relation between H and D for the intended application may be determined empirically without undue experimentation by one of ordinary skill in the art.  
         [0055]    Noting that θ 5  has minor variations along the contact curve  45 , θ 5AVE  denotes an average value of value of θ 5 ; i.e., an average contact angle along the outer contact curve  45 . The aforementioned low value of θ 5  prevents cracks from forming during thermal cycling on the surface  13  of the substrate  12  in a vicinity of the planar area bounded by the outer contact curve  45 , as explained supra in conjunction with the analogous contact angle θ 2  of FIG. 5.  
         [0056]    Next, the high-thixotropic adhesive material of the bead  42  is cured at an elevated temperature. The elevated temperature is application dependent and is a function of the high-thixotropic adhesive material of the bead  42 . The time for substantial completion of curing is a decreasing function of the cure temperature. A representative cure temperature and cure time is 130° C. for 4 hours. A cure temperature and associated cure time suitable for the intended application may be determined empirically without undue experimentation by one of ordinary skill in the art. The curing does not change the contact angle θ 5.    
         [0057]    While particular embodiments of the present invention have been described herein for purposes of illustration, many modifications and changes will become apparent to those skilled in the art. Accordingly, the appended claims are intended to encompass all such modifications and changes as fall within the true spirit and scope of this invention.

Technology Category: 5