Abstract:
A vacuum carrier can be employed to provide a partial vacuum on a back side surface of a substrate thereby holding the substrate flat against a rigid surface of the carrier throughout the duration of a bonding process. The magnitude of vacuum can be optimized to limit the warping of the substrate during and after bonding with another substrate, and to limit the mechanical stress induced in the solder balls during cooling. The vacuum carrier can include a base plate, a seal plate with at least one opening configured to accommodate at least one substrate, and vacuum seal elements configured to create a vacuum environment that pushes the substrate against the base plate when the vacuum carrier is under vacuum. The configuration of the vacuum carrier is chosen to avoid distortion of the substrate due to the vacuum seal elements, while allowing adjustment of the magnitude of the partial vacuum.

Description:
RELATED APPLICATIONS 
     The present application is related to copending U.S. patent application Ser. No. 13/437,309 filed on Apr. 2, 2012, the entire contents of which are incorporated herein by reference. 
     BACKGROUND 
     The present disclosure relates to bonding substrates, and particularly, to a method of bonding substrates while minimizing substrate warping, a vacuum carrier for effecting the same, and a structure for implementing the same. 
     Substrate warping poses a challenge for the attachment of a semiconductor chip to a packaging substrate. A large substrate warp at reflow is a cause for unreliable C 4  bonding, leading to potential non-wets or unequal C 4  solder heights. Even for a population of substrates having a nominal mean warp, there is usually a large variation (sigma) in the warp which can be a problem during bond and assembly. The thermal warp, i.e., the change in warp with temperature, is another undesirable problem for bond and assembly. A large thermal warp means that the packaging substrate changes shape during the critical cool down period after the reflow of solder balls. Such change in the shape of the solder balls could lead to defects in the solder ball joints such as hot tears. 
     SUMMARY 
     A vacuum carrier can be employed to provide a partial vacuum on a back side surface of a substrate thereby holding the substrate flat against a rigid surface of the carrier throughout the duration of a bonding process. The magnitude of vacuum can be optimized to limit the warping of the substrate during and after bonding with another substrate, and to limit the mechanical stress induced in the solder balls during cooling. The vacuum carrier can include a base plate, a seal plate with at least one opening configured to accommodate at least one substrate, and vacuum seal elements configured to create a vacuum environment that pushes the substrate against the base plate when the vacuum carrier is under vacuum. The configuration of the vacuum carrier is chosen to avoid distortion of the substrate due to the vacuum seal elements, while allowing adjustment of the magnitude of the partial vacuum. 
     According to an aspect of the present disclosure, a structure includes a vacuum carrier and at least one substrate. The vacuum carrier includes a base plate, a seal plate having at least one opening, at least one first vacuum seal element, and a second vacuum seal element. The at least one substrate contacts a planar surface of the base plate and underlies each of the at least one opening. The at least one first vacuum seal element provides a seal at each gap between the at least one substrate and the seal plate. The second vacuum seal element provides another seal between the base plate and the seal plate. The vacuum carrier and the at least one substrate includes a reduced pressure environment therein. 
     According to another aspect of the present disclosure, a method of bonding substrates is provided. At least one stack is mounted on a vacuum carrier. Each of the at least one stack includes a first substrate, an array of solder balls, and a second substrate such that the array of solder balls is not bonded to at least one of the first substrate and the second substrate. A partial vacuum is provided within an enclosure defined by the vacuum carrier and the at least one stack. Each of the at least one first substrate is pushed against a surface of the vacuum carrier by a pressure differential between the partial vacuum and atmospheric pressure. The pressure differential is in a range from 0.4 atmospheric pressure to 1.0 atmospheric pressure. Bonding is induced within the at least one stack by reflowing the at least one array of solder balls at an elevated temperature. The at least one stack is dismounted from the vacuum carrier after the at least one stack is bonded by releasing the partial vacuum. 
     According to yet another aspect of the present disclosure, a vacuum carrier is provided, which is configured to hold vacuum upon mounting of at least one substrate thereupon and upon pumping out of ambient gas therefrom. The vacuum carrier includes a base plate, a seal plate, at least one first vacuum seal element, and a second vacuum seal element. The base plate includes a planar surface and a vacuum manifold, and is connected to a sealable pumping port. The seal plate has at least one opening therein and is configured to overlie the base plate. The at least one first vacuum seal element is configured to provide a seal between at least one substrate and the seal plate upon mounting of the at least one substrate on the base plate, upon placement of the at least one first vacuum seal element upon the at least one substrate and upon placement of the seal plate upon the at least one first vacuum seal element. The second vacuum seal element is configured to provide another seal between the base plate and the seal plate upon placement of the second vacuum seal element on the base plate and upon placement of the seal plate upon the second vacuum seal element. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         FIG. 1  is a vertical cross-sectional view of a first exemplary structure including a vacuum carrier and a stack of substrates according to an embodiment of the present disclosure. 
         FIG. 2  is a vertical cross-sectional view of a second exemplary structure including a vacuum carrier and a stack of substrates according to an embodiment of the present disclosure. 
         FIG. 2A  is a photo of a physical implementation of the second exemplary structure. 
         FIG. 3  is a vertical cross-sectional view of a third exemplary structure including a vacuum carrier and a stack of substrates according to an embodiment of the present disclosure. 
         FIG. 4  is a vertical cross-sectional view of a fourth exemplary structure including a vacuum carrier and a stack of substrates according to an embodiment of the present disclosure. 
         FIG. 4A  is a vertical cross-sectional view of the fourth exemplary structure in which the differential pressure is schematically illustrated and a second substrate and solder balls are omitted for the sake of clarity. 
         FIG. 5  is a schematic vertical cross-sectional view of an exemplary apparatus that can be employed for bonding substrates according to an embodiment of the present disclosure. 
         FIG. 6  is a graph illustrating the temperature of an oven as a function of time during an exemplary bonding process. 
         FIG. 7  is a vertical cross-sectional view of a fifth exemplary structure including a vacuum carrier and a stack of substrates according to an embodiment of the present disclosure. 
         FIG. 8  is a vertical cross-sectional view of a sixth exemplary structure including a vacuum carrier and a stack of substrates according to an embodiment of the present disclosure. 
         FIG. 9A  is a bird&#39;s eye view of a seventh exemplary structure including a vacuum carrier and stacks of substrates prior to placement of a seal plate according to an embodiment of the present disclosure. 
         FIG. 9B  is a vertical cross-sectional view of the seventh exemplary structure after placement of the seal plate according to an embodiment of the present disclosure. 
         FIG. 10A  is a bottom-up view of the seal plate of the seventh exemplary structure according to an embodiment of the present disclosure. 
         FIG. 10B  is a side view of the seal plate of the seventh exemplary structure in  FIG. 10A  in an upside-down position according to an embodiment of the present disclosure. 
         FIG. 10C  is a magnified vertical cross-sectional view of the seal plate of the seventh exemplary structure along the plane C-C′ in  FIG. 10A . 
         FIG. 11  is a bird&#39;s eye view of an eighth exemplary structure including a vacuum carrier and substrates prior to placement of a seal plate according to an embodiment of the present disclosure. 
         FIG. 12A  is a bottom-up view of the seal plate of the eighth exemplary structure according to an embodiment of the present disclosure. 
         FIG. 12B  is a side view of the seal plate of the eighth exemplary structure in  FIG. 12A  in an upside-down position according to an embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     As stated above, the present disclosure relates to a method of bonding substrates while minimizing substrate warping, a vacuum carrier for effecting the same, and a structure for implementing the same. Aspects of the present disclosure are now described in detail with accompanying figures. It is noted that like and corresponding elements are referred to by like reference numerals. The drawings are not in scale. As used herein, ordinals such as “first” and “second” are employed merely to distinguish similar elements, and different ordinals may be employed to designate a same element in the specification and/or claims. 
     Referring to  FIGS. 1-4 , a first exemplary structure, a second exemplary structure, a third exemplary structure, and a fourth exemplary structure are shown according to various embodiments of the present disclosure. Each exemplary structure includes a vacuum carrier and a stack of substrates. The vacuum carrier is configured to hold vacuum upon mounting of at least one substrate thereupon and upon pumping out of ambient gas therefrom. The vacuum carrier includes a base plate  410  including a vacuum manifold therein. The vacuum manifold can include, for example, an enclosed cavity  421  configured to hold vacuum therein and connected to a sealable pumping port  422 . A cavity enclosure  420  defines the volume of the enclosed cavity  421 . The portion of the base plate  410  that defines a boundary of the enclosed cavity  421  is herein referred to as a cavity enclosure  420 . 
     In one embodiment, the cavity enclosure  420  can include two openings. A first opening in the cavity enclosure  420  provides a passage to the sealable pumping port  422 . A second opening in the cavity enclosure  420  can be a connection to a vacuum distribution manifold ( 431 ,  441 ), which can include, for example, horizontal vacuum distribution manifold portions  431  that extend along horizontal directions and vertical vacuum distribution manifold portions  441  that extend along a vertical direction. The horizontal vacuum distribution manifold portions  431  can be embedded entirely within the base plate  410 , and the vertical vacuum distribution manifold portions  441  can extend to openings in a planar top surface of the base plate  410 . 
     In some embodiments, the vertical vacuum distribution manifold portions  441  can be located only in regions that do not underlie any of the at least one first substrate  100  as illustrated in  FIGS. 1 and 3 . The planar top surface of the base plate  410  can have a surface roughness that allows formation of channels  461  at a microscopic level through which a gas can be pumped out and so allows the vacuum to permeate beneath the at least one first substrate  100 . In this case, the root mean square (RMS) surface roughness of the planar top surface of the base plate  410  that contacts the at least one first substrate  100  can be in a range from 10 nm to 10,000 nm, although lesser or greater RMS surface roughness can also be employed. 
     In some other embodiments, the vertical vacuum distribution manifold portions  441  can also be located in regions that underlie the at least one first substrate  100  as illustrated in  FIGS. 2 and 4 . The planar top surface of the base plate  410  can have a surface roughness that further allows the vacuum to permeate beneath the at least one first substrate  100 . 
     In all of the above cases the pressure differential, due to the pressure of the ambient acting on the exposed top surface of the at least one first substrate  100  and the pressure of the partial vacuum acting on the complete lower surface of the at least one first substrate  100 , can apply a force to the at least one first substrate  100 , that presses the at least one first substrate  100  against the planar top surface of the base plate  410  as shown in  FIG. 4A . 
     The sealable pumping port  422  includes a means of connecting, and disconnecting, a passage to an ambient that is at atmospheric pressure. One end of the sealable pumping port  422  can be connected to the enclosed cavity  421 , and the other end of the sealable pumping port  422  can be connected to an orifice  424 , which can be connected to a vacuum pump (not shown) for the purpose of reducing the pressure in the vacuum manifold, and can be disconnected from the vacuum pump and exposed to the atmospheric ambient at the time of releasing the vacuum in the vacuum manifold. 
     The planar top surface of the base plate  410  is a planar surface having an area large enough to accommodate a first substrate  100 . The first substrate  100  can be a packaging substrate, a transposer substrate, an interposer substrate, or a semiconductor substrate. As used herein, a packaging substrate refers to a substrate that can be bonded to a semiconductor chip to facilitate permanent mounting of the semiconductor chip to a circuit board or an equivalent thereof. As used herein, a transposer substrate refers to a substrate that can be employed to provide temporary electrical connections between a semiconductor chip and a circuit board. As used herein, an interposer substrate refers to an intermediate substrate that provides electrical interface routing between a semiconductor chip and a packaging substrate. The semiconductor substrate can be a semiconductor chip. 
     While  FIGS. 1-4  illustrate embodiments in which a single first substrate  100  is mounted on a vacuum carrier, embodiments are expressly contemplated herein in which a vacuum carrier can be configured to mount a plurality of first substrates  100 . Thus, at least one first substrate  100  can be mounted on each vacuum carrier. 
     Optionally, a second substrate  200  and an array of solder balls  300  can be present on the top surface of the first substrate  100 . The second substrate  200  can be a semiconductor chip configured to be mounted on the first substrate  100 . Each array of solder balls  300  can be located on a top surface of a first substrate  100 . Each second substrate  200  can be located on, and over, an array of solder balls  300 . 
     In one embodiment, the bottom surface of the second substrate  200  and the top surface of the first substrate  100  can include a commensurate pattern of bonding pads (not shown) to allow bonding between the first substrate  100  and the second substrate  200  through the array of solder balls  300 . The array of solder balls  300  can be, for example, C 4  balls as known in the art. At this step, the array of solder balls  300  is not bonded to at least one of the first substrate  100  and the second substrate  200 . In one embodiment, the array of solder balls  300  can be bonded to the first substrate  100  and not bonded to the second substrate  200 . In another embodiment, the array of solder balls  300  can be bonded to the second substrate  200  and not bonded to the first substrate  100 . In yet another embodiment, the array of solder balls  300  can be bonded to neither of the first substrate  100  and the second substrate  200 . 
     Each exemplary structure can include a first substrate  100  without a second substrate thereupon, or can include a vertical stack including a first substrate  100  and a second substrate  200 . Each first substrate  100  alone, if a second substrate  200  is not present thereabove, or a combination of a first substrate  100  and a second substrate  200  having an array of solder balls  300  therebetween, is herein referred to as at least one substrate ( 100 ,  200 ). 
     The vacuum carrier further includes a seal plate  500 . The seal plate  500  has at least one opening therein. The number of openings in the seal plate  500  corresponds to the number of stacks of substrates that can be mounted on the base plate  410 . For example, if the base plate is configured to mount N stacks of substrates (in which N is any positive integer), the seal plate  500  can include N openings such that a peripheral portion of the seal plate  500  overlies a peripheral portion of the first substrate  100 . The contiguous periphery of each opening in the seal plate  500  can overlie a first substrate  100  such that, in a top-down view, a set of contiguous edges of the seal plate  500  that define the opening can be entirely within an area defined by a contiguous outer periphery of the first substrate  100 . 
     Vacuum seal elements ( 510 ,  520 ) are employed to provide a vacuum environment that holds the first substrate  100  against the planar top surface of the base plate  410 . The vacuum seal elements ( 510 ,  520 ) can be any mechanical structure that can provide an air-tight seal. For example, the vacuum seal elements ( 510 ,  520 ) can be o-rings or gaskets, and include a material that can withstand a thermal cycling at a reflow temperature of solder balls  300 . A typical reflow temperature is in a range from 200 degrees Celsius to 280 degrees Celsius. If o-rings are employed for the vacuum seal elements ( 510 ,  520 ), the o-rings can be polymer-based o-rings such as Viton™ o-rings or Kalrez™ o-rings. 
     The vacuum seal elements ( 510 ,  520 ) include at least one first vacuum seal element  510  and a second vacuum seal element  520 . The at least one first vacuum seal element  510  is configured to provide a seal between at least one substrate ( 100 ,  200 ) and the seal plate  500  upon mounting of the at least one substrate ( 100 ,  200 ) on the base plate  410 , upon placement of the at least one first vacuum seal element  510  onto the at least one substrate ( 100 ,  200 ) and upon placement of the seal plate  500  upon the at least one first vacuum seal element  510 . The at least one first vacuum seal element  510  can be a single vacuum seal element if only a single first substrate  100  is mounted on the vacuum carrier, or can be a plurality of vacuum seal elements if a plurality of first substrates  100  is mounted on the vacuum carrier. 
     The second vacuum seal element  520  is configured to provide another seal between the base plate  410  and the seal plate  500  upon placement of the second vacuum seal element  520  on the base plate  410  and upon placement of the seal plate  500  upon the second vacuum seal element  520 . During mounting of each first substrate  100 , the first substrate  100  is placed on the planar top surface of the base plate  410 . One of the at least one first vacuum seal element  510  is placed on a top surface of the first substrate  100  such that the placed first vacuum seal element  510  contiguously extends around a periphery of the top surface of the first substrate  100  in a closed shape. As used herein, a closed shape refers to a three-dimensional shape that is topologically homeomorphic to a torus. Before, or after, placement of all of the at least one first vacuum seal elements  510 , the second vacuum seal element  520  is placed on a top surface of the base plate  410 . Finally, the seal plate  500  is placed on top of the at least one first vacuum seal elements  510  and the second vacuum seal element  520 . 
     In one embodiment, the bottom surface of the seal plate  500  can be coplanar across the regions overlying the at least one first vacuum seal element  510  and across regions overlying the second vacuum seal element  520 . For example, the top surface of the base plate  410  on which the second vacuum seal element  520  is placed may protrude above the top surface on which the first substrate  100  is placed as illustrated in  FIGS. 1 and 2 . In one embodiment, the vertical distance between the interface between the second vacuum seal element  520  and the base plate  410  and the interface between the first substrate  100  and the base plate  410  can be substantially the same as the thickness of the first substrate  100 . As used herein, two dimensions are substantially the same if the difference in the two dimensions is less than 1% of the average of the two dimensions 
     In another embodiment, the seal plate  500  can have different bottom surfaces for contacting the at least one first vacuum seal element  510  and for contacting the second vacuum seal element  520 . In this case, the top surface of the base plate  410  on which the second vacuum seal element  520  is placed can be coplanar with the top surface on which the first substrate  100  is placed as illustrated in  FIGS. 3 and 4 . In one embodiment, a first bottom surface of the seal plate overlying the at least one first vacuum seal element could be vertically offset relative to a second bottom surface of the seal plate overlying the second vacuum seal element by an amount substantially the same as the thickness of the first substrate  100 . 
     A cavity  451  can laterally surround each first substrate  100 . Each cavity  451  is enclosed by, and is defined by, the base plate  410 , the seal plate  500 , the at least one first vacuum seal element  510 , and the second vacuum seal element  520 . The cavity  451  can be present around each of the at least one first substrate  100 . Each cavity  451  can be a toroidal cavity, i.e., a cavity that is topologically homeomorphic to a torus. 
     During the operation of the exemplary structures, at least one stack can be mounted on the vacuum carrier. Each of the at least one stack can include a first substrate  100  by itself, or a stack of a first substrate  100 , an array of solder balls  300 , and a second substrate  200 . A partial vacuum can be provided within an enclosure defined by the vacuum carrier and the at least one stack. As used herein, a “partial vacuum” refers to a reduced pressure environment in which the pressure is greater than 0 atmospheric pressure (atm), and is less than 0.6 atmospheric pressure. Each of the at least one first substrate  100  is pushed against a surface of the vacuum carrier by a pressure differential between the partial vacuum and atmospheric pressure. The pressure differential can be in a range from 0.4 atmospheric pressure to 1.0 atmospheric pressure. 
     It is well known that the pressure of an encapsulated volume increases linearly with absolute temperature. If a confined environment is sealed at room temperature (e.g., 20 degrees Celsius), heating up to a temperature around 200 degrees Celsius increases the pressure inside the confined environment by about 60%. In order to prevent the pressure of the confined environment from going above atmospheric pressure at the temperature of a reflow, the confined environment needs to start off at a pressure lower than 0.6 atmospheric pressure at room temperature. 
     All of the above exemplary structures can be connected to a vacuum pump via the sealable pumping port  422  and the orifice  424 . The gas within the vacuum manifold ( 421 ,  431 ,  441 ) and the at least one cavity  451  can be pumped so that a reduced pressure environment is formed within the vacuum manifold ( 421 ,  431 ,  441 ) and the at least one cavity  451 . In one embodiment, the sealable pumping port  422  includes a seal switch configured to isolate the vacuum manifold ( 421 ,  431 ,  441 ) and the at least one cavity  451  from the ambient in which the vacuum carrier is placed. 
     Once the reduced pressure environment is provided within the vacuum manifold ( 421 ,  431 ,  441 ) and the at least one cavity  451 , the seal plate presses against the at least one first vacuum seal element  510  and the second vacuum seal element  520 . The at least one first vacuum seal element  510  provides a seal at each gap between the at least one substrate ( 100 ) and the seal plate  500 . The second vacuum seal element  520  provides another seal between the base plate  410  and the seal plate  500 . Surfaces of the base plate  410  and the seal plate  500  define the outer boundary of a volume in which a vacuum environment is to be formed. 
     While the at least one substrate ( 100 ,  200 ) is pushed against the planar surface of the base plate  410  of the vacuum carrier by a pressure differential between the reduced pressure environment and the ambient at an atmospheric pressure, any of the exemplary structures can be loaded into a bonding apparatus, which can be, for example, an oven or a furnace. 
     An exemplary bonding apparatus is illustrated in  FIG. 5 . The exemplary bonding apparatus can be a furnace including heating means (not shown explicitly). The exemplary bonding apparatus can include an enclosure  600 , which includes enclosure walls  610  and a door  620 , which can be configured to form a sealed volume when the door  620  is shut. The exemplary bonding apparatus can further include a shelf  630  onto which one or more of the exemplary structures of  FIGS. 1-4  can be loaded. Alternatively, the enclosure  600  can be an open-ended system, such as a reflow oven, that is configured to continuously process multiple combinations of a vacuum carrier and a stack of substrates ( 100 ,  200 ) through a reflow process and a subsequent cool down process. 
     The heating means can be any type of heater element known in the art. The heating means can be embedded in the enclosure walls  610  and/or the door  620 , located within the cavity of the enclosure  600 , or located outside the enclosure walls  610  and the door  620 . The heating means is configured to heat structures loaded within the enclosure  600 . Thus, the heating means is configured to heat each stack of a first substrate  100 , an array of solder balls  300 , and a second substrate  200  and a vacuum carrier holding the stack simultaneously. The enclosure  600  is configured to confine heat at least during the bonding process. 
     Bonding between each pair of a first substrate  100  and a second substrate  200  through an array of solder balls  300  within each of the at least one stack is induced within the bonding apparatus by heating a combination of the vacuum carrier and the at least one stack at an elevated temperature. The temperature profile of the bonding process is illustrated in  FIG. 6 . The combination of the vacuum carrier and the at least one stack ( 100 ,  200 ,  300 ) can start at room temperature TR, which refers to a temperature range between 10 degrees Celsius and 30 degrees Celsius. 
     Heating of the combination of the vacuum carrier and the at least one stack ( 100 ,  200 ,  300 ) can be performed by placing the combination within a bonding apparatus such as an oven. Upon loading of the combination of the vacuum carrier and the at least one stack ( 100 ,  200 ,  300 ) into the bonding apparatus, the temperature of the combination of the vacuum carrier and the at least one stack ( 100 ,  200 ,  300 ) can be ramped to a standby temperature TA, which can be lower than the melting temperature of the solder balls  300  by 3-30 degrees. Because each array of solder balls  300  is not bonded to at least one of the underlying first substrate  100  and the overlying second substrate  200 , each first substrate  100  and each second substrate  200  can freely expand laterally during a temperature ramp step of the bonding process during which the temperature of the combination of the vacuum carrier and the at least one stack ( 100 ,  200 ,  300 ) is ramped from room temperature TR to the standby temperature TA. 
     Once the temperature of the combination of the vacuum carrier and the at least one stack ( 100 ,  200 ,  300 ) becomes uniform across the entire of the combination of the vacuum carrier and the at least one stack ( 100 ,  200 ,  300 ), the temperature of the combination of the vacuum carrier and the at least one stack ( 100 ,  200 ,  300 ) can be ramped to a reflow temperature TB, which can be higher than the melting temperature of the solder balls by 1-10 degrees. 
     The temperature of the combination of the vacuum carrier and the at least one stack ( 100 ,  200 ,  300 ) is held at the reflow temperature TB for a duration sufficient to induce reflow of each array of solder balls  300 . Because each first substrate  100  is held flat against the top surface of the base plate  410  of the vacuum carrier by the combination of the differential pressure acting uniformly over the exposed top surface of each first substrate  100  and the seal plate  500  that applies a uniform pressure around the periphery of each first substrate  100 , each first substrate  100  can have a substantially planar top surface at the reflow temperature as illustrated in Inset X. The duration of the reflow process can be in a range from 1 second to 60 seconds, although lesser and greater durations can also be employed. 
     Once each of the at least one stack ( 100 ,  200 ,  300 ) is bonded through the reflow of the solder balls  300  at the reflow step, the combination of the vacuum carrier and the at least one stack ( 100 ,  200 ,  300 ) is cooled to room temperature TR or to a temperature lower than the solidification temperature of the solder. The cooling of each bonded stack ( 100 ,  200 ,  300 ), which is also referred to as a bonded assembly ( 100 ,  200 ,  300 ), can be performed within the bonding apparatus or outside the bonding apparatus. 
     The reduced pressure environment is maintained within the vacuum manifold ( 421 ,  431 ,  441 ) and the at least one cavity  451  at least until the temperature of each bonded assembly ( 100 ,  200 ,  300 ) is lowered to room temperature TR, or to a temperature lower than the solidification temperature of the solder. 
     Since each array of solder balls  300  is bonded to the underlying first substrate  100  and the overlying second substrate  200 , the first and second substrates ( 100 ,  200 ) cannot freely shrink laterally. Instead, the differential between the thermal expansion coefficients of the first and second substrates ( 100 ,  200 ) causes each bonded assembly of a first substrate  100 , a second substrate  200 , and an array of solder balls  300  to warp. This warp is caused by a build up of stresses in the solder balls  300  due to the first and second substrates ( 100 ,  200 ) shrinking at different rates. By warping, the bonded assembly lowers the stresses that would otherwise build-up in the structure if the first and second substrates ( 100 ,  200 ) were not allowed to warp. The vacuum carrier restrains the warping of the stack during cool-down due to the differential pressure pushing the first substrate  100  against the base plate  410 . The vacuum carrier enables a build up of a higher stress in the solder balls  300  relative to methods that allow free bending of a bonded assembly. For those structures that are vulnerable to damage by the extra build-up of stresses, it is beneficial to reduce the differential pressure in the vacuum carrier to the lowest level that is necessary to maintain the flatness of the substrates during reflow. Alternately it may be beneficial to release the vacuum during cool-down at a temperature higher than room temperature provided that the solder balls have resolidified and the stresses have not built-up to a level capable of structurally damaging the bonded assembly. 
     Thus, in one embodiment, the magnitude of the pressure differential between the ambient and the reduced pressure environment can be selected to allow warping of the bonded assembly ( 100 ,  200 ,  300 ) during the cool down step during which the temperature of each bonded assembly ( 100 ,  200 ,  300 ) is lowered to room temperature TR or to a temperature lower than the solidification temperature of the solder. In this case, the bonded assembly ( 100 ,  200 ,  300 ) can warp in a manner illustrated in Inset Y. 
     Use of the partial vacuum allows reduction of the applied force on the bonded assembly ( 100 ,  200 ,  300 ) relative to the force that would be applied to the bonded assembly ( 100 ,  200 ,  300 ) if the vacuum manifold ( 421 ,  431 ,  441 ) and the at least one cavity  451  were in full vacuum, i.e., a vacuum environment in which the total pressure is less than 0.01 atm. In one embodiment, the pressure differential across each first substrate  100  can be in a range from 0.4 atm to 0.55 atm. In yet another embodiment, the pressure differential across each first substrate  100  can be in a range from 0.55 atm to 0.7 atm. In one embodiment, the pressure differential across each first substrate  100  can be in a range from 0.7 atm to 0.9 atm. The selection of the pressure differential between the reduced pressure environment and the atmospheric ambient can be based on the stiffness and the thermal expansion coefficient mismatch between the first substrate  100  and the second substrate within each bonded assembly ( 100 ,  200 ,  300 ), and the magnitude of the maximum allowable stress in the bonded assembly ( 100 ,  200 ,  300 ). The ability to choose the pressure differential between the reduced pressure environment and the atmospheric ambient can be advantageously employed to control the force applied to the bonded assembly ( 100 ,  200 ,  300 ) during the cooling step. 
     It is noted that release of vacuum at a temperature greater than 100 degrees Celsius is typically required in a system employing full vacuum to hold substrates during a bonding process because the force applied to a bonded structure is proportional to the difference between the atmospheric pressure and the full vacuum. Use of partial vacuum allows delayed release of the partial vacuum at least until the temperature of each bonded assembly ( 100 ,  200 ,  300 ) is lowered to room temperature TR or to a temperature lower than 50 degrees Celsius because less force due to the pressure differential is applied to the bonded assembly ( 100 ,  200 ,  300 ) relative to a comparative exemplary system in which full vacuum is employed to hold the substrates. Thus, the release of the partial vacuum can be performed after the bonded assembly ( 100 ,  200 ,  300 ), i.e., the bonded at least one stack, cools to a temperature below the solidification temperature of the solder material of the solder balls  300 . 
     The at least one bonded assembly ( 100 ,  200 ,  300 ) can be dismounted from the vacuum carrier after the cool down step is completed or after the temperature of the at least one bonded assembly ( 100 ,  200 ,  300 ) decreases sufficiently below the solidification temperature of the solder material of the solder balls  300 . The dismounting of the at least one bonded assembly ( 100 ,  200 ,  300 ) can be performed by releasing the partial vacuum. The release of the partial vacuum can be employed, for example, employing a seal switch provided as a component of the sealable pumping port  422 . The seal switch can be configured to release vacuum within the vacuum carrier upon activation of the seal switch. In one embodiment, the release of the partial vacuum can be performed after the at least one stack is taken out of the oven. 
     In one embodiment, the magnitude of the pressure differential can be decreased as a function of time while the bonded assembly ( 100 ,  200 ,  300 ) cools from the elevated temperature. The magnitude of the pressure differential can have an exponential decay as a function of time once the combination of the vacuum carrier and the at least one stack of substrates ( 100 ,  200 ) is disconnected from the vacuum pump. The time constant of the exponential decay can be in a range from 0.5 times the duration of the bonding process (i.e., from the initiation of heating to the end of cooling at which the partial vacuum can be released) to 2 times the duration of the bonding process. For example, the time constant of the exponential decay can be in a range from 5 minutes to 60 minutes. 
     In one embodiment, the leakage path between the enclosure including the partial vacuum and defined by the vacuum carrier and the at least one stack of substrates ( 100 ,  200 ) and the atmospheric ambient at the atmospheric pressure can be provided by a leak valve embedded within the sealable pumping port  422 . In another embodiment, the leakage path can be provided by one or more microscopic grooves and/or rough surfaces of the base plate  410  or the seal plate  500  at which the at least one first vacuum seal element  510  and/or the second vacuum seal element  520  contacts the base plate  410  or the seal plate  520 . 
     The bonding process illustrated in  FIGS. 5 and 6  can be performed employing different types of vacuum carriers. The vacuum carriers in the first through fourth exemplary structures provide sealing between mating surfaces of the at least one first substrate  100  and the vacuum carrier such that no bending force is applied to the first substrate(s)  100  during the reflow process. In case the at least one first substrate  100  includes any resin (as in the case of an organic packaging substrate), the resin in the at least one substrate  100  becomes soft above its glass transition temperature. With the resin in such a soft state, the at least one first substrate  100  can be easily deformed permanently by a small force. Since the effectiveness of seals requires pressure between the sealing material and the mating surfaces, it is important that the pressure be applied in a manner that does not induce deformation in the at least one first substrate  100 . Within the first through fourth exemplary structures, the sealing force is applied on the at least one substrate  100  in a manner that presses the at least one first substrate  100  against the mating surface of the vacuum carrier, thereby eliminating any bending force on the at least one first substrate  100  and preventing deformation of the at least one first substrate  100 .  FIGS. 7 and 8  illustrate fifth and sixth exemplary structures, respectively that can be used for substrates that do not deform easily at reflow temperatures. The base plate  410  can include a recessed surface that is vertically recessed from a planar top surface that contacts the at least one first substrate  100 . A vacuum seal element  530  can be placed between the recessed surface and a periphery of each first substrate  100  to provide a vacuum seal. This placement of the seal element  530  causes an unsupported upward force on the periphery of the at least one first substrate  100 , which could cause deformation for materials that become soft at the reflow temperature. 
       FIGS. 9A ,  9 B,  10 A,  10 B, and  10 C illustrate a seventh exemplary structure including a vacuum carrier and a plurality of substrate stacks ( 100 ,  200 ,  300 ). Each substrate stack ( 100 ,  200 ,  300 ) can include a first substrate  100 , a second substrate  200 , and an array of solder balls  300 . The vacuum carrier in the seventh exemplary structure is configured to hold four substrate stacks ( 100 ,  200 ,  300 ) in a 2×2 configuration. 
       FIG. 10C  provides a magnified view in which recessed regions in the seal plate  500  for accommodating the at least one first vacuum seal element  510  and the second vacuum seal element  520  can be placed. The recessed regions can be grooves that extend along the direction of the at least one first vacuum seal element  510  and the second vacuum seal element  520 . Each groove can have a width that is at least the same as the width of the at least one first vacuum seal element  510  or the width of the second vacuum seal element  520  so that the at least one first vacuum seal element  510  or the second vacuum seal element  520  can fit into the groove. Each groove can have a depth that is less than the height of the at least one first vacuum seal element  510  and the second vacuum seal element  520  so that at least a portion of the at least one first vacuum seal element  510  or the second vacuum seal element  520  protrudes out of the bottom surface of the seal plate  500  (or the topmost surface in an upside-down view such as  FIG. 10C ). 
       FIGS. 11 ,  12 A, and  12 B illustrate an eighth exemplary structure including a vacuum carrier and a plurality of substrate stacks ( 100 ,  200 ,  300 ). Each substrate stack ( 100 ,  200 ,  300 ) can include a first substrate  100 , a second substrate  200 , and an array of solder balls  300 . The vacuum carrier in the eighth exemplary structure is configured to hold four substrate stacks ( 100 ,  200 ,  300 ) in a 1×4 configuration. 
     While the disclosure has been described in terms of specific embodiments, it is evident in view of the foregoing description that numerous alternatives, modifications and variations will be apparent to those skilled in the art. Each of the various embodiments of the present disclosure can be implemented alone, or in combination with any other embodiments of the present disclosure unless expressly disclosed otherwise or otherwise impossible as would be known to one of ordinary skill in the art. Accordingly, the disclosure is intended to encompass all such alternatives, modifications and variations which fall within the scope and spirit of the disclosure and the following claims.