Patent Publication Number: US-11027479-B2

Title: Thermal control mold for making three-dimensional microstructures

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Application No. 62/397,402, filed on Sep. 21, 2016. The entire disclosure of the above application is incorporated herein by reference. 
    
    
     GOVERNMENT CLAUSE 
     This invention was made with government support under grant number W31P4Q-11-1-0002 awarded by the Department of Defense/Defense Advanced Research Projects Agency (DARPA). The government has certain rights in the invention. 
    
    
     FIELD 
     The present disclosure relates to three-dimensional (3-D) microstructures and fabrication processes thereof. 
     BACKGROUND 
     Micro-scale three-dimensional (3-D) shell structures have applications in a variety of areas such as inertial sensors, chemical sensors, biological sensors, and optical components. For example, micro-scale three-dimensional (3-D) shell structures play an important role in the instances of high-performance vibratory gyroscopes. A vibratory gyroscope is a sensor that measures angular speed and angular orientation and may be used in a variety of applications, such as an inertial measurement unit (IMU) for autonomous cars, drones, space satellites, and airplanes in GPS-denied environments. 
     A vibratory gyroscope comprises a vibratory resonator and electrodes configured to actuate and sense the motion of the vibratory resonator. The performance of the vibratory gyroscope, including accuracy and resolution, is heavily dependent on the quality and symmetry of a resonator. For a vibratory gyroscope to obtain high performance, the vibratory resonator comprising the vibratory gyroscope should have a comparatively high mechanical quality factor (Q) and substantial mechanical symmetry. In particular, stiffness and damping constants of the vibratory resonator should be the same along all directions perpendicular to a sensing axis of the vibratory gyroscope. An axisymmetric vibratory resonator comprising materials having low internal energy loss, such as fused silica, is attractive due to its excellent mechanical quality factor (Q) and high structural symmetry. However, such materials, such as fused silica, may be difficult to machine using conventional micromachining techniques. 
     A hemispherical resonator gyroscope (HRG) comprises an axisymmetric shell resonator having a comparatively high mechanical quality factor (Q). The hemispherical resonator gyroscope (HRG) resonator comprises fused silica and has a shape resembling a wineglass (size ˜30 cc). To achieve an improved high mechanical quality factor (Q) (e.g., ˜20 million) and substantially perfect structural symmetry, the hemispherical resonator gyroscope (HRG) resonator is manufactured using precision grinding and polishing processes. However, such manufacturing processes are expensive (&gt;$100,000/unit), slow, and inaccurate for making micro-scale (&lt;1cc) structures. To overcome these challenges, micro-electromechanical system (MEMS) fabrication processes have been used to fabricate micro-scale axisymmetric shell resonators. A micro-electromechanical system (MEMS) process can form highly accurate components at a low cost. However, conventional micro-electromechanical system (MEMS) processes have some disadvantages, such as a limited number of available materials, difficulty in depositing films or substrates with large thicknesses, and forming components with high surface roughness. 
     Three-dimensional (3D) micro-reflowing molding processes provide an attractive alternative. However, three-dimensional (3D) micro-reflowing molding is disadvantaged by dependency on temperature uniformity of the mold and the temperature uniformity of a heating source. More particularly, the uniform distribution of heat from the heat source is dependent on the alignment of the heat source with the mold and the symmetry of the mold itself. Most of the available heating sources (e.g., blowtorch, laser, plasma torch, induction heating) have a fairly non-uniform temperature distribution profile in the radial direction with respect to their center axes. In some instances, uniform heating of the mold can be achieved when a heating source is aligned accurately with the center of the mold. However, the alignment accuracy for achieving the level of symmetry from a reflow molded shell for high-value applications, such as a high-performance vibratory gyroscope, is extremely high (e.g., better than 5 μm). This level of accuracy is comparable with a lithography process and is difficult to obtain using a low-cost fabrication setup. A furnace could be used to uniformly heat the mold. However, it is difficult to apply a large enough pressure gradient for deforming a substrate and to rapidly cool a reflowed shell to prevent the shape of the shell from deviating in a furnace environment. 
     Further, it is difficult to precisely control the temperature of the mold during the reflow process, in part, because of the time required for the mold temperature to reach a steady state (e.g., thermal response time). Such complicates the temperature control of the reflow molding process because the temperature of the mold changes while the substrate is being reflowed. A poorly controlled molding temperature causes shells to have large variations in their sizes and mechanical properties. Thus, there remains a need for microfabrication techniques to fabricate three-dimensional (3D) micro-sensors with reflowable materials having good accuracy. 
     This section provides background information related to the present disclosure, which is not necessarily prior art. 
     SUMMARY 
     This section provides a general summary of the disclosure, and is not a comprehensive disclosure of its full scope or all of its features. 
     In various aspects, the present disclosure provides an exemplary method for fabricating three-dimensional microstructures. The method includes disposing a substantially planar reflow material on a mold having a molding region, a boundary region, and a thermal-isolating region disposed therebetween; heating the reflow material while the reflow material is disposed on the mold; and reflowing the reflow material. The molding region of the mold includes a cavity centered therein, and a protrusion projects upwards from a bottom surface of the cavity. The thermal-isolating region includes at least one pocket that is formed adjacent to and along a perimeter of the cavity of the molding region. The thermal-isolating region divides the thermal masses of the molding region and the boundary region and consequently during heating of the reflow material the molding region has a first temperature that is higher than a second temperature of the boundary region. The reflow material is reflowed towards the bottom surface of the cavity by creating a pressure gradient across the reflow material. The protrusion extending from the bottom surface of the cavity helps to shape the reflow material and thereby to form a three-dimensional microstructure. 
     In one variation, the formed three-dimensional microstructure has a diameter of equal to or less than about 120 cm. 
     In one variation, the thermal resistance within the at least one pocket of the thermal-isolating region is equal to or greater than the thermal resistance of the molding region. 
     In one variation, the thermal resistance of the thermal-isolating region is proportional to 
                   R   3     -     R   2         T   -     D     recess   ⁢           ⁢   2           ,         
where R 3  is an outer radius of the thermal-isolating region, R 2  is an inner radius of thermal-isolating region, T is a thickness of the mold, and D recess2  is a depth of the at least one pocket of the thermal-isolating region.
 
     In one variation, the mold has a geometrical relationship defined by one of [(R 3 −R 2 )/(T−D recess2 )], [(R 2 −R 1 )/D recess1 ], [(R 2 −R 1 )/D recess2 ], or a combination thereof, where R 1  is an outer radius of the cavity of the molding region, R 2  is an inner radius of thermal-isolating region, R 3  is an outer radius of the thermal-isolating region, D recess1  is a depth of the cavity of the molding region, D recess2  is a depth of the at least one pocket of the thermal-isolating region, and T is a thickness of the mold. 
     In one variation, the thermal mass of the molding region is proportional to [(R 2 −R 1 )×D recess1 ] and [(R 2 −R 1 )×D recess2 ], where R 2  is an inner radius of thermal-isolating region, R 1  is an outer radius of the cavity of the molding region, T is a thickness of the mold, D recess1  is a depth of the cavity of the molding region, and D recess2  is a depth of the at least one pocket of the thermal-isolating region. 
     In one variation, the thermal mass of the molding region is proportional to a thermal response time of the molding region. 
     In one variation, the at least one pocket of the thermal-isolating region is a ring shaped recess that surrounds the cavity of the molding region. The ring shaped recess has a first depth that is substantially equal to a second depth of the cavity. 
     In one variation, the at least one pocket of the thermal-isolating region has a first base surface at a first depth that is substantially equal to a second depth of the cavity and at least one through-hole extending through the first base surface and a second base surface of the mold. 
     In one variation, the at least one pocket of the thermal-isolating region includes an array of pockets that are distributed in a substantially uniformed manner around the cavity of the molding region. 
     In one variation, the at least one pocket of the thermal-isolating region includes an array of interdigitated pockets that are distributed in a substantially uniformed manner around the cavity of the molding region. 
     In one variation, the at least one pocket of the thermal-isolating region extends through a base surface of the mold. 
     In one variation, the method further includes controlling the pressure gradient across the reflow material independently from the heating of the reflow material. 
     In one variation, at least one through-hole extends from a bottom surface of the cavity through a base surface of the mold and the method further includes fluidly coupling the at least one through-hole to a pressure source. 
     In one variation, the molding region has a first temperature that is higher than a second temperature of the boundary region. 
     In other aspects, the present disclosure provides a thermal control reflow mold for fabricating three-dimensional microstructures. The thermal control reflow mold includes a first mold component having a first substantially planar surface opposing a second substantially planar surface and comprising a molding region having a cavity substantially centered therewithin and a pillar projecting upwards from a centered bottom surface of the cavity; a boundary region surrounding the molding region; and a thermal-isolating region disposed between the molding region and the boundary region and including at least one pocket formed adjacent to and along a perimeter of the cavity of the molding region and an interior border of the boundary region. The thermal-isolating region divides the thermal masses of the molding region and the boundary region. 
     In one variation, the at least one pocket of the thermal-isolating region is a ring shaped recess that surrounds the cavity of the molding region. The ring shaped recess has a first depth that is substantially equal to a second depth of the cavity. 
     In one variation, the at least one pocket of the thermal-isolating region has a first base surface at a first depth that is substantially equal to a second depth of the cavity and at least one through-hole extending through the first base surface and a second base surface of the mold. 
     In one variation, the at least one pocket of the thermal-isolating region includes an array of pockets that are distributed in a substantially uniformed manner around the cavity of the molding region. 
     In one variation, the at least one pocket of the thermal-isolating region includes an array of interdigitated pockets that are distributed in a substantially uniformed manner around the cavity of the molding region. 
     In one variation, the at least one pocket of the thermal-isolating region extends through a base surface of the mold. 
     In one variation, the thermal control reflow mold further comprises a second mold and a substrate to be molded is disposed between the first mold and the second mold. 
     In other aspects, the present disclosure provides a mold for fabricating three-dimensional microstructures. The mold includes a molding region having a cavity formed therewithin and a projection projecting upwards from a bottom surface of the cavity; a boundary region surrounding the molding region; and a thermal-isolating region disposed between the molding region and the boundary region and including at least one pocket formed adjacent to and along a perimeter of the cavity of the molding region. The molding region has a first temperature higher than a second temperature of the boundary region. 
     In one variation, the thermal-isolating region divides thermal masses of the molding region and the boundary region and controls varying thermal resistances therebetween. 
     In one variation, a thermal resistance of the thermal-isolating region is proportional to 
                   R   3     -     R   2         T   -     D     recess   ⁢           ⁢   2           ,         
where R 3  is an outer radius of the thermal-isolating region, R 2  is an inner radius of thermal-isolating region, T is a thickness of the mold, and D recess2  is a depth of the at least one pocket of the thermal-isolating region.
 
     In one variation, the mold has a geometrical relationship defined by one of [(R 3 −R 2 )/(T−D recess2 )], [(R 2 −R 1 )/D recess1 ], [(R 2 −R 1 )/D recess2 ], or a combination thereof, where R 1  is an outer radius of the cavity of the molding region, R 2  is an inner radius of thermal-isolating region, R 3  is an outer radius of the thermal-isolating region, D recess1  is a depth of the cavity of the molding region, D recess2  is a depth of the at least one pocket of the thermal-isolating region, and T is a thickness of the mold. 
     In one variation, a thermal mass of the molding region is proportional to [(R 2 −R 1 )×D recess1 ] and [(R 2 −R 1 )×D recess2 ], where R 2  is an inner radius of thermal-isolating region, R 1  is an outer radius of the cavity of the molding region, T is a thickness of the mold, D recess1  is a depth of the cavity of the molding region, and D recess2  is a depth of the at least one pocket of the thermal-isolating region. 
     Further areas of applicability will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure. 
    
    
     
       DRAWINGS 
       The drawings described herein are for illustrative purposes only of selected embodiments and not all possible implementations, and are not intended to limit the scope of the present disclosure. 
         FIGS. 1A-1D  illustrate an example reflow molding technique for fabricating three-dimensional microstructures. 
         FIGS. 2A-2B  illustrate an example reflow mold having a molding region and a boundary region for use in the fabrication of three-dimensional microstructures, for example, in accordance with the processes illustrated in  FIGS. 1A-1D .  FIG. 2A  is a top-down view of the reflow mold and  FIG. 2B  is a side-view of the reflow mold. 
         FIG. 3A-3C  illustrates an example thermal control reflow mold for fabricating three-dimensional microstructures having a thermal-isolating region disposed between a molding region and a boundary region.  FIG. 3A  is a perspective view of the thermal control reflow mold;  FIG. 3B  is a side-view of the mold; and  FIG. 3C  is a top-down view of the mold. 
         FIG. 4A  illustrates an equivalent electrical circuit representation of the reflow molding process using the thermal control mold illustrated in  FIGS. 3A-3B . 
         FIG. 4B  illustrates the electrical circuitry of the equivalent electrical components of  FIG. 4A . 
         FIG. 5  illustrates a thermal control reflow mold having multiple sub-molds, where each sub-mold includes a molding region, a boundary region, and a thermal-isolating region disposed therebetween. 
         FIGS. 6A-6B  illustrate another example thermal control reflow mold, wherein the thermal-isolating region includes a plurality of pockets distributed around the molding region, the pockets having a depth equal to the depth of the cavity of the molding region.  FIG. 6A  is a top-down view of the thermal control mold, and  FIG. 6B  is a side-down view of the mold. 
         FIGS. 7A-7B  illustrate another example thermal control reflow mold, wherein the thermal-isolating region includes a plurality of pockets distributed around the molding region, the pockets extending through a bottom surface of the thermal control reflow mold.  FIG. 7A  is a top-down view of the thermal control mold, and  FIG. 7B  is a side-down view of the thermal control reflow mold. 
         FIGS. 8A-8B  illustrate another example thermal control reflow mold, wherein the thermal-isolating region includes a plurality of pockets distributed around the molding region and a through-hole extending from each pocket through a bottom surface the thermal control reflow mold.  FIG. 8A  is a top-down view of the thermal control mold, and  FIG. 8B  is a side-down view of the mold. 
         FIGS. 9A-9B  illustrate another example thermal control reflow mold, wherein the thermal-isolating region includes a substantially uniformed polygonal-shaped recess around the molding region.  FIG. 9A  is a top-down view of the thermal control mold, and  FIG. 9B  is a side-down view of the mold. 
         FIGS. 10A-10B  illustrate another example thermal control reflow mold, wherein the thermal-isolating region includes an array of interdigitated pockets around the molding region, the interdigitated pockets extending through a bottom surface of the thermal control reflow mold.  FIG. 10A  is a top-down view of the thermal control mold, and  FIG. 10B  is a side-down view of the mold. 
     
    
    
     Corresponding reference numerals indicate corresponding parts throughout the several views of the drawings. 
     DETAILED DESCRIPTION 
     The present disclosure will now be described with reference to the accompanying drawings. 
     The present disclosure provides a mold having substantially complete symmetry and uniformity for low-cost reflow molding of a substrate into a variety of complex three-dimensional (3-D) microstructures. More particularly, the reflow molding process described herein uses a thermal control mold comprising a molding region, a boundary region, and a thermal-isolating region positioned therebetween. In various aspects, the mold may be used for the fabrication of a micro-scale shell resonator having an improved quality factor (Q) for a high-performance vibratory gyroscope. While reference is made throughout this disclosure to gyroscopes, it is understood that the fabrication techniques described herein may be used to construct microstructures for use in a variety of other applications such as RF filters, RF resonators, RF switches, physical sensors and actuators, optical sensors and actuators, chemical sensors, gas sensors, biological sensors and actuators, or combinations thereof. 
     By way of non-limiting background,  FIGS. 1A-1D  depict a general reflow molding process for molding a micro-birdbath shell. A detailed description of the depicted reflow molding process is provided in pending U.S. patent application Ser. No. 14/985,859, the disclosure of which is incorporated herein by reference. 
       FIG. 1A  illustrates a mold  30  comprising a top or first mold  10  member or portion and a bottom or second mold  12  member or portion having a first substantially planar surface  21  opposing a first substantially planar surface  23  of the top mold  10 . The first and second mold members  10 ,  12  are formed by machining recesses within substrates and comprise materials having melting temperatures higher than the softening temperature of a substrate material or materials  20  to be reflowed. The top mold  10  has a through-hole  14 . The bottom mold  12  has a cylindrical recess or cavity  16 , a pillar  18  extending from a bottom surface  17  of the cavity  16 , and one or more through-holes  19  defined in the bottom surface  17  of the cavity  16 . 
     As seen in  FIG. 1B , the material or substrate  20  to be reflowed is disposed on the first substantially planar surface  21  of the bottom mold  12  and fixed to the bottom mold member  12  using the top mold  10  to press thereagainst. In other embodiments, the substrate  20  may be fixed to the bottom mold member  12  by applying a vacuum pressure inside the cavity  16  thereby creating a downward pressure on the thermally-reflowable substrate  20 . For example, the through-holes  19  may be fluidly coupled to a vacuum that creates a negative pressure between the bottom surface  17  of the cavity  16  and the substrate  20 . In such instances, the top mold member  10  may not be needed. 
     As seen in  FIG. 1C , a heating source (e.g., fuel-oxygen blowtorch)  24  is used to heat the substrate  20  above its softening temperature. The reflow molding occurs either above the glass transition (T g ) for non-crystalline material or above the melting point (T M ) of the source material (e.g., quartz)  20 . A vacuum pressure is applied inside the cavity  16  between the substrate  20  and the bottom surface  17  of the bottom mold member  12  creating a pressure gradient across the substrate  20 . The pressure of the cavity  16  below the substrate  20  (P cavity ) is made lower than the ambient pressure (P ambient ) outside the cavity  16 . The softened substrate is reflowed down into the cavity  16  and toward the bottom surface  11  of the bottom mold member  12  as a result of the downward pressure gradient generated across the substrate  20 . The substrate  20  either partially or negligibly touches the upper corners of the sidewalls  25  forming the cavity  16  and the sidewalls  26  forming the pillar  18 . The substrate  20  is deformed into the shape of a birdbath (or a hemi-toroidal) shell  28 . As seen in  FIG. 1D , the shell  28  is cooled down below the softening temperature and subsequently separated from the molds  10  and  12 . 
     As seen in  FIGS. 2A-2B , mold  30  can be divided into two regions: a molding region  32  and a boundary region  34 .  FIG. 2A  illustrates a top view of mold  30 , and  FIG. 2B  illustrates a cross-sectional view of mold  30 . Reflow molding takes place in the molding region  32 , the hottest part of the mold  30 . The molding region  32  includes the middle pillar  18 , cavity  16 , and through-hole  19  of the bottom mold member  12  and the through-hole  14  of the top mold member  10 . The boundary region  34  surrounds the molding region  32  and may have a controlled temperature lower than that of the molding region  32  (e.g., below the softening temperature of the reflow material  20 ). 
     The symmetry of a molded shell  28  is affected by both the symmetry and the temperature uniformity of the mold  30 . Asymmetry of a mold  30  can be reduced to a negligible level when the mold  30  is made using a precision machining technique, such as micro-milling and a combination of lithography and etching. However, these techniques are prohibitedly expensive. Most commonly, the most dominant cause of structural asymmetry is non-uniform temperature distribution near the upper corners  27 A and  27 B of the sidewalls  25  of the recess  16 . The upper corner regions  27 A and  27 B may touch the substrate  20  and control its local temperatures. Viscosity of a material near its softening temperature strongly depends on temperature and non-uniform temperature distribution at the upper corners  27 A and  27 B can cause imperfections in the local viscosities of the substrate  20  in this region causing the substrate  20  to deform by different amounts ultimately forming an asymmetrically-shaped shell  28 . Further, the corners  27 A and  27 B of the sidewalls  25  of the mold  30  are located near the rim of the formed birdbath shell resonator  28 . The mechanical properties of a shell resonator  28  (e.g., stiffness and damping constants) are dependent on rim geometry because this region has the highest mechanical energy density when a resonator vibrates. Therefore, in order to create a highly symmetric shell  28 , it is crucial that the temperatures in the upper corners of the sidewalls of the mold be kept uniform. 
     The present disclosure uses a thermal control mold comprising a molding region, a boundary region, and a thermal-isolating for low-cost reflow molding of a substrate into a variety of complex three-dimensional (3-D) microstructures. The thermal control reflow mold of the present disclosure optimizes or improves the temperature uniformity and controllability of the reflow molding process.  FIGS. 3A-3C  illustrates an example thermal control reflow mold  50  for fabricating three-dimensional microstructures (not shown) having a thermal-isolating region  56  disposed between a molding region  52  and a boundary region  54 . The thermal control reflow mold  50  has a substantially planar first or top surface  60  opposing a substantially planar second or bottom surface  61 . 
     The molding region  52  is configured to form three-dimensional micro-birdbath shells  69  by reflow molding. However, it is recognized that the molding region  52  of the thermal control reflow mold  50  may take a variety of other shapes. The teachings herein should not be limited to the shape or shapes presently illustrated. In accordance with various aspects of the present disclosure, molding region  52  includes a cavity  58  formed into the top surface  60  of the thermal control reflow mold  50  and a pillar or protrusion  62  formed therewithin. The pillar  62  extends from a bottom surface  64  of the molding region  52  towards the top surface  60  of the thermal control reflow mold  50 . One or more through-holes  65  may be formed in the bottom surface  64  of the molding region  52 . The molding region  52  is used in conjunction with a heating source  80  to heat and mold a substrate or powder  20  into two or three dimensional microstructures  69  at a temperature above the substrates  20  reflowing temperature. 
     The thermal-isolating region  56  defines one or more pockets or recesses  66  formed into the top surface  60  of the thermal control reflow mold  50  that increase a distance between the molding region  52  and the boundary region  54  of the thermal control reflow mold  50  and thereby reduces contact between the same. In the present illustration, a pocket  66  extends along a perimeter  72  of the molding region  52  and an interior border  74  of the boundary region  54 . However, it is recognized that the thermal-isolating region  56  may take a variety of other shapes, including for example recesses or through-holes having circular, partially circular, polygonal, or partially polygonal top or bottom sides and cross-sections, or a combination thereof. The teachings herein should not be limited to the shape or shapes presently illustrated. In accordance with various aspects of the present disclosure, the thermal-isolating region  56  comprises pocket  66  having a cylindrical or ring shape and that surrounds the molding region  52  forming a cylindrical wall  68  between the pocket  66  and the cavity  58 . The boundary region  54  is the region that surrounds the thermal-isolating region  56 . The temperature of the boundary region  54  is lower than that of the molding region  52 , and the thermal-isolating region  56  controls the thermal conductivity between the molding region  52  and the boundary region  54 . 
     The thermal-isolating region  56  controls the thermal resistance between the molding region  52  and the boundary region  54 . More particularly, the thermal resistance within the pocket  66  of the thermal-isolating region  56  is greater than the thermal resistance within the molding region  52 . The heat provided by the heat source  80  to the molding region  52  is stored or retained in the molding region  52  and not dissipated to the boundary region  54  because the pocket  66  of the thermal-isolating region  56  effectively divides the thermal masses of the molding region  52  from the boundary region  54 . Thus, heat flowing from the molding region  52  into the thermal-isolating region  56  is neutralized allowing the molding region  52  to achieve temperature uniformity when the mold  50  is not heated uniformly. 
     As seen in  FIG. 4A , during the reflow molding process, similar to the reflow molding process illustrated in  FIGS. 1A-1D , a substrate  67  is disposed on the first surface  60  of the thermal control reflow mold  50 . The disposed substrate  67  extends across the molding region  52 , the thermal-isolating region  56 , and the boundary region  54 . A heat source  80  is subsequently brought close to the molding region  52  and a vacuum pressure applied inside the cavity  58  between the substrate  67  and the bottom surface  64  thereof. The softened substrate  67  reflows down into the cavity  58  toward the bottom surface  64  and deforms into the shape of the thermal control reflow mold  50 . The deformed substrate  67  may be trimmed or removed to form the desired final three-dimensional (3-D) microstructure  69 . 
     The symmetry of a shell  69  formed using the thermal control reflow mold  50  is controlled or regulated by the thermal resistance of the thermal-isolating region  56 . More particularly, in the example embodiment as seen in  FIG. 3B , R anchor  is the outer radius of the pillar  62  of the molding region  52 . The pillar  62  and molding region each have a cylindrical shape. R 1  is the outer radius of the cavity  58  of the molding region  52 . The cavity  58  has a cylindrical shape. R 2  is the inner radius of thermal-isolating region  56 , and R 3  is the outer radius of the thermal-isolating region  56 . The thermal-isolating region  56  has a ring or cylindrical shape. D recess1  is the depth of cavity  58  of the molding region  52 , and D recess2  is the depth of the pocket  66  of the thermal-isolating region  56 . As seen in  FIG. 4A , the geometry of the shell  69  is determined by the R 1  and R anchor , while the symmetry of the shell is controlled by the thermal resistance of the thermal-isolating region  56 . The thermal resistance of the thermal-isolating region  56  is proportional to 
                   R   3     -     R   2         T   -     D     recess   ⁢           ⁢   2           ,         
where T is the thickness of the thermal control reflow mold  50 . The thermal mass of the molding region  52  is proportional to (R 2 −R 1 )×D recess1  and (R 2 −R 1 )×D recess2 . Thus, the dimensions and symmetry of the reflow-molded shell  69  can be independently controlled.
 
     The temperature distribution and heat flow characteristics of thermal control reflow mold  50  can be further characterized using an equivalent electrical circuit model. For example, as seen in  FIG. 4A , the heat source  80  may be a blowtorch  81  having an imperfect temperature distribution profile and modeled as a perfect single-point heat source misaligned from the center of the mold  50 . It is recognized that a variety of other heat sources  80  may be employed in conjunction with the present disclosure, including for example only fuel-oxygen blowtorch, plasma torch, laser heating, resistive heating, induction heating, or combinations thereof. The blowtorch  81  discussion herein is understood to be illustrative and not limiting of the potential heat sources  80 . 
     The misalignment between the heat source  80  and the center of the mold  50  is modeled using two resistors (R AirR  and R AirL ) between the blowtorch  81  and the opposing upper corners  70 A and  70 B of the cylindrical walls  68 . R AirR  and R AirL  are inversely proportional to the distance between the blowtorch  81  and respective mold  50  regions. The blowtorch  80  is modeled as a DC voltage source having a voltage V Blowtorch . The thermal resistance between the molding region  52  and the thermal-isolating region  56  is modeled as R Mold-Isolate  and the thermal mass between the molding region  52  and the thermal-isolating region  56  is modeled as C Mold-Isolate . R Mold-Isolate  is inversely proportional to the thickness of the cylindrical wall  68  and proportional to the height of the cylindrical wall  68   
               (     ∝         D     recess   ⁢           ⁢   1           R   2     -     R   1         ⁢           ⁢   and   ⁢           ⁢       D     recess   ⁢           ⁢   2           R   2     -     R   1             )     .         
C Mold-Isolate  is proportional to the mass of the cylindrical wall  68  (≥(R 2 −R 1 )×D recess1  and (R 2 −R 1 )×D recess2 ). The thermal resistance between the opposing upper corners  70 A and  70 B of the cylindrical wall  68  is modeled as R Mold-Mold  and the thermal mass between the upper corners  70 A and  70 B of the cylindrical wall  68  is modeled as C Mold-Mold . R Mold-Mold  is proportional to the average radius of the cylindrical wall  68  and inversely proportional to thickness and height (e.g., D recess1 ; D recess2 ) of the cylindrical wall  68 
 
               (     ∝           R   1     +     R   2           (       R   2     -     R   1       )     ⁢     D     recess   ⁢           ⁢   1           ⁢           ⁢   and   ⁢           ⁢         R   1     +     R   2           (       R   2     -     R   1       )     ⁢     D     recess   ⁢           ⁢   2               )     .         
C Mold-Mold  is proportional to the mass of the cylindrical wall  68  (∝(R 2 −R 1 )×D recess1  and (R 2 −R 1 )×D recess2 ). The thermal resistance between the molding region  52  and the boundary region  54  is modeled as R isolate . R isolate  is proportional to the width and inversely proportional to a bridge between the molding region  52  and the boundary region  54 
 
     
       
         
           
             
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             . 
           
         
       
     
       FIG. 4B  illustrates the electrical circuitry of the equivalent electrical components of  FIG. 4A . The voltage of nodes V Mold_R  and V Mold_L  represent the temperatures of the respective corners  70 A and  70 B of the cylindrical wall  68 . The non-uniformity in temperature in these regions is proportional to V Mold_R  V Mold_L . The current that flowing from the DC source, voltage V Blowtorch  (=(i Blowtorch ), is proportional to the total amount of heat provided by the blowtorch  80 . 
     Table 1 below summarizes the equivalent electrical components and relationship of the components to the physical parameters of the blowtorch molding setup of  FIG. 4A . 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Summarizing Table of Electrical Components 
               
            
           
           
               
               
               
            
               
                   
                 Equivalent 
                   
               
               
                   
                 Circuit 
                 Relationship to 
               
               
                 Parameter 
                 Representation 
                 Physical Dimensions 
               
               
                   
               
               
                 Temperature of blowtorch 
                 V Blowtorch   
                 ∝ Temperature of blowtorch 
               
               
                 Thermal resistance 
                 R AirR   
                 ∝ (Distance between the 
               
               
                 between blowtorch and 
                   
                 blowtorch 81 and the upper 
               
               
                 upper right corner of wall 
                   
                 corner 70B of the cylindrical 
               
               
                   
                   
                 wall 68) −1   
               
               
                 Thermal resistance 
                 R AirL   
                 ∝ (Distance between 
               
               
                 between blowtorch and 
                   
                 blowtorch 81 and the 
               
               
                 upper left corner of wall 
                   
                 uppercorner 70A of the 
               
               
                   
                   
                 cylindrical wall 68) −1   
               
               
                 Thermal resistance 
                 R Mold-Isolate   
                 ∝ D recess1 /(R 2  − R 1 ) &amp; 
               
               
                 between molding region to 
                   
                 D recess2 /(R 2  − R 1 ) 
               
               
                 thermal-isolating region 
                   
                   
               
               
                 Thermal mass between 
                 C Mold-Isolate   
                 ∝ (R 2  − R 1 ) × D recess1  &amp; 
               
               
                 molding region to 
                   
                 (R 2  − R 1 ) × D recess2   
               
               
                 thermal-isolating region 
                   
                   
               
               
                   
               
               
                 Thermal resistance between the two upper corners of the wall 
                 R Mold-Mold   
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   ∝ 
                                   
                                     
                                       
                                         R 
                                         1 
                                       
                                       + 
                                       
                                         R 
                                         2 
                                       
                                     
                                     
                                       
                                         ( 
                                         
                                           
                                             R 
                                             2 
                                           
                                           - 
                                           
                                             R 
                                             1 
                                           
                                         
                                         ) 
                                       
                                       ⁢ 
                                       
                                         D 
                                         
                                           recess 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           1 
                                         
                                       
                                     
                                   
                                 
                                 &amp; 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     R 
                                     1 
                                   
                                   + 
                                   
                                     R 
                                     2 
                                   
                                 
                                 
                                   
                                     ( 
                                     
                                       
                                         R 
                                         2 
                                       
                                       - 
                                       
                                         R 
                                         1 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     D 
                                     
                                       recess 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                   
                                 
                               
                             
                           
                         
                           
                       
                     
                   
                 
               
               
                   
               
               
                 Thermal capacitance 
                 C Mold-Mold   
                 ∝ (R 2  − R 1 ) × D recess1  &amp; 
               
               
                 between the two upper 
                   
                 (R 2  − R 1 ) × D recess2   
               
               
                 corners of the wall 
                   
                   
               
               
                 Thermal resistance 
                 R Isolate   
                 ∝ (R 3  − R 2 )/(T − D recess2 ) 
               
               
                 between molding and 
                   
                   
               
               
                 boundary regions 
               
               
                   
               
            
           
         
       
     
     When a mold is heated uniformly, the same amount of heat is provided from the blowtorch  81  to both upper corners  70 A and  70 B of the cylindrical wall  68  and R AirR =R AirL . When a mold  50  is perfectly symmetrical, R Mold-Isolate , C Mold-Isolate , and R Mold-Isolate  connected to both the upper corner  70 B of the cylindrical wall  68  (i.e., node R) and the upper corner  70 A of the cylindrical wall  68  (i.e., node L) are the same and V Mold_R =V Mold_L . The temperatures of the opposing upper corners  70 A and  70 B are the same and the shell  69  formed using reflow molding can have perfect symmetry. 
     Typically, however the mold  50  is heated non-uniformly and different amounts of heat arrive from the blowtorch  81  to the upper corners  70 A and  70 B of cylindrical wall  68  and R AirR ≠R AirL . An approximate solution for |V Mold_R −V Mold_L | is found to be: 
     
       
         
           
             
                
               
                 
                   V 
                   
                     Mold 
                     ⁢ 
                     _ 
                     ⁢ 
                     R 
                   
                 
                 - 
                 
                   V 
                   
                     Mold 
                     ⁢ 
                     _ 
                     ⁢ 
                     L 
                   
                 
               
                
             
             ≈ 
             
               
                 
                    
                   
                     
                       R 
                       AirR 
                     
                     - 
                     
                       R 
                       AirL 
                     
                   
                    
                 
                 ⁢ 
                 
                   V 
                   Blowtorch 
                 
               
               
                 ( 
                 
                   
                     R 
                     
                       Mold 
                       - 
                       Isolate 
                     
                   
                   + 
                   
                     R 
                     Isolate 
                   
                 
                 ) 
               
             
           
         
       
     
     Thus, for a given |R AirR −R AirL |, a smaller |V Mold_R −V Mold-L | can be achieved by increasing R Mold-Isolate +R isolate . More particularly, as R Mold-Isolate +R Isolate  increases it becomes increasingly easier for electrical current to flow from Node R to Node L or vice versa if there is a voltage difference between these nodes. The current that flows across the nodes reduces the voltage difference. In other words, when the thermal resistance at the thermal-isolating region  56  (R Mold-Isolate ) is raised more heat flows across locally hot regions to locally cold regions within the molding region  52  to neutralize the temperatures differences. 
     The geometry of the thermal control reflow mold  50  controls the geometry of the reflow-molded shell  69  and the rigidity and durability of the thermal control reflow mold  50 . Increases in the thermal resistance of the thermal isolating region  56  and reductions in the mass of the molding region  52  improve the structural symmetry of the reflow-molded shell  69 . Reductions in the mass of the molding region  52  improve the structural symmetry of the reflow-mold shell  69  by decreasing the time required to reach a steady-state temperature value. Thus, the improved symmetry of the reflow-molded shell  69  occurs when [(R 3 −R 2 )/(T−D recess2 )] increases and [(R 2 −R 1 )×D recess1 ] or [(R 2 −R 1 )×D recess2 ] decreases. 
     The height of a reflow-molded shell  69 , when under a same applied heat, pressure gradient, and molding duration, decreases as the thermal resistance of the thermal-isolating region  56  increases (e.g., ∝(R 3 −R 2 )/(T−D recess2 )) and the mass of the molding region  52  decreases (e.g., ∝[(R 2 −R 1 )×D recess1 ] and [(R 2 −R 1 )×D recess2 ]) because the temperature of the molding region  52  reaches a temperature that is closer to the temperature of the reflow-molded substrate  67 . Conversely, the temperature of a reflow-molded substrate near a molding region is generally higher than the temperature of the molding region of the mold because the substrate is located closer to the heat source. As the temperature difference between the reflow-molding substrate  67  and the molding region  52  decreases, the substrate  67  reflows at a closer distance to the molding region  52  because the amount of thermal energy transferred from the reflow-molding substrate  37  to the molding region  52  through thermal conduction, convection, and radiation decreases. The temperature of the reflow-molding substrate  67  is maintained above its glass transition temperature when the substrate  67  reflows closer to the molding region  52 . As a result the amount of friction between the shell  69  and the mold  50  increases and the height of the shell  69  decreases. The height of the shell  69  may be increased by increasing the amount of heat applied by the heat source  80 , the pressure gradient across the shell  69 , and the duration of reflow molding. However, the applied heat need be maintained so the substrate  67  does not become uncontrollably soft and the pressure gradient maintained so the shell  69  is not inadvertently deformed. 
     The rigidity and durability of the mold  50  decreases with an increase in the thermal resistance of the thermal-isolating region  56  and a decrease in the mass of the molding region  52  (e.g., (cc [(R 2 −R 1 )×D recess1 ] and [(R 2 −R 1 )×D recess2 ]). For a mold comprising graphite having a particle size of less than 100 μm, geometrical parameters of the mold can result in a tall, symmetric shell where [(R 3 −R 2 )/(T−D recess2 )] is equal to about 0.001-100 and [(R 2 −R 1 )/D recess1 ] or [(R 2 −R 1 )/D recess2 ] are equal to about 0.001-100. 
     While mold  50  illustrated in  FIGS. 3A-4A  is configured to form one shell  69 , a mold  100  can have a plurality of sub-mold patterns  102  for reflow molding multiple shells (not shown). For example,  FIG. 5  illustrates a mold  100  comprising a plurality of sub-mold patterns  102  each having a molding region  104 , a boundary region  106 , and a thermal-isolating region  108  disposed therebetween as described above. In various aspects, the mold  100  may create multiple shells simultaneously from a single substrate that extends across the sub-mold patterns  102 . 
     As noted above, the thermal-isolating region (e.g.,  56 ,  108 ) may take a variety of configurations. The configuration of the thermal-isolating region including recesses therein controls or regulates the thermal conductivity between the molding region (e.g.  52 ,  104 ) and boundary region (e.g.,  54 ,  106 ). 
     For example,  FIGS. 6A-6B  illustrate a thermal control reflow mold  120  comprising a molding region  122 , a boundary region  124 , and a thermal-isolating region  126  disposed therebetween. The thermal-isolating region  126  has an array of pockets or circular recesses  128  evenly distributed around the molding region  122 . The pockets  128  of the thermal-isolating region  126  have a first depth  132  substantially equal to a second depth  131  of the cavity  130  of the molding region  122 . 
       FIGS. 7A-7B  illustrate a thermal control reflow mold  134  having a first or top surface  146  opposing a second or bottom surface  144  and comprising a molding region  136 , a boundary region  138 , and thermal-isolating region  140  disposed therebetween. The thermal-isolating region  140  has an array of pockets  142  evenly distributed to surround the molding region  136  that extend through the bottom or base surface  144  of the thermal control reflow mold  134 . 
       FIGS. 8A-8B  illustrate a thermal control reflow mold  150  having a first or top surface  152  opposing a second or bottom surface  154  and comprising a molding region  156 , a boundary region  158 , and a thermal-isolating region  160  disposed therebetween. The thermal-isolating region  160  has an array of pockets  162  evenly distributed to surround the molding region  156 . Each pocket  162  has a first depth  167  substantially equal to a second depth  168  of a cavity  165  of the molding region  156 . The thermal-isolating region  160  further includes a through-hole  164  extending from a base or bottom surface  166  of the pocket  162  through the bottom surface  154  of the mold  150 . 
       FIGS. 9A-9B  illustrate a thermal control reflow mold  170  comprising a molding region  172 , a boundary region  174 , and a thermal-isolating region  176  disposed therebetween. The thermal-isolating region  176  comprises a substantially uniformed polygonal-shaped recess or pocket  177  that surrounds the molding region  156 . The polygonal-shaped pocket  177  has a first depth  173  substantially equal to a second depth  175  of a cavity  178  of the molding region  172 . 
       FIGS. 10A-10B  illustrate a thermal control reflow mold  180  having a first or top surface  190  opposing a second or bottom surface  192  and comprising a molding region  182 , a boundary region  184 , and a thermal-isolating region  186  disposed therebetween. The thermal-isolating region  186  has an array of interdigitated pockets  188  that extend through the bottom surface  192  of the mold. The pockets  188  are arranged to form a first surrounding region  194  and a second surrounding region  196 . The first surrounding region  194  is positioned between the molding region  182  and the second surrounding region  196 . 
     In each example embodiment, the thermal control reflow molds of the present disclosure have a thermal-isolating region configured to control the thermal resistance across the molding region (e.g., a region where reflow molding takes place) and the boundary region (e.g., a region whose temperature is kept lower than that of the molding region). The thermal resistance in the thermal-isolating region is high to prevent heat dissipation from the molding region to the boundary region. Specifically, the thermal-isolating region forms a barrier to store a large amount of heat within the molding region and to neutralize the temperature within the molding region. The molding region therefore obtains high temperature uniformity when the mold is heated non-uniformly. Also, the thermal-isolating region controls the thermal mass of the molding region, such that the thermal mass is lowered to reduce the thermal response time of the molding region, thus improving the temperature controllability of the molding region. 
     The thermal control reflow mold design of the present disclosure can be used to create a wide variety of three-dimensional microstructures. 
     The foregoing description of the embodiments has been provided for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but, where applicable, are interchangeable and can be used in a selected embodiment, even if not specifically shown or described. The same may also be varied in many ways. Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure. 
     Example embodiments are provided so that this disclosure will be thorough, and will fully convey the scope to those who are skilled in the art. Numerous specific details are set forth, such as examples of specific components, devices, and methods, to provide a thorough understanding of embodiments of the present disclosure. It will be apparent to those skilled in the art that specific details need not be employed, that example embodiments may be embodied in many different forms, and that neither should be construed to limit the scope of the disclosure. In some example embodiments, well-known processes, well-known device structures, and well-known technologies are not described in detail. 
     The terminology used herein is for the purpose of describing particular example embodiments only, and is not intended to be limiting. As used herein, the singular forms “a,” “an,” and “the” may be intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms “comprises,” “comprising,” “including,” and “having,” are inclusive and therefore specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. The method steps, processes, and operations described herein are not to be construed as necessarily requiring their performance in the particular order discussed or illustrated, unless specifically identified as an order of performance. It is also to be understood that additional or alternative steps may be employed. 
     Although the terms first, second, third, etc. may be used herein to describe various elements, components, regions, layers, and/or sections, these elements, components, regions, layers, and/or sections should not be limited by these terms. These terms may only be used to distinguish one element, component, region, layer, or section from another region, layer, or section. Terms such as “first,” “second,” and other numerical terms when used herein do not imply a sequence or order unless clearly indicated by the context. Thus, a first element, component, region, layer, or section discussed below could be termed a second element, component, region, layer, or section without departing from the teachings of the example embodiments. 
     Spatially relative terms, such as “inner,” “outer,” “beneath,” “below,” “lower,” “above,” “upper,” and the like, may be used herein for ease of description to describe one element or feature&#39;s relationship to another element(s) or feature(s) as illustrated in the figures. Spatially relative terms may be intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the example term “below” can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations), and the spatially relative descriptors used herein interpreted accordingly.