PATENT DOCUMENT

Publication Number: US-9705432-B2
Application Number: US-201414503065-A
Country: US
Kind Code: B2

Title: Micro pick up array pivot mount design for strain amplification

Abstract:
Systems and methods for aligning a transfer head assembly with a substrate are disclosed. In an embodiment a pivot mount is used for generating a feedback signal in a closed-loop motion control system. In an embodiment, the pivot mount includes primary spring arms and secondary spring arms extending between a pivot platform and a base of the pivot mount. The secondary spring arms are characterized by a lower stiffness than the primary spring arms, and strain sensing elements are located along the secondary spring arms.

Claims:
What is claimed is: 
     
       1. A pivot mount comprising:
 a pivot platform; 
 a base; 
 a primary spring arm fixed to the pivot platform at a primary inner root, fixed to the base at a primary outer root, and characterized by a corresponding primary axis length spanning between the primary outer root and primary inner root; and 
 a secondary spring arm fixed to the pivot platform at a secondary inner root, fixed to the base at a secondary outer root, and characterized by a secondary axis length spanning between the secondary outer root and secondary inner root; and 
 a strain sensing element along the secondary spring arm; 
 wherein the secondary spring arm is characterized as having a lower stiffness than the primary spring arm. 
 
     
     
       2. The pivot mount of  claim 1 , wherein the primary axis length is greater than the secondary axis length. 
     
     
       3. The pivot mount of  claim 2 , wherein an average width of the primary spring arm along the primary axis length is wider than an average width of the secondary spring arm along the secondary axis length. 
     
     
       4. The pivot mount of  claim 3 , wherein an average thickness of the primary spring arm along the primary axis length is substantially equal to an average thickness of the secondary spring arm along the secondary axis length. 
     
     
       5. The pivot mount of  claim 3 , wherein the primary spring arm and the secondary spring arm are formed of a same material. 
     
     
       6. The pivot mount of  claim 3 , wherein the secondary spring arm includes a switch-back along the secondary axis length such that a first beam segment and a second beam segment of the secondary spring arm immediately adjacent the switch-back are parallel to each other. 
     
     
       7. The pivot mount of  claim 6 , wherein the strain sensing element is a first strain sensing element at the first beam segment of the secondary spring arm; and further comprising a second strain sensing element at the second beam segment of the secondary spring arm. 
     
     
       8. The pivot mount of  claim 7 , further comprising a first reference gauge adjacent the first strain sensing element at the first beam segment of the secondary spring arm, and a second reference gauge adjacent the first strain sensing element at the first beam segment of the secondary spring arm. 
     
     
       9. The pivot mount of  claim 6 , further comprising a plurality of switch-backs along the secondary axis length. 
     
     
       10. The pivot mount of  claim 9 , wherein the plurality of switch-backs along the secondary axis length are parallel. 
     
     
       11. The pivot mount of  claim 9 , wherein the second beam segment is longer than the first beam segment. 
     
     
       12. The pivot mount of  claim 3 , wherein the secondary spring arm includes a plurality of switch-backs along the secondary axial length, a plurality of beam segments of a first length along the secondary axial length, and a beam segment of a second length longer than the first length along the secondary axial length. 
     
     
       13. The pivot mount of  claim 1 , wherein an average thickness of the primary spring arm along the primary axis length is greater than an average thickness of the secondary spring arm along the secondary axis length. 
     
     
       14. The pivot mount of  claim 2 , comprising:
 a pair of secondary spring arms laterally between a pair of primary spring arms, wherein each of the secondary spring arms is characterized as having a lower stiffness than each of the primary spring arms. 
 
     
     
       15. A transfer tool comprising:
 an articulating transfer head assembly; 
 a pivot mount, mountable onto the articulating transfer head assembly comprising:
 a pivot platform; 
 a base; 
 a primary spring arm fixed to the pivot platform at a primary inner root, fixed to the base at a primary outer root, and characterized by a corresponding primary axis length spanning between the primary outer root and primary inner root; and 
 a secondary spring arm fixed to the pivot platform at a secondary inner root, fixed to the base at a secondary outer root, and characterized by a secondary axis length spanning between the secondary outer root and secondary inner root; and 
 a strain sensing element along the secondary spring arm; 
 wherein the secondary spring arm is characterized as having a lower stiffness than the primary spring arm; and 
 
 a micro pick up array mountable onto the pivot platform of the pivot mount, the micro pick up array including an array of transfer heads. 
 
     
     
       16. The pivot mount of  claim 15 , wherein the secondary spring arm includes a plurality of switch-backs along the secondary axial length, a plurality of beam segments of a first length along the secondary axial length, and a beam segment of a second length longer than the first length along the secondary axial length. 
     
     
       17. The transfer tool of  claim 15 , wherein each transfer head has a localized contact point characterized by a maximum dimension of 1-100 μm in both x- and y-dimensions. 
     
     
       18. The transfer tool of  claim 15 , wherein the primary axis length is greater than the secondary axis length. 
     
     
       19. The transfer tool of  claim 18 , wherein an average width of the primary spring arm along the primary axis length is wider than an average width of the secondary spring arm along the secondary axis length. 
     
     
       20. The transfer tool of  claim 15 , wherein the pivot platform comprises a plurality of compliant voltage contacts, and the micro pick up array comprises a plurality of voltage contacts arranged to mate with the plurality of compliant voltage contacts of the pivot platform. 
     
     
       21. The transfer tool of  claim 15 , wherein an average thickness of the primary spring arm along the primary axis length is greater than an average thickness of the secondary spring arm along the secondary axis length.

Description:
BACKGROUND 
     Field 
     Embodiments relate to an alignment system. More particularly embodiments relate to a micro pick up array pivot mount with integrated strain sensing elements for aligning an electrostatic transfer head array with a target substrate. 
     Background Information 
     The feasibility of commercializing miniature devices such as radio frequency (RF) microelectromechanical systems (MEMS) microswitches, light-emitting diode (LED) display systems, and MEMS or quartz-based oscillators is largely constrained by the difficulties and costs associated with manufacturing those devices. Miniaturized device manufacturing processes typically include processes in which miniaturized devices are transferred from one wafer to another. In one such implementation, a transfer wafer may pick up an array of miniaturized devices from a donor wafer and bond the miniaturized devices to a receiving wafer. Methods and apparatuses for aligning two flat surfaces in a parallel orientation have been described, and may be applied to miniaturized device transfer. 
     SUMMARY 
     A pivot mount and transfer tool are described. In an embodiment a pivot mount includes a pivot platform, a base, a primary spring arm, a secondary spring arm characterized as having a lower stiffness than the primary spring arm, and a strain sensing element along the secondary spring arm. The primary spring arm is fixed to the pivot platform at a primary inner root, fixed to the base at a primary outer root, and characterized by a corresponding primary axis length spanning between the primary outer root and primary inner root. The secondary spring arm is fixed to the pivot platform at a secondary inner root, fixed to the base at a secondary outer root, and characterized by a corresponding secondary axis length spanning between the secondary outer root and secondary inner root. The relative stiffness of the primary spring arm and secondary spring arm may be selected by adjusting the length, width, or thickness of the spring arm designs. For example, the primary axis length may be greater than the secondary axis length. An average width along the primary axis length may be wider than an average width along the secondary axis length. The primary spring arm and secondary spring arm may also share the same average thickness along their respective axial lengths. In an embodiment, the primary spring arm and the secondary spring arm are formed of the same material. For example, each may be formed from the same silicon substrate, and each may be integrally formed. In an embodiment, the secondary spring arm has a lower average thickness along its axial length than the primary spring arm. In this manner the relative stiffness can be selected by modulating thickness of the spring arms. In an embodiment, the relative stiffness of the primary spring arms and secondary spring arms is modulated by selectively etching the secondary spring arms. In an embodiment, the relative stiffness of the primary spring arms and secondary spring arms is modulated by adding one or more layers with differentiated features. The pivot mount may include a plurality of primary spring arms and secondary spring arms. 
     The primary spring arms and/or secondary spring arms may include one or more switch-backs along an axial length. In an embodiment, a secondary spring arm includes a switch-back along the secondary axis length such that a first beam segment and a second beam segment of the secondary spring arm immediately adjacent the switch-back are parallel to each other. In an embodiment, a first strain sensing element is at the first beam segment, and a second strain sensing element is at the second beam segment. First and second reference gages may also be located adjacent the first and second strain sensing elements at the first and second beam segments. In an embodiment, the second beam segment is longer than the first beam segment. The secondary spring arm may include a plurality of switch-backs along the secondary axis length. In an embodiment, the secondary spring arm includes a plurality of beam segments of a first length along the secondary axis length, and a beam segment of a second length longer than the first length along the secondary axis length. The primary spring arm may also include a plurality of switch-backs along the primary axis length. In an embodiment, a pair of secondary spring arms is laterally between a pair of primary spring arms, with each secondary spring arm characterized as having a lower stiffness than each of the primary spring arms. 
     The pivot mount may be integrated into a transfer tool. In an embodiment, the transfer tool includes an articulating transfer head assembly, a pivot mount, and a micro pick up array (MPA) mountable onto the pivot platform of the pivot mount. The MPA includes an array of transfer heads, such as electrostatic transfer heads. In an embodiment, each transfer head has a localized contact point characterized by a maximum dimension of 1-100 μm in both x- and y-dimensions. In an embodiment, the pivot platform includes a plurality of compliant voltage contacts, and the micro pick up array includes a plurality of voltage contacts arranged to mate with the plurality of compliant voltage contacts of the pivot platform. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is perspective view illustration of a mass transfer tool in accordance with an embodiment. 
         FIG. 2  is a perspective view illustration of a micro pick up array and pivot mount mounted onto a transfer head assembly in accordance with an embodiment. 
         FIG. 3  is an exploded cross-sectional side view illustration of a transfer head assembly, pivot mount, and micro pick up array in accordance with an embodiment. 
         FIG. 4  is a schematic top view illustration of a micro pick up array in accordance with an embodiment. 
         FIGS. 5A-5E  are cross-sectional side view illustrations of a method of forming a pivot mount including compliant voltage contacts in accordance with an embodiment. 
         FIG. 6A  is a top view illustration of a pivot mount and a primary axial length of a primary spring arm in accordance with an embodiment. 
         FIG. 6B  is a top view illustration of a pivot mount and a secondary axial length of a secondary spring arm in accordance with an embodiment. 
         FIG. 6C  is a close-up top view illustration of Detail B in  FIG. 6B  in accordance with an embodiment. 
         FIG. 6D  is a close-up top view illustration of Detail B in  FIG. 6B  in accordance with an embodiment. 
         FIG. 6E  is a close-up top view illustration of Detail D in  FIG. 6D  in accordance with an embodiment. 
         FIGS. 6F-6H  are cross-sectional side view illustrations along section A-A in  FIGS. 6A-6B  of a method of modulating stiffness by reducing layer thickness in accordance with an embodiment. 
         FIGS. 6I-6J  are cross-sectional side view illustrations along section A-A in  FIGS. 6A-6B  of a method of modulating stiffness with layer build up in accordance with an embodiment. 
         FIG. 7  is a top view illustration of a pivot mount including various structural features and electrical routing in accordance with an embodiment. 
         FIG. 8A  is an illustration of strain components in a body. 
         FIG. 8B  is an illustration of strain components in a thin structure. 
         FIG. 9  is an illustration of a spring arm under pure bending in accordance with an embodiment. 
         FIG. 10  is an illustration of a spring arm under simultaneous bending and torsion in accordance with an embodiment. 
         FIGS. 11A-11B  are perspective view illustrations of a pivot platform of a pivot mount deflected with a uniform z displacement in accordance with an embodiment. 
         FIG. 11C  is a perspective view illustration of strain modeling for normal strain in the x direction for a pivot platform deflected with a uniform z displacement in accordance with an embodiment. 
         FIG. 11D  is a perspective view illustration of strain modeling for normal strain in the y direction for a pivot platform deflected with a uniform z displacement in accordance with an embodiment. 
         FIG. 11E  is a perspective view illustration of strain modeling for equivalent strain magnitude for a pivot platform deflected with a uniform z displacement in accordance with an embodiment. 
         FIG. 11F  is a perspective view illustration of strain modeling for surface shear strain for a pivot platform deflected with a uniform z displacement in accordance with an embodiment. 
         FIG. 12  is a schematic illustration of an idealized beam of length L with one end fixed and subject to simultaneous transversely applied force and bending moment at the free end and with zero slope boundary conditions at both ends. 
         FIG. 13  depicts shear force and bending moment diagrams for an idealized beam of length L with one end fixed and subject to simultaneous transversely applied force and bending moment at the free end and with zero slope boundary conditions at both ends. 
         FIG. 14  is a top view illustration with detail view of a strain amplifying secondary spring arm structure with each beam segment labeled sequentially starting at the inner root to the outer root in accordance with an embodiment. 
         FIG. 15A  depicts a bending moment diagram along the axial length of the secondary spring arm structure of  FIG. 14  in accordance with an embodiment. 
         FIG. 15B  depicts a bending moment diagram along the axial length of the secondary spring arm structure of  FIG. 14  with an applied loading of equal magnitude and opposite sense to the loading presumed in  FIG. 15A  in accordance with an embodiment. 
         FIG. 16  is a top view illustration with detail view strain amplifying secondary spring arms including correlated strain sensors in accordance with an embodiment. 
         FIG. 17  is top view illustration of a pivot mount in accordance with an embodiment. 
         FIG. 18A  is a schematic illustration of a control scheme for regulating a transfer head assembly in accordance with an embodiment. 
         FIG. 18B  is a schematic illustration of a method of generating a synthesized output signal in accordance with an embodiment. 
         FIG. 18C  is a schematic illustration of a method of generating a synthesized output signal in accordance with an embodiment. 
         FIG. 19  is a flowchart illustrating a method of aligning a micro pick up array relative to a target substrate in accordance with an embodiment. 
         FIG. 20  is a schematic illustration of a computer system in accordance with an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments describe a pivot mount including a base, a pivot platform, primary spring arms extending between the pivot platform and the base, and secondary springs arm extending between the pivot platform and the base. The secondary spring arms are characterized as having a lower stiffness than the primary spring arms, and strain sensing elements are located along the secondary spring arms. In this manner, when the pivot mount is moved in a direction orthogonal to a contact surface of the pivot platform normal strain is created at the surface of the spring arms. Since the secondary spring arms have a lower stiffness than the primary spring arms, the secondary spring arms undergo more strain for a given pivot platform displacement. By locating the strain sensing elements along the secondary spring arms a larger amount of strain is measured. Thus, in an embodiment, the primary spring arms provide stiffness for the pivot mount, for example to support the MPA and achieve the operational amount of deflection during the pick and place operations of the transfer tool, while the secondary spring arm provides strain amplification, and therefore signal amplification, enabling higher sensitivity of the pivot mount. 
     The pivot mount can be coupled to an articulating head assembly of a mass transfer tool for accurate and repeatable alignment in 6 spatial degrees of freedom between the transfer tool and a target substrate. When accurately aligning two planar surfaces, lateral (x and y) and rotational (θz) alignments are relatively straightforward to achieve through use of a high-precision x-y stage and rotationally-positioned substrate chucks. The remaining three degrees of freedom, θx, θy, (or, “tilt” and “tip”) and z are difficult to independently control. Any changes to the tip and tilt angle necessarily change the distance z to any point not located at the center of rotation. While parallelism between two planes can be accomplished through use of a passive pivot mount, the pressure distribution between the two planar surfaces will not be centered or uniform unless the two surfaces were parallel to begin with. A transfer tool including a pivot mount in accordance with embodiments described herein may redistribute the pressure distribution to achieve a uniform pressure field. By placing strain sensing elements (strain gages) at high-strain locations on the pivot mount secondary spring arms, a feedback signal of the position error can be generated and input to the transfer tool for operation in a closed-loop motion control system. Because strain is related to the stress state through Hooke&#39;s Law, both displacement and forces acting on the pivot mount can be known by measuring strain. 
     In one aspect, embodiments describe a pivot mount configuration including primary spring arms to provide stiffness for the pivot mount, and secondary spring arms to provide strain amplification, and therefore signal amplification, enabling higher sensitivity of the pivot mount. In an embodiment, the length of the secondary spring arms is less than the length of the primary spring arms. In such a configuration where an amount of deflection for the primary and secondary spring arms is equivalent for a given pivot platform displacement, the strain resulting from the given loading is greater in the secondary spring arms than in the primary spring arms. As a result, the sensitivity of the pivot mount as a displacement sensing device is increased. 
     In one aspect, embodiments describe a pivot mount configuration that achieves a high strain sensing sensitivity and generates a feedback signal with a high signal to noise ratio. As a result the pivot mount can provide a position feedback signal with increased effective resolution to the transfer tool. By locating the strain sensing elements near the inner and outer roots or on opposite sides of switch-backs in an axial length of a spring arm, equal and opposite strain responses are measured. In this manner a strain signal for a given platform displacement may be effectively doubled. Such a configuration can also reduce noise for a given strain signal. Due to the differential sensing at the inner and outer roots and the switch-backs the measured noise is effectively canceled. Accordingly, higher strain sensing sensitivity may be accomplished with a higher signal to noise ratio, and an increased effective resolution of the position feedback signal may be provided to the transfer tool. 
     In another aspect, embodiments describe pivot mount spring arm configurations that minimize the torsion applied to a spring arm at the roots where a spring arm is fixed to a pivot platform at one end and fixed to a base at another end. This creates a more uniform bending moment in the high strain regions of the spring arm with reduced strain variation and torsion in the spring arms, which allows the strain sensing elements to be located in the high strain regions near the roots. By comparison, in other configurations with spring arms that undergo both bending and torsional loading, the area of maximum strain may include both bending and torsion. Torsion in the spring arms is parasitic to surface strain sensing since it manifests as strain at the surface of the spring arm having components in both the x and y directions. Because the total strain energy distributed through the spring arms is constant for a given pivot platform displacement, the presence of strain components perpendicular to the strain sensing elements reduces the ratio of strain components that are aligned with the strain sensing elements. As a result, strain sensing elements located near areas of torsion may produce a lower effective feedback signal and sensitivity. In an embodiment, a pivot mount is arranged to create boundary conditions at the roots of the spring arms with a uniform bending moment, in which strain is substantially perpendicular to the roots and substantially parallel to strands in the strain sensing elements, which may be parallel to axial lengths of the spring arms in the high strain regions. Such a configuration directs substantially all of the strain energy from a given pivot platform displacement into strain components aligned with the strain sensing elements. As a result, higher strain may be measured and sense feedback signal strength may be increased for a given pivot platform displacement. Reduction of the torsional moment at the roots may additionally allow more freedom in stiffness requirements of the spring arms. In turn, reduced stiffness requirements allow for greater bending, resulting in increased normal strain at the surface of the spring arms and sense feedback signal strength. 
     In another aspect, reduction of the torsional moment applied to the spring arms at the roots may also increase the effectiveness of the reference gage(s) positioned adjacent the strain sensing elements. In an embodiment, each strain sensing element is located in a high strain region of a spring arm that sees only normal strain at the surface in the gage direction of the strain sensing element and sees no normal strain at the surface lateral to the gage direction. This allows the location of a reference strain gage adjacent to each strain sensing element with the result that the reference gages do not see strain caused by mechanical loading of the pivot platform. This in turn allows the reference gages to compensate for temperature variations in the system, and increase the signal to noise ratio. Since the strain sensing elements and reference gages are adjacent, they are exposed to the same temperature, meaning the thermal strain is identical in both a strain sensing element and a corresponding reference gage. Since the reference strain gages are not subjected to strain resulting from mechanical load, any strain signal they produce can be attributed to temperature (as noise), which is then subtracted as background noise from the strain measured by the adjacent strain sensing element. In an embodiment, strands in the reference gages are oriented perpendicular to strands in the strain sensing elements. In such a configuration, the normal strain at the surface of the spring arms is substantially parallel to the strands in the strain sensing elements, and perpendicular to the strands in the reference strain gages. Thus, by reducing the torsional moment and creating uniform bending moments in the spring arms in which normal strain at the surface of the spring arms is substantially perpendicular to the roots, the reference strain gages may be more accurate and a higher strain sensing sensitivity may be accomplished with a higher signal to noise ratio. 
     In another aspect, embodiments describe an arrangement of strain sensing elements into distributed, correlated pairs. In an embodiment, a correlated pair of strain sensing elements (and reference gages, if present) forms a sensor. The sensors may also be arranged into distributed, correlated sensors. In an embodiment, each sensor includes one or more correlation sensors. In these manners, the loss of a strain sensing element or sensor does not prohibit use of the pivot mount, and the lifetime of the pivot mount use with a transfer tool can be extended. In essence, redundancy is obtained by having pairs of the same signal. For example, a correlated pair of strain sensing elements or sensors may each sense a same z-deflection. In another situation, a correlated pair may sense a same or equal but opposite θx, θy, (or, “tilt” and “tip”). In either situation, the loss of one of the correlated strain sensing element or sensor may reduce the overall signal to noise ratio generated from the pivot platform, yet the remaining signal to noise ratio remains adequate for operation of the transfer tool. 
     In yet another aspect, embodiments describe a pivot mount with compliant voltage contacts, for providing a low contact resistance connections of the voltage contacts to a micro pick up array (MPA) that is mounted onto the pivot platform of the pivot mount. The compliant voltage contacts may protrude from the pivot platform such that they are elevated above the pivot platform, yet are compliant such that they exert a pressure upon the MPA contacts when the MPA is clamped onto the pivot mount pivot platform, for example, using an electrostatic clamp contact on the pivot mount platform. 
     Referring to  FIG. 1 , a perspective view of a mass transfer tool is shown. Mass transfer tool  100  may include a transfer head assembly  200  for picking up an array of micro devices from a carrier substrate held by a carrier substrate holder  104  and for transferring and releasing the array of micro devices onto a receiving substrate held by a receiving substrate holder  106 . Embodiments of a mass transfer tool are described in U.S. Patent Publication No. 2014/0071580, titled “Mass Transfer Tool”, filed on Sep. 7, 2012. Operation of mass transfer tool  100  and transfer head assembly  200  may be controlled at least in part by a computer  108 . Computer  108  may control the operation of transfer head assembly  200  based on feedback signals received from various sensors, strain sensing elements, reference gages located on a pivot mount. For example, transfer head assembly  200  may include an actuator assembly for adjusting an associated MPA  103  with at least three degrees of freedom, e.g., tipping, tilting, and movement in a z direction, based on feedback signals received from sensors associated with a pivot mount that carries MPA  103 . Similarly, the carrier substrate holder  104  and receiving substrate holder  106  may be moved by an x-y stage  110  of mass transfer tool  100 , having at least two degrees of freedom, e.g., along orthogonal axes within a horizontal plane. Additional actuators may be provided, e.g., between mass transfer tool  100  structural components and transfer head assembly  200 , carrier substrate holder  104 , or receiving substrate holder  106 , to provide movement in the x, y, or z direction for one or more of those sub-assemblies. For example, a gantry  112  may support transfer head assembly  200  and move transfer head assembly  200  along an upper beam, e.g., in a direction parallel to an axis of motion of x-y stage  110 . Thus, an array of electrostatic transfer heads on MPA  103 , supported by transfer head assembly  200 , and an array of micro devices supported by a carrier substrate held by carrier substrate holder  104  may be precisely moved relative to each other within all three spatial dimensions. 
     Referring to  FIG. 2 , a perspective view of a transfer head assembly  200  is shown in accordance with an embodiment. A transfer head assembly  200  may be used in combination with mass transfer tool  100  to transfer micro devices to or from a substrate, e.g., receiving substrate or carrier substrate, using MPA  103  which is supported by a pivot mount  300 . More particularly, transfer head assembly  200  may provide for negligible lateral or vertical parasitic motion for small movements of MPA  103 , e.g., motion less than about 5 mrad about a neutral position. Accordingly, transfer head assembly  200  may be incorporated in mass transfer tool  100  to adjust an MPA  103  relative to mass transfer tool  100 . Thus, transfer head assembly  200  may be fixed to a chassis of mass transfer tool  100 , e.g., at a location along an upper beam or support. 
     As illustrated, the pivot mount  300  may include a base  302 , a pivot platform  304 , a plurality of primary spring arms  306 , and a plurality of secondary spring arms  307 , and the MPA  103  supporting a transfer head array  115  is mounted on the pivot platform  304 . In an embodiment, the transfer head array  115  is an electrostatic transfer head array  115 , where each transfer head operates in accordance with electrostatic principles to pick up and transfer a corresponding micro device. In an embodiment each electrostatic transfer head has a localized contact point characterized by a maximum dimension of 1-100 μm in both the x- and y-dimensions. In an embodiment, the pivot mount  300  may communicate and send feedback signals to the mass transfer tool  100  through one or more electrical connections, such as a flex circuit  308 . As described below, feedback may include analog signals from various sensors, strain sensing elements, reference gages that are used in a control loop to regulate actuation and spatial orientation of the transfer head assembly  200 . In an embodiment, the feedback signals are sent to a position sensing module located near the pivot mount  300  to reduce signal degradation by limiting a distance that analog signals must travel from a strain sensing element to the position sensing module. In an embodiment, the position sensing module is located within the transfer head assembly  200 . 
     Referring now to  FIG. 3 , an exploded cross-sectional side view illustration is provided of a transfer head assembly  200 , pivot mount  300 , and MPA  103 . Generally, the pivot mount  300  is mounted onto the transfer head assembly  200 . This may be accomplished using a variety of manners such as using tabs or lips to press the pivot mount against the transfer head assembly  200 , bonding, vacuum, or electrostatic clamping. A deflection cavity  202  may be formed in the transfer head assembly  200  to allow a specified z-deflection distance of the pivot platform  200  along the z-axis. 
     As illustrated in  FIG. 3 , the pivot mount  300  may include channels  310  formed through a body of the pivot mount from a front surface  312  to back surface  314 . Channels  310  may be used to form a variety of compliant features of the pivot mount  300 , including defining the primary spring arms  306 , secondary spring arms  307 , and pivot platform  304 , as well as the compliant voltage contacts  316 , described in more detail in the following description. The compliant voltage contacts  316  may provide a low contact resistance connection to voltage contacts  120  of the MPA  103 . In the embodiment illustrated, the compliant voltage contacts  316  protrude from the pivot platform such that they are raised above the pivot platform. Upon clamping the MPA  103  onto the pivot platform of the pivot mount  300  with the opposing electrostatic clamp contacts  318 ,  122 , the compliant voltage contacts  316  exert a pressure upon the MPA contacts  120 . Additional features may be located on or in the pivot mount  300 . For example, strain sensing elements  320  (strain gages) and reference gages  340  may be located at high strain regions of the secondary spring arms  307 , as described in further detail in the following description. Strain sensing elements  320  and reference gages  340  may also be located at high strain regions of primary spring arms  306 . 
     Referring now to  FIG. 4 , a schematic top view illustration of an MPA  103  is shown in accordance with an embodiment. In an embodiment, an area of the electrostatic clamp contact  122  on a back side of the MPA is larger than an area of the transfer head array  115  on the front surface of the MPA. In this manner, the alignment and planarity across the transfer heads in the transfer head array  115  can be regulated by alignment of the transfer head assembly. In such an embodiment, a plurality of voltage contacts  120  for supplying an operating voltage to the transfer head array  115  is located outside the periphery of the transfer head array  115 . 
     Referring now to  FIGS. 5A-5E , cross-sectional side view illustrations are shown for a method of forming a pivot mount  300  including compliant voltage contacts  316 . The processing sequence may begin with a commercially available silicon wafer  301  including a top oxide layer  330 , and bottom oxide layer  332  as illustrated in  FIG. 5A . While the following description is made with regard to a silicon wafer, embodiments are not so limited, and other suitable substrates can be used to form pivot mount  300 , such a silicon carbide, aluminum nitride, stainless steel, and aluminum, amongst others. In an embodiment illustrated in  FIG. 5B , the top oxide layer  330  is then removed, with bottom oxide layer  330  remaining. Referring to  FIG. 5C , the top and bottom surfaces of the wafer  301  may then be oxidized further resulting in a top oxide layer  334 , and bottom oxide layer  336  that is thicker than the previous bottom oxide layer  332  and thicker than the top oxide layer  334 . For example, this may be accomplished with a wet thermal oxidation operation. Following the formation of oxide layers  334 ,  336  various layers may be formed over the top oxide layer  334  to form the strain gages  320 , reference gages  340 , electrostatic clamp contact(s)  318 , and electrodes  317  for the compliant voltage contacts. In an embodiment, these various layers may be formed by one or more metal deposition processes. In an embodiment, the electrodes  317  for the compliant voltage contacts are thicker than other metallization layers used to form the strain gages  320 , reference gages  340 , and electrostatic clamp contact(s)  318 . Referring to  FIG. 5E , the bottom oxide layer  336  is removed and channels  310  are etched through the silicon wafer  301  and top oxide layer  334  to define the primary spring arms  306 , secondary spring arms  307 , pivot platform  304 , and compliant voltage contacts  316 . As shown in  FIG. 5E , the contact surfaces including the electrodes  317  for the compliant voltage contacts  316  protrude from the pivot platform such that they are elevated above the surrounding pivot platform, including the strain gages  320 , reference gages  340 , and electrostatic clamp contact(s)  318 . This may be the result of releasing residual stress within the silicon wafer  301  during formation of the channels  310 . In an embodiment, the residual stress was created in the silicon wafer  301  during the oxidation and removal operation described and illustrated in  FIGS. 5A-5C . In accordance with embodiments, the channels  310  forming the compliant voltage contacts  316  may assume a variety of configurations such as switch-backs or a winding contour. In an embodiment, the channels forming the compliant voltage contacts  316  are made in a spiral configuration which can achieve a high amount of compliance within a small area. 
     Referring again to  FIG. 4 , the voltage contacts  120  of the MPA  103  align with the compliant voltage contacts  316  in the pivot platform  304  of the pivot mount  300 . Once the MPA is clamped onto the pivot mount pivot platform, for example, using an electrostatic clamp contact on the pivot mount platform, the compliant voltage contacts  316  exert a pressure upon the MPA voltage contacts  120  to achieve low contact resistance connections. 
       FIGS. 6A-7  illustrate various structural aspects of a pivot mount  300 . In an embodiment pivot mount  300  includes a base  302 , a pivot platform  304 , a plurality of primary spring arms  306 , and a plurality of secondary spring arms  307 . Referring to  FIG. 6A , in an embodiment each primary spring arm  306  is fixed to the pivot platform  304  at a corresponding inner root  350 , and fixed to the base  302  at a corresponding outer root  352 . Each primary spring arm  306  includes at least one switch-back along an axial length  354  of the primary spring arm such that a pair of lengths of the primary spring arm adjacent the switch-back are parallel to each other. In the embodiment illustrated in  FIG. 6A , each primary spring arm  306  includes an inner switch-back  356  along an inner length of the spring arm and an outer switch-back  358  along an outer length of the spring arm. In an embodiment, an inner length  370  of the spring arm extending from the pivot platform  304  (along the axial length  354  of the spring arm  306 ) is perpendicular to the inner root  350 . In an embodiment, an outer length  372  of the spring arm extending from the base  302  (along the axial length  354  of the spring arm  306 ) is perpendicular to the outer root  352 . 
     Referring now to  FIG. 6B , in an embodiment each secondary spring arm  307  is fixed to the pivot platform  304  at a corresponding inner root  351 , and fixed to the base  302  at a corresponding outer root  353 . Each secondary spring arm  307  includes at least one switch-back along an axial length  355  of the secondary spring arm such that a pair of lengths of the secondary spring arm adjacent the switch-back are parallel to each other. 
       FIGS. 6C-6D  are close-up top view illustrations of Detail B in  FIG. 6B  in accordance with embodiments. In the embodiment illustrated in  FIG. 6C , each secondary spring arm  307  includes an inner switch-back  357  along an inner length of the secondary spring arm and an outer switch-back  359  along an outer length of the secondary spring arm. Each secondary spring arm  307  may additionally include one or more intermediate switch-backs  349 A,  349 B along a length of the secondary spring arm between the inner and outer switch-backs  357 ,  359 . As illustrated in  FIG. 6C , an inner length  371  of the secondary spring arm extending from the pivot platform  304  (along the axial length  355  of the secondary spring arm  307 ) is perpendicular to the inner root  351 . In an embodiment, an outer length  373  of the spring arm extending from the base  302  (along the axial length  355  of the secondary spring arm  307 ) is perpendicular to the outer root  353 . In the embodiments illustrated, each switch-back along the axial length of the primary spring arm and secondary spring arm results in a parallel pair of lengths of the spring arm adjacent the switch-back. 
     In the embodiment illustrated in  FIG. 6D , a portion of the secondary spring arm immediately adjacent the intermediate switch-back  349 A includes a first length  361 A and a second length  363 A of the secondary spring arm that are parallel to each other. A portion of the secondary spring arm immediately adjacent the intermediate switch-back  349 B includes a first length  361 B and a second length  363 B of the secondary spring arm that are parallel to each other. Similarly, a portion of the secondary spring arm immediately adjacent the inner root  351  includes a first length  365  and a portion of the secondary spring arm immediately adjacent the outer root  353  includes a second length  367  of the secondary spring arm that are parallel to each other. Referring briefly to  FIG. 14 , in an embodiment each primary spring arm and secondary spring arm is characterized as including a series of spring arm segments with endpoints characterized by a boundary condition of slope θ equal to zero. As described in further detail with regard to  FIGS. 15A-15B , the endpoints of the spring arm segments correspond to local maxima or local minima bending moments, where the slope of the deformed spring arm segment changes in sign between positive and negative for a given deflection of the pivot platform. In the particular embodiments illustrated in  FIG. 6D  and  FIG. 14  length  365  is within secondary spring arm segment  1 , length  361 A is within secondary spring arm segment  2 , lengths  363 A,  363 B are within secondary spring arm segment  3 , length  361 B is within secondary spring arm segment  4 , length  367  is within secondary spring arm segment  5 . In the particular embodiment illustrated, the secondary spring arm  307  is characterized by a right angle omega (Ω) shape, with each secondary spring arm segment having an axial length parallel to each other, and secondary spring arm segment  3  being longer than secondary spring arm segments  1 ,  2 ,  4 ,  5 . 
     In accordance with embodiments, strain sensing elements may be located along the lengths of the secondary spring arm adjacent switch-backs or roots. Furthermore, reference gages may be located adjacent the strain sensing elements.  FIG. 6E  is a close-up top view illustration of Detail D in  FIG. 6D  in accordance with an embodiment. In the particular embodiment illustrated in  FIG. 6E , a first strain sensing element  320  is located at the first length of  361 B the secondary spring arm adjacent the intermediate switch-back  349 B, and a second strain sensing element  320  is located at the second length  363 B of the secondary spring arm adjacent the intermediate switch-back  349 B. Furthermore, first reference gage  340  is located adjacent the first strain sensing element  320  at the first length  361 B, and a second reference gage  340  is located adjacent the second strain sensing element  320  at the second length  363 B. Referring again to  FIG. 6D , reference gages  340  are also located adjacent the strain sensing elements  320  at the lengths  365 ,  367  located near and perpendicular to the inner and outer roots  351 ,  353  and at lengths  361 A,  363 A adjacent intermediate switch-back  349 A. As illustrated, the strain sensing elements  320  and reference gages  340  are located a certain distance away from the roots and switch-backs to avoid stray strain regions, where some stress concentrations may be present due to patterning the substrate. Further detail regarding placement of the strain sensing elements  320  and reference gages is provided in the following description with regard to  FIGS. 14-16 . 
     Referring again to  FIG. 6E , in the particular embodiment illustrated the strain sensing elements  320  and reference gages  340  along the first and second lengths  361 B,  363 B of the secondary spring arm adjacent an intermediate switch-back  349 B are shown in more detail. In an embodiment, strain sensing elements  320  may be strain gages that measure deformation of secondary spring arm  307 . The strain gages may exhibit an electrical resistance that varies with material deformation. More specifically, the strain gages may deform when secondary spring arm  307  deforms. That is, the strain gage design may be selected based on environmental and operating conditions associated with the transfer of micro devices from a carrier substrate, to achieve the necessary accuracy, stability, cyclic endurance, etc. Accordingly, the strain gages may be formed from various materials and integrated with the spring arm in numerous ways to achieve this goal. Several such embodiments are described below. 
     A strain gage may be separately formed from secondary spring arm  307  and attached thereto. In an embodiment, the strain gage includes an insulative flexible backing that supports a foil formed from polysilicon and electrically insulates the foil from secondary spring arm  307 . The foil may be arranged in a serpentine pattern, for example. An example of an attachable strain gage is a Series 015DJ general purpose strain gage manufactured by Vishay Precision Group headquartered in Malvern, Pa. A strain gage that is separately formed from secondary spring arm  307  may be attached to secondary spring arm  307  using numerous processes. For example, the strain gage backing may be directly attached to secondary spring arm  307  with an adhesive or other bonding operation. More specifically, strain gage backing may be fixed to a surface of secondary spring arm  307  using solder, epoxy, or a combination of solder and a high-temperature epoxy. 
     In another embodiment, a strain gage may be formed on secondary spring arm  307  in a desired pattern, such as a serpentine pattern. In an embodiment, a strain gage may be formed directly on secondary spring arm  307  using a deposition process. For example, constantan copper-nickel traces may be sputtered directly on secondary spring arm  307  in a serpentine pattern. The dimensions of a strand of a sputtered strain gage having a serpentine pattern may be about 8 micron width with about an 8 micron distance between strand lengths and may be deposited to a thickness of about 105 nanometers. 
     In another embodiment, the material of secondary spring arm  307  may be modified to form an integrated strain gage. More specifically, secondary spring arm  307  may be doped so that the doped region of the spring arm exhibits piezoresistive behavior. As an example, the surface of secondary spring arm  307  may be doped silicon. The doped material may be in a serpentine pattern, having dimensions that vary with an applied strain. Thus, the strain gage may be fully integrated and physically indistinct from the remainder of secondary spring arm  307 . 
     During the transfer of micro devices from a carrier substrate, secondary spring arm  307  and strain sensing elements  320  may be subjected to elevated temperatures, and thus, temperature compensation may be necessary. In an embodiment, strain sensing element  320  (strain gage) may be self-temperature compensated. More specifically, strain gage material may be chosen to limit temperature-induced apparent strain over the operating conditions of the transfer process. However, in an alternative embodiment, other manners for temperature compensation may be used. For example, temperature compensation may be achieved using a reference gage technique. 
     In an embodiment, strain sensing element  320  may be a strain gage on secondary spring arm  307  having a pattern (e.g. serpentine) of lengthwise strands that align in a direction of anticipated normal strain at the surface of the spring arm. Referring to  FIGS. 6D-6E , in an embodiment, a reference gage technique utilizes a reference gage  340  to compensate for strain sensing element  320 . More particularly, reference gage  340  may be located adjacent strain sensing element  320  in the same area of strain. While strands of strain sensing element  320  may align with the direction of applied strain, strands of reference gage  340  may extend perpendicular to the strands of strain sensing element  320  and to the direction of applied strain. Alternatively, reference gage  340  may be located in a non-strain area of the pivot mount  300 , apart from strain sensing element  320 , which is located in a high strain area of secondary spring arm  307 . For example, reference gage  340  may be located on base  302  or pivot platform  304 . In each configuration, strain sensing element  320  detects a strain applied to secondary spring arm  307  and reference gage  340  detects strain from thermal effects on the pivot mount  300 . Accordingly, a comparison of strain in the strain sensing element  320  and reference gage  340  may be used to determine, and compensate for, strain related to thermal expansion of secondary spring arm  307 . 
     In particular, the strands  341  in the references gages  340  are oriented perpendicular to strands  321  in the strain sensing elements  320 . As will become more apparent in the following description, the normal strain at the surface that results at the first and second lengths  361 B,  363 B of the secondary spring arm during operation of the pivot mount is substantially parallel to the strands  321  in the strain sensing elements, and perpendicular to the strands  341  in the reference strain gages. Similar strain relationships are found at the other described locations (e.g.  365 ,  361 A,  363 A,  367 ) for strain sensing elements where normal strain at the surface that occurs during operation of the pivot mount is substantially parallel to the strands in the strain sensing elements  320 . 
     In accordance with embodiments, the one or more secondary spring arms  307  are characterized as having a lower stiffness than the one or more primary spring arms  306 . As such, a greater amount of strain can be measured in the secondary spring arms than the primary spring arms, resulting in strain signal amplification. The relative stiffness of the primary spring arms and secondary spring arms may be selected by adjusting the length, width, or thickness of the spring arms or materials of the spring arms. For example, referring to  FIGS. 6A-6B  the primary axis length  354  may be greater than the secondary axis length  355 . An average width along the primary axis length  354  may be wider than an average width along the secondary axis length  355 . The primary spring arm  306  and secondary spring arm  307  may also share the same average thickness along their respective axial lengths. In an embodiment, the primary spring arm and the secondary spring arm are formed of the same material. For example, each may be formed from the same silicon substrate, and each may be integrally formed. 
     In an embodiment, the secondary spring arm  307  has a lower average thickness along its axial length  355  than the primary spring arm  306  has along its axial length  354 . In this manner the relative stiffness can be selected by modulating thickness of the spring arms.  FIGS. 6F-6H  are cross-sectional side view illustrations along section A-A in  FIGS. 6A-6B  of a method of modulating stiffness by reducing layer thickness in accordance with an embodiment. Referring to  FIG. 6F , the process may start with a patterned base substrate  301  such as a silicon substrate including the base  302 , pivot platform  304 , primary spring arms  306  and secondary spring arms  307 . The relative thicknesses may then be modulated by selectively etching away a thickness of the secondary spring arm  307  as illustrated in  FIG. 6G , resulting in the pivot platform configuration shown in  FIG. 6H  in which the primary spring arms  306  are thicker than the secondary spring arms  307 . 
     In an embodiment, one or more additional layers with differentiated features are built up along the primary spring arms  306  compared to the secondary spring arms  307 .  FIGS. 6I-6J  are cross-sectional side view illustrations along section A-A in  FIGS. 6A-6B  of a method of modulating stiffness with layer build up in accordance with an embodiment. Referring to  FIG. 6I , the process may start with a patterned base substrate  301  such as a silicon substrate including the base  302 , pivot platform  304 , primary spring arms  306 , and secondary spring arms  307  of a first thickness. A stiffener layer  601  may then be formed on the base substrate  301  as illustrated in  FIGS. 6I-6J . In an embodiment, the stiffener layer  601  is bonded to the base substrate  301 , for example by wafer bonding. The stiffener layer  601  may be formed of the same material or a different material than the base substrate  301  in order to achieve the desired stiffness. Likewise, thickness of the stiffener layer  601  may be modulated. As shown, the stiffener layer  601  may be patterned similarly as the base substrate  301 , including the base  302 , pivot platform  304 , and primary spring arms  306  of a second thickness. In an embodiment, a gap or a reduced thickness of the stiffener layer  601  exists where the secondary spring arms  307  exist in the base substrate  301  in order to modulate the thickness. In the embodiment illustrated, a composite pivot mount structure is formed by bonding the base substrate  301  and stiffener layer  601 . The resultant structure includes primary spring arms  306  with a total thickness including the sum of the first and second thicknesses, with the secondary spring arms having only the first thickness. 
       FIG. 7  is a top view illustration of a pivot mount including electrical routing in accordance with an embodiment. As illustrated, wiring can be routed on the top surface of the pivot mount for operation of various components. In an embodiment wiring  380  is provided for operation of the strain sensing elements  320  and reference gages  340 . In an embodiment wiring  382  is provided for operation of the electrostatic clamp contacts  318 . In an embodiment wiring  384  is provided for operation of the compliant voltage contacts  316 . In the particular embodiment illustrated, the wiring  384  connects with the electrodes  317  for the compliant voltage contacts  316 , where the electrodes form a spiral pattern within the spiral channels  310  forming the compliant voltage contacts. Wiring  380 ,  382 , and  384  can run over one or more portions of the pivot mount including the base  302 , primary spring arms  306 , secondary spring arms  307 , and pivot platform  304 . Wiring  380 ,  382 , and  384  may be formed using a suitable technique such s sputtering or e-beam evaporation, or may be a wire that is bonded to the pivot mount. 
     Wiring  380 ,  382 , and  384  may be routed to an electrical connection, such as a flex circuit  308 , at an edge of the base  302  of the pivot mount. For example, an operating voltage can be applied trough the flex circuit  308  to operate the electrostatic clamp contacts  318  to clamp the MPA onto the pivot mount  300 . Another operating voltage can be applied through the flex circuit  308  to operate the compliant voltage contacts  316  which transfer an operational voltage to the array of electrostatic transfer heads in order to provide a grip pressure to pick up micro devices. Additionally, the flex circuit  308  can transfer the feedback signals from the strain sensing elements  320  and reference gages  340  to a position sensing module or computer  108  to regulate actuation and spatial orientation of the transfer head assembly  200 . 
     Referring now to  FIG. 8A , strain at any point in a body may be described by nine strain components. These include three normal strains (εx, εy, εz) and six shear strain components (εxy, εxz, εyx, εyz, εzx, and εzy). Strain components in a thin structure are illustrated in  FIG. 8B . For a thin pivot mount structure shear strains on the surface (εzx and εzy) and out-of-plane normal strain (εz) are not significant. This idealization is known as plane stress. Accordingly, in an embodiment the strain gages (strain sensing elements and reference gages) on the surface of the pivot mount will measure components of the normal strains εx and εy. In an embodiment, the pivot mount includes regions of strain loaded only in either pure εx or pure εy and directs substantially all available strain into measurable strain. 
     Referring now to  FIGS. 9-10 , the idealization of plane stress is illustrated as realized in accordance with embodiments.  FIG. 9  is an illustration of a spring arm under pure bending in accordance with an embodiment. In such an embodiment, the spring arm undergoing pure bending may have a single normal strain component aligned with the spring arm axial length. A reference gage  340  may be oriented perpendicular to the spring arm axial length and not measure any strain due to bending.  FIG. 10  is an illustration of a spring arm in both bending and torsion. In such a configuration, normal strain components and shear strain components are produced in multiple directions. In this case both the strain gage  320  and reference gage  340  may measure non-zero strain, which may reduce the ability of the reference gage  340  to compensate for temperature changes. 
     In order to illustrate strain confinement within the pivot mount, a pivot mount with a uniform z displacement of the pivot platform  304  is illustrated in  FIGS. 11A-11E  along with modeling data for strain fields located within the pivot mount. Referring to  FIG. 11A , a pivot platform  304  of pivot mount  300  is deflected with a uniform z displacement. Such deflection may be typical during a normal pick and place operation with the mass transfer tool, though the amount of deformation illustrated in  FIG. 11A  is exaggerated for illustrational purposes. In the particular embodiment illustrated in  FIG. 11A , the primary spring arm  306  along the first length  366  of the spring arm adjacent the outer switch-back  358  and the first length  360  of the spring arm adjacent the inner switch-back  356  have a negative curvature and are in a condition of negative (compressive) normal strain at the surface. In the particular embodiment illustrated in  FIG. 11A , the primary spring arm  306  along the second length  364  the spring arm adjacent the outer switch-back  358  and the second length  362  of the spring arm adjacent the inner switch-back  356  have a positive curvature and are in a condition of positive (tensile) normal strain at the surface. 
     Referring to  FIG. 11B , a pivot platform  304  of pivot mount  300  is deflected with a uniform z displacement as described with regard to  FIG. 11A . As illustrated in  FIG. 11B , the secondary spring arm  307  includes lengths  361 A,  363 B,  367  that are in condition of negative (compressive) normal strain at the surface, and lengths  365 ,  363 A,  361 B that are in a condition of positive (tensile) normal strain at the surface. 
     In accordance with embodiments, a pivot mount structure achieves a high strain sensing sensitivity and generates a feedback signal with a high signal to noise ratio by locating strain sensing elements on secondary spring arms that have a lower stiffness than the primary spring arms. In this manner secondary spring arms undergo more strain for a given pivot platform displacement than the primary spring arms and a higher strain signal is produced. The strain sensing sensitivity and feedback signal may be further increased by locating strain sensing elements at locations of the secondary spring arms where equal and opposite strain responses are measured, such as at inner and outer roots and/or on opposite sides of switch-backs. In this manner, strain signal for a given platform displacement may be effectively doubled, while also reducing noise for a given strain signal since the differential sensing can be used to effectively cancel the noise. 
     Referring to  FIG. 11C , modeling data is provided for the z displacement illustrated in  FIGS. 11A-11B  illustrating normal strain at the outer surface of the pivot mount in the x direction, εx. As shown, when in the condition of uniform z displacement, the high εx strain regions are located along lengths of the secondary spring arms extending in the x-direction between the base and pivot platform, while minimal or no εx strain is located along the secondary spring arms extending in the y-direction between the base and pivot platform. In addition, the high strain regions are concentrated in the secondary spring arms rather than the primary spring arms. Specifically, regions in a condition of positive (tensile) normal strain at the surface with the highest εx are located at lengths  365 ,  363 A,  361 B, and regions in a condition of negative (compressive) normal strain at the surface with the highest εx are located at lengths  361 A,  363 B,  367 . 
     In the embodiment illustrated in  FIG. 11C , lengths  361 A,  363 A adjacent the switch-back  349 A have equal and opposite normal strains, and lengths  361 B,  363 B adjacent the switch-back  349 B have equal and opposite normal strains. In an embodiment, length  365  adjacent the inner root  351  and length  367  adjacent outer root  353  have equal and opposite normal strains. 
     In an embodiment a pair of adjacent secondary spring arms is located between a pair of primary spring arms. For example, the pair of adjacent secondary spring arms may be mirror images of each other, providing additional redundancy of the strain gauges. In an embodiment, strain at length  361 A is the same in pair of adjacent mirror image secondary spring arms. Lengths  363 B,  367 ,  365 ,  363 A,  361 B in the pair of adjacent mirror image secondary spring arms may also have the same corresponding strains. 
     In an embodiment, a pair of opposite secondary spring arms is located on opposite sides of the pivot platform. For example, the pair of opposite secondary spring arms may be mirror images of each other, providing additional redundancy of the strain gauges. In an embodiment, strain at length  361 A is the same in pair of opposite mirror image secondary spring arms. Lengths  363 B,  367 ,  365 ,  363 A,  361 B in the pair of opposite mirror image secondary spring arms may also have the same corresponding strains. 
     Referring to  FIG. 11D , modeling data is provided for the z displacement illustrated in  FIGS. 11A-11B  illustrating normal strain at the outer surface of the pivot mount in the y direction, εy. As shown, when in the condition of uniform z displacement, the high εy strain regions are located along lengths of the secondary spring arms extending in the y-direction between the base and pivot platform, while minimal or no εy strain is located along the secondary spring arms extending in the x-direction between the base and pivot platform. In addition, the high strain regions are concentrated in the secondary spring arms rather than the primary spring arms. Specifically, regions in a condition of positive (tensile) normal strain at the surface with the highest εy are located at lengths  365 ,  363 A,  361 B, and regions in a condition of negative (compressive) normal strain at the surface with the highest εx are located at lengths  361 A,  363 B,  367 . Thus, the highest εy regions illustrated in  FIG. 11D  are similar to the highest εx regions illustrated in  FIG. 11C , rotated 90 degrees. Furthermore, the description of equal and opposite normal strains, and mirror images of the spring arms is the same in  FIG. 11D , rotated 90 degrees. 
       FIG. 11E  is an illustration of modeling data for equivalent strain magnitude at the outer surface of the pivot mount in both εx and εy for the z displacement illustrated in  FIGS. 11A-11B . As shown, substantially equal strain magnitudes are measured at each of the secondary spring arms.  FIG. 11F  is an illustration of modeling data for shear strain at the outer surface of the pivot mount for the z displacement illustrated in  FIGS. 11A-11B . As illustrated, there is substantially no measurable shear strain at the surface. Thus, the modeling data provided in  FIGS. 11C-11E  illustrates a pivot mount configuration with substantially uniform bending moments in the high strain regions of the spring arms, in which strain is substantially parallel to axial lengths of the spring arms. 
       FIG. 12  is a schematic illustration of an idealized beam of length L with one end fixed and subject to simultaneous transversely applied force F and bending moment M L  at the free end and with zero slope boundary conditions at both ends. In the case shown, the boundary conditions at both ends are such that the slope θ of the deformed beam is equal to zero. The beam and loading shown in  FIG. 12  is in essence a simplification and idealization of the individual spring arm segments comprising the primary spring arms and secondary spring arms in the pivot mount when under load. While the pivot mount spring arm structures in the described embodiments include switch-backs, the underlying behavior of each beam segment in the secondary spring arms can be represented in simplified form by the idealized beam shown in  FIG. 12 . Both the primary and secondary spring arms in the pivot mount can each be thought of as two or more of such idealized beams arranged in series with switch-backs forming the union between each serial beam segment. Further, the ends of the idealized beam in  FIG. 12  are similarly analogous to the inner and outer roots of the spring arms. 
     It can be shown that the moment M L  applied at a point x=L at the end of the beam shown in  FIG. 12  that meets the boundary conditions of zero slope at each end is, in terms of the applied force, F: 
                     M   L     =     FL   2             (   1   )               
Further, it can be shown that the displacement δ of the beam of length L shown in  FIG. 12  at a point x=L is given by:
 
                   δ   =       FL   3       12   ⁢           ⁢   EI               (   2   )               
where E is the Young&#39;s Modulus of the beam and I is the area moment of inertia about the neutral axis. The bending stress σ in a beam is given by:
 
                   σ   =     My   I             (   3   )               
where M is the bending moment at a point along the length of the beam and y is the distance from the neutral plane. This equation shows that this stress will be maximum at a point y=c, where c is the distance from the neutral plane to the outer surface of the beam.
 
     Referring to  FIG. 13 , the shear force and bending moment diagrams for the idealized beam depicted in  FIG. 12  is shown. Such diagrams are derived using elementary mechanics of materials methods. Referring to the bending moment diagram, it is evident that the bending moment is equal but of opposite sign at each end of the beam, and further, that the absolute value of the bending moment is maximum at the ends of the beam. Because the value of bending moment M is maximum and the ends of the beam, the stress σ will also be maximum at the ends of the beam shown in  FIG. 12 , or when M=M L . Regions of the beam in which the bending moment has a positive value will have positive or tensile stress. Correspondingly, regions of the beam in which the bending moment has a negative value will have a negative or compressive stress. The sign of the shear force and bending moment is dependent on the sense of the load applied to the beam. If the sense of the applied load is reversed, the sign of the shear force and bending moment is reversed while the absolute values of the shear force and bending moment will remain unchanged. Thus, if the sense of the applied load is reversed the sign of the resulting stress will also reverse. Stress can be related to strain c through Hooke&#39;s Law:
 
σ= Eε   (4)
 
Combining equations 3 and 4, strain at the outer surface of the beam can be expressed as:
 
                   ε   =     Mc   EI             (   5   )               
Rearranging equation 2 and inserting the result into equation 1:
 
                   F   =       12   ⁢   EI   ⁢           ⁢   δ       L   3               (   6   )                 M   L     =       6   ⁢   EI   ⁢           ⁢   δ       L   2               (   7   )               
Inserting the expression for the bending moment at the end of the beam in equation 7 into equation 5 it can be shown that the normal strain c at the surface of the beam at a position x=L for a given loading will be:
 
                   ε   =       6   ⁢           ⁢   c   ⁢           ⁢   δ       L   2               (   8   )               
Recognizing that the distance from the neutral axis c to the surface of the spring arm and deflection δ will be identical for both the primary and secondary spring arms, the above expression for strain can be expressed as the following proportionality, in which the resulting strain c is inversely proportional to the length L of the beam squared:
 
     
       
         
           
             
               
                 
                   ε 
                   ∝ 
                   
                     1 
                     
                       L 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Hence, an ideal strain amplifying secondary spring arm structure will have a total length L that is substantially shorter than the primary spring arms of the pivot mount. For example, if the secondary spring arms of the pivot mount are half the composite length of the primary spring arms, the strain resulting from a given loading in the secondary spring arm will be four times the strain in the primary spring arms. Thus, a strain gage placed on a secondary spring arm having a total length half the length of a primary spring arm may produce a signal four times as a large as a strain gage placed at a corresponding position on the primary spring arm for the same displacement of the pivot mount platform. Stated another way, the sensitivity of a pivot mount as a displacement sensing device may improve fourfold by incorporating such structures. 
     Referring to  FIG. 14 , a detail view of a strain amplifying secondary spring arm structure with each beam segment labeled sequentially starting at the inner root to the outer root is shown in accordance with an embodiment. Further, the endpoints of each beam segment are identified. For example, spring arm beam segment  1  has corresponding endpoints  1   a  and  1   b . Additionally, it will be apparent that endpoint  1   a  corresponds to the inner root of the secondary spring arm and that endpoint  5   b  corresponds to the outer root of the secondary spring arm. 
     Referring to  FIG. 15A , the bending moment diagram along the length of the strain amplifying secondary spring arm structure depicted in  FIG. 14  resulting from a load applied to the pivot mount platform is shown in accordance with an embodiment. As with the diagrams shown in  FIG. 13 , this diagram is derived using elementary mechanics of materials methods. The bending moment diagram shown has been divided into regions corresponding to the individual beam segments defined for the secondary spring arm structure shown in  FIG. 14 . Referring to the diagram, the absolute value of the bending moment is maximum at end points  1   a ,  2   b ,  3   a ,  3   b ,  4   a , and  5   b . By extension, the absolute value of strain is also a maximum at end points  1   a ,  2   b ,  3   a ,  3   b ,  4   a , and  5   b.    
     The sign of the shear force and bending moment is dependent on the sense of the load applied to the beam. If the sense of the applied load is reversed, the sign of the shear force and bending moment is reversed while the absolute values of the shear force and bending moment will remain unchanged. Thus, if the sense of the applied load is reversed the sign of the resulting stress and, it follows, strain will also reverse. Referring to  FIG. 15B , the bending moment diagram for the secondary spring arm of  FIG. 14  for the case of equal applied load with opposite sense to that depicted in  FIG. 15A  is shown in accordance with an embodiment. Note that the bending moment for both load cases is equal among the grouping of endpoints  1   a ,  3   b , and  4   a  and that the bending moment is also equal among the grouping of endpoints  2   b ,  3   a , and  5   b . Further, note that the magnitude of the bending moment and, hence, strain response is always equal but of opposite sign between the grouping of endpoints  1   a ,  3   b , and  4   a  and the grouping of endpoints  2   b ,  3   a , and  5   b . It is possible to form “correlated pairings” or, generally, “correlated groupings” of strain gages by combining the signals from stain gages that are subjected to a correlated strain response. 
     In accordance with embodiments, some amount of localized strains are found at various locations within the pivot mount due to local stress concentrations, however these do not affect the strain measurement because the strain gages are located away from the localized strain regions. For example, local stress concentrations may be found at the ends of channels  310  defining the switch-backs or roots near end points  1   a ,  2   b ,  3   a ,  3   b ,  4   a , and  5   b . Accordingly, while strain may reach a theoretical maximum at the segment endpoints, in an embodiment strain gages and reference gages are located a specific distance away from the end points  1   a ,  2   b ,  3   a ,  3   b ,  4   a , and  5   b  so that they are not located at fringe strain regions associated with local stress concentrations yet still be located at or near the regions of highest strain. 
     Strain sensing elements  320  and reference gages  340  may be arranged into sensors so that the resulting sensor signals are correlated. A set of sensors is considered correlated, or dependent, if the signal of a missing or broken gage in the sensor may be approximated from the remaining set of signals. A minimum set of independent strain signals equal to the number of desired position measurements is required to calculate those measurements. Correlated strain signals in excess of the minimum required set may be included in the position calculation and used to improve the signal to noise ration of the measurement. If a strain gage ( 320 ,  340 ) or sensor failure occurs the calculation may be adjusted to maintain position output albeit with a reduced signal to noise ratio. In this way correlated signals provide redundancy as well as an improved signal to noise ratio. 
     Referring to  FIG. 16 , a pivot mount including 24 correlated strain sensors is illustrated in accordance with an embodiment. Specifically,  FIG. 16  is an exemplary illustration similar to  FIG. 7  described above, including 48 total strain sensing elements  320  (strain gages) and 48 total reference gages  340 . In such a configuration, a pair of strain sensing elements (strain gages) and references gauges on opposite sides of a switch-back or at the inner/outer roots may correspond to a single strain sensor. As previously described, these pairs of strain sensing elements  320  on opposite sides of a switch-back or at the inner/outer roots measure opposite strain types, of equal magnitude. Accordingly, these pairs of strain gages (as well as the corresponding reference gages  340 ) can also be considered strain sensors, which may be correlated with other strain sensors. The strain sensors illustrated in  FIG. 16  may be linearly dependent sets (correlated pairs) depending upon whether the pivot platform is rotated about the x-axis, rotated about the y-axis, or is subjected to a vertical displacement. Table I below describes certain correlated pairs of the exemplary embodiment. 
     
       
         
           
               
             
               
                 TABLE I 
               
               
                   
               
               
                 Correlated pair strain sensors 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Under rotation about the y-axis 
               
               
                   
                 signal 1 = −signals 7, 10 
               
               
                   
                 signal 2 = −signals 9, 12 
               
               
                   
                 signal 3 = −signals 8, 11 
               
               
                   
                 signal 1 = signal 4 
               
               
                   
                 signal 2 = signal 5 
               
               
                   
                 signal 3 = signal 6 
               
               
                   
                 Under rotation about the x axis 
               
               
                   
                 signal 13 = −signals 19, 22 
               
               
                   
                 signal 14 = −signals 21, 24 
               
               
                   
                 signal 15 = −signals 20, 23 
               
               
                   
                 signal 13 = signal 16 
               
               
                   
                 signal 14 = signal 17 
               
               
                   
                 signal 15 = signal 18 
               
               
                   
                 Under vertical displacement 
               
               
                   
                 signal 1 = signals 4, 7, 10, 13, 16, 19, 22 
               
               
                   
                 signal 2 = signals 5, 9, 12, 15, 18, 20, 23 
               
               
                   
                 signal 3 = signals 6, 8, 11, 14, 17, 21, 24 
               
               
                   
                   
               
            
           
         
       
     
     In the above exemplary embodiment, several correlated pairs are described for a 24 channel (signal) operation, with each channel corresponding to a signal produced by a pair of strain gages and references gages. Under normal operation, the feedback signal produced by the exemplary pivot mount operating under normal operation can be converted into a synthesized output signal by a transformation matrix. A generalized transformation matrix for converting a pivot mount feedback signal to a synthesized output signal is represented in equation (10) for n strain signal inputs to 3 position measurement outputs (e.g. tilt, tip, z): 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             Out 
                             1 
                           
                         
                       
                       
                         
                           
                             Out 
                             2 
                           
                         
                       
                       
                         
                           
                             Out 
                             3 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               A 
                               1 
                             
                           
                           
                             
                               A 
                               2 
                             
                           
                           
                             
                               A 
                               3 
                             
                           
                           
                             … 
                           
                           
                             
                               A 
                               n 
                             
                           
                         
                         
                           
                             
                               B 
                               1 
                             
                           
                           
                             
                               B 
                               2 
                             
                           
                           
                             
                               B 
                               3 
                             
                           
                           
                             … 
                           
                           
                             
                               B 
                               n 
                             
                           
                         
                         
                           
                             
                               C 
                               1 
                             
                           
                           
                             
                               C 
                               2 
                             
                           
                           
                             
                               C 
                               3 
                             
                           
                           
                             … 
                           
                           
                             
                               C 
                               n 
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               S 
                               1 
                             
                           
                         
                         
                           
                             
                               S 
                               2 
                             
                           
                         
                         
                           
                             
                               S 
                               3 
                             
                           
                         
                         
                           
                             … 
                           
                         
                         
                           
                             
                               S 
                               n 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     While embodiments of pivot mounts have been described thus far in a square configuration, with secondary spring arms extending along the x-direction or y-direction, embodiments are not so limited. Indeed, the strain sensing elements and reference gages can be located along a number of directions. In an embodiment illustrated in  FIG. 17 , a pivot mount  300  includes a base  302 , pivot platform  304 , primary spring arms  306  and secondary spring arms  307 . Each secondary spring arm  307  is fixed to the pivot platform  304  at a corresponding inner root  351 , and fixed to the base  302  at a corresponding outer root  353  as previously described. The pivot mount illustrated in  FIG. 17  differs from other embodiments of pivot mounts described herein in that the secondary spring arms  306 ,  307  are arranged in a generally equilateral triangular configuration, rather than a generally square configuration. As a result, strain measured is not located within the only the εx and εy directions. Nevertheless, the same results of equal and opposite strain, uniform bending moments in the high strain regions, and distributed, correlated pairs is achieved. Accordingly, while embodiments have been described specific to creating and measuring strain in the εx and εy directions, embodiments are not so limited, and pivot mount feedback signals may be converted into a synthesized output signal for a variety of geometries. 
     In accordance with embodiments, the transfer head assembly  200  may adjust the orientation of the MPA  103  until a desired amount of and/or a desired distribution of pressure across pivot mount  300  is sensed by the pivot mount  300  strain sensing elements  320 . Thus, the transfer head array  115  on MPA  103  may be actively aligned with an array of micro devices on a mating substrate. For example, the spatial orientation representing alignment may be predetermined to include a plane passing through the transfer head array  115  being parallel to a plane passing through the array of micro devices. Alternatively, the spatial orientation representing alignment may include the planes not being parallel, but rather, being in some predetermined mutual orientation, such as angled such that only a portion of the transfer head array  115  make contact with respective micro devices when the arrays are brought together. More particularly, the spatial orientation representing alignment of the transfer head array  115  with the array of micro devices may be any predetermined spatial orientation. Such spatial orientation may be monitored, sensed, and measured to determine system characteristics such as distribution of pressure across pivot mount  300 . Thus, the measured system characteristics may be used as a proxy to represent alignment. Active alignment may increase the transfer rate of micro devices, since fine-alignment may be accomplished while picking up, and similarly while releasing, the micro devices. Furthermore, active alignment may be made on-the-fly without parasitic translation of the transfer head array  115  that may otherwise smear and damage the array of micro devices. Such on-the-fly adjustments may be useful when a donor substrate, e.g., carrier substrate, and/or a display substrate, e.g., receiving substrate, include surface irregularities and non-planar contours. 
     Referring to  FIG. 18A , a schematic illustration of a control scheme for regulating a transfer head assembly is shown in accordance with an embodiment. More particularly, the control loop may include multiple sub-loops that process a combination of position and strain inputs. The actuators of transfer head assembly may be driven by the sub-loops, first toward an initial desired location, and if contact between MPA  103  and a target substrate is sensed, then the initial desired location may be modified to move MPA  103  toward a desired stress state, e.g., to evenly distribute pressure across MPA  103  and/or to achieve a desired level of pressure at one or more locations on pivot mount  300  based on a deflection of the pivot mount  300  secondary spring arms  307 . 
     A primary input  1802  may define a set of reference signals that correspond to an initial desired state of MPA  103 . More specifically, primary input  1802  may define a target spatial location of MPA  103  relative to an anticipated location of a micro device array or substrate surface. Primary input  1802  may be fed into one of several inner loops, each of which may correspond to an individual actuator. For example, x-actuator inner loop  1804  may correspond to a control loop for controlling an x-actuator of the transfer head assembly, and thus MPA  103 , to tip about a remote rotational center. Similarly, y-actuator inner loop  1806  may correspond to a control loop for controlling a y-actuator of the transfer head assembly, and thus MPA  103 , to tilt about the remote rotational center. Also, z-actuator inner loop  1808  may correspond to a control loop for controlling a z-actuator of the transfer head assembly and thus a location of MPA  103  along a z-axis. Therefore, the combination of inner loops allow for the control of actuators that adjust a tip, tilt, and z-spatial orientation of MPA  103 . 
     In an embodiment, inner loop control of transfer head assembly  200  actuators results in a primary output  1810 . More specifically, primary output  1810  may be an instantaneous geometric configuration of transfer head assembly  200  resulting from actuator movement. The geometric configuration may be inferred from data supplied by encoders or other sensors that track spatial position of individual transfer head assembly  200  components. That is, the geometric configuration may include a combination of individual geometric configurations such as a tip position, tilt position, and z-position. Primary output  1810  may also relate to a spatial position of MPA  103  as inferred from known physical dimensions of transfer head assembly  200  components. Alternatively, MPA  103  surface location may be sensed directly using, e.g., laser micrometers, accelerometers, etc., to provide spatial orientation feedback that may be included directly in primary output  1810 . Thus, a position of MPA  103  may be inferred or sensed to determine whether primary output  1810  has been achieved, i.e., equals the intended primary input  1802 . However, although MPA  103  may be driven toward a target substrate to achieve the positional command of primary input  1802 , in some cases, MPA  103  may contact the target substrate. Furthermore, once contact is detected, primary input  1802  may be modified by additional commands from several actuator outer loops, to achieve a neutral tip and tilt deformation of pivot mount  300  with a desired pressure distribution across pivot mount  300 . Accordingly, MPA array  103  may be driven to a tip deflection, tilt deflection, and z-compression target within an accuracy in the submicron range, e.g., on the order of less than about 250 nm. 
     After contact between a transfer head array  115  of MPA  103  and a micro device has been made, MPA  103  may be finely adjusted based on pressure feedback from the pivot mount  300 . More particularly, fine adjustment of MPA  103  may be enabled in response to system recognition of a contact disturbance  1812 . In an embodiment, enable logic is included to determine whether a contact disturbance  1812  is sensed prior to MPA  103  achieving the desired primary input  1802 , and if a contact disturbance  1812  is sensed, additional control loops may be closed to permit fine adjustment of the transfer head assembly  200 . More specifically, additional control loops may be closed to drive MPA  103  toward tip deflection, tilt deflection, and z-compression targets, rather than toward the initial positional target of primary input  1802 . 
     In an embodiment, a contact disturbance  1812  is sensed when, e.g., MPA  103  contacts a mating substrate out of alignment. For example, if MPA  103  and the mating substrate make contact in perfect alignment, the primary output  1810  may equal the primary input  1802  and micro devices may then be gripped by transfer head array  115  without requiring additional adjustment. However, if MPA  103  and the mating substrate are not perfectly aligned, displacement or strain measurements from each strain sensing element  320  on pivot mount  300  may be substantially different from each other and/or the desired level of pressure may not be achieved. That is, in an embodiment, an expected or desired tip, tilt, and compression state must be satisfied prior to initiating electrostatic gripping. If the desired state is not achieved, displacement or strain measurements may be fed as feedback signals  1814 . 
     In an embodiment, feedback signals  1814  correspond to analog signals from the strain sensing elements  320  and references gages  340 . In the exemplary embodiment above, feedback signals  1814  may include twenty four sensor signals from forty eight separate strain sensing elements  320  and forty eight reference gages  340 . The feedback signals  1814  may be conditioned by a signal conditioning and combination logic  1815  to transform the analog signals into a synthesized output signal representing a strain state of a respective strain sensing element. These synthesized output signals may furthermore be combined by signal conditioning and combination logic  1815  to synthesize one or more of a pivot mount  300  compression synthesized output signal, a pivot mount  300  tilt deflection synthesized output signal, and a pivot mount  300  tip deflection synthesized output signal represented by a transformation matrix equation, such as equation (10) described above. The synthesized output signals may be provided as inputs to dynamic control enable logic  1816 . More particularly, dynamic control enable logic  1816  may observe the one or more synthesized output signals to determine that a contact disturbance  1812  has occurred in one or more of a tip, tilt, or z-direction. For example, if a non-zero compression signal is synthesized by signal conditioning and combination logic  1815  that exceeds predetermined limits, dynamic control enable logic  1816  may recognize the contact disturbance  1812 . 
     In response to observing that a contact disturbance  1812  exists, dynamic control enable logic  1816  may close respective outer loops, each of which may be configured to provide output commands to modify the positional command of primary input  1802 . Thus, closing the outer loops may drive the actuators to achieve a desired state of pressure and orientation, rather than driving them to achieve an initial position command. For example, if dynamic control enable logic  1816  observes that a compression contact disturbance  1812  exists, z-actuator outer loop  1818  may be closed to respond to the contact disturbance  1812  by adjusting a z-actuator. Likewise, dynamic control enable logic  1816  may respond to tip deflection signals or tilt deflection signals by enabling x-actuator outer loop  1820  or y-actuator outer loop  1822 , respectively. 
     Deflection and compression feedback signals may be passed from signal conditioning and combination logic  1815  as synthesized output signals to respective outer loops for comparison with deflection command inputs  1840  provided to respective outer loops. In an embodiment, pivot mount  300  deflection command inputs  1840  may correspond to a desired pressure distribution across pivot mount  300  or MPA  103 . Thus, pivot mount  300  deflection command inputs  1840  may represent tip deflection, tilt deflection, and z-compression targets of pivot mount  300 . These targets may be compared to the synthesized output signals from signal conditioning and combination logic  1815 , which indicate an instantaneous pressure distribution across pivot mount  300 , to determine a difference. The difference, if any, may then be fed as an error signal to drive respective transfer head assembly  200  actuators. For example, if tipping of pivot mount  300  is sensed as a contact disturbance  1812  and dynamic control enable logic  1816  observes that the tipping exceeds an allowable amount, x-actuator outer loop  1820  may be closed and the tipping deflection signal may be compared with a pivot mount  300  tip deflection command  1840  to generate a motion control signal that will tip pivot mount  300  toward a desired stress state. The motion control signal may be fed to a servo filter and passed through inverse kinematics calculations to generate an outer loop command output  1830 . In an embodiment, the motion control signal may also be added with other transfer head assembly motion control signals at one or more of motion summation nodes  1850 . This may be the case, for example, when movement of multiple actuators is required to cause tipping. 
     In order to close the control loop, the outer loop command outputs  1830  may be combined with primary input  1802  and passed back into actuator inner loops. For example, a tipping outer loop command  1830  may be summed with primary input  1802  for an x-actuator and passed through x-actuator inner loop  1804 , thereby controlling an x-actuator in such a manner that pivot mount  300  tips toward a physical state of more even pressure distribution. Respective outer loop commands may be passed through to any actuator inner loop for which a contact disturbance  1812  was sensed. 
     The above control methodology may be performed and repeated until the transfer head assembly  200  is moved to a location at which pressure distribution across pivot mount  300 , and hence MPA  103 , is uniform and achieves a desired amount of pressure. Thus, transfer head assembly  200  may be controlled to bring an array of electrostatic transfer head array  115  on MPA  103  into contact with an array of micro devices on a mating substrate. Using the control system described above, if alignment between MPA  103  and the mating substrate is not initially perfect, which would be true of almost every transfer operation, pressure distribution control may be implemented to fine tune the alignment. The control methodology may be performed quickly, e.g., on the order of about 50 ms to sense a contact disturbance  1812 , enable the appropriate outer loop(s), and feed appropriate outer loop control commands to actuators, and thus, complete contact may be rapidly achieved between an electrostatic transfer head array  115  and an array of micro devices, enabling efficient transfer between a carrier substrate and a receiving substrate. 
     Referring now to  FIG. 18B , a schematic illustration is provided for a method of generating a synthesized output signal in an embodiment. As illustrated, feedback signals  1814  are received by a signal conditioning and combination logic  1815 , which combines the incoming feedback signals  1814  from the pivot mount  300  and generates synthesized output signals. In the simplest case, feedback signals received from the pivot mount (e.g. from sensors  1 - 24  described above with regard to  FIG. 16 ) are linearly combined by multiplication with a transformation matrix to form a set of output measurements (synthesized output signals). 
     Referring to the embodiment illustrated in  FIG. 18C , in a more complex implementation, correlated sets of strain sensors may be checked for signal quality. As illustrated, feedback signals  1814  are received by a signal conditioning and combination logic  1815 . At  1815 A, the feedback signals  1814  are checked to determine if they are within a predefined normal operating range. Sensors (including gages  320 ,  340 ) that are outside of the normal operating range are flagged as failed sensors. Failed sensor signals may then be rejected requiring a change in the transformation matrix. At  1815 B signals are checked for variation within the normal operating range. Sensors (including gages  320 ,  340 ) with variation that is greater or less than a normally operating sensor are flagged as failed sensors. Based on the sensors flagged as failed, a transformation matrix is selected that is able to synthesize the outputs from the remaining signals, and the transformation matrix is used to convert the resulting sensor signal vector into synthesized output signals (position measurement output) at  1815 C. In this way synthesized output signals are maintained at a reduced signal to noise ratio rather than sensor failure causing output failure. 
     Referring to  FIG. 19 , a flowchart illustrating a method of aligning an MPA  103  coupled with a pivot mount  300  on a transfer head assembly  200  relative to a target substrate is shown in accordance with an embodiment. The method may be performed, e.g., during a pick-up or a placement operation as micro devices are transferred from a carrier substrate to a receiving substrate. At operation  1902 , mass transfer tool  100  moves transfer head assembly  200  along a z-axis toward a target substrate, e.g., carrier substrate held by carrier substrate holder  104  or receiving substrate held by receiving substrate holder  106 , according to primary input  1302 . More specifically, the MPA  103  and pivot mount  300  are moved toward the target substrate along the z-axis. Movement of MPA  103  along z-axis  510  may be achieved by actuating various actuators of mass transfer tool  100  or a substrate holder. 
     Initially, there may be no compressive loading applied to MPA  103  or pivot mount  300 . This initial state may correspond to a range of travel over which array of micro devices are physically separated from the electrostatic transfer head array. During this travel, MPA  103  and the target substrate may have misaligned surfaces, but there may be no indication of this misalignment since the pressure distribution state of pivot mount  300  may be uniform, i.e., all strain sensing elements may be outputting signals indicating zero strain. 
     At operations  1904  and  1906 , an electrostatic transfer head in the electrostatic transfer head array  103  may contact a micro device while other electrostatic transfer heads may remain separated from corresponding micro devices. That is, contact may be made while MPA  103  is misaligned with the target substrate. This positional misalignment may be sensed as uneven pressure distribution in pivot mount  300 . For example, a first strain output value from one strain sensing element  320  on pivot mount  300  and a different second strain output value from another strain sensing element  320  in pivot mount  300  may differ. The strain signals may be provided as feedback signals  1814  and conditioned and combined by into synthesized output signals (e.g. tip deflection, tilt deflection, and compression signals) by signal conditioning and combination logic  1815  indicating a contact disturbance  1812 . 
     Dynamic enable control logic  1816  may observe that the contact disturbance  1812  exists, and depending upon the level of contact disturbance  1812 , may activate actuator outer loops to determine driving signals for actuating various actuators of transfer head assembly  200  in order to adjust an orientation of MPA  103  such that pressure distribution across pivot mount  300  is uniform. For example, at operation  1908 , in response to the tip signal being recognized as a contact disturbance  1812  above a threshold, x-actuator outer loop  1820  may feed command signals  1830  to x-actuator inner loop  1804  in order to actuate an x-actuator to tip MPA  103  about remote rotational center. Similarly, at operation  1910 , in response to the tilt deflection signal being recognized as a contact disturbance  1812  above a threshold, y-actuator outer loop  1822  may feed command signals to y-actuator inner loop  1806  in order to actuate a y-actuator  708  to tile MPA  103  about remote rotational center. 
     At operation  1912 , in response to actuation of the x- and y-actuators based on the tip and tilt deflection signals MPA  103  may be rotated into alignment with the target substrate. Furthermore, with remote rotational center co-located with the contact surface of MPA  103 , the electrostatic transfer head array  115  may experience pure rotation about remote rotational center. Thus, as MPA  103  is aligned with the target substrate, the electrostatic transfer head array  115  may experience minimal parasitic lateral motion and micro devices may remain undamaged. 
     Actuation of transfer head assembly  200  according to synthesized output signals (tip, tilt, and z-compression signals) may continue until the electrostatic transfer head array  115  is in contact with micro devices on the target substrate. More particularly, actuation may continue until primary output  1810  is within the limits set by primary input  1802 , at which point actuation may be stopped. As discussed above, primary output  1810  may be a positional output that is modified to reach a desired pivot mount  300  state. For example, actuation of transfer head assembly  200  may continue until primary positional input is achieved and/or pressure distribution across pivot mount  300  is uniform. 
     After contact between the electrostatic transfer head array  115  and the micro devices is made, a voltage may be applied to the electrostatic transfer head array  115  to create a grip pressure on the array of micro devices. An electrostatic voltage may be applied to electrostatic transfer head array  115  compliant voltage contacts  316  and voltage contacts  120 . Additional electrical contacts and connectors may be integrated within transfer head assembly  200  and powered by voltage supplies based on control signals from computer  108 . For example, computer  108  may implement a control algorithm instructing that electrostatic transfer head array  115  be activated if a predefined deformation is simultaneously sensed by each strain sensing element on pivot mount  300  during a pick up process. As a result, the array of electrostatic transfer head array  115  may apply a gripping pressure to the array of micro devices after the entire array surface is in contact and uniform pressure is applied across the array. 
     After gripping the micro devices with electrostatic transfer head array  115 , the micro devices may be picked up from carrier substrate. During pick up, the electrostatic voltage supplied to the electrostatic transfer head array  115  may persist, and thus, the array of micro devices may be retained on the electrostatic transfer head array  115  and removed from the carrier substrate. 
     During the pick up operation, a heating element may direct heat toward pivot mount  300  and/or MPA  103 . Thus, the micro devices may be heated through contact with electrostatic transfer head array  115  on MPA  103  during pick up. For example, a heating element adjacent to pivot mount  300  may be resistively heated to transfer heat to MPA  103 , and thus, to the micro devices through the electrostatic transfer head array  115 . Heat transfer may occur before, during, and after picking up the array of micro devices from carrier substrate. 
     Although a pick up process is described in relation to  FIG. 19 , a similar methodology may be used to control the placement of micro devices onto a receiving substrate, such as a display substrate, held by receiving substrate holder  106 . For example, as the micro devices are gripped by the electrostatic transfer head array  115 , mass transfer tool  100  may move the MPA  103  over a receiving substrate, and align MPA with a target region of the receiving substrate. MPA  103  may be advanced toward, and aligned with, the receiving substrate using the control sequence described above until the array of micro devices held by the electrostatic transfer head array  115  are placed in uniform contact with the target region. Uniform contact may be inferred by sensing a strain state of pivot mount  300 . Subsequently, voltage may be removed from the electrostatic transfer head array  115  to release the micro devices onto the receiving substrate and complete the transfer operation. 
     Referring to  FIG. 20 , a schematic illustration of a computer system is shown that may be used in accordance with an embodiment. Portions of embodiments are comprised of or controlled by non-transitory machine-readable and machine-executable instructions that reside, for example, in machine-usable media of a computer  108 . Computer  108  is exemplary, and embodiments may operate on or within, or be controlled by a number of different computer systems including general purpose networked computer systems, embedded computer systems, routers, switches, server devices, client devices, various intermediate devices/nodes, stand-alone computer systems, and the like. Furthermore, although some components of a control system, e.g., signal conditioning and combination logic  1815  and dynamic control enable logic  1816 , have been broken out for discussion separately above, computer  108  may integrate those components directly or include additional components that fulfill similar functions. 
     Computer  108  of  FIG. 20  includes an address/data bus  2002  for communicating information, and a central processor  2004  coupled to bus  2002  for processing information and instructions. Computer  108  also includes data storage features such as a computer usable volatile memory, e.g. random access memory (RAM)  2006 , coupled to bus  2002  for storing information and instructions for central processor  2004 , computer usable non-volatile memory  2008 , e.g. read only memory (ROM), coupled to bus  2002  for storing static information and instructions for the central processor  2004 , and a data storage device  2010  (e.g., a magnetic or optical disk and disk drive) coupled to bus  2002  for storing information and instructions. Computer  108  of the present embodiment also includes an optional alphanumeric input device  2012  including alphanumeric and function keys coupled to bus  2002  for communicating information and command selections to central processor  2004 . Computer  108  also optionally includes an optional cursor control  2014  device coupled to bus  2002  for communicating user input information and command selections to central processor  2004 . Computer  108  of the present embodiment also includes an optional display device  2016  coupled to bus  2002  for displaying information. 
     The data storage device  2010  may include a non-transitory machine-readable storage medium  2018  on which is stored one or more sets of instructions (e.g. software  2020 ) embodying any one or more of the methodologies or operations described herein. For example, software  2020  may include instructions, which when executed by processor  2004 , cause computer  108  to control mass transfer tool  100  or remote center robot  500  according to the control scheme described above for aligning an MPA  103  with a target substrate. Software  2020  may also reside, completely or at least partially, within the volatile memory, non-volatile memory  2008 , and/or within processor  2004  during execution thereof by computer  108 , volatile memory  2006 , non-volatile memory  2008 , and processor  2004  also constituting non-transitory machine-readable storage media. 
     In utilizing the various aspects of the embodiments, it would become apparent to one skilled in the art that combinations or variations of the above embodiments are possible for forming a pivot mount with integrated strain sensing elements. Although the embodiments have been described in language specific to structural features and/or methodological acts, it is to be understood that the appended claims are not necessarily limited to the specific features or acts described. The specific features and acts disclosed are instead to be understood as embodiments of the claims useful for illustration.

Metadata:
Filing Date: 20140930
Publication Date: 20170711
Grant Date: 20170711
Priority Date: 20140930
Inventors: BATHURST STEPHEN P.
PARKS PAUL ARGUS
LIGHT NILE ALEXANDER
Assignee: APPLE INC
CPC Classifications: [{"code": "B81C99/002", "inventive": true, "first": false, "tree": "[]"}, {"code": "H02N13/00", "inventive": true, "first": true, "tree": "[]"}, {"code": "H01L21/6833", "inventive": true, "first": false, "tree": "[]"}, {"code": "B81C99/002", "inventive": true, "first": false, "tree": "[]"}, {"code": "H02N13/00", "inventive": true, "first": true, "tree": "[]"}, {"code": "B81C99/002", "inventive": true, "first": false, "tree": "[]"}, {"code": "H01L21/6833", "inventive": true, "first": false, "tree": "[]"}, {"code": "B81C99/002", "inventive": true, "first": true, "tree": "[]"}, {"code": "H02N13/00", "inventive": true, "first": true, "tree": "[]"}]
Family ID: 54140678