Assembly of flexible interconnects using sedimentation

Abstract

Embodiments of interplanar interconnects, intraplanar interconnects, and methods for forming the same in rigid, flexible, and stretchable substrates are described. In one example, a method for forming interplanar interconnects in a substrate includes injecting a solution into a mold cavity of a molding structure. The solution includes a polymer matrix and liquid metal elements. The method further includes performing a curing process on the solution to form an interplanar interconnect in the polymer matrix. The curing process includes exposing different regions of the solution to light while the molding structure is positioned in different orientations to cause selective sedimentation of the liquid metal elements in the solution.

Description

ASSEMBLY OF FLEXIBLE INTERCONNECTS USING SEDIMENTATION STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0001] This invention was made with government support under grant number 2119105 awarded by the National Science Foundation (NSF) and grant number N000142112699 awarded by the Office of Naval Research (ONR). The government has certain rights in the invention. CROSS REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of and priority to U.S. Provisional Application Serial No. 63 / 535,919, filed August 31, 2023, titled “CONCURRENT AND RAPID THREE- DIMENSIONAL ASSEMBLY OF LIQUID METAL FLEXIBLE INTERCONNECTS USING GRAVITATIONAL SEDIMENTATION,” the entire contents of which are hereby incorporated herein by reference. BACKGROUND

[0003] The development of complex computer architectures and advanced electrical systems has increased the demand for highly integrated circuit design. Additionally, the development of flexible and stretchable electronics has increased the need for complex flexible electrical circuits. To make a highly integrated electric circuit, a multi-layer three-dimensional (3D) circuit architecture is necessary. An essential technique for fabricating such a complex and intricate 3D circuit architecture is the use of “vias” to link conductive elements that are disposed in two different layers. In theory, single-layer circuit designs that include open curves can connect all components without crossing lines. However, in practice, electrical resistance, the area of the material, and the physical size of the medium limit this approach. Using a via can minimize the complexity of printed circuit boards (PCBs) that typically include numerous electronic components. In addition to rigid circuit boards, vias may also be used in flexible circuit boards that are implemented in devices such as soft robotics, wearable electronics, and flexible displays, among others. The application of via techniques can substantially improve flexible circuit design.SUMMARY

[0004] Described herein is method for forming flexible interplanar (multi-layer) interconnects and cross pattern planar interconnects in a stretchable and flexible substrate. Specifically, the present disclosure is directed to forming flexible traces, interplanar interconnects, and cross pattern planar interconnects in various types of rigid, flexible, and stretchable circuit boards by using selective sedimentation of liquid metal microdroplets within a photoresin-dilutant solution and leveraging photoresin curing behaviors. By using one or more fabrication processes described in examples herein, conductive elements formed in two different planes of a substrate can be connected in under one minute in most cases, regardless of the size and number of connection points. The fabrication processes of the present disclosure have the potential to transform the way complex flexible electronic devices are designed and produced, unlocking new opportunities for use in a variety of industries.

[0005] According to one embodiment, a device includes a substrate and a porous metal element extending between a first plane and a second plane in the substrate. The porous metal element includes a formation of liquid metal elements.

[0006] According to another embodiment, a device includes a substrate. The device further includes a first porous metal element extending in a first plane in the substrate in a first direction. The first porous metal element includes a first formation of liquid metal elements. The device further includes a second porous metal element extending in a second plane in the substrate in a second direction that is different from the first direction. The second plane is different from the first plane and the second porous metal element includes a second formation of liquid metal elements.

[0007] According to another embodiment, a method for forming interplanar interconnects in a substrate includes injecting a solution into a mold cavity of a molding structure. The solution includes a polymer matrix and liquid metal elements. The method further includes performing a curing process on the solution to form an interplanar interconnect in the polymer matrix. The curing process includes exposing different regions of the solution to light while the molding structure is positioned in different orientations to cause selective sedimentation of the liquid metal elements in the solution.BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Many aspects of the present disclosure can be better understood with reference to the following figures. The components in the figures are not necessarily to scale, with emphasis instead being placed upon clearly illustrating the concepts of the disclosure. Moreover, repeated use of reference characters or numerals in the figures is intended to represent the same or analogous features, elements, or operations across different figures. Repeated description of such repeated reference characters or numerals is omitted for brevity.

[0009] FIG. 1A illustrates a cross-sectional view of an example device according to various aspects and embodiments of the present disclosure.

[0010] FIG. 1B illustrates a cross-sectional view of the device of FIG. 1A in a bent position according to various aspects and embodiments of the present disclosure.

[0011] FIG. 2 illustrates a cross-sectional view of another example device according to various aspects and embodiments of the present disclosure.

[0012] FIG. 3A illustrates a cross-sectional view of another example device according to various aspects and embodiments of the present disclosure.

[0013] FIG. 3B illustrates a top view of the device of FIG. 3A according to various aspects and embodiments of the present disclosure.

[0014] FIG. 4 illustrates a perspective view of another example device according to various aspects and embodiments of the present disclosure.

[0015] FIG. 5 illustrates a perspective view of another example device according to various aspects and embodiments of the present disclosure.

[0016] FIG. 6 illustrates a cross-sectional view of another example device according to various aspects and embodiments of the present disclosure.

[0017] FIG. 7A illustrates an example method for forming interplanar interconnects in a substrate according to various aspects and embodiments of the present disclosure.

[0018] FIG. 7B illustrates views of an example implementation of the method of FIG. 7A according to various aspects and embodiments of the present disclosure.

[0019] FIG. 8 illustrates a flow diagram of an example cross pattern planar interconnect fabrication process according to various aspects and embodiments of the present disclosure.

[0020] FIG. 9 illustrates a flow diagram of an example interplanar interconnect and cross pattern planar interconnect fabrication process according to various aspects and embodiments of the present disclosure.

[0021] FIG. 10A illustrates two different LM-STAIR fabricated circuits that are stacked together to form another example device according to various aspects and embodiments of the present disclosure.

[0022] FIG. 10B illustrates another example device including the two different LM-STAIR fabricated circuits of FIG. 10A according to various aspects and embodiments of the present disclosure.

[0023] FIGS. 11A and 11B illustrate diagrams of example peel test results of an example fabricated flexible circuit during 11 cycles according to one embodiment of the present disclosure.

[0024] FIG.12A illustrates chemical structure diagrams of an example photocurable polymer and an example diluting agent according to one embodiment of the present disclosure.

[0025] FIG. 12B illustrates a diagram of an example shear mixing process according to one embodiment of the present disclosure.

[0026] FIG.12C illustrates a diagram of an example analysis of LM microdroplets size based on shear mixing revolutions per minute (RPM) and processing time according to one embodiment of the present disclosure.

[0027] FIG. 12D illustrates a diagram of example circuit feature size based on LM microdroplets diameter according to one embodiment of the present disclosure.

[0028] FIG.12E illustrates a bar chart of various example Young’s modulus values based on different ratios of photoresin, diluent, and LM volume percentage according to one embodiment of the present disclosure.

[0029] FIG.12F illustrates a bar chart of various example strain values at maximum based on different ratios of photoresin, diluent, and LM volume percentage according to one embodiment of the present disclosure.

[0030] FIG. 12G illustrates reconstructed micro CT images of example unactivated and activated samples and volume fraction for each cluster according to one embodiment of the present disclosure.

[0031] FIG. 12H illustrates an example cluster index according to one embodiment of the present disclosure.

[0032] FIG.12I illustrates an optical microscopic image of an example minimal gap between electrically conductive electrodes according to one embodiment of the present disclosure.

[0033] FIG. 13A illustrates a diagram of example sheet resistance values of an example line patterned flexible circuit based on three different LM volume percentages according to one embodiment of the present disclosure.

[0034] FIG. 13B illustrates a diagram of an example electrical resistance variation of an example flexible circuit patterned in line according to compressive strain in accordance with one embodiment of the present disclosure.

[0035] FIG. 13C illustrates a diagram of an example electrical resistance variation of an example flexible circuit patterned in line according to tensile strain in accordance with one embodiment of the present disclosure.

[0036] FIG. 13D illustrates a diagram of example sheet resistance values of example interplanar interconnects based on three different percentages of LM volume according to one embodiment of the present disclosure.

[0037] FIG. 13E illustrates a diagram of an example electrical resistance variation of an example interplanar interconnect flexible circuit depending on compressive strain according to one embodiment of the present disclosure.

[0038] FIG. 13F illustrates a diagram of an example electrical resistance variation of an example interplanar interconnects flexible circuit depending on tensile strain according to one embodiment of the present disclosure.

[0039] FIG.13G illustrates a diagram of an example durability test of an example interplanar interconnects flexible circuit for 100 cycles of compressive strain 50% according to one embodiment of the present disclosure.

[0040] FIG. 13H illustrates a diagram of an example durability test of an example flexible interplanar interconnect circuit for 100 cycles of 50% tensile strain according to one embodiment of the present disclosure.

[0041] FIG.14A illustrates a top view of an example magnet sensing and indicating flexible circuit according to one embodiment of the present disclosure.

[0042] FIG. 14B illustrates a bottom view of the example magnet sensing and indicating flexible circuit of FIG.14A according to one embodiment of the present disclosure.

[0043] FIG.14C illustrates a side view of the example magnet sensing and indicating flexible circuit of FIG.14A according to one embodiment of the present disclosure.

[0044] FIG. 14D illustrates a circuit diagram of the example magnet sensing and indicating flexible circuit of FIG.14A according to one embodiment of the present disclosure.

[0045] FIG. 14E illustrates a diagram of an example Hall effect sensor working mechanism according to one embodiment of the present disclosure.

[0046] FIG. 14F illustrates a bar chart of output data of a Hall effect sensor obtained with different magnet height according to one embodiment of the present disclosure.

[0047] FIGS. 14G, 14H, and 14I illustrate images of LEDs in the example magnet sensing and indicating circuit of FIG.14A being illuminated by varying the position of a rectangular shape magnet behind the circuit according to one embodiment of the present disclosure.

[0048] FIG. 14J illustrates a deformed example flexible circuit being illuminated using a magnet according to one embodiment of the present disclosure. DETAILED DESCRIPTION

[0049] As noted above, in addition to rigid circuit boards, vias may also be used in flexible circuit boards that are implemented in devices such as soft robotics, wearable electronics, and flexible displays, among others. The application of via techniques can substantially improve flexible circuit design; however, vias in flexible electronics still present several challenges. First, due to the nature of flexible substrates, vias can function as structural flaws. Second, rigid metallic electrodes on the via in stretchable substrates can cause mechanical failure due to the modulus mismatch between the substrate and the electrode. Third, the current fabrication techniques for creating a via typically involve a multi-step procedure with epoxy resin and copper filling or electroless plating. Due to these challenges, via fabrication in flexible and stretchable electronics has been carried out by manually drilling a via hole and filling it with metallic fillers rather than a systematic approach that can enable automation and scale up.

[0050] To address these challenges, researchers have focused on stretchable and flexible conductive materials, such as liquid metals (LMs). LMs are known for their tunable fluidity as well as thermal and electrical conductivity. Due to their exceptional fluid characteristics as metal species that allow for a large degree of physical deformation, they have been adopted as electrode materials for a variety of stretchable and flexible electronics. LMs are used not only for electrodes but also as via materials to avoid differences in modulus between the electrode and substrate. One set of researchers utilized LM as traces to make three different electrical components and also as interconnects between the components. Other researchers have used LM traces as interconnects between different circuit layers and other electrical components using various methods, such as wetting or filling the vias, lift-off patterning, and iron wires. However, all these methods use viafabrication techniques that have holes in the plane. Through holes can be structural failure points during mechanical deformation. Also, the general via fabrication process involves multiple steps to create individual holes with a drill or a laser cutter, making it complicated. To achieve highly integrated flexible and stretchable circuits, via techniques need to be overhauled.

[0051] To address the aforementioned problems associated with forming vias in flexible and stretchable substrates in general and with respect to existing approaches, the present disclosure provides a via fabrication process referred to herein as the “Liquid Metal Sedimentation for Three- dimensional Assembly of electrical InteRconnects” or “LM-STAIR” process. The LM-STAIR process is a rapid and scalable approach that can be universally applied to vertically connect circuit layers and enable 3D interconnected complex circuit designs in soft and flexible devices through photoresin and LM. The LM-STAIR process leverages an LM selective sedimentation process that occurs throughout a substrate in less than a minute, which creates hundreds of vias regardless of the size and number of connection points. Also, the choice of photoresin for the LM-STAIR process can be adapted to different materials.

[0052] The LM-STAIR process can be implemented to interconnect conductive elements of two different circuit planes in an entirely new approach compared to any other previously reported methods. Furthermore, to realize flexible and stretchable mechanical characteristics, the photoresin (typically stiff and rigid after curing) is mixed with an aliphatic monofunctional acrylate diluting agent in some cases to soften the cured photoresin illustrated by the mechanical and electromechanical properties of the fabricated samples. A magnetic field-indicating circuit with different functions (magnetic field indication and detection) on each side is demonstrated in one example using the LM-STAIR process described herein. The LM-STAIR process can be implemented to create multi-layer circuits without through holes that offer a versatile and efficient solution for a wide range of applications, unlike other conventional methods, such as through hole and wire bonding. The LM-STAIR process of the present disclosure is an innovative approach to revolutionize the design and fabrication of flexible and stretchable circuits and can lead to a paradigm shift in new opportunities and advancements in fields such as wearable technology, healthcare, and robotics, among others.

[0053] Turning now to the figures, FIG. 1A illustrates a cross-sectional view of an example device 100 according to various aspects and embodiments of the present disclosure. The device 100 is an example embodiment of an interconnect device or other device described herein that includes a flexible, stretchable, electrically and thermally conductive interplanar interconnectformed in and extending between multiple layers of a substrate (e.g., at least one of a rigid, flexible, or stretchable substrate). In some cases, the interplanar interconnect of the device 100 or the device 100 itself can be embodied and implemented as a flexible and stretchable via formed in a circuit board (e.g., at least one of a rigid, flexible, or stretchable circuit board). In other examples, the device 100 can be embodied as at least one of a rigid, flexible, stretchable, printed, or wearable circuit board or electronic device (e.g., soft robotics electronic device, healthcare electronic device) that includes such a flexible and stretchable interplanar interconnect or via. The device 100 can include a substrate and at least one of a rigid, flexible, stretchable, or wearable functional component that can be coupled to the substrate in still other examples.

[0054] The interplanar interconnect of the device 100 is embodied as a continuous porous metal structure formed as a collection of individual liquid metal elements (e.g., micro-scale liquid metal particles). When included in at least one of a flexible or stretchable substrate, the flexible and stretchable interplanar interconnect of the device 100 allows for the entire device to have at least one of flexible or stretchable properties. FIG. 1B illustrates a cross-sectional view of the device 100 in a bent position to demonstrate flexible and stretchable properties of the device 100 according to various aspects and embodiments of the present disclosure.

[0055] Referring to FIGS.1A and 1B, the device 100 includes a substrate 103. The substrate 103 can be embodied as at least one of a rigid substrate, a flexible substrate, or a stretchable substrate. In FIGS.1A and 1B, the substrate 103 is embodied as a flexible and stretchable substrate. In one example, the substrate 103 is embodied as at least one of a cured photocurable polymer or a cured photopolymer resin and diluent composite, although other materials may be relied upon to form the substrate 103 in other examples.

[0056] The substrate 103 includes an interplanar interconnect 105 that is at least partly formed in and extends between multiple layers or planes in the substrate 103. The interplanar interconnect 105 includes a first porous metal element 110 extending in a first plane (1stPlane) or layer in the substrate 103. The porous metal element 110 includes and is embodied as a first formation of the liquid metal elements 112. Only a single liquid metal element 112 is denoted in FIG.1A for clarity. The substrate 103 further includes a second porous metal element 120 extending in a second plane (2ndPlane) or layer in the substrate 103. The second plane or layer extending in the substrate 103 is different from the first plane or layer. The porous metal element 120 includes and is embodied as a second formation of liquid metal elements 122. Only a single liquid metal element 122 is denoted in FIG. 1A for clarity. The substrate 103 further includes a third porous metal element130 extending between the first plane or layer and the second plane or layer in the substrate 103. The porous metal element 130 includes and is embodied as a third formation of liquid metal elements 132. Only a single liquid metal element 132 is denoted in FIG.1A for clarity.

[0057] The interplanar interconnect 105 of the device 100 is embodied as a continuous porous metal structure formed as a collection of the porous metal elements 110, 120, 130. Each of the porous metal elements 110, 120, 130 is also embodied as a continuous porous metal structure formed as a collection of the liquid metal elements 112, 122, 132, respectively. When included in at least one of a flexible or stretchable substrate 103, the flexible and stretchable interplanar interconnect 105 of the device 100 allows for the entire device to have at least one of flexible or stretchable properties.

[0058] The porous metal elements 110, 120, 130 and the liquid metal elements 112, 122, 132 are each embodied as at least one of a flexible, stretchable, electrically conductive, or thermally conductive metal element. Individual liquid metal elements 112, 122, 132 respectively forming the porous metal elements 110, 120, 130 include at least one of liquid gallium, liquid indium, a liquid gallium alloy, a liquid indium alloy, liquid gallium-indium, or another liquid metal in various examples. Individual liquid metal elements 112, 122, 132 respectively forming the porous metal elements 110, 120, 130 include 70 percent liquid gallium and 30 percent liquid indium in one example, although different percentage ratios may be relied upon in some cases. Individual liquid metal elements 112, 122, 132 respectively forming the porous metal elements 110, 120, 130 include a gallium to indium ratio of at least one of 75 percent gallium and 25 percent indium or 75 wt% gallium and 25 wt% indium in another example. Individual liquid metal elements 112, 122, 132 respectively forming the porous metal elements 110, 120, 130 are also embodied as micro- scale liquid metal elements in some examples. The liquid metal elements 112, 122, 132 in the example shown are individually embodied as a micro-scale liquid metal element (e.g., a micro- sized liquid metal particle or droplet) including a gallium to indium ratio of at least one of 75 percent gallium and 25 percent indium or 75 wt% gallium and 25 wt% indium.

[0059] Any or all of the porous metal elements 110, 120, 130 or individual liquid metal elements 112, 122, 132 can include or be incorporated with (e.g., embedded or integrated with) solid filler elements in some embodiments. Examples of the solid filler elements include, but are not limited to, at least one of solid metal micro elements, carbon-based microfibers, carbon-based micro elements, or other solid filler elements.

[0060] The porous metal element 130 includes a first end that is coupled to the porous metal element 110 in the first plane or layer extending in the substrate 103. At least one of the liquid metal elements 132 positioned at the first end of the porous metal element 130 is coupled (e.g., electrically, mechanically, thermally) to at least one of the liquid metal elements 112 of the porous metal element 110 in the first plane or layer of the substrate 103. The porous metal element 130 further includes a second end that is coupled to the porous metal element 120 in the second plane or layer extending in the substrate 103. The second end of the porous metal element 130 is opposite the first end. At least one of the liquid metal elements 132 positioned at the second end of the porous metal element 130 is coupled (e.g., electrically, mechanically, thermally) to at least one of the liquid metal elements 122 of the porous metal element 120 in the second plane or layer of the substrate 103.

[0061] The device 100 can further include one or more conductive elements in some cases. Example conductive elements can include, but are not limited to, an electrode, a light emitting diode (LED), a Hall effect sensor, a passive component, a resistor, a capacitor, an inductor, a transformer, an integrated circuit (IC), or another conductive element. The conductive element or elements in these examples can be positioned in or on the substrate 103 and can be coupled to at least one of the porous metal elements 110, 120, 130.

[0062] In one example, the device 100 can include a first conductive element that can be positioned in or on the substrate 103 and coupled to the first end of the porous metal element 130. The first conductive element can be coupled (e.g., electrically, mechanically, thermally) to at least one of the liquid metal elements 132 positioned at the first end of the porous metal element 130. The device 100 can further include a second conductive element that can be positioned in or on the substrate 103 and coupled to the second end of the porous metal element 130. The second conductive element can be coupled (e.g., electrically, mechanically, thermally) to at least one of the liquid metal elements 132 positioned at the second end of the porous metal element 130. The first conductive element can be embodied as an LED in this example and the second conductive element can be embodied as a Hall effect sensor.

[0063] In another example, the device 100 can include a first conductive element that can be positioned in or on the substrate 103 and coupled to the porous metal element 110. The first conductive element can be coupled (e.g., electrically, mechanically, thermally) to at least one of the liquid metal elements 112 of the porous metal element 110. The device 100 can further include a second conductive element that can be positioned in or on the substrate 103 and coupled to theporous metal element 120. The second conductive element can be coupled (e.g., electrically, mechanically, thermally) to at least one of the liquid metal elements 122 of the porous metal element 120. The first conductive element can be embodied as an LED in this example and the second conductive element can be embodied as a Hall effect sensor.

[0064] FIG. 2 illustrates a cross-sectional view of another example device 200 according to various aspects and embodiments of the present disclosure. The device 200 is an example embodiment of an interconnect device or other device described herein that includes a flexible, stretchable, electrically and thermally conductive cross pattern planar interconnect formed in multiple layers of a substrate (e.g., at least one of a rigid, flexible, or stretchable substrate). In some cases, the cross pattern planar interconnect of the device 200 or the device 200 itself can be embodied and implemented as a flexible and stretchable cross pattern planar interconnect formed in a circuit board (e.g., at least one of a rigid, flexible, or stretchable circuit board). In other examples, the device 200 can be embodied as at least one of a rigid, flexible, stretchable, printed, or wearable circuit board or electronic device (e.g., soft robotics electronic device, healthcare electronic device) that includes such a flexible and stretchable cross pattern planar interconnect. The device 200 can include the substrate 103 and at least one of a rigid, flexible, stretchable, or wearable functional component that can be coupled to the substrate 103 in still other examples.

[0065] The device 200 includes the substrate 103. The substrate 103 in this example includes a cross pattern planar interconnect 205 that is at least partly formed in multiple layers or planes in the substrate 103. The cross pattern planar interconnect 205 includes a first porous metal element 210 extending in a first direction (e.g., into and out of the sheet of FIG.2) in a first plane (1stPlane) or layer in the substrate 103. The porous metal element 210 includes and is embodied as a first formation of liquid metal elements 212. Only a single liquid metal element 212 is denoted in FIG. 2 for clarity. The substrate 103 in this example further includes a second porous metal element 220 extending in a second direction (e.g., left to right or vice versa across the sheet of FIG. 2) in a second plane (2ndPlane) or layer in the substrate 103. The second plane or layer extending in the substrate 103 is different from the first plane or layer and the second direction of the porous metal element 220 is different from the first direction of the porous metal element 210. The porous metal element 220 includes and is embodied as a second formation of liquid metal elements 222. Only a single liquid metal element 222 is denoted in FIG.2 for clarity.

[0066] The porous metal element 220 can extend in the second plane in the substrate 103 in a direction that is greater than 0 degrees (°) and less than or equal to 90° offset from the firstdirection of the porous metal element 210 extending in the first plane in the substrate 103. The porous metal element 220 in the example shown extends in the second plane in the substrate 103 in a direction that is 90° offset from the first direction of the porous metal element 210 extending in the first plane in the substrate 103.

[0067] Each of the porous metal elements 210, 220 is embodied as a continuous porous metal structure formed as a collection of the liquid metal elements 212, 222, respectively. When included in at least one of a flexible or stretchable substrate 103, the flexible and stretchable cross pattern planar interconnect 205 of the device 200 allows for the entire device to have at least one of flexible or stretchable properties.

[0068] The porous metal elements 210, 220 and the liquid metal elements 212, 222 are each embodied as at least one of a flexible, stretchable, electrically conductive, or thermally conductive metal element. Individual liquid metal elements 212, 222 respectively forming the porous metal elements 210, 220 include at least one of liquid gallium, liquid indium, a liquid gallium alloy, a liquid indium alloy, liquid gallium-indium, or another liquid metal in various examples. Individual liquid metal elements 212, 222 respectively forming the porous metal elements 210, 220 include 70 percent liquid gallium and 30 percent liquid indium in one example, although different percentage ratios may be relied upon in some cases. Individual liquid metal elements 212, 222 respectively forming the porous metal elements 210, 220 include a gallium to indium ratio of at least one of 75 percent gallium and 25 percent indium or 75 wt% gallium and 25 wt% indium in another example. Individual liquid metal elements 212, 222 respectively forming the porous metal elements 210, 220 are also embodied as micro-scale liquid metal elements in some examples. The liquid metal elements 212, 222 in the example shown are individually embodied as a micro-scale liquid metal element (e.g., a micro-sized liquid metal particle or droplet) including a gallium to indium ratio of at least one of 75 percent gallium and 25 percent indium or 75 wt% gallium and 25 wt% indium in another example.

[0069] Either or both of the porous metal elements 210, 220 or one or more of the liquid metal elements 212, 222 can include or be incorporated with (e.g., embedded or integrated with) solid filler elements in some embodiments. Examples of the solid filler elements include, but are not limited to, at least one of solid metal micro elements, carbon-based microfibers, carbon-based micro elements, or other solid filler elements.

[0070] The device 200 can further include one or more conductive elements in some cases. Example conductive elements can include, but are not limited to, an electrode, a light emittingdiode (LED), a Hall effect sensor, a passive component, a resistor, a capacitor, an inductor, a transformer, an integrated circuit (IC), or another conductive element. The conductive element or elements in these examples can be positioned in or on the substrate 103 and can be coupled to at least one of the porous metal elements 210, 220.

[0071] In one example, the device 200 can include a first conductive element that can be positioned in or on the substrate 103 and coupled to the porous metal element 210. The first conductive element can be coupled (e.g., electrically, mechanically, thermally) to at least one of the liquid metal elements 212 of the porous metal element 210. The device 200 can further include a second conductive element that can be positioned in or on the substrate 103 and coupled to the porous metal element 220. The second conductive element can be coupled (e.g., electrically, mechanically, thermally) to at least one of the liquid metal elements 222 of the porous metal element 220. The first conductive element can be embodied as an LED in this example and the second conductive element can be embodied as a Hall effect sensor.

[0072] FIG.3A illustrates a cross-sectional view of another example device 300 according to various aspects and embodiments of the present disclosure. FIG. 3B illustrates a top view of the device 300 according to various aspects and embodiments of the present disclosure. The device 300 is an example alternative embodiment of each of the devices 100, 200 described herein and illustrated in FIGS.1A, 1B, and 2. The device 300 is an example embodiment of an interconnect device or other device described herein that includes a flexible, stretchable, electrically and thermally conductive interplanar interconnect extending between multiple layers of a substrate (e.g., at least one of a rigid, flexible, or stretchable substrate) and a flexible, stretchable, electrically and thermally conductive cross pattern planar interconnect formed in such layers of the substrate. In some cases, the interplanar and cross pattern planar interconnects of the device 300 or the device 300 itself can be embodied and implemented as flexible and stretchable interplanar and cross pattern planar interconnects formed in a circuit board (e.g., at least one of a rigid, flexible, or stretchable circuit board). In other examples, the device 300 can be embodied as at least one of a rigid, flexible, stretchable, printed, or wearable circuit board or electronic device (e.g., soft robotics electronic device, healthcare electronic device) that includes such flexible and stretchable interplanar and cross pattern planar interconnects. The device 300 can include the substrate 103 and at least one of a rigid, flexible, stretchable, or wearable functional component that can be coupled to the substrate 103 in still other examples.

[0073] Referring to FIGS. 3A and 3B, the device 300 includes the substrate 103. The device 300 further includes the interplanar interconnect 105 of the device 100 and the cross pattern planar interconnect 205 of the device 200. The interplanar interconnect 105 is coupled to the cross pattern planar interconnect 205 in the substrate 103. At least one of the liquid metal elements 122 of the porous metal element 120 is coupled (e.g., electrically, mechanically, thermally) to at least one of the liquid metal elements 222 of the porous metal element 220 in the second plane.

[0074] Each of the porous metal elements 110, 120, 130, 210, 220 is embodied as a continuous porous metal structure formed as a collection of the liquid metal elements 112, 122, 132, 212, 222, respectively. When included in at least one of a flexible or stretchable substrate 103, the flexible and stretchable interplanar and cross pattern planar interconnects 105, 205 of the device 300 allow for the entire device to have at least one of flexible or stretchable properties.

[0075] FIG. 4 illustrates a perspective view of another example device 400 according to various aspects and embodiments of the present disclosure. The device 400 is an example embodiment of an interconnect device or other device described herein that includes a flexible, stretchable, electrically and thermally conductive interplanar interconnect extending between multiple layers of a substrate (e.g., at least one of a rigid, flexible, or stretchable substrate), a flexible, stretchable, electrically and thermally conductive cross pattern planar interconnect formed in such layers of the substrate, and one or more conductive elements. In some cases, the interplanar and cross pattern planar interconnects of the device 400 or the device 400 itself can be embodied and implemented as flexible and stretchable interplanar and cross pattern planar interconnects formed in a circuit board (e.g., at least one of a rigid, flexible, or stretchable circuit board). In other examples, the device 400 can be embodied as at least one of a rigid, flexible, stretchable, printed, or wearable circuit board or electronic device (e.g., soft robotics electronic device, healthcare electronic device) that includes such flexible and stretchable interplanar and cross pattern planar interconnects. The device 400 can include the substrate 103 and at least one of a rigid, flexible, stretchable, or wearable functional component that can be coupled to the substrate 103 in still other examples.

[0076] The device 400 is an example alternative embodiment of the device 300 described herein and illustrated in FIGS. 3A and 3B. The device 400 has the same or similar structure, components, materials, and functions as that of the device 300. A difference between the devices 300, 400 is that the device 400 includes a first conductive element 440 coupled to the interplanar interconnect 105 in a first plane (1stPlane) or layer of the substrate 103 of the device 400 and asecond conductive element 450 coupled to the cross pattern planar interconnect 205 in a second plane (2ndPlane) or layer of the substrate 103. The conductive element 440 is coupled (e.g., electrically, mechanically, thermally) to at least one of the liquid metal elements 112 of the porous metal element 110 in the first plane or layer of the substrate 103. The conductive element 450 is coupled (e.g., electrically, mechanically, thermally) to at least one of the liquid metal elements 222 of the porous metal element 220 in the second plane or layer of the substrate 103. The conductive elements 440, 450 are each embodied as a light emitting diode (LED) in the example shown. In other examples, either or both of the conductive elements 440, 450 can be embodied as another type of conductive element such as an electrode, a Hall effect sensor, a passive component, a resistor, a capacitor, an inductor, a transformer, an integrated circuit (IC), or another conductive element, for instance.

[0077] Illustrated in FIG. 4 is an example LM interplanar interconnect of a circuit formed in a substrate according to one embodiment of the present disclosure. In addition to the LM interplanar interconnect 105, the circuit of the example LM interplanar interconnect device shown in FIG.4 also includes parallelly crossing top and bottom electrodes according to one embodiment of the present disclosure.

[0078] FIG. 5 illustrates a perspective view of another example device 500 according to various aspects and embodiments of the present disclosure. The device 500 is an example embodiment of an interconnect device or other device described herein that includes multiple flexible, stretchable, electrically and thermally conductive interplanar interconnects respectively extending between multiple layers of a substrate (e.g., at least one of a rigid, flexible, or stretchable substrate). In some cases, the interplanar interconnects of the device 500 or the device 500 itself can be embodied and implemented as flexible and stretchable interplanar interconnects formed in a circuit board (e.g., at least one of a rigid, flexible, or stretchable circuit board). In other examples, the device 500 can be embodied as at least one of a rigid, flexible, stretchable, printed, or wearable circuit board or electronic device (e.g., soft robotics electronic device, healthcare electronic device) that includes such flexible and stretchable interplanar interconnects. The device 500 can include the substrate 103 and at least one of a rigid, flexible, stretchable, or wearable functional component that can be coupled to the substrate 103 in still other examples.

[0079] The device 500 is an example alternative embodiment of the device 100 described herein and illustrated in FIGS. 1A and 1B. The device 500 has the same or similar structure, components, materials, and functions as that of the device 100. A difference between the devices100, 500 is that the device 500 includes multiple rows of individual interplanar interconnects 105 coupled to one another. The rows of interplanar interconnects 105 are embodied as electrodes 505a, 505b, 505c, 505d, 505e, 505f, 505g, 505h, 505i, 505j (or “electrodes 505”). Only the electrodes 505a, 505f, 505g, 505h, 505j are denoted in FIG. 5 for clarity. Each of the electrodes 505 includes twenty interplanar interconnects 105a to 105t for a total of 200 interplanar interconnects 105 in the device 500. Only the interplanar interconnects 105a, 105b, 105c, 105d for the electrode 505f are denoted in FIG. 5 for clarity. While individual interplanar interconnects 105a to 105t are electrically, mechanically, and thermally coupled to one another within each electrode 505, individual interplanar interconnects 105a to 105t of one electrode 505 are at least electrically and mechanically isolated and insulated from interplanar interconnects 105a to 105t of all other electrodes 505.

[0080] FIG. 6 illustrates a cross-sectional view of another example device 600 according to various aspects and embodiments of the present disclosure. The device 600 is an example embodiment of an interconnect device or other device described herein that includes multiple flexible, stretchable, electrically and thermally conductive interplanar interconnects respectively extending between multiple layers of a substrate (e.g., at least one of a rigid, flexible, or stretchable substrate). In some cases, the interplanar interconnects of the device 600 or the device 600 itself can be embodied and implemented as flexible and stretchable interplanar interconnects formed in a circuit board (e.g., at least one of a rigid, flexible, or stretchable circuit board). In other examples, the device 600 can be embodied as at least one of a rigid, flexible, stretchable, printed, or wearable circuit board or electronic device (e.g., soft robotics electronic device, healthcare electronic device) that includes such flexible and stretchable interplanar interconnects. The device 600 can include the substrate 103 and at least one of a rigid, flexible, stretchable, or wearable functional component that can be coupled to the substrate 103 in still other examples.

[0081] The device 600 is an example alternative embodiment of the device 100 described herein and illustrated in FIGS. 1A and 1B. The device 600 has the same or similar structure, components, materials, and functions as that of the device 100. A difference between the devices 100, 600 is that the device 600 includes multiple layers of individual interplanar interconnects 105 coupled to one another. The layers of interplanar interconnects 105 are embodied as circuit layers 605a, 605b, 605c, 605d, 605e, 605f (or “circuit layers 605”). The circuit layers 605 include interplanar interconnects 105a, 105b, 105c, 105d, 105e respectively extending between the circuit layers 605a and 605b, 605b and 605c, 605c and 605d, 605d and 605e, 605e and 605f.

[0082] Sedimentation-based 3D Assembly of Interplanar Interconnect.

[0083] FIG.7A illustrates a flow diagram of an example interplanar interconnect fabrication process 700 according to various aspects and embodiments of the present disclosure. FIG. 7B illustrates real-time views of an example implementation of the interplanar interconnect fabrication process 700 (or “fabrication process 700”) according to various aspects and embodiments of the present disclosure. The fabrication process 700 can be implemented to fabricate one or more devices described herein or illustrated in the figures. The fabrication process 700 can be implemented to fabricate devices 100, 200, 300, 400, 500, 600 described herein with reference to FIGS.1A to 6.

[0084] The fabrication process 700 includes performing a curing process on uncured regions 701 (or “uncured 701”) of a solution including a polymer matrix and liquid metal elements (e.g., the liquid metal elements 112, 122, 132). The curing process can be implemented to ultimately form an interplanar interconnect (e.g., the interplanar interconnect 105) from liquid metal elements (LMEs) that become fixed in cured regions 703 (or “cured 703”) of the polymer matrix that become cured when exposed to light (e.g., ultraviolet (UV) light, infrared light, visible light). The curing process includes exposing different masked and unmasked regions of the solution inside a molding structure to light while the molding structure is positioned in different orientations to cause selective sedimentation of the liquid metal elements in the solution and the polymer matrix. The curing process further includes forming porous metal elements (e.g., the porous metal elements 110, 120, 130) in the cured regions 703 of the polymer matrix. The porous metal elements can be individually formed in the cured regions 703 such that they collectively extend as a continuous structure between at least two planes of the polymer matrix. In some cases, at least one of the porous metal elements can be formed such that it is coupled to at least one conductive element (e.g., electrode, LED, Hall effect sensor, passive component, resistor, capacitor, inductor, transformer, IC).

[0085] In one example, the aforementioned curing process includes curing one or more regions of the polymer matrix with one or more regions of liquid metal elements (e.g., the liquid metal elements 112, 122, 132) being located in the one or more regions of the polymer matrix at one or more curing times, and the curing being based on exposing the different regions of the solution to the light while the molding structure is positioned in the different orientations. The curing process further includes solidifying the one or more regions of the polymer matrix based on the curing. The curing process further includes fixing in place the one or more regions of liquidmetal elements in the one or more regions of the polymer matrix based on the curing and coupling the one or more regions of liquid metal elements in the one or more regions of the polymer matrix based on the curing. The curing process further includes forming at least one porous metal element (e.g., any or all of the porous metal elements 110, 120, 130) in the one or more regions of the polymer matrix based on coupling the one or more regions of liquid metal elements located in the one or more regions of the polymer matrix at the one or more curing times.

[0086] At 702, the fabrication process 700 includes performing a solution preparation process to prepare a solution and performing first layer curing of an unmasked portion of the solution. The solution preparation process at 702 includes shear mixing liquid metal elements (e.g., the liquid metal elements 112, 122, 132) with at least one of a photocurable polymer, a photoresin, or a diluent to prepare a solution that includes a polymer matrix and the liquid metal elements. The polymer matrix includes a photoresin and a diluent in several examples.

[0087] Examples of the photoresin include, but are not limited to, acrylate-based photopolymers (e.g., including monomers, diacrylates, triacrylates, and methacrylate derivatives), epoxy-based photopolymers (e.g., including cycloaliphatic epoxides and glycidyl ethers), vinyl ether photopolymers (e.g., including divinyl ethers and polyvinyl ethers), thiol-ene systems (e.g., including thiol-acrylate and thiol-ene formulations), silicone-based photopolymers (e.g., including vinyl-terminated polydimethylsiloxane (PDMS) and silicone acrylates), polyurethane acrylates (e.g., including aliphatic and aromatic urethane acrylates), polyester acrylates (e.g., including bisphenol A ethoxylate diacrylate and neopentyl glycol diacrylate), photocurable polycarbonates, polyfluorinated acrylates, and polyphosphazenes (e.g., including poly[bis(trifluoroethoxy)phosphazene] with methacrylate groups), dendritic polymers and hyperbranched polymers with photoreactive groups (e.g., including dendritic acrylates and dendritic polyesters), photo-crosslinkable polyurethanes, methacrylamide photopolymers, and polycaprolactone acrylates (e.g., including aromatic and aliphatic polyester urethane acrylates).

[0088] Examples of the diluent include, but are not limited to, reactive diluents (e.g., including monoacrylates, diacrylates, and triacrylates), non-reactive diluents (e.g., including solvents such as acetone, isopropanol, and ethyl acetate), plasticizers (e.g., including phthalates, adipates, and trimellitates), surfactants (e.g., including non-ionic, anionic, and cationic surfactants), viscosity modifiers (e.g., including poly(ethylene glycol) (PEG) and poly(propylene glycol) (PPG)), co-solvents (e.g., including butyl acetate, toluene, and xylene), dispersing agents (e.g., including polyvinyl alcohol (PVA) and polyvinylpyrrolidone (PVP)), wetting agents (e.g.,including silicone surfactants and fluorosurfactants), leveling agents (e.g., including poly(dimethylsiloxane) (PDMS) and alkylphenol ethoxylates), stabilizers (e.g., including hindered amine light stabilizers (HALS) and UV absorbers), chain transfer agents (e.g., including thiols and isopropanol), antifoaming agents (e.g., including silicone oils and fatty alcohols), rheology modifiers (e.g., including fumed silica and clay minerals), coupling agents (e.g., including silanes and titanates), and antioxidants (e.g., including butylated hydroxytoluene (BHT) and butylated hydroxyanisole (BHA)).

[0089] The first layer curing at 702 includes injecting the solution of the polymer matrix and liquid metal elements into a mold cavity of a molding structure. The first layer curing further includes masking a region of the solution in the mold cavity to define a masked solution region and an unmasked solution region. The mold cavity is at least partly defined by a first acrylic plate (e.g., polyvinyl alcohol (PVA) plate) and a second acrylic plate (e.g., PVA plate) positioned vertically above the first acrylic plate. The first layer curing further includes exposing the masked solution region and the unmasked solution region to light to respectively create an uncured photoresin region 701 (or “uncured 701”) and a cured photoresin region 703 (or “cured 703”) in the mold cavity. Based on such light exposure, a first porous metal element (e.g., the porous metal element 110) of an interplanar interconnect (e.g., the interplanar interconnect 105) is formed from a first subset of the liquid metal elements (e.g., the liquid metal elements 112) in the cured photoresin region 703.

[0090] At 704, the fabrication process 700 further includes performing gravitational sedimentation. The gravitational sedimentation includes positioning the molding structure in another orientation (e.g., an inverted, flipped position) to cause a second subset of the liquid metal elements (e.g., the liquid metal elements 122, 132) to settle in the uncured photoresin region 701 under force of gravity along a side portion of the cured photoresin region 703 and in a bottom portion of the uncured photoresin region 701.

[0091] At 706, the fabrication process 700 further includes performing second layer curing. The second layer curing includes exposing the cured photoresin region 703 and the uncured photoresin region 701 to light to transform the uncured photoresin region 701 to a second cured photoresin region 703. Based on such light exposure, a second porous metal element (e.g., the porous metal elements 120, 130) of the interplanar interconnect is formed from the second subset of the liquid metal elements settled along the side portion of the cured photoresin region 703 and in the bottom portion of the uncured photoresin region 701.

[0092] Based on the gravitational sedimentation at 704, the first porous metal element (e.g., the porous metal element 110) is coupled to the second subset of the liquid metal elements (e.g., the liquid metal elements 122, 132) in the uncured photoresin region 701. At 706, the first porous metal element is coupled to the second porous metal element (e.g., the porous metal elements 120, 130) based on exposing the cured photoresin region 703 and the uncured photoresin region 701 to the light.

[0093] At 702, the fabrication process 700 further includes forming a first portion of a substrate (e.g., the substrate 103) based on exposing the unmasked solution region to the light to create a first cured photoresin region 703. At 706, the fabrication process 700 further includes forming a second portion of the substrate based on exposing the uncured photoresin region 701 to the light to create a second cured photoresin region 703. The aforementioned first and second cured photoresin regions 703 respectively cured at 702 and 706 of the fabrication process 700 collectively form a substrate described herein (e.g., the substrate 103).

[0094] In some examples, at 702 and / or 706 the fabrication process 700 can include exposing the different masked, unmasked, cured, and uncured regions to a confined optical light path while the molding structure is positioned in the different orientations to cause the selective sedimentation of the liquid metal elements in the solution. The confined optical light path can be generated by at least one of an optical device, a beam projector, or a photolithography machine.

[0095] In some examples, the fabrication process 700 can further include performing a pressure-based activation process on the solution to disrupt gallium oxide shell regions in the polymer matrix located between the liquid metal elements. The fabrication process 700 in these examples can further include forming the aforementioned interplanar interconnect (e.g., the interplanar interconnect 105) as a percolated network in the polymer matrix based on performing such a pressure-based activation process.

[0096] FIGS. 7A and 7B illustrate a flow diagram of an example LM-STAIR process (FIG. 7A) and corresponding real-time images (FIG.7B) of an example implementation of the example LM-STAIR process according to one embodiment of the present disclosure. The images of FIGS. 7A and 7B show LM microdroplets being formed into an interplanar interconnect during an example LM microdroplet sedimentation process described herein that leverages sedimentation and photoresin curing behaviors.

[0097] The LM-STAIR process of the present disclosure includes three major steps: solution preparation, substrate preparation, and the curing procedure (e.g., the fabrication process 700).When a solution mixed with the photoresin / diluent and LM microparticles is exposed to light such as, for instance, ultraviolet (UV) light, infrared light, visible light, or another light, photoresin is solidified and the position of LM microparticles is fixed within the cured region. However, areas not exposed to the light remain in liquid state, allowing LM microdroplets to move freely inside the low viscosity photoresin solution. Additionally, due to the higher density of LM microdroplets (e.g., 6.25 grams (g) / cubed-centimeter (cm3)) compared to photoresin solution (e.g., 1.05 g / cm3), LM microdroplets can settle due to gravity and do not have any effect from buoyancy force. A component of LM-STAIR is the convex profile of cured photoresin formed by its own curing behavior. When photoresin is exposed to light (e.g., UV, infrared, visible), the curing reaction is focused in the center of the exposed area rather than the edges, resulting in a convex shape in the cured photoresin profile. The slope of convex profile provides continuous foundation for LM microdroplets to settle from the top to the bottom plane (FIG. 7B). By combining these two phenomena, gravitational settlement and photoresin curing behavior, an intricate flexible double- layer circuit with two different planes connected without a through-hole can be realized (e.g., any of the devices 100, 200, 300, 400, 500, 600). The example circuit illustrated in FIG.4 has parallel top and bottom sides of electrodes that cross each other without causing a short circuit, resulting in illumination of both light-emitting diodes (LEDs) on the top and bottom sides of the plane.

[0098] To show the sedimentation in real time, the gravitational sedimentation of LM microparticles was recorded (FIG. 7B). As shown in the images of FIG. 7B, at 5.17 seconds (s), LM microparticles inside the cured photoresin region 703 are fixed in position. However, LM microparticles inside the uncured photoresin region 701 settle down in the direction of gravity. One of the interesting aspects of LM-STAIR process is that the LM settlement behavior is completed in less than a minute. Compared to the processing time of conventional methods of through-hole or wire bonding that must be performed for all connection points individually, the LM-STAIR process is not affected by the number and size of the interconnects. Since the LM- STAIR process is based on photocuring, it can be controlled by modifying the stencil and shadow mask. In this way, complexity of the circuit does not affect the processing time. Thus, the LM- STAIR process of the present disclosure can achieve high scalability with short processing time and unrestricted areal coverage. To demonstrate the high scalability of the LM-STAIR process, the 200 interplanar interconnects included in the device 500 described herein and illustrated in FIG.5 were fabricated in less than a minute in one example.

[0099] Cross-Pattern Fabrication Method and Adhesion Characteristics of Flexible Circuit.

[0100] FIG. 8 illustrates a flow diagram of an example cross pattern planar interconnect fabrication process 800 (or “fabrication process 800”) according to various aspects and embodiments of the present disclosure. The fabrication process 800 can be implemented to fabricate one or more devices described herein or illustrated in the figures. The fabrication process 800 can be implemented to fabricate devices 100, 200, 300, 400, 500, 600 described herein with reference to FIGS.1A to 6.

[0101] The fabrication process 800 can be implemented to successfully link upper and lower layers (e.g., the porous metal elements 110, 120, 130, 210, 220 and / or conductive elements in upper and lower layers) of various ridged and / or flexible devices such as flexible and / or stretchable circuit boards. However, if electrodes in such top and bottom layers cannot intersect, the circuit structure would be similar to that of a single-layer circuit. This can be addressed by utilizing adhesion between the photoresin and a polyvinyalcohol (PVA) layer or layers. This can be achieved by implementing the fabrication process 800 illustrated in FIG.8.

[0102] At 802, by performing first layer curing a crossing part is first partially cured (e.g., 2.5 seconds of UV exposure) from the bottom side by way of UV ray exposure to adhere LMEs and portions of photoresin to a surface of the second acrylic PVA plate in FIG. 8, fixing a partial amount of LMEs in place to form an electrode (e.g., to form the porous metal element 220 of the cross pattern planar interconnect 205). From this bottom curing, a partial amount of photoresin is cured, and the LM microparticles within this region are fixed.

[0103] At 804, by performing gravitational sedimentation the layer is flipped upside down to allow the uncured parts of the composite to settle. Due to the partial curing of the crossing region, the cured part remains in the bottom layer, while other uncured regions layer (e.g., settle), in the direction of gravity (e.g., the other uncured regions settle by force of gravity).

[0104] At 806, by performing second layer curing the entire composite is cured. As a result of the partial curing process performed at 802 and 806 that limits the amount of LM microparticles deposited at both the top and bottom layers, the region where electrodes are crossing each other has fewer LM microparticles on both sides (e.g., on both plates). Although the cross-pattern section has fewer LM microparticles, because of the high concentration of LM in the confined dimension, it is sufficient to make a conductive electrode.

[0105] In one example implementation, the cross pattern planar interconnect fabrication process 800 was used to fabricate an embodiment of the device 400 as an LED circuit with a cross- pattern. The circuit in this example featured LEDs on the top and bottom sides. The fabricationprocess 800 allows for the fabrication of complex, intertwined flexible circuits without limitations. In addition to complex circuit fabrication capability, the fabricated device 400 embodied as a flexible circuit also had adhesion characteristics as a result of the diluent. The low-modulus surface of the flexible circuit of the device 400 derives interesting reversible adhesion characteristics similar to those of polydimethylsiloxane (PDMS).

[0106] FIG. 9 illustrates a flow diagram of an example interplanar interconnect and cross pattern planar interconnect fabrication process 900 (or “fabrication process 900”) according to various aspects and embodiments of the present disclosure. The fabrication process 900 can be implemented to fabricate one or more devices described herein or illustrated in the figures. The fabrication process 900 can be implemented to fabricate devices 100, 200, 300, 400, 500, 600 described herein with reference to FIGS. 1A to 6. The fabrication process 900 is an example alternative embodiment of both the fabrication process 700 and the fabrication process 800 described herein and illustrated in FIGS.7A, 7B, and 8.

[0107] At 902, the fabrication process 900 includes performing first and second layer curing of unmasked portions of a solution that includes a polymer matrix and liquid metal elements (e.g., the liquid metal elements 112, 122, 132, 212, 222). The polymer matrix includes at least one of a photocurable polymer or a photoresin and a diluent in several examples. The first and second layer curing at 902 includes injecting the solution of the polymer matrix and liquid metal elements into a mold cavity of a molding structure. The first and second layer curing further includes masking regions of the solution in the mold cavity to define a masked solution region and an unmasked solution region. The mold cavity is at least partly defined by a first acrylic plate (e.g., polyvinyl alcohol (PVA) plate) and a second acrylic plate (e.g., PVA plate) positioned vertically above the first acrylic plate. The first and second layer curing further includes exposing the masked solution regions and the unmasked solution regions to light to respectively create uncured photoresin regions 901 (or “uncured 901”) and cured photoresin regions 903 (or “cured 903”) in the mold cavity. Based on such light exposure, a first porous metal element (e.g., the porous metal element 210) is formed from a first subset of the liquid metal elements (e.g., the liquid metal elements 212) in one of the cured photoresin regions 903.

[0108] At 904, the fabrication process 900 further includes performing gravitational sedimentation and directed stratification. The gravitational sedimentation and directed stratification includes positioning the molding structure in another orientation (e.g., an inverted, flipped position) to cause additional subsets of the liquid metal elements (e.g., the liquid metalelements 122, 132, 222) to respectively settle under force of gravity into bottom portions of respective uncured photoresin regions 901 and along a side portion of one of the cured photoresin regions 903 formed at 902 of the fabrication process 900.

[0109] At 906, the fabrication process 900 further includes performing second layer curing. The second layer curing includes exposing the cured photoresin regions 903 and the uncured photoresin regions 901 to light to transform the uncured photoresin regions 901 to cured photoresin regions 903. Based on such light exposure, additional porous metal elements (e.g., the porous metal elements 120, 130, 220) are formed from the aforementioned additional subsets of the liquid metal elements settled in bottom portions of respective uncured photoresin regions 901 and along a side portion of one of the cured photoresin regions 903 formed at 902 of the fabrication process 900.

[0110] In some examples, at 902 and / or 906 the fabrication process 900 can include exposing the different masked, unmasked, cured, and uncured regions to a confined optical light path while the molding structure is positioned in the different orientations to cause the selective sedimentation of the liquid metal elements in the solution. The confined optical light path can be generated by at least one of an optical device, a beam projector, or a photolithography machine.

[0111] The fabrication process 900 can be implemented to create circuits across multiple layers of a substrate and couple (e.g., electrically, mechanically, thermally) different components across these circuit layers. Through implementation of the fabrication process 900, the circuit layout within multiple layers and control connectivity across these layers can also be independently controlled. To achieve this, the curing direction and sequence can be modified to specifically discretize a single layer of LMEs into multiple layers. This allows planar interconnects to be created that can cross each other in different layers / planes without being electrically connected except at specified locations where the fabrication process 900 places soft vias.

[0112] At 902 of the fabrication process 900, a single crossing planar interconnect can be created by partially UV curing through a layer of LMEs (e.g., UV exposes through the bottom side). Because LMEs function as UV blockers, the curing of the photoresin is limited to a shallow depth. As a result, this only partially cures the layer of LMEs. The LMEs at a greater depth remain in uncured photoresin regions 901, which function as the source of LMEs for the second crossing planar interconnect. The UV exposure time can be used to control this discretization process. Too much curing time locks nearly all LMEs into the upper position while too little curing time does not lock nearly any LMEs into the upper position, while an intermediate curing time is able tostratify a single layer of LMEs into multiple layers. The fabrication process 900 at 902 further includes exposing the top side to UV with a shadow mask placed in a defined region where the top and bottom planar interconnects will cross. During this step, the crossing region is still partially uncured.

[0113] At 904 of the fabrication process 900, the LMEs in the uncured areas (e.g., the crossing region and unexposed regions) of the composite are directionally stratified by flipping the layer upside down, while the cured part in the crossing region remains in position. Finally, the entire composite is cured at 906 of the fabrication process 900.

[0114] The fabrication process 900 extends LM-STAIR and allows for the fabrication of intricate intertwined flexible circuits with high complexity. In one example, the fabrication process 900 can be implemented to create an arbitrary number of soft circuit layers by combining top and bottom curing. Following the normal curing procedure and stratification, by adding another layer of uncured LMEs / photoresin followed by sequential top and bottom curing, six soft circuit layers with five vias can be created within a single device structure (e.g., the device 600 illustrated in FIG.6).

[0115] In addition to the ability to make three-dimensional interconnects, fabricated flexible circuits described in examples herein can also be stacked together through intrinsic adhesion. The low-modulus surface of the flexible circuits allows for reversible adhesion characteristics. To demonstrate this, two different LM-STAIR fabricated circuits 1000a, 1000b are stacked together in one example (FIGS.10A and 10B). The stacked circuits 1000a, 1000b are flexed with no signs of detachment (FIG. 10B), indicating sufficient adhesion strength to maintain the bond between each layer. After bending, the stacked circuits 1000a, 1000b can be intentionally separated by initiating a crack at an edge and then peeling apart. This adhesion characteristic can be applied to stack multiple flexible circuits such as those described herein.

[0116] FIGS. 11A and 11B illustrate diagrams of example peel test results of an example fabricated flexible circuit during 11 cycles according to one embodiment of the present disclosure. FIG. 11A illustrates a plot of adhesion energy (in units of Newtons / meter (N / m)) against displacement (mm) for the 11 cycles and FIG.11B illustrates a bar chart having data presented as mean values ± standard deviation of each cycle’s adhesion energy from 40 to 60 mm displacement. Additionally, a series of photos in the bar chart of FIG.11B show two example circuits adhered to each other, bent, and detached from one another. FIGS.11A and 11B also provide an analysis and determination of the adhesion characteristics of such an example LM-STAIR interplanarinterconnect formed using the cross-pattern fabrication method according to one embodiment of the present disclosure.

[0117] As shown in FIGS. 11A and 11B, peel tests of the fabricated circuit were performed on an acrylic surface for 11 cycles in one example. During the cycle test, the fabricated flexible circuit in this example maintains its adhesion energy around 6 N / m. These adhesion characteristics can be useful when vertical stacking of the fabricated circuit. The adhesion between the two different layers was tested in one example by adhering two different LM-STAIR fabricated circuits stacked together (inset photos of FIG. 11B). After adhering the circuits, the stacked device was bent several times in one example to see if any detachment occurred between the two layers and there were no signs of detachment between the two layers. Also, two individual layers were detached after the bending test in this example, which shows that the adhesion is not too strong, allowing for this example LM-STAIR fabricated device to be used as a modular layer structure for flexible electronics in the future. Conventional polyimide-based flexible circuits need additional bonding between each layer, but using the reversible adhesion behavior described above, stacking of fabricated flexible electric circuits as described herein can be easily achieved.

[0118] Physical Characterization of Interplanar Interconnect.

[0119] FIGS. 12A to 12I collectively provide an analysis and determination of the physical characteristics of assembled straight line and interplanar interconnects formed according to example embodiments of the present disclosure. FIG.12A illustrates chemical structure diagrams of an example photocurable polymer and an example diluting agent according to one embodiment of the present disclosure. FIG. 12B illustrates a diagram of an example shear mixing process according to an example embodiment of the present disclosure. FIG. 12C illustrates a diagram of an example analysis of LM microdroplets size based on shear mixing revolutions per minute (RPM) and processing time according to one embodiment of the present disclosure. Data is collected from the individual LM microparticles Feret diameter and number of samples for each bar is 41, 133, 448, and 493.

[0120] FIG. 12D illustrates a diagram of example circuit feature size based on LM microdroplets diameter according to one embodiment of the present disclosure.

[0121] FIG.12E illustrates a bar chart of various example Young’s modulus values based on different ratios of photoresin, diluent, and LM volume percentage according to one embodiment of the present disclosure. The ratio presented as legend represents the weight ratio (expressed as a weight-percentage (wt%)) of photoresin and diluent (e.g., 30:70 denotes 30 wt% of photoresin and70 wt% of diluent). LM is added to the solution of photoresin and diluent as the total volume percentage of solution in one example.

[0122] FIG.12F illustrates a bar chart of various example strain values at maximum based on different ratios of photoresin, diluent, and LM volume percentage according to one embodiment of the present disclosure. Data in FIGS. 12E and 12F are presented in these examples as mean values ± standard deviation for three different samples.

[0123] FIG. 12G illustrates reconstructed micro CT images of example unactivated and activated samples (left) and volume fraction for each cluster (right) according to one embodiment of the present disclosure.

[0124] FIG. 12H illustrates an example cluster index according to one embodiment of the present disclosure.

[0125] FIG.12I illustrates an optical microscopic image of an example minimal gap between electrically conductive electrodes according to one embodiment of the present disclosure.

[0126] With reference to FIGS. 12A to 12I, collectively, the physical characteristics of circuits fabricated by using the LM-STAIR process described were analyzed according to at least one embodiment of the present disclosure. Photoresin formulation is composed of acrylate and methacrylate-based polymer, and dibutyltin dilaurate in one example (FIG. 12A). In some cases, the LM-STAIR process can include adding a diluting agent, aliphatic monofunctional acrylate, to give extra space to move and soften the cured photoresin. In various examples, the formulation of the photoresin and the diluting agent can be modified to meet the desired mechanical characteristics requirement unless the viscosity of the photoresin is exceptionally high so that LM microdroplets cannot move in the uncured solution.

[0127] LM microdroplets inside the photoresin are made using a shear mixing process (FIG. 12C, left schematic). The effect of shear mixing speed on the size of LM microdroplets is measured in one example by performing an image analysis on the optical microscopy images. The results indicate that the LM droplet diameter plateaus at approximately 100 micrometers (μm) for the mixing condition of 2000 parts-per-million (PPM) after 2 minutes of mixing. Using a different combination of diluent and viscosity modifier, smaller microdroplet sizes can be achieved to decrease the minimum electrode width of the circuit electrodes (FIG. 12D). In one example, the smallest LM microdroplets that can be made using the current shear mixing setup and chemical formulation (2000 RPM, 2 minutes) can be chosen for one or more example experiments.

[0128] To understand the mechanical properties, Young’s modulus was measured for a planar line shape electrode (line electrode) with a LM-STAIR interconnect using a universal testing machine (FIG.12E) in one example. Young’s modulus of cured pristine photoresin (100:0, Φ= 0% LM, Φ= volume fraction of LM microdroplets = volume of LM droplets / volume of (LM microdroplets + photoresin + diluent)) was measured as 1100 megapascals (MPa) in one example, considering that most soft electronics have Young’s modulus in the range of 50 kilopascals (kPa) to 3 MPa, the bare photoresin may be further modified to become more suitable for soft and stretchable electronics. The cured polymer matrix remains rigid up to 50 wt% of the diluent being mixed into the photoresin. At 50 wt% of the diluent, Young’s modulus decreased to 35 MPa in one example, which is similar to rubber. As the diluent increases to 90 wt%, the modulus decreases further (2 MPa) in another example. To make flexible and stretchable circuits, formulations containing less than or equal to (≤ ) 50 wt% photoresin were chosen in one example to test Young’s modulus of the composite that includes LM microdroplets.

[0129] Both the line electrode and the interplanar interconnects were fabricated and their mechanical properties were tested in various examples (FIG.12E). The results show that both the Φ of the LM and the type of electrode result in a minimal variation in mechanical behavior of the cured composite compared to photoresin / diluent pristine matrix without LM. There was a small decrease in Young’s modulus observed in examples when LM microdroplets were added, which is consistent with the general behavior observed when liquid fillers were introduced to a polymer or elastomer matrix. In order to minimize the effect of the variation in LM concentration on mechanical and electrical characteristics, the LM / photoresin solution applied to the top of the stencil mask was subjected to mechanical vibration in at least one example (Supplementary Notes, Solution Preparation). As a result, in at least one example, the difference in packing density between the different concentrations of LM was minimized and the Young’s modulus difference between the samples with Φ= 10 and 20% LM was minimized.

[0130] The strain at break for the selected samples was obtained from the same test in one example (FIG.12F). For a line electrode, the strain at break was slightly higher, 23.57% ( Φ= 10% LM) and 19.953% (Φ= 10% LM) compared to a strain of 17.7% for Φ= 0% LM (50:50 photoresin / diluent). LM microdroplets are expected to mitigate crack propagation in the composite during fracture due to their liquid nature. In one implementation, the LM-STAIR interconnects of the present disclosure showed a negligible difference in strain at break of 16.76 % at Φ= 20% LM compared to the non-LM photoresin (17.77%). A small decrease in the strain at break may be dueto the interconnect point between two layers being relied on the porous polymer matrix occupied by the LM microdroplets which could partially weaken the area connecting different layers. However, the decrease in the strain at break is minimal and indicates that the inclusion of LM microdroplets does not affect the maximum strain that the samples can endure, regardless of differences in the volume fraction of LM in the composite. These results obtained from example implementations of the LM-STAIR fabrication method described herein confirm that the method can, in fact, mitigate structural flaws.

[0131] To characterize the effective volume fraction of LM, micro CT scans of the line electrode were taken and images were reconstructed in one example. From the reconstructed micro CT image, the LM volume fraction inside the composite was calculated. The line electrode has Φ= 16.4% LM inside the path, while the interplanar interconnect has Φ= 14.5% LM in this example.

[0132] The process of percolation network formation was also observed using micro CT in one example (FIG. 12G). To make a percolated network, a mechanical embossing method (i.e., activation process) was used in one example to apply a small amount of pressure (83 kPa) to break the gallium oxide shell and connect the individual LM microdroplets. The microstructural difference between the unactivated and activated states in this example can be clearly seen through the difference in color in the visualization created through micro CT data. Each color in this example denotes a cluster that can be defined as a single connected network. Therefore, a single- colored image means that the LM microdroplets are connected as a percolated network. In the case of an unactivated sample in this example, the largest cluster in one example occupies 20 % of the total 3D reconstructed volume, whereas the largest cluster of the activated sample has 99.26% volume.

[0133] LM microdroplet percolation network analysis was performed in one example implementation. The activated and unactivated samples were segmented into individual particles using the random-walk distance transforms in this example. Unactivated sample shape factor, perfect sphere = 1) shows a smaller distribution and lower average values compared to activated samples in this example, indicating that the pressure activation procedure broke the spherical shape of the LM microdroplets and transformed to a more irregular shape. Accordingly, a coordination number that refers to the number of connections between different LM micro- droplets increases in this example due to activation. An interesting observation is the fact that in at least this example larger LM microdroplets tend to settle at thebottom of the composite and have a higher coordinate number. This settlement of larger LM microdroplets at the bottom of the composite agrees with the settling velocity equation based on Stoke’s law that larger LM microdroplets have higher settling velocity. Also, larger LM microdroplets form a higher coordinate number that indicates the percolation network is tending to form more on the larger microdroplets than the smaller ones. Since in general conductive polymer composites are mostly based on solid particles, conductive liquid filler percolation network analysis has not been studied.

[0134] It is a different kind of percolation network compared to conventional solid filler based composite system. That are all connected through the point-to-point contact. Connection between the individual particles is more of a volume-to-volume contact.

[0135] Further, the minimum feature size of the stencil mask patterning method was also investigated in at least one example. As shown in FIG. 12I, the minimum gap between line electrodes, and the minimum width of line electrode were 126 μm and 208 μm, respectively, in one example. Additionally, the electrical resistance of the minimum feature size line electrode (5 cm length) was measured to ensure that the LM microdroplets were electrically connected to each other. Electrical isolation between each planar interconnect was measured to ensure that traces are conductive but isolated from each other. In some cases, the resolution of the stencil mask patterning method can be further improved using a more advanced stencil fabrication method and smaller LM droplets. The LM-STAIR fabrication process described in examples herein can be implemented using different types of acrylic and silicon-based photoresins.

[0136] Electromechanical Characterization of Interplanar Interconnect.

[0137] FIGS. 13A to 13H collectively provide an analysis and determination of the electromechanical characteristics of a via holeless flexible circuit formed according to example embodiments of the present disclosure.

[0138] FIG. 13A illustrates a diagram of example sheet resistance values of an example line patterned flexible circuit based on three different LM volume percentages according to one embodiment of the present disclosure. Data of FIG. 13A are presented as mean values ± standard deviation for 5 different samples.

[0139] FIG. 13B illustrates a diagram of an example electrical resistance variation of an example flexible circuit patterned in line according to compressive strain in accordance with one embodiment of the present disclosure.

[0140] FIG. 13C illustrates a diagram of an example electrical resistance variation of an example flexible circuit patterned in line according to tensile strain in accordance with one embodiment of the present disclosure.

[0141] FIG. 13D illustrates a diagram of example sheet resistance values of example interplanar interconnects based on three different percentages of LM volume according to one embodiment of the present disclosure. Data of FIG. 13D are presented as mean values ± standard deviation for 5 different samples.

[0142] FIG. 13E illustrates a diagram of an example electrical resistance variation of an example interplanar interconnect flexible circuit depending on compressive strain according to one embodiment of the present disclosure. The inset of FIG. 13E shows the resistance behavior, depending on the measured bending radius of the specimen in this example.

[0143] FIG. 13F illustrates a diagram of an example electrical resistance variation of an example interplanar interconnects flexible circuit depending on tensile strain according to one embodiment of the present disclosure.

[0144] FIG.13G illustrates a diagram of an example durability test of an example interplanar interconnects flexible circuit for 100 cycles of compressive strain 50% according to one embodiment of the present disclosure. The inset of FIG.13G shows the initial and final 7 seconds of the cycle in this example.

[0145] FIG. 13H illustrates a diagram of an example durability test of an example flexible interplanar interconnect circuit for 100 cycles of 50% tensile strain according to one embodiment of the present disclosure. The inset of FIG.13H shows the initial and final 7 seconds of the cycle in this example.

[0146] With reference to FIGS. 13A to 13H, collectively, along with the physical characteristics, the electromechanical properties of fabricated samples of the LM interplanar interconnect device described herein were determined in example implementations. During electromechanical test in one example, 50:50 photoresin / diluent composite was used for the polymer matrix. To measure the electromechanical response of the fabricated samples, dog bone- shaped samples that include single electrodes were made in at least one example. First, to see the effects of Φ, line electrodes with different Φ LM were tested in one example (FIG. 13A). Composites with Φ = 10, 15 and 20% LM show a sheet resistance of less than 0.1 Ω / Ƒ in this example. After measuring the sheet resistance, the electromechanical response of Φ= 20% LM sample during compressive loading up to 50% strain was measured in one example (FIG. 13B).When compressive strain was applied in this example, the sample buckled, as shown in the inset of the graph of FIG. 13B. The buckling that occurs during compressive strain is similar to the bending behavior that is widely used in flexible electronics, such as foldable smartphones and flexible displays. Based on observing the buckling behavior and electromechanical response in this example, it can be expected that the fabricated material of embodiments described herein can be utilized in flexible electronics. During the compressive test, the resistance of the electrode maintained a constant level of 12 Ω in one example. This trend is consistent with the results of the uniaxial tensile testing up to 10% strain (FIG.13C).

[0147] Fabricated samples of the LM-STAIR interplanar interconnects described in examples herein were tested in the similar set up as the straight LM trace samples in one example (FIG. 13D). The sheet resistance of the interplanar interconnect was less than 0.3 Ω / Ƒ in this example for the three LM volume fractions. The slight increase in sheet resistance compared to the line electrodes in this example may be due to the longer path length and less volume concentration of the interconnect region as shown in the inset of FIG. 13D. Compressive and tensile strain tests were conducted in at least one example with an interplanar interconnect sample described herein (FIGS. 13E and 13F). The compressive strain bending radius in one example was measured as shown in the inset of FIG 13E. The minimum bending radius of the sample during the test was measured at 3.17 millimeters (mm) and the resistance remained constant throughout the test. Furthermore, results of the tensile test up to 10% strain in this example show the same consistent electromechanical response as the bending test. These results show that the developed interplanar interconnect fabricated using the LM-STAIR process of the present disclosure is robust and can withstand different modes of deformation including folding and stretching.

[0148] To test the durability of the LM-STAIR interconnects, cyclic bending tests with each compressive strain cycle up to 50% and tensile strain cycle up to 10% strain were performed in several examples on a dog bone-shaped sample with an interplanar interconnect. From both types of strain tests each of 100 cycles, the LM-STAIR interconnect’s electrical resistance showed a consistent response, with no noticeable change from beginning to end in at least one example implementation. Along with the electrical conductivity of the composite, the dielectric constant of the cured photopolymer / diluent composite, which is a critical factor for signal integrity and impedance matching to make the high-performance electric circuit, was measured in at least one example. The dielectric constant was measured for a frequency range of 0.1 to 100 kilohertz (kHz) in one example and was found to be in the range of 3.5 to 4.3 in this example. Considering that thedielectric constant of polyimide is between 3.1 and 3.6, the composite formulation described in example embodiments herein is suitable to be an electrical circuit substrate material. Further, environmental stability of the electrical resistance of an example LM-STAIR interplanar interconnect was examined in one example without any additional encapsulation under two different conditions: i) 80 °C elevated temperature and ii) 45 °C underwater (tap water). Over 7 days in 80 °C, a slight decrease was observed in normalized resistance (R / R0=0.87 ± 0.12) while in the elevated temperature the resistance increased slightly the first day then stabilized (R / R0=1.31 ± 0.27). This agrees with recent work that has shown the stability of LM-based soft composites in adverse underwater environments and could likely be further improved with encapsulation if needed. The electromechanical tests show that the LM-STAIR process of the present disclosure can be implemented to form and maintain robust electrical interconnections for reliable and flexible circuits.

[0149] Demonstration of Magnet Sensing and Indicating Circuit.

[0150] FIGS. 14A to 14F provide an overview of an example magnet sensing and indicating circuit demonstration according to one embodiment of the present disclosure.

[0151] FIG.14A illustrates a top view of an example magnet sensing and indicating flexible circuit according to one embodiment of the present disclosure.

[0152] FIG. 14B illustrates a bottom view of the example magnet sensing and indicating flexible circuit of FIG.14A according to one embodiment of the present disclosure.

[0153] FIG.14C illustrates a side view of the example magnet sensing and indicating flexible circuit of FIG.14A according to one embodiment of the present disclosure.

[0154] FIG. 14D illustrates a circuit diagram of the example magnet sensing and indicating flexible circuit of FIGS.14A to 14C according to one embodiment of the present disclosure.

[0155] FIG. 14E illustrates a diagram of an example Hall effect sensor working mechanism according to one embodiment of the present disclosure.

[0156] FIG. 14F illustrates a bar chart of output data of the Hall effect sensor obtained with different magnet height according to one embodiment of the present disclosure. Data in the bar chart of FIG. 14F are presented as mean values ± standard deviation for 14000 data points equivalent of 1.4 second.

[0157] FIGS. 14G, 14H, 14I illustrate images of LEDs in the example magnet sensing and indicating circuit being illuminated by varying the position of a rectangular shape magnet behind the circuit according to one embodiment of the present disclosure.

[0158] FIG. 14J illustrates a photo of a deformed example flexible circuit being illuminated using a magnet according to one embodiment of the present disclosure.

[0159] With reference to FIGS. 14A to 14J, collectively, the LM-STAIR process of the present disclosure can be implemented to electrically connect two different planes (e.g., electrically conductive elements in two different planes) of various ridged and / or flexible devices such as flexible and / or stretchable circuit boards in a facile manner. To demonstrate an example capability of the LM-STAIR process, a flexible magnetic field sensing circuit that embodied the indication function was fabricated in one example (FIG. 14A). As shown in FIGS. 14A to 14C, the fabricated flexible magnetic field sensing circuit in this example has two different layers, a top layer and a bottom layer. The top layer and bottom layer in this example have 9 white LEDs to indicate the magnitude of the magnetic field and 9 Hall effect sensors to sense the magnetic field, respectively. The outputs of hall effect sensors are individually connected to the top layer LED cathode through the interplanar interconnects in this example. Connections between the soft circuit and rigid components can be made with a paste formed from LM and copper (Cu) particles. Even with the complex connection of the electrical components, the thickness of the flexible circuit remained thin (0.33 mm) in this example. Using the LM-STAIR process of the present disclosure, the flexible circuit with multilayer and multicomponents that have two different functions was fabricated in this example without using a manual drilling procedure or conductive material filling process but instead by using LM microdroplets, photoresin solution and shadow mask as described herein. FIG.14D illustrates a circuit diagram showing how the Hall effect sensor and the LED are electrically connected in this example. The Hall effect sensor output is connected to the cathode of the LED, while the sensor anode is attached to the LED anode in this example. This connection is achieved using 21 interplanar interconnects that were fabricated simultaneously using LM- STAIR (12 for the cathodes and 9 for the outputs) in this example. These interplanar interconnects allow for the magnet field sensing and indicating circuit to be embodied as a flexible circuit having two different functionalities.

[0160] The circuit’s on and off state is depicted in FIG. 14E to help with comprehension of the magnetic field sensing and indicating circuit. If the magnetic field is weak (magnet at a distance of 50 mm), the Hall effect sensor output is half of the applied voltage (4 volts (V)) in this example, which can be seen in FIG.14F. When a magnet is placed at 50 mm, the output voltage of the Hall effect sensor is around 2.1 V in this example. Due to the threshold of the LED, at low output voltage, the LED does not turn on. By decreasing the distance of the magnet from the Hall effectsensor, the output of the Hall effect sensor increases to 4 V in this example which surpasses the threshold of the LED and turns on the LED as illustrated in FIG. 14E bottom diagram. To demonstrate the fabricated circuit of this example, a rectangular magnet is placed beneath the circuit and gradually moved from one end to another end of the circuit (FIGS. 14G, 14H, 14I). It can be clearly seen in FIGS.14G, 14H, 14I that the LEDs that are right above the magnet turn on. Furthermore, the fabricated circuit was bent in an "S" shape and tested to show the flexibility of the circuit as illustrated in FIG. 14J. Similar to the flat-state circuit, the bent circuit showed the same magnet sensing and indicating functionality seamlessly in this example. From the series of demonstrations, it can be concluded that the LM-STAIR method of the present disclosure can be implemented to fabricate a flexible complex electric circuit that seamlessly connects two different planes, unlike any conventional connection method.

[0161] Methods.

[0162] Physical characterization as described herein was performed in at least one example using a universal testing machine to measure stress applied to a specimen during application of tensile strain. During electromechanical measurement as described herein, a custom designed linear stage with the servo motor was used in at least one example.

[0163] Electric characterization and electromechanical measurement as described herein was performed in at least one example by using a custom-designed linear stage with a servo motor. A specimen was cut into the shape of a dog bone in at least one example and dimensions of the dog bone sample is illustrated in FIG. 13A. To measure the electric response of a specimen in at least one example, a source measurement unit was used. For the demonstration, a direct current (DC) power supply was used in at least one example to power the LED and Hall effect sensor circuitry.

[0164] Micro CT scanning (or Micro CT) as described herein was performed in at least one example on a liquid metal composite trimmed from the dog bone-shaped sample and placed on a Kapton with an energy of 60 kilovolts (kV) and a resolution of 1.57 μm per voxel using a Micro- CT scanner. An image stack of reconstructed slides in at least one example was imported into Avizo software and then threshold segmented to visualize the 3D volume of the liquid metal phase and the general STL surface. The color rendering of the LM phase was performed in at least one example using open-source software Blender.

[0165] Fabrication of LM via Junction.

[0166] Solution Preparation.

[0167] The compound (or solution) described herein was made of two main parts in various examples, a polymer matrix and liquid metal (LM) (e.g., LM particles such as LM microdroplets). The polymer matrix consists of two parts in these examples, diluent (Ebecryl 113) and photoresin (Black R2, B9 creations). The LM particles were composed of 70 wt% gallium and 30 wt% indium in one example and 75 wt% gallium and 25 wt% indium in another example. To control the stretchability and flexibility of the polymer matrix, wt% of diluent and photoresin was adjusted in some examples. The LM was added as the volume percentage (Φ) of the total volume of the solution in at least one example. First, in one example, the diluent and LM were poured into the plastic cup according to the final total volume, wt% and Φ of the composite. Before shear mixing was performed, the diluent and photoresin were mixed with a wooden tongue depressor in this example to break large LM into small droplets. Second, in this example, using a planetary shear mixer, LM was broken into micro sized particles in the diluent at 500 RPM for 20 seconds and 2000 RPM for 2 minutes. Shear mixing was performed in a vacuum environment (30 millibars (mbar)) in this example to eliminate bubbles. After the shear mixing process, the LM / diluent solution was cooled to room temperature in this example and mixed with photoresin based on the final wt% of the polymer matrix using a wooden tongue depressor. Finally, in this example, the LM / photoresin / diluent solution was placed on the vibration plate for 5 minutes to avoid micro bubbles inside. Additionally, same wt% of photoresin / diluent solution without LM was prepared in one example by shear mixing procedure using a planetary shear mixer under the same conditions.

[0168] Substrate Preparation.

[0169] To make a flexible and stretchable thin film in which example LM-STAIR interplanar interconnects of the present disclosure can be formed, two transparent acrylic plates were used in one example as substrates on either side of the fabricated film (e.g., on either side of a space in which the fabricated film is to be formed as described herein). Transparent acrylic plates (3 mm thickness) were cut into a rectangular shape (15 centimeters (cm) × 7 cm) in one example with a laser cutter. Before the polyvinylalcohol (PVA) coating procedure was performed, the acrylic plates were cleaned in various examples using isopropyl alcohol (IPA). After cleaning, the acrylic plate was placed on a flat surface and a small amount of PVA water solution (20 wt%) was applied to the top side of the acrylic plate in at least one example. To spread the PVA solution uniformly, a mayer rod (RD specialties, groove size #12) was used in one example. After coating the PVA on the acrylic plate, it (the PVA coated acrylic plate) was placed in a convection oven at 80 degreesCelsius (°C) for 5 minutes in at least one example. The same process was performed on the second acrylic plate as well in at least one example.

[0170] Stencil Mask Preparation.

[0171] A stencil mask according to embodiments described herein was cut using a laser cutter in at least one example. The stencil mask film was composed of 4 layers in at least one example, adhesives / substrate / adhesives / protective film. The protective film of the stencil mask film was not removed in one or more examples until the curing preparation procedure. Prior to laser cutting, the stencil mask film was attached to the top of the metal plate in one example for precise cutting. The laser cutting machine was set to 8-10% laser power with 15% speed in this example. To achieve the small feature size, a High-Power Density Focusing Optics (HPDFO) lens was used in this example. By changing the lens, the current system could make the feature size smaller than 200 μm in this example. After the stencil mask was prepared, it was attached to the top of the acrylic plate (PVA-coated side) in this example. The intricate design of the stencil mask at the center can cause unwanted warping of the stencil mask in some cases. To avoid this, first the complicated part of the stencil mask may be gently pressed using a rubber roller in one example to fix it. Then adhesion of the entire stencil mask with a PVA-coated surface using the rubber roller can be achieved in this example.

[0172] Curing Preparation Procedure.

[0173] Before the fabrication procedure, the LM / photoresin solution was mixed in one example using a wooden tongue depressor until the LM microparticles within the solution dispersed uniformly. Next, the LM / photoresin solution was poured on top of an acrylic plate with a stencil mask in this example. The LM / photoresin solution was uniformly spread out using the wood stick in this example. After the solution was spread, a vibrational plate was used to pack the LM microparticles in this example. By using this vibrational dense packing procedure, the concentration difference of the LM microparticles inside the confined electrode between 10 to 30 vol% of LM solution became similar and resulted in similar physical and electromechanical properties between different Φ in this example. After the LM microparticle packing procedure, an excessive solution was scraped off in this example using a glass slide in one continuous motion without pause. At this stage in this example, the LM / photoresin solution remained only in the confined path. To prevent incomplete electrodes, the quality of the circuit was inspected from the backside of the acrylic plate. In areas where there were imperfect areas, the LM / photoresin solution pouring and scraping procedure was repeated in this example until there was no transparent areain the circuit. Next, in this example, the protective film of the stencil was peeled off to expose the adhesives and put the spacer film (PET, 0.4 mm) on top of the adhesives of the stencil mask. The photoresin / diluent solution was then poured on top of the surface in this example. The surface of the Meniscus in various examples should be higher than the top of the spacer plate to avoid bubbles. Then, an acrylic top plate may be gently placed on top of the spacer (PVA coated side should contact the solution) in at least one example. Four sides of acrylic plates were secured using binder clips in one example to avoid imperfect film due to volume shrinkage during the UV curing procedure.

[0174] Curing Procedure.

[0175] To cure the LM / photoresin solution, in one example an UV ramp (380-420 nanometers (nm), 1000 milliwatts (mW)) was located above the top surface of the acrylic plate 15 cm high. A shadow mask was placed on top of the acrylic surface and the UV ramp was turned on for 10 seconds in this example. The entire substrate was then flipped to cause the LM particles to detach from the PVA surface and settled down to the bottom acrylic plate in this example. The settlement process took less than one minute in this example. For LM particles that did not detach from the PVA surface, a vibration plate or a small amount of mechanical impact was used to accelerate the procedure in this example. After settlement was done, the top side of the substrate was exposed to UV for 15 seconds to cure the circuit in this example. The entire substrate was then cured for 1 minute in this example after removal of the shadow mask. Finally, the fabricated sample in this example was extracted by peeling off the acrylic plates.

[0176] Conclusions.

[0177] The embodiments described herein demonstrate that a combination of LM and photo- curable resin can enable a facile fabrication method (LM-STAIR) to rapidly create 3D interconnects between two different circuit planes. The LM-STAIR technique is independent of the chemical composition of LM or photoresin but is rather a function of flow and cure characteristics of the photoresin. The insights gained from the embodiments of the present disclosure will drive the design of electronic materials with expanded freedom of choice in resin material to tune stretchability or functionality, such as biocompatibility or biodegradability. Concurrently, there will be similar freedom of choice in LM composition, which can be tuned by a variety of dopants or particles for specialized applications, LM doped with iron particles to enable a magneto-responsive droplets for instance. This facilitates a highly tunable, versatile, rapid, and economically viable process and material to advance flexible electronic manufacturingbeyond the development of individual vias through drilling and filling processes. Furthermore, the LM-STAIR process described herein can lead to a paradigm shift and substantial advancement for flexible, hybrid electronics manufacturing, integration, and packaging to complement and replicate the photofabrication technologies of silicon-based chips and devices. As such, some embodiments could leverage a range of different chemistries or inclusion characteristics to broaden the functionality, including responsive systems, biocompatible or biodegradable materials, or multi- material systems. One challenge that may arise within materials selection is the modification of photoresin viscosity with various functional inclusions. As the loading of inclusions increases viscosity typically increases, which could require longer times for the particles to settle. This could be supplemented with techniques to accelerate particle settling such as centrifuge or by increasing the temperature to reduce viscosity. However, the LM-STAIR process effectively concentrates inclusions. Therefore, low inclusion loadings at the start of processing become more concentrated during processing, which maintains a working viscosity for rapid processing. Other embodiments can include further down-scaling of feature size through the use of higher resolution patterning methodologies such as photolithography or E-beam lithography. It may also be possible to automate fabrication steps described herein to enable mass production of the multilayer soft electronic devices of various examples. Thus, the resulting materials and LM-STAIR methodology can serve as the foundation for integrated soft and flexible electronic systems for a variety of functional devices.

[0178] Disjunctive language, such as the phrase “at least one of X, Y, or Z,” unless specifically stated otherwise, is to be understood with the context as used in general to present that an item, term, or the like, can be either X, Y, or Z, or any combination thereof (e.g., X, Y, and / or Z). Thus, such disjunctive language is not generally intended to, and should not, imply that certain embodiments require at least one of X, at least one of Y, or at least one of Z to be each present. As referenced herein in the context of quantity, the terms “a” or “an” are intended to mean “at least one” and are not intended to imply “one and only one.”

[0179] As referred to herein, the terms “include,” “includes,” and “including” are intended to be inclusive in a manner similar to the term “comprising.” As referenced herein, the terms “or” and “and / or” are generally intended to be inclusive, that is (i.e.), “A or B” or “A and / or B” are each intended to mean “A or B or both.” As referred to herein, the terms “first,” “second,” “third,” and so on, can be used interchangeably to distinguish one component or entity from another and are not intended to signify location, functionality, or importance of the individual components orentities. As referenced herein, the terms “couple,” “couples,” “coupled,” and / or “coupling” refer to chemical coupling (e.g., chemical bonding), communicative coupling, electrical and / or electromagnetic coupling (e.g., capacitive coupling, inductive coupling, direct and / or connected coupling), mechanical coupling, operative coupling, optical coupling, and / or physical coupling.

[0180] It should be emphasized that the above-described embodiments of the present disclosure are merely possible examples of implementations set forth for a clear understanding of the principles of the disclosure. Many variations and modifications can be made to the above- described embodiment(s) without departing substantially from the spirit and principles of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims.

Claims

CLAIMS Therefore, at least the following is claimed:

1. A device, comprising: a substrate; and a porous metal element extending between a first plane and a second plane in the substrate, the porous metal element comprising a formation of liquid metal elements.

2. The device of claim 1, further comprising: a second porous metal element extending in the first plane in the substrate and coupled to the porous metal element in the first plane in the substrate, the second porous metal element comprising a second formation of liquid metal elements.

3. The device of claim 1, further comprising: a second porous metal element extending in the first plane in the substrate and coupled to the porous metal element in the first plane in the substrate, the second porous metal element comprising a second formation of liquid metal elements; and a third porous metal element extending in the second plane in the substrate and coupled to the porous metal element in the second plane in the substrate, the third porous metal element comprising a third formation of liquid metal elements.

4. The device of claim 1, further comprising: a conductive element positioned in or on the substrate and coupled to the porous metal element.

5. The device of claim 4, wherein the conductive element comprises an electrode, a light emitting diode, a Hall effect sensor, a passive component, a resistor, a capacitor, an inductor, a transformer, or an integrated circuit.

6. The device of claim 1, further comprising: a first conductive element positioned in or on the substrate and coupled to a first end of the porous metal element; anda second conductive element positioned in or on the substrate and coupled to a second end of the porous metal element, the second end of the porous metal element being opposite the first end.

7. The device of claim 6, wherein the first conductive element comprises a light emitting diode and the second conductive element comprises a Hall effect sensor.

8. The device of claim 1, further comprising: a second porous metal element extending in the first plane in the substrate and coupled to the porous metal element in the first plane in the substrate, the second porous metal element comprising a second formation of liquid metal elements; and a conductive element positioned in or on the substrate and coupled to the second porous metal element.

9. The device of claim 8, further comprising: a third porous metal element extending in the second plane in the substrate and coupled to the porous metal element in the second plane in the substrate, the third porous metal element comprising a third formation of liquid metal elements; and a second conductive element positioned in or on the substrate and coupled to the third porous metal element.

10. The device of claim 9, wherein the conductive element comprises a light emitting diode and the second conductive element comprises a Hall effect sensor.

11. The device of claim 1, wherein the substrate comprises a rigid substrate, a flexible substrate, or a stretchable substrate.

12. The device of claim 1, wherein the substrate comprises at least one of a cured photocurable polymer or a cured photopolymer resin and diluent composite.

13. The device of claim 1, wherein each of the porous metal element and the formation of liquid metal elements comprises at least one of a flexible, stretchable, electrically conductive, or thermally conductive metal element.

14. The device of claim 1, wherein individual liquid metal elements in the formation of liquid metal elements comprise at least one of liquid gallium, liquid indium, a liquid gallium alloy, a liquid indium alloy, or liquid gallium-indium.

15. The device of claim 1, wherein individual liquid metal elements in the formation of liquid metal elements comprise a gallium to indium ratio of at least one of 75 percent gallium and 25 percent indium or 75 wt% gallium and 25 wt% indium.

16. The device of claim 1, wherein liquid metal elements in the formation of liquid metal elements comprise micro-scale liquid metal elements.

17. The device of claim 3, wherein each of the porous metal element, the second porous metal element, the third porous metal element, the formation of liquid metal elements, the second formation of liquid metal elements, and the third formation of liquid metal elements comprises at least one of a flexible, stretchable, electrically conductive, or thermally conductive metal element.

18. The device of claim 3, wherein individual liquid metal elements in each of the formation of liquid metal elements, the second formation of liquid metal elements, and the third formation of liquid metal elements comprise at least one of liquid gallium, liquid indium, a liquid gallium alloy, a liquid indium alloy, or liquid gallium-indium.

19. The device of claim 3, wherein individual liquid metal elements in each of the formation of liquid metal elements, the second formation of liquid metal elements, and the third formation of liquid metal elements comprise a gallium to indium ratio of at least one of 75 percent gallium and 25 percent indium or 75 wt% gallium and 25 wt% indium .

20. The device of claim 3, wherein liquid metal elements in each of the formation of liquid metal elements, the second formation of liquid metal elements, and the third formation of liquid metal elements comprise micro-scale liquid metal elements.

21. A device, comprising: a substrate; a first porous metal element extending in a first plane in the substrate in a first direction, the first porous metal element comprising a first formation of liquid metal elements; and a second porous metal element extending in a second plane in the substrate in a second direction that is different from the first direction, the second plane being different from the first plane and the second porous metal element comprising a second formation of liquid metal elements.

22. The device of claim 21, wherein the second porous metal element extends in the second plane in the substrate in a direction that is between 0 degrees and 90 degrees offset from the first direction of the first porous metal element extending in the first plane in the substrate.

23. The device of claim 21, wherein the second porous metal element extends in the second plane in the substrate in a direction that is 90 degrees offset from the first direction of the first porous metal element extending in the first plane in the substrate.

24. The device of claim 21, further comprising: a conductive element positioned in or on the substrate and coupled to the first porous metal element or the second porous metal element.

25. The device of claim 24, wherein the conductive element an electrode, a light emitting diode, a Hall effect sensor, a passive component, a resistor, a capacitor, an inductor, a transformer, or an integrated circuit.

26. The device of claim 21, further comprising: a first conductive element positioned in or on the substrate and coupled to the first porous metal element; anda second conductive element positioned in or on the substrate and coupled to the second porous metal element.

27. The device of claim 26, wherein the first conductive element comprises a light emitting diode and the second conductive element comprises a Hall effect sensor.

28. The device of claim 21, wherein the substrate comprises a rigid substrate, a flexible substrate, or a stretchable substrate.

29. The device of claim 21, wherein the substrate comprises at least one of a cured photocurable polymer or a cured photopolymer resin and diluent composite.

30. The device of claim 21, wherein each of the first porous metal element, the second porous metal element, the first formation of liquid metal elements, and the second formation of liquid metal elements comprises at least one of a flexible, stretchable, electrically conductive, or thermally conductive metal element.

31. The device of claim 21, wherein individual liquid metal elements in each of the first formation of liquid metal elements and the second formation of liquid metal elements comprise at least one of liquid gallium, liquid indium, a liquid gallium alloy, a liquid indium alloy, or liquid gallium-indium.

32. The device of claim 21, wherein individual liquid metal elements in each of the first formation of liquid metal elements and the second formation of liquid metal elements comprise a gallium to indium ratio of at least one of 75 percent gallium and 25 percent indium or 75 wt% gallium and 25 wt% indium.

33. The device of claim 21, wherein liquid metal elements in each of the first formation of liquid metal elements and the second formation of liquid metal elements comprise micro-scale liquid metal elements.

34. The device of claim 21, further comprising:a third porous metal element extending between the first plane and the second plane in the substrate, the third porous metal element comprising a third formation of liquid metal elements, wherein a first end of the third porous metal element is coupled to the first porous metal element in the first plane in the substrate and a second end of the third porous metal element is coupled to the second porous metal element in the second plane in the substrate.

35. The device of claim 34, further comprising: a fourth porous metal element extending between the second plane and a third plane in the substrate, the fourth porous metal element comprising a fourth formation of liquid metal elements; and a fifth porous metal element extending in the third plane in the substrate, the fifth porous metal element comprising a fifth formation of liquid metal elements, wherein a first end of the fourth porous metal element is coupled to the second porous metal element in the second plane in the substrate and a second end of the fourth porous metal element is coupled to the fifth porous metal element in the third plane in the substrate.

36. The device of claim 21, wherein each of the first porous metal element and the second porous metal element comprises an electrically conductive flexible and stretchable metal trace.

37. The device of claim 34, wherein: each of the first porous metal element and the second porous metal element comprises an electrically conductive flexible and stretchable metal trace; and the third porous metal element comprises an electrically conductive flexible and stretchable metal interplanar interconnect.

38. The device of claim 35, wherein: each of the first porous metal element, the second porous metal element, and the fifth porous metal element comprises an electrically conductive flexible and stretchable metal trace; and each of the third porous metal element and the fourth porous metal element comprises an electrically conductive flexible and stretchable metal interplanar interconnect.

39. The device of claim 21, wherein the device comprises at least one of a rigid circuit board, a flexible circuit board, a stretchable circuit board, a printed circuit board, a wearable circuit board, a wearable electronic device, a soft robotics electronic device, or a healthcare electronic device.

40. The device of claim 21, further comprising: at least one of a rigid, flexible, stretchable, or wearable functional component coupled to the substrate.

41. A method for forming interplanar interconnects in a substrate, the method comprising: injecting a solution into a mold cavity of a molding structure, the solution comprising a polymer matrix and liquid metal elements; and performing a curing process on the solution to form an interplanar interconnect in the polymer matrix, the curing process comprising: exposing different regions of the solution to light while the molding structure is positioned in different orientations to cause selective sedimentation of the liquid metal elements in the solution.

42. The method of claim 41, wherein: performing the curing process further comprises forming a porous metal element in the polymer matrix; and the porous metal element extends between at least two planes of the polymer matrix and is coupled to at least one conductive element.

43. The method of claim 41, wherein performing the curing process further comprises: curing one or more regions of the polymer matrix, one or more regions of liquid metal elements being located in the one or more regions of the polymer matrix at one or more curing times, and the curing being based on exposing the different regions of the solution to the light while the molding structure is positioned in the different orientations.

44. The method of claim 43, wherein performing the curing process further comprises: solidifying the one or more regions of the polymer matrix based on the curing; fixing in place the one or more regions of liquid metal elements in the one or more regions of the polymer matrix based on the curing; and coupling the one or more regions of liquid metal elements in the one or more regions of the polymer matrix based on the curing.

45. The method of claim 44, wherein performing the curing process further comprises: forming at least one porous metal element in the one or more regions of the polymer matrix based on coupling the one or more regions of liquid metal elements located in the one or more regions of the polymer matrix at the one or more curing times.

46. The method of claim 41, further comprising: masking a region of the solution in the mold cavity to define a masked solution region and an unmasked solution region.

47. The method of claim 46, wherein: the mold cavity is at least partly defined by a first plate and a second plate positioned vertically above the first plate; and masking the region of the solution further comprises masking a portion of an outer surface of the second plate to define a masked region and an unmasked region on an outer surface of the second plate, the masked region and the unmasked region respectively corresponding to the masked solution region and the unmasked solution region.

48. The method of claim 46, wherein performing the curing process further comprises: exposing the masked solution region and the unmasked solution region to the light to respectively create an uncured photoresin region and a cured photoresin region in the mold cavity, the cured photoresin region comprising a first porous metal element of the interplanar interconnect formed from a first subset of the liquid metal elements in the cured photoresin region.

49. The method of claim 48, wherein performing the curing process further comprises:positioning the molding structure in another orientation to cause a second subset of the liquid metal elements to settle in the uncured photoresin region under force of gravity along a side portion of the cured photoresin region and in a bottom portion of the uncured photoresin region.

50. The method of claim 49, wherein performing the curing process further comprises: exposing the cured photoresin region and the uncured photoresin region to the light to transform the uncured photoresin region to a second cured photoresin region, the second cured photoresin region comprising a second porous metal element of the interplanar interconnect, the second porous metal element being formed from the second subset of the liquid metal elements settled along the side portion of the cured photoresin region and in the bottom portion of the uncured photoresin region.

51. The method of claim 50, wherein performing the curing process further comprises: coupling the first porous metal element to the second subset of the liquid metal elements in the uncured photoresin region based on gravitational sedimentation; and coupling the first porous metal element to the second porous metal element based on exposing the cured photoresin region and the uncured photoresin region to the light.

52. The method of claim 50, wherein performing the curing process further comprises: forming the substrate based on exposing the unmasked solution region to the light to create the cured photoresin region and exposing the uncured photoresin region to the light to create the second cured photoresin region.

53. The method of claim 41, wherein the substrate comprises a rigid substrate, a flexible substrate, or a stretchable substrate.

54. The method of claim 41, wherein the polymer matrix comprises at least one of photocurable polymer, a photoresin, or a diluent.

55. The method of claim 41, further comprising:performing a physical characterization process to determine one or more physical properties or parameters of at least one of the polymer matrix, the liquid metal elements, the substrate, or the interplanar interconnect, wherein performing the physical characterization process comprises altering a composition of the solution by adjusting at least one of a weight percentage of a photoresin in the polymer matrix, a weight percentage of a diluent in the polymer matrix, or a volume percentage of the liquid metal elements.

56. The method of claim 41, further comprising: performing an electromechanical characterization process to determine one or more electromechanical properties or parameters of at least one of the polymer matrix, the liquid metal elements, the substrate, or the interplanar interconnect, wherein performing the electromechanical characterization process comprises performing various mechanical tests on at least one of the substrate or the interplanar interconnect to determine an electromechanical response of at least one of the substrate or the interplanar interconnect.

57. The method of claim 41, further comprising: performing a solution preparation process to prepare the solution, the solution preparation process comprising: shear mixing the liquid metal elements with at least one of a photocurable polymer of the polymer matrix or a photoresin or a diluent of the polymer matrix.

58. The method of claim 41, wherein performing the curing process further comprises: exposing masked and unmasked regions of the solution to the light while the molding structure is positioned in the different orientations to cause the selective sedimentation of the liquid metal elements in the solution.

59. The method of claim 41, wherein performing the curing process further comprises: exposing the different regions of the solution to a confined optical light path while the molding structure is positioned in the different orientations to cause the selective sedimentation of the liquid metal elements in the solution, the confined optical light path being generated by at least one of an optical device, a beam projector, or a photolithography machine.

60. The method of claim 41, further comprising: performing a pressure-based activation process on the solution to disrupt gallium oxide shell regions in the polymer matrix located between the liquid metal elements; and forming the interplanar interconnect as a percolated network in the polymer matrix based on performing the pressure-based activation process.

61. The method of claim 41, further comprising: performing a peeling-based activation process to disrupt gallium oxide shell regions in the polymer matrix located between the liquid metal elements; and forming the interplanar interconnect as a percolated network in the polymer matrix based on performing the peeling-based activation process.

62. The method of claim 52, further comprising: exposing the cured photoresin region and the second cured photoresin region to an ultrasound signal; and forming the interplanar interconnect as a percolated network in the substrate based on exposing the cured photoresin region and the second cured photoresin region to the ultrasound signal.

63. A device, comprising: a substrate; and a porous metal element extending in a plane in the substrate, the porous metal element comprising a formation of liquid metal elements.

64. The device of claim 1, wherein at least one of the porous metal element or individual ones of the liquid metal elements are incorporated with solid filler elements.

65. The device of claim 64, wherein the solid filler elements comprise at least one of solid metal micro elements, carbon-based microfibers, or carbon-based micro elements.

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