Integrated electronic device with flexible and stretchable substrate

Abstract

A flexible and stretchable integrated electronic device comprising a substrate having a stiffness gradient, wherein a rigid electronic device is embedded within the substrate. The stiffness gradient within the substrate prevents delamination at the interface between the substrate and the embedded device. A method of fabricating an integrated electronic device having a stiffness gradient comprises applying a curing agent to an uncured polymer base material.

Claims

1. A method of making an integrated electronic device having a stiffness gradient, the method comprising: embedding a rigid electronic device in a substrate comprising an uncured polymer base, and applying a curing agent to the substrate in a pattern, wherein applying the curing agent in the pattern creates a portion of the substrate adjacent the embedded electronic device with a modulus in between a modulus of a portion of the substrate not adjacent to the embedded electronic device and the modulus of the rigid electronic device.

2. The method of claim 1, wherein the curing agent is applied to a surface of the substrate using an inkjet device, an aerosol jetting device, or a 3D printer.

3. The method of claim 2, further comprising: thinning the curing agent using a solvent.

4. The method of claim 3, wherein the solvent is selected from the group consisting of xylene, trichlorobenzene, hexane, and isopropyl alcohol.

5. The method of claim 1: wherein the substrate comprises polydimethylsiloxane; wherein applying the curing agent to the substrate in the pattern comprises: applying the curing agent to a first section adjacent to the rigid electronic device at a ratio of base-to-curing agent of 5:1; and applying the curing agent to a second section not adjacent to the rigid electronic device at a ratio of base-to-curing agent of 20:1.

6. The method of claim 1, wherein the pattern comprises: a first area of the substrate adjacent to the rigid electronic device and a second area not adjacent to the rigid electronic device, wherein the first area receives a greater amount of the curing agent.

7. The method of claim 1, wherein the pattern comprises a continuous gradient.

8. The method of claim 1, wherein applying the curing agent to the substrate comprises: applying the curing agent to a surface of the substrate; and allowing the curing agent to diffuse into the substrate.

9. The method of claim 1, wherein the curing agent is applied manually.

10. The method of claim 2, wherein the substrate is heated as the curing agent is applied to the substrate.

11. The method of claim 2, wherein the inkjet device, aerosol jetting device, or 3D printer applies the curing agent in the pattern comprising a plurality of overlapping areas of increasing size, each of the plurality of overlapping areas located in part over the rigid electronic device, thereby creating a gradient in the amount of the curing agent applied to the substrate.

12. The method of claim 2, further comprising: controlling diffusion of the curing agent by adjusting at least one of: a temperature of the substrate, a viscosity of the curing agent, and a surface tension of the curing agent.

13. The method of claim 2, wherein the pattern replicates a wiring pattern of the electronic device.

14. The method of claim 1, wherein applying the curing agent to the substrate in the pattern comprises: applying the curing agent to a first section adjacent to the rigid electronic device to create a first base-to-curing agent ratio; applying the curing agent to a second section not adjacent to the rigid electronic device at a second base-to-curing agent ratio; wherein the first ratio is less than the second ratio.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

(1) FIGS. 1A-1C show the integrated device, according to one embodiment.

(2) FIG. 2 is an image showing delamination at the interface of the rigid device and the substrate.

(3) FIG. 3 is a graph depicting the stiffness of various components of the integrated device.

(4) FIGS. 4-5 are graphs showing the energy release rate for integrated devices with varying parameters.

(5) FIGS. 6A-6B show the strain in the device as a function of the distance from a center.

(6) FIGS. 7A-7B are graphs depicting energy release rates.

(7) FIG. 8 shows the failure strain at various interfaces.

(8) FIGS. 9-11 are graphs depicting energy release rates.

(9) FIGS. 12A-12C depict a fabrication method of the integrated device according to one embodiment.

(10) FIGS. 13A-13C depict an alternative fabrication method.

(11) FIGS. 14A-14C show another fabrication method.

(12) FIGS. 15A-15D depict a fabrication method with the inclusion of passive electronic devices.

(13) FIGS. 16A-16C are schematics of the Young's modulus of the materials as a function of location along the length of the stretchable substrate, according to different embodiments.

DETAILED DESCRIPTION

(14) According to one embodiment of the present invention is an integrated electronic device 100 comprising a flexible and stretchable substrate 110 and a rigid electronic device 120. As shown in the embodiment depicted in FIG. 1A, the substrate 110 comprises a plurality of sections, where each section has a different stiffness. More specifically, the substrate 110 of the embodiment shown in FIG. 1A comprises a first section 111 and a second section 112, where the first section 111 has a greater stiffness than the second section 112. As further shown in FIGS. 1A-1B, the rigid electronic device 120 is embedded within the first section 111 of the substrate 110.

(15) By providing a gradient in the stiffness of the substrate 110, delamination at the interface 130 between the rigid electronic device 120 and the substrate 110 can be reduced by controlling the strain and stress contours at the interface 130 of the rigid electronic device 120 and substrate 110 when the substrate 110 is stretched. That is, the presence of the intermediate soft material (first section 111) with a Young's modulus between that of the primary soft material (second section 112) and the embedded device 120 decreases the risk of delamination as the majority of the strain will be accommodated in the second section 112 or outer regions of the substrate 110. Because of this, the substrate material near interface 130 with the rigid electronic device 120 experiences relatively low strain and stress.

(16) While example embodiments will be discussed in terms of a first section 111 and a section 112, the substrate 110 ay comprise additional sections to further smooth the stiffness gradient. In alternative embodiments, a continuous stiffness gradient is employed on the substrate 110 without distinct sections. In yet another embodiment, a first section 111 has a uniform stiffness while the second section 112 has a stiffness gradient. The presence of distinct sections or a continuous gradient in the substrate depends, in part, on the particular fabrication method employed.

(17) As previously stated, the stiffness gradient aims to prevent delamination at the interface 130 of the embedded device 120 and the flexible substrate 110. To quantify the delamination characteristic of the interface 130, the energy release rate, G in units of J/m.sup.2, is used to guide the fabrication of the integrated flexible electronic device 100. In testing, the energy introduced to a pre-formed crack, which causes it to increase in size, must be balanced by the amount of energy lost due to the formation of new surfaces and other dissipative processes, such as plasticity. The crack size increases when the energy release rate equals a critical value, the fracture energy denoted as .

(18) The risk of delamination at the interface 130 between a soft material and rigid material is significant and this risk increases when the system is stretched and thus subjected to mechanical strain. Therefore, if the structure has sufficiently high stress at the interface 130 between the two materials, delamination occurs (see FIG. 2). To address this challenge, the amount of strain and strain energy in the soft material (i.e. substrate 110) at the interface 130 should be minimized to prevent delamination. This minimization is accomplished using the intermediate material gradient such that the mechanical stiffness properties between the soft and rigid materials are changed gradually (see FIG. 3). Adding a single intermediate material in the first section 111 of the substrate 110, where the first section 111 has a stiffness value between the soft second section 112 and the rigid embedded device 120, has a significant effect in reducing delamination and allows for the integration of rigid devices 120, such as CMOS chips.

(19) In one embodiment, the substrate 110 that surrounds the silicon-based electronic device 120 is made of two soft polymers with different Young's modulus, E.sub.1 and E.sub.2 (E.sub.2>E.sub.1). The stiffer intermediate polymer (Young's Modulus E.sub.2) is in contact with the silicon-based device 120 while the softer material (Young's Modulus E.sub.1) occupies the outer domain. When the composite substrate 110 is strained, the outer, second portion 112 has a higher strain when compared to the intermediate inner first portion 111. The value of Young's modulus (E.sub.2) of the intermediate material has an effect in minimizing the delamination in the flexible integrated device 100.

(20) For example, the effect of the ratio, E.sub.2/E.sub.1, can be determined by calculating the energy release rates using techniques such as a two-dimensional finite element analysis (FEA). The two conditions E.sub.2/E.sub.1=10 and E.sub.2/E.sub.1=100 shown in FIG. 4 indicate the significance of the Young's modulus ratio on delamination of layers. The energy release rate values for additional ratios are shown in FIG. 5. As shown in FIG. 4, the system having the higher Young's modulus ratio has the lowest energy release rate for all values of L.sub.2, which corresponds to the length or radius of the first section 111. As the energy release rate rises with external applied strain, the system with the higher Young's modulus ratio results in a larger safe region where delamination does not occur. Of note, for any case where a first portion 111 and second portion 112 are used, the energy release rate is lower when compared to just a single soft material having either Young's modulus E.sub.1 or E.sub.2.

(21) Results from an example finite-element analysis are shown in FIGS. 6A-6B. Maximum principal elastic strain for two structures without (FIG. 2A) and with (FIG. 2B) the engineered two-section substrate 110, indicate the amount of strain in the cut-plane coinciding with the top surface of silicon device 120. The strain at the interface 130 between the silicon electronic device 120 and the intermediate first portion 111 in the engineered substrate 110 is approximately six times smaller than in the example substrate 110 having only a single material. This lower strain region at the chip interface 130 to the engineered substrate 110 reduces the onset of delamination from the embedded electronic device 120.

(22) In the example shown in FIG. 6B, the highest strain occurs at the interface between the first section 111 and the second section 112. Accordingly, this region is the most susceptible to delamination. However, by selecting two materials with strong bonding capability, the substrate 110 can be designed to withstand higher strains before delamination. In one embodiment, the substrate comprises polydimethylsiloxane (PDMS) with a differing amount of elastomer base-to-curing agent mixing ratio in each section. PDMS with different base-to-curing agent mixing ratios exhibit strong bonding. In addition, the bonding between the two sections 111, 112 can be enhanced by selecting materials with high surface adhesion. Also, in general, an enhanced roughness at the border between the two has a positive effect on bonding between the two soft materials. In alternative embodiments, other elastic polymers are used in the substrate 110. For example, the substrate 110 may comprise two-part silicone elastomers, including but not limited to: RTV (room-temperature-vulcanizing) silicone rubber, tin-catalyzed silicones, and platinum-catalyzed silicones (e.g., Ecoflex from Smooth-On, Inc., Macungie, Pa.).

(23) In order to compare variations in the two-section substrate 110, three example embodiments (listed in Table 1) are analyzed. In these examples, the rigid electronic device 120 is a 1 mm1 mm50 m silicon chip. For the compliant substrate 110, two mixtures of PDMS with a base-to-curing agent ratios of 5:1 and 20:1 are used. The Young's modulus of PDMS relates to the ratio of monomer (base) and hardener (curing agent). Using PDMS with different ratios of base and curing agent for the materials of the first section 111 and second section 112 allows the Young's modulus values to be modified between regions while still achieving strong bonding at their interface. The substrate 110 in examples #1 and #2 are made completely of a single type of PDMS, while the substrate 110 in example #3 implements the composite structure with a first section 111 and a second section 112 of PDMS each having different stiffness.

(24) TABLE-US-00001 TABLE 1 Sample 1.sup.st Material 2.sup.nd Material Energy Release #1 PDMS (5:1), none 10.99 J/m.sup.2 L = 3 mm #2 PDMS (20:1), none 1.493 J/m.sup.2 L = 3 mm #3 PDMS (20:1), PDMS (5:1), 0.689 J/m.sup.2 L = 2 mm L = 1 mm

(25) The energy release rate, which indicates the likelihood of delamination, was determined for a given interface using a FEA with a symmetric quarter model of the entire substrate. A fine mesh was placed on an initial 10 m-wide separation (i.e., a crack initiator) located at the interface 130 between the sidewall of the rigid device 120 and the surrounding PDMS substrate 110. The crack with the highest degree of stress was located at the corner of the device 120. The energy release rate was determined by subtracting the strain energy before and after crack growth, while dividing by the area of the crack. Mesh refinements were used to verify numerical convergence.

(26) Table 1 indicates that the energy release rate in the stiffest substrate (PDMS (5:1)) used in sample #1 is over 7 times higher than the energy release rate in the intermediate stiffness substrate 110 (PDMS (20:1)) used in sample #2. The energy release rate for sample #3 was found to be approximately two times lower than the next best case of sample #2. When the energy release rate exceeded a critical value, as determined empirically, the crack propagated and the substrate 110 delaminated from the embedded rigid device 120. As a result of the lowest energy release rate occurring for sample #3, the risk of delamination at the interface 130 was low and the bonding at the interface 130 remained intact.

(27) To compare FEA predictions shown in Table 1 and to quantify the onset of strain failure, tensile tests were performed for all three sample types. In many applications, the rigid device 120 will often be no greater than 1 mm in size and sparsely embedded within the substrate 110, while the radius of bending curvature of the soft substrate 110 is expected to be much greater than 1 mm. Tensile strain loading at each end of the substrate was applied as a series of small incremental step functions. The system was elongated at a low strain rate (0.001 s.sup.1) to achieve a pseudo steady-state and the strain failure was examined through optical microscopy imaging. Delamination for sample #1 occurred at 20% strain, as indicated by a crack initiation and subsequent growth. The strain for delamination for sample #2 was higher, occurring at 30% strain at the interface 130 and in line with the finite-element predictions (see Table 1). The silicon-PDMS (5:1) interface 130 in sample #3 did not delaminate. Instead, crack growth occurred at the interface of the PDMS (5:1) and PDMS (20:1) materials between the first section 111 and second section 112, rather than at the interface 130 with the embedded device 120, and initiated at 100% strain. This strain failure threshold was six times larger than that of sample #1 (with the silicon-PDMS (5:1) interface). Further, the strain cycling performance of sample #3 up to 100 cycles under maximum 50% strain was studied and delamination was not detected at either interface.

(28) While the foregoing analyzes the effect of material stiffness on the risk of delamination, the relative length of each section 111, 112 of the substrate 110 also have an effect. To minimize the delamination risk, the substrate 110 can be analyzed based on the ratio of the length of first section, L.sub.2, to the total substrate length, L=L.sub.1+L.sub.2. The energy release rates for different values of the L.sub.2/L ratio at the interface 130 of silicon-PDMS (5:1) and at the interface 130 of PDMS (5:1)-PDMS (20:1) were calculated.

(29) At these interfaces, material properties and geometric design parameters affect the energy release rate function:
G=f(a, E.sub.1, E.sub.2, , L.sub.1, L.sub.2, h.sub.1, h.sub.2, h.sub.3)(1)
where a is crack length, is the applied strain, h.sub.1 is the thickness of the material in the second section 112 of substrate 110 on top of the embedded device 120, h.sub.2 is the thickness of the material in the first section 111 on top of the embedded device 120, and h.sub.3 is the thickness of the embedded device 120.

(30) For this comparison, all parameters except L.sub.2 are fixed. The energy release rate increases with increasing applied strain with approximately quadratic dependence. This nonlinear dependence of G on strain arises in FIG. 7A, which also illustrates a nonlinear dependence on L.sub.2. A comparison in FIG. 7B of energy release rates at 20% strain for the interface 130 (top line) and for the first section 111/second section 112 (PDMS (5:1)/PDMS (20:1)) interface (bottom line) indicates that G for the silicon-PDMS interface 130 is roughly two times higher than for the PDMS-PDMS interface. In FIG. 7B, L.sub.2/L=0 represents the sample #1 case and L.sub.2/L=1 represents the sample #2 case, with these endpoint values corresponding to those in Table 1. For intermediate values of L.sub.2/L, the energy release rate at the silicon-PDMS interface 130 decreases significantly.

(31) FIG. 8 shows the tensile responses of integrated devices 100 with different L.sub.2/L (0.05, 0.15, 0.25, 0.35, 0.45) and a fixed L=10 mm. The graph of FIG. 8 shows the quantified the strain level at the onset of delamination and indicates in all cases that the interface between the first section 111 and second section 112 failed first. The failure strain values for the example without an intermediate stiffness first section 111 (L.sub.2/L=0 and L.sub.2/L=1) were relatively small. The highest failure strain of 140% occurred with the geometric condition of L.sub.2/L=0.05 (see FIG. 8). The effects on G of h.sub.3/h.sub.2, h.sub.1/h.sub.2, and E.sub.2/E.sub.1 are shown in FIGS. 9, 10, and 11, respectively. Delamination typically happens at corners, edges and regions of the device/substrate interface 130 where there is high strain. Having rounded corners or circular chips can reduce the energy release rate.

(32) It is estimated that the adhesion energy of Si-PDMS interfaces is about 0.05-0.4 J/m.sup.2. The work of adhesion for a PDMS-PDMS interface is in the range of about 250-300 J/m.sup.2. Therefore, the PDMS-PDMS bonding is stronger than Si-PDMS bonding by four orders of magnitude. While the Si-PDMS adhesion could possibly be enhanced through a geometric interlock design or through use of adhesion promoters, the substrate 110 of the present invention moves the critical interface to the interface of the first section 111 and the second section 112, enabling exploitation of the natural adhesion between similar polymers.

(33) To create a substrate 110 having a gradient, PDMS with mixing ratios of base to curing agent of (5:1) and (20:1) were used in the example embodiment described above. However, in alternative embodiments, other mixing ratios, additional materials, or distinct materials can be used to create the gradient. In the example embodiment, the Young's modulus values are E.sub.2=1.98 MPa for PDMS (5:1) and E.sub.1=0.26 MPa for PDMS (20:1).

(34) One fabrication method comprises embedding a 1 mm1 mm50 m silicon chip (E=170 GPa) as the rigid device 120 into a 90 m-thick PDMS sheet as the substrate 110. To make the two-material substrate 110, a handle wafer as a base 141 is spin coated with 10 m-thick PDMS (5:1), which will become part of the first portion 111 of the substrate 110. The coating step can be followed by partial curing at 80 C. for 20 minutes to allow the film to solidify without losing its adherent nature. Next, the silicon chip (i.e. device 120) is then transferred to this first layer, and a second 60 m-thick PDMS (5:1) layer is spin coated and then cured at 80 C. for 4 hrs., thereby embedding the rigid device 120 in the first portion 111 of the substrate 110. This composite structure is then etched (for example, reactive ion etching using SF.sub.6 and O.sub.2 plasma) into a 1 mm diameter circle and released from the base 141 and subsequently transferred to a second base 141 having an initial 10 m-thick spin-coat PDMS (20:1) layer, which will be part of the second portion 112. The composite structure is then embedded into PDMS (20:1) by spin coating an additional 80 m-thick PDMS (20:1) layer followed by 4 hrs. curing at 80 C. The soft PDMS (20:1) material of the second portion 112 covers the first portion 111 by approximately 10 m on its top and bottom surfaces. Thus, in this embodiment of the method of fabrication, there are two general stages: first, embedding the rigid device 120 into the first portion 111 of the substrate 110; and, second, embedding the combined structure into the second portion 112 of the substrate 110.

(35) In an alternative embodiment, the base 141 is coated with a submicron layer of gelatin (1%). Gelatin is used as a sacrificial layer 143 (see FIG. 1B) since it is soluble in water and it aids in release of the device 100. For example, the device 100 can be released in hot water (70 C.) since gelatin is highly soluble at this temperature level. In yet another embodiment, the combined embedded device 120/first portion 111 composite structure is patterned into a circular shape using a hard mask through reactive-ion etching using SF.sub.6/O.sub.2 plasma for 3 hrs.

(36) In an alternative fabrication method, as shown in FIGS. 12A-12C, the embedded device 120 is placed on a cured layer of the second portion 112 of the substrate 110. Next, as shown in FIG. 12A, drops of the material for the first portion 111 (PDMS (5:1), for example) are deposited around the device 120. The material can be added manually, or with the aid of equipment such as an inkjet or 3D printer. FIG. 12B shows the material of the second portion 112 of the substrate 110 added. The released integrated device 100 is shown in FIG. 12C.

(37) FIGS. 13A-13C depict another alternative embodiment of the fabrication method. First, the rigid electronic device 120 and the first portion 111 of the substrate 110 are fabricated, similar to the method described above, and place on a cured layer of the second portion 112. The composite structure is then surrounded with uncured polymer base, as shown in FIG. 13B. The uncured polymer base may comprise a base material without a curing agent or a base material pre-mixed with a curing agent. As a person having skill in the art will appreciate, the uncured polymer base is generally in a liquid state prior to curing. Drops of curing agent, base material/curing agent mixture, or base material are then deposited at the interface between the first portion 111 and the second portion 112, creating a gradient at the interface of the two portions 111, 112.

(38) In one example of the fabrication process depicted in FIGS. 13A-13C, the rigid device 120 is encapsulated in PDMS (20:1). Next, PDMS (5:1) droplets are deposited manually, such as by a micro-pipette, around the rigid device 120 before curing the PDMS (20:1) substrate 110. The PDMS (5:1) drops diffuse into the surrounding PDMS (20:1). Since the PDMS droplets are located in the center of the structure and PDMS flows from the center to the sides, the concentration of PDMS (5:1) at the center is higher than the edges. In other words, there is a concentration gradient of PDMS (5:1) across the soft substrate 110. Therefore, the mixture of PDMS (20:1) and (5:1) form PDMS (x:1), where x varies between 5 and 20 across the substrate 110.

(39) In yet another alternative, the gradient in stiffness starts at the edge of the first section 111. The fabrication process is similar to the process used to create a two-region substrate, except that for the formation of the gradient in stiffness, where PDMS (5:1) droplets are injected to the center of the structure at the end of the process before curing the second section 112.

(40) FIGS. 14A-14C show embodiment of the fabrication method with a continuous gradient without a distinct first section 111 and second section 112. In this method, the gradient in stiffness in the substrate 110 is created by diffusing a curing agent into the substrate 110. For example, as shown in FIG. 14A, the device 120 is embedded within the substrate 110, which can be cured or semi-cured. If semi-cured, the substrate 110 may have some portion of the curing agent pre-mixed with the base material. Once the device 120 is embedded in the substrate 110, drops of the curing agent are deposited onto the substrate 110, which will then diffuse into the material comprising the substrate 110. As previously stated, the drops can be added manually or by using an inkjet or 3D printer, where it can diffuse into the substrate 110. The curing agent may be applied by other techniques, such as through the use of an aerosol jet printers or spray jetting systems.

(41) If using a printer or jetting system, the pattern of drops can be programmed digitally to provide any gradient pattern. For example, the printer can make a first pass of depositing a curing agent at the interface 130. A second pass can cover the same area, but also extend beyond the area of the first pass. Subsequent passes can enlarge the area covered by the curing agent in the previous pass. In this manner, the first area will be covered by the most passes and, thus, will have the highest concentration of curing agent, leading to a higher stiffness in the substrate 110.

(42) When using an inkjet printer or aerosol jet printer, additional steps may be performed to aid the process. For example, in one alternative embodiment the curing agent is combined with a solvent, such as xylene, trichlorobenzene, hexane, isopropyl alcohol, or similar solvents to reduce the viscosity of the curing agent. Alternatively, the curing agent could be heated to reduce the viscosity. Other variations of these techniques can be employed to develop an appropriate viscosity and surface tension to allow printing of the curing agent.

(43) Additional steps may also include heating the substrate 110 to control the rate of diffusion of the curing agent into the substrate 110. For example, when the curing agent is printed onto the substrate comprising an uncured base material, the curing agent will diffuse into the base material until cured. The extent of diffusion of the curing agent can be limited by heating the substrate 110, which decreases the curing time. In some embodiments where the substrate 110 is heated sufficiently, the uncured base material will cure upon impact by the curing agent deposited by the printer. Using this technique, the precision of gradients in the stiffness of the substrate 110 can be improved.

(44) FIGS. 16A-16C show schematics of devices created by several of the processes described above. For example, FIG. 16A shows a device with a substrate 110 comprising a first section 111 and a second section, each having a uniform stiffness. FIG. 16B shows a device with a substrate 110 having a stiffness gradient beginning at the edge of the rigid device 120. FIG. 16C shows a device with a first section 111 having a uniform stiffness and a second section 112 having a stiffness gradient. Further depicted in FIGS. 16A-16C are graphs depicting the Young's modulus of the materials as a function of location along the length of the stretchable substrate 110. The approach depicted in FIG. 16C results in a smoother strain contour with a lower strain around the silicon chip compared to other approaches.

(45) FIGS. 15A-15D show an alternative fabrication embodiment where antennas, coils, and other passive devices 150 are embedded in the substrate 110. As a person having skill in the art will appreciate, several fabrication methods to create a gradient in the substrate 110 can be employed.

(46) In addition to delamination at the interface 130 of the rigid device 120, wiring of the electronic components in an elastic substrate 110 poses an additional challenge. Wires are made of conducting materials having a different Young's modulus from the substrate 110; therefore, these connections experience levels of strain and stress that also require soft substrate engineering. The interfaces between the regions of the substrate 110 are often locations where wires can break. A composite structure of two regions having different values of Young's modulus causes a step in the strain level at the interface. This step in strain induces wire breakage. With gradients in stiffness, the step in the strain level can be reduced, thereby minimizing breakage.

(47) Several of the substrates 110 described herein address the wiring failure that can happen where the wire passes across the substrate regions having different stiffness values. Regions in the substrate 110 experience different levels of expansion and contraction in the direction perpendicular to the applied load. Shear stress at the edges of the interfaces can break the wires. In order to address this issue, the substrate 110 material stiffness can be smoothly transitioned from one region to another. This material gradient reduces the sharp shear stress at the interface between regions. For example, in the embodiment where the first section 111 of the substrate 110 has a uniform stiffness and the second section has a stiffness gradient, there is a smoother strain contour with a lower strain around the rigid electronic device 120. Moreover, a wire embedded in the substrate 110 can remain intact without failure approaching 135% strain. For complicated circuits, curing agent or uncured base material could be applied along wires to create a stiffness gradient around each wire. In one embodiment, the curing agent is printed around the wires prior to curing. In yet another alternative, the curing agent can be printed onto the substrate 110 prior to fabrication of the wires, where the curing agent is deposited in a pattern that replicates the path of the wires. In other words, the curing agent can be applied in a pattern that replicates the wiring pattern in the electronic device 100.

(48) While the disclosure has been described in detail and with reference to specific embodiments thereof, it will be apparent to one skilled in the art that various changes and modification can be made therein without departing from the spirit and scope of the embodiments. Thus, it is intended that the present disclosure cover the modifications and variations of this disclosure provided they come within the scope of the appended claims and their equivalents.