Mechanically resilient integrated electronics realized using interconnected 2D gold-nanosheet elastomeric electrodes

With the growing interest in wearable devices in recent decades, considerable effort has been devoted to developing mechanical elastomeric devices such as sensors, transistors, logic circuits, and integrated circuits. To successfully implement elastomeric devices subjected to large mechanical deformations or stretching, all the components, including conductors, semiconductors, and dielectrics, must have high stability and mechanical sustainability. Elastomeric conductors, which exhibit excellent electrical performances under mechanical deformations, are key components of elastomeric devices. Herein, we prepared fully elastomeric electrodes based on interconnected 2D gold nanosheets (AuNSs) to develop mechanically resilient integrated electronics. The AuNS elastomeric electrodes exhibited a sheet resistance of less than 2 Ω/sq under 50% stretching and sustained 100,000 stretching–releasing cycles. These electrodes with a dedicated design were used in combination with elastomeric semiconductors of P3HT nanofibrils in the PDMS elastomer (P3NF/PDMS) and an ion gel as a dielectric to realize elastomeric transistors, inverters, and NOR and NAND logic gates. Additionally, an elastomeric 8 × 8 transistor array that can sustain various types of mechanical stimuli was successfully demonstrated. Furthermore, the elastomeric electronic devices implemented on a soft robot showed no interfering performances during robot gripping motion. The proposed framework is expected to aid in the rapid development and broaden the application scope of soft electronics. Bendable but resilient electrodes made from nanometer-thick sheets of gold have been developed by researchers in South Korea. Flexible electronic materials are opening the way to foldable phones and wearable devices. Elastomers, elastic polymers with rubber-like physical properties, are particularly interesting materials for these applications. A crucial requirement, however, is a way to electrically connect the various elastomer components. Hae-Jin Kim and co-workers from the Gyeongsang National University in Jinju used interconnected two-dimensional gold nanosheets to create elastomeric electrodes. The team demonstrated that these electrodes had low electrical resistance and were structurally resilient even after 100,000 stretch-and-release cycles. They then used these electrodes in combination with an elastomeric semiconductor to create basic electronic components such as an elastomeric transistor to demonstrate the practical viability of their approach. A mechanically percolated network of 2D gold nanosheets embedded within a PDMS elastomer enables the realization of elastomeric electrodes with superior mechanical sustainability and high electrical conductivity. Owing to such highly durable elastomeric electrodes facilitate the development of elastomeric electronics, including transistors, inverters, NOR, and NAND, which is expected to broaden the scope of soft electronic applications.


Introduction
With advances in sophisticated techniques for material design and structural engineering, the paradigm of electronics is shifting from conventional rigid devices to soft devices through form factor innovations [1][2][3] . To satisfy the novel requirements of soft elastomeric devices, research in the electronics domain has focused on the development of elastomeric devices, such as multifunctional sensors [4][5][6][7] , power conversion/storage sources (e.g., photovoltaics, nanogenerators, supercapacitors, and batteries) [8][9][10][11] , and operating logic circuits 12,13 . Although considerable effort has been expended in developing soft electronics, several challenges must be overcome to enable the scaling of soft electronics from laboratory prototypes to industrial manufacturing.
There has been growing interest in the development of elastomeric electronics (e.g., inverters, NOR, NAND logic gates, oscillators, and flip-flops) to implement logical operating functions in elastomeric sensors, thereby broadening the application scope of soft electronics [14][15][16] . The incorporation of elastomeric electronics with sensors can facilitate the dynamic acquisition of signals over a large area, ensure low interference between the pixels in the active matrix array system, and achieve high power efficiency [17][18][19][20][21] . Nevertheless, the realization of fully elastomeric electronics remains challenging, as all the components must be elastic and exhibit satisfactory performance when subjected to mechanical stimuli.
Among the various nanomaterials used to develop elastomeric electrodes, gold nanomaterials exhibit high intrinsic conductivity, a low injection barrier at the metal-semiconductor interface, superior chemical stability, and ease of surface modification 33,34 . Furthermore, gold-based elastomeric electrodes are chemically inert, which facilitates the long-term use of the electrodes on human skin without any irritation or inflammation. Stateof-the-art gold-based elastomeric electrodes exhibit a conductivity of more than 100 S/cm 2 at a mechanical strain of 500% 35 .
Due to the effective formation of mechanical percolation of 2D materials within the elastomer, the use of 2D gold nanosheets (AuNSs) has been proposed to develop elastomeric electrodes. Table S1 (Supplementary Information) summarizes the up-to-date AuNS-based stretchable electrodes. These electrodes can be developed either by transferring or embedding AuNSs on the elastomer surface or within the elastomer, respectively. Compared to the state-of-the-art AuNS-based elastomeric electrodes, the AuNS elastomeric electrodes developed in this work exhibited the lowest electrical sheet resistance (0.15 Ω/sq) and showed the smallest increase to 1.8 Ω/sq upon a 50% mechanical strain. Additionally, embedding percolated AuNSs within the elastomeric PDMS resulted in a sustainable electrical performance even after 100,000 cycles of the stretch-release cycles, which have never been tested before. Furthermore, the patterning capability owing to the unique manufacturing process greatly widens the application scope, as proven in this study with the development of mechanically resilient integrated electronics and arrays.
In this study, we prepared mechanically durable and reliable elastomeric electrodes by using interconnected AuNSs. In the manufacturing process, the hot-pressing conditions were optimized to enhance the electrical conductivity and mechanical sustainability under stretching. The resulting AuNS elastomeric electrodes maintained a sheet resistance of less than 2 Ω/sq at a mechanical strain of 50% and sustained 100,000 cycles without any observable hysteresis. By exploiting the patterning ability of the AuNS elastomeric electrodes, elastomeric electronic devices, such as transistors, inverters, NOR and NAND gates, and arrays, were devised. The excellent performance of the elastomeric electronic devices could be attributed to the following aspects: (i) the use of mechanically resilient AuNS elastomeric electrodes; (ii) the use of highly crystalline π-π stacking P3HT nanofibrils in the PDMS elastomer (P3NF/PDMS); (iii) the small hole-injection barrier between AuNS and P3NF; and (iv) the use of an elastomeric ion-gel dielectric. The elastomeric transistor had field-effect mobility of 19.8 cm 2 /V s, which did not significantly decrease at a 50% mechanical strain. Moreover, the electronic devices exhibited stable static and dynamic performance under various types of mechanical stimuli. A high-performance elastomeric transistor 8 × 8 array was prepared to illustrate the application of integrated circuits for soft electronics. To date, the performances of our developed AuNS stretchable electrodes have surpassed those of previous AuNS stretchable electrodes, which aided in realizing fully elastomeric integrated electronics. In addition, a soft robot equipped with integrated electronics on its skin was demonstrated, with the objective of contributing to the development of intelligent robots. The development of mechanically resilient electronics based on AuNS elastomeric electrodes can foster the realization of next-generation wearable devices that are imperceptible, comfortable, durable, lightweight, and cost-effective.

Synthesis of AuNSs
First, HAuCl 4 •3H 2 O (≥99.9%, Merck, Korea) aqueous solution (8 mL, 17 mM) and L-arginine (≥98%, Sigma Aldrich) aqueous solution (20 mL, 1.98 mM) were heated to~95°C in an oil bath for 1 h. After mixing the two solutions, the mixture was placed in an oil bath for 2 h until the AuNS precipitation was complete. Next, the solution was thoroughly washed with deionized (DI) water three times and purified by centrifugation. Finally, the precipitated AuNSs were dispersed in 2 mL of 1-butanol for further fabrication. The dimension and electrical conductivity of the AuNSs were characterized using AFM (Anton-Paar, TOSCA-200). To measure the electrical conductivity of the AuNSs, a conductive Arrow TM Si AFM probe (Nanoworld, C = 2.8 M/m, f = 75 kHz) was used at an applied voltage of 1 V. The AFM equipment provided current compliance of up to 2 nA to ensure safe use.

Fabrication of the AuNS elastomeric electrodes
To fabricate the AuNS elastomeric electrodes, precleaned glass with a stencil polyimide mask was prepared.
The stencil mask was fabricated using a programmable cutting machine (Silhouette, USA). The stencil mask was designed as desired by using the commercial computeraided software AutoCAD ® . A few drops of the AuNS dispersed solution were dropped onto the water surface, which led to the natural formation of an AuNS monolayer. The AuNSs were transferred to the glass by repeatedly stamping the sample. The AuNS transfer process was repeated eight times to ensure a low sheet resistance (<2 Ω/sq) for the AuNS electrodes. After removing the stencil mask, the AuNS electrodes were subjected to hot pressing at 10 kPa and 250°C. According to our previous study, high electrical conductivity and mechanical durability of the AuNS electrodes could be ensured under these hot-pressing conditions 36,37 . PDMS (10:1 = prepolymer:curing agent) was spin-coated on the AuNS electrodes at 300 rpm and cured for 2 h in an 80°C oven. Finally, the PDMS was detached from the glass to yield 300-μm-thick AuNS elastomeric electrodes.
The P3HT/PDMS elastomeric semiconductor was synthesized by storing a P3HT/DCM solution (2 mg/mL) in a freezer (−20°C) for 10 min to form self-assembled P3NF. After mixing the P3NF/DCM solution with the PDMS/ DCM solution with a weight ratio of 8:2, the mixture was spin-coated at 2000 rpm for 30 s to prepare the elastomeric semiconductor. The ratio was selected to attain high-performance in terms of the mechanical stretchability and electrical conductivity of the elastomeric semiconductor, as examined in our previous work 33 . To synthesize the ion-gel elastomeric dielectric, poly(vinylidene fluoride)-co-hexafluoropropylene (PVDF-HFP), 1ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide (EMIM-TFSI), and acetone were blended with a weight ratio of 1:4:7. The solution was then spin-coated on a precleaned glass at 300 rpm and stored in a 70°C vacuum oven for 12 h. The prepared ion gel could be easily shaped using a razor and picked up from the glass.

Fabrication of the elastomeric devices and array
To construct the transistors, inverters, NOR, and NAND, AuNS elastomeric electrodes consisting of a source, a drain, and a gate were fabricated using the aforementioned method. The channel length was 50 μm. The P3NF/PDMS elastomeric semiconductor was patterned on the AuNS elastomeric electrodes by using the polyimide stencil mask. A piece of the 100-μm-thick iongel elastomeric dielectric was aligned and laminated on the P3HT/PDMS layer. Finally, the diluted PDMS solution (400 mg/mL) in dichloromethane (DCM) was dropcast and solidified to encapsulate the elastomeric devices. To construct the 8 × 8 transistor elastomeric array, two layers of elastomeric electrodes were stacked and connected with an EGaIn via-hole. The constructed array consisted of eight gates, eight drains, and a common source. Next, the P3NF/PDMS semiconductor and ion-gel layers were sequentially patterned on the elastomeric electrode array by using the aforementioned method. Finally, a thin layer of PDMS was spin-coated to encapsulate the elastomeric array. The fabrication process is illustrated in Fig. S1 (Supplementary Information). The performance of the array was evaluated using a custombuilt connecting module, as shown in Fig. S2 (Supplementary Information). To further examine the mechanical resilience of the array, the ON current of the transistors was measured in real-time under various types of mechanical stimuli.

Fabrication of the soft robot
The elastomeric devices, such as NOR and NAND logic gates, were incorporated with a soft robot to examine the feasibility of using the elastomeric devices for soft robot operations. The soft robot was developed following the procedure described in ref. 38 . Briefly, a mixture of Ecoflex ® 0030 prepolymer and curing agent (1:1 in weight) was poured into a 3D printed mold (Fig. S3, Supplementary Information). After removing the part from the mold, a thin layer of PDMS (t =~300 μm) was placed on the part as a bottom cover. Next, the PDMS top cover with the elastomeric devices was placed on the other side of the soft robot. A thin layer of Ecoflex was used as glue to ensure that the covers adhered well to the middle part of the soft robot. An air-supply tube was connected to the soft robot to complete the soft robot fabrication.

Electrical performance characterization
To characterize the effect of the hot-pressing conditions on the elastomeric electrode performance, the sheet resistance of 2 mm × 10 mm AuNS elastomeric electrodes was measured under different levels of mechanical stretching strain by using a four-point-probe method 39,40 . The samples were stretched in cyclic and endurance tests using a custom-built mechanical stretcher. The elastomeric devices were characterized using a semiconductor analyzer (4200-SCS, Keithley Instruments Inc.) equipped with 3700 A systems, a function generator (33210 A, Keysight Technologies), and a digital oscilloscope (DSO-X 2002A, Agilent Technologies).

FEA mechanical simulation
To investigate the stress and strain distribution over the AuNSs at different orientation angles and 50% mechanical stretching, the commercial FEA software ABAQUS ® was used. The angles of the embedded AuNSs with respect to the horizontal axis were 0°, 30°, 45°, 60°, and 90°. The elastic modulus and Poisson's ratio of Au and purely elastic PDMS were 60 GPa and 0.3 and 2 MPa and 0.4, respectively 41,42 . Isotropic mechanical properties were considered for simplification. All features meshed with quadratic tetrahedral elements (C3D10). Moreover, automatic stabilization was implemented to minimize the mesh distortion that may lead to unstable responses during the calculation.

Results and discussion
Mechanically resilient AuNS elastomeric electrodes Before fabricating the elastomeric electrodes, AuNSs were synthesized by following the procedure described in our previous work 36 . Figure S4 (Supplementary Information) shows atomic force microscopy (AFM) images of the synthesized AuNSs. The average diameter and thickness of the polygonal AuNSs were 30 µm and 120 nm, respectively. Because the AuNS elastomeric electrodes were simply manufactured using a stencil mask, the electrodes could be easily patterned with a sophisticated design. Figure 1a shows the AuNS elastomeric electrodes with the word "Resilience" patterned in cursive. The resolution of the pattern was sufficiently high to clearly express the curves and vertices of the word on the AuNS elastomeric electrodes (Fig. S5, Supplementary Information). Figure 1a shows that the resulting electrode could power a commercial red LED without any brightness variation when subjected to twisting and stretching motions. This outcome could be attributed to the mechanically percolated AuNSs embedded in the PDMS elastomer, as illustrated in the inset of Fig. 1a.
This performance of the AuNS elastomeric electrodes could be achieved through a simple manufacturing process, as illustrated in Fig. 1b. In brief, the manufacturing process started with preparing a stencil mask with the desired design using a programmable cutting machine. The AuNSs were then transferred printed on the sample, followed by removing the stencil mask. Next, hotpressing treatment was conducted to increase the electrical conductivity of the electrodes by removing the organic ligand and increasing the conformal contact between the AuNSs. Observations of the AuNS surface morphology confirmed an increase in the conformal contact between the AuNSs under optimal hot-pressing conditions. As shown in Fig. S6 (Supplementary Information), the surface roughness of the elastomeric electrodes prepared from the hot-pressed AuNSs was significantly lower than that of the AuNS elastomeric electrodes subjected to insufficient hot pressing. Although the AuNS elastomeric electrodes subjected to hot-pressing conditions of 350°C and 20 kPa resulted in low surface roughness, considerable AuNS residue was observed on the counter Si wafer surface owing to the excessive hot-pressing conditions, as shown in Fig. S7 (Supplementary Information). Furthermore, a slight loss in the electrical performance was observed when a mechanical strain was applied, as discussed in the following section.
The final manufacturing step involved spin-coating, curing, and detaching the PDMS from the glass to develop the AuNS elastomeric electrodes. The thicknesses of the AuNS embedded region and overall AuNS elastomeric electrodes were 30 and 300 μm, respectively (Fig. S8, Supplementary Information). In general, compared with preparation via a simple transfer on the elastomer 43 , embedding AuNSs in elastomeric PDMS can help prevent delamination of AuNSs during repetitive contact-release cycles in wearable applications. This aspect was confirmed through an adhesion test, as shown in Fig. S9 (Supplementary Information). Compared to a simple transfer of AuNSs on PDMS, elastomeric electrodes from AuNSs embedded within PDMS exhibited not only higher electrical conductivity but also superior sustainability under the 3 M tape adhesion test.
Note that hot-pressing treatment must be implemented to effectively manufacture mechanically durable and reliable AuNS elastomeric electrodes. To investigate the effect of the hot-pressing treatment on the change in the AuNS conductivity, the conductivity of a single AuNS subjected to hot pressing under different conditions was evaluated using a conductive force microscope (CFM). Figure 1c shows the conductivity mapping images (upper) and corresponding current profile (yellow dotted line) in the CFM images of triangular AuNSs subjected to different hotpressing conditions. The treatment was sequentially applied to the same AuNS to monitor the variation in the current over the surface under different treatment conditions. The CFM measurement was performed with an applied voltage of 1 V. For the as-transferred AuNS, no detectable current was obtained over the entire AuNS surface. The AuNS subjected to hot-pressing conditions of 150°C and 20 kPa exhibited an average current of up to 1 nA, while the AuNS subjected to hot-pressing conditions of 250°C and 20 kPa reached device compliance of up to 2 nA. This phenomenon could be attributed to the effective removal of the organic ligand formed on the surface during AuNS synthesis 32,36 .
Finite element analysis (FEA) was conducted to investigate the mechanical sustainability of the embedded AuNSs by observing the stress and strain distribution under stretching. In the simulation, the stress and strain of the embedded AuNSs with different orientation angles were evaluated in the case of 50% PDMS stretching. The orientation angle of the embedded AuNSs with respect to the horizontal axis varied from 0°to 360°. In Fig. 1d, the orange dot in one of the triangle vertices indicates the orientation criterion. Figure 1d shows the results of the averaged von Mises stress σ (red) and strain ε (green) generated on the embedded AuNSs under the 50% stretched PDMS condition. The averaged von Mises stress and strain generated on the AuNSs were 0.5 MPa and 7 × 10 −6 , respectively, for all AuNS orientation angles. All the results corresponded to the elastic regime of the AuNSs. This outcome could be attributed to the large mismatch in the mechanical properties of the AuNSs and PDMS, which induced the island effect during PDMS stretching 44 .
Considering the results derived from a single AuNS, as shown in Fig. 1c, d, we attempted to optimize the performance of the elastomeric electrodes fabricated with mechanically percolated AuNSs. Thus, various AuNS elastomeric electrodes subjected to different hot-pressing conditions were fabricated using the aforementioned procedure. The temperature and pressure ranged from 25°C (Ambient) to 250°C and from 0 to 20 kPa, respectively. Figure 1e shows the sheet resistance map of the various AuNS elastomeric electrodes subjected to different levels of a mechanical strain of up to 50%. The sheet resistance of the resulting electrodes was less than 5 Ω/sq for all hot-pressing conditions. A significant change in the electrical performance was observed when the electrodes were subjected to a mechanical strain of up to 50%. Under hot-pressing conditions involving an inadequate temperature and pressure (i.e., <150°C and <10 kPa, respectively), the sheet resistance exceeded 20 Ω/sq when the sample was subjected to a 50% mechanical strain, leading to a significant loss in the device performance. Thus, the AuNS elastomeric electrodes treated with hot pressing at 250°C and 20 kPa were optimal for simultaneously maximizing their mechanical sustainability and electrical performance. In the scanning electron microscopy (SEM) images of the AuNS elastomeric electrodes subjected to mechanical stretching of up to 50%, shown in Fig. 1f, severe damage or visible cracks were not observed, which is consistent with the FEA results.
To further examine the mechanical integrity of the AuNS elastomeric electrodes, the electrodes were subjected to various endurance tests. The sheet resistance of the AuNS elastomeric electrodes prepared under optimized hot-pressing conditions increased from 0.15 to 1.8 Ω/sq when stretched up to a 50% mechanical strain, as shown in Fig. 1g (left). The electrodes exhibited almost no hysteresis in the mechanical stretching and releasing cycle. The corresponding I-V curves are presented in Fig. S10a (Supplementary Information). Figure 1g (right) shows the relative electrical resistance (R/R o ) under different consecutive mechanical strains. While the applied stretching strain ranges from 10 to 50%, the resistance changes accordingly from~0.7 to~11.4.
To perform the static cyclic test, the electrode was mounted in a custom-built mechanical stretcher, which stretched up to 30% and could be released at a rate of 1 Hz. As presented in Fig. 1h (left), the electrodes maintained a sheet resistance of less than 2 Ω/sq even after 100,000 stretching-releasing cycles. The corresponding I-V curves of the cyclic test are presented in Fig. S10b (Supplementary Information).
In the dynamic stretching-releasing cycles at a rate of 1 Hz with increasing strain, the electrodes demonstrated excellent resilience in terms of electrical resistance with no severe hysteresis, as shown in Fig. 1h (right). Additionally, no severe drift or any changes in the relative resistance of the electrodes were observed, consistent with the results of the static measurement. Overall, the AuNS elastomeric electrodes exhibited excellent performance and could function as mechanically resilient and elastomeric electrodes in all soft electronics applications.

Performance characterization of the elastomeric transistors
Elastomeric transistors were developed using highly stretchable, durable, and reliable AuNS elastomeric electrodes. The transistor consisted of AuNS elastomeric electrodes (source, drain, and gate), P3NF/PDMS semiconductor nanocomposites, an ion gel, and a PDMS encapsulation layer, as illustrated in Fig. 2a. The channel length and width of the transistor were 50 μm and 5 mm, respectively. To ensure the mechanical stretchability and enhanced electrical performance of the P3HT organic semiconductor, the following aspects were implemented: (i) highly crystalline P3NFs were obtained using a cooling process, (ii) a P3NF/PDMS solution (2:8 = w:w) was used to facilitate patterning, and (iii) a percolated P3NF network was embedded in the PDMS structure with the aim of enhancing the electrical conductivity during stretching. Consequently, the embedded P3NF network maintained its form in the PDMS during mechanical stretching of up to 50%, as demonstrated by the AFM images shown in Fig. S11 (Supplementary Information). Figure 2b shows the representative transfer characteristics of the elastomeric transistor, with the drain current obtained at a sweep gate voltage ranging from 0 to −3 V and a constant drain voltage of −1 V. The averaged fieldeffect mobility and on/off ratio were 19.8 cm 2 /V s and 4.1 × 10 4 , respectively. The output characteristics were obtained by varying the gate voltage from 0 to −3 V with a step of −0.2 V and sweeping the drain voltage from 0 to −1 V (Fig. 2c). No electrode-semiconductor contact issue was observed.
After determining the basic characteristics of the elastomeric transistor, the transistor was subjected to mechanical stretching to verify its mechanical sustainability. Figure 2d shows the representative transfer curves of the elastomeric transistor at various levels of mechanical strain (up to 50%) along the channel length. A small change in the transfer curves during mechanical stretching resulted in a marginal decrease in the fieldeffect mobility and a small change in the threshold voltage (V TH ) of the elastomeric transistors, as presented in Fig. 2e. The V TH ranged from −2.1 to −2.3 V at a mechanical strain ranging from 0 to 50%. The inset optical images show the transistors subjected to mechanical strains of up to 50%. The values recovered to nearly the original values when the transistors were released to a 0% strain. Notably, the field-effect mobility of the elastomeric transistors recovered to 18.1 ± 2.5 cm 2 /V s when released to a 0% mechanical strain.
To validate the repeatability of and discrepancy in the elastomeric transistor performance under mechanical strain, a statistical approach was followed. The transfer curves and corresponding field-effect mobilities of 30 transistors were determined, as shown in Fig. 2f and Fig. S12a (Supplementary Information). The average fieldeffect mobility at a 0% mechanical strain was 19.8 ± 3.6 cm 2 /V s, and the corresponding average values at a 30 and 50% mechanical strain along the channel length were 14.2 ± 3.2 cm 2 /V s and 11.3 ± 2.1 cm 2 /V s, respectively. The distribution of the field-effect mobility values at a 0% mechanical strain was statistically similar to those at a 30 and 50% mechanical strain, and thus, all p values were higher than 0.05.
A similar performance characterization was conducted to examine the mechanical sustainability when the device was stretched perpendicular to the channel length. The transfer curves, field-effect mobilities, and their statistical distributions are shown in Fig. 2g-i, respectively. The transfer curves of the elastomeric transistors at different levels of mechanical strain perpendicular to the channel length are presented in Fig. S12b (Supplementary  Information). The electrical performance remained nearly constant when the sample was subjected to a mechanical strain of up to 50%. The average field-effect mobilities at a 30 and 50% mechanical strain perpendicular to the channel length were 14.5 ± 4.8 cm 2 /V s and 10.0 ± 3.3 cm 2 /V s, respectively. A comparative statistical analysis of the three groups yielded p values higher than 0.05, demonstrating the mechanical sustainability of the elastomeric transistors.
In addition, the dynamic electrical performance of the elastomeric transistor was investigated by determining the drain current (−I D ) in real-time corresponding to various types of mechanical stimuli, such as stretching, twisting, and poking. Figure 2j shows the ON and OFF currents of the transistor measured for 60 s when subjected to continuous and sequential mechanical stimuli (see Video S1, Supplementary Information). Although the current slightly fluctuated every time a mechanical stimulus was applied, almost no current variation was observed over the entire measurement time. Overall, the fabricated elastomeric transistor exhibited high mechanical sustainability and durability with excellent electrical performance.

Elastomeric integrated electronics and logic gates
To expand the application scope of the transistors, elastomeric integrated electronics and logic gates were developed. In general, networked inverters and logic gates are basic components in integrated electronics used to compute Boolean logic operations. Elastomeric integrated electronics that can formulate digital logic from mechanically sustainable and compliant materials can complement conventional electronics, thereby broadening the application scope, especially in the domains of soft robots, health monitoring sensors, and medical devices. In this study, an elastomeric load-type inverter, zero-V GS load inverter, and NOR and NAND gates were fabricated using the methods described in the Materials and methods section. Figure 3a shows the exploded schematic illustration, corresponding optical photograph, and circuit diagram of the elastomeric load-type inverter. A commercial 100-kΩ resistor was serially connected to the drain electrodes of the transistor. Figures 3b and c  The dynamic response of the elastomeric load-type inverter was characterized by generating a square wave input voltage (blue line), as presented in Fig. 3d. The frequency of the square wave input voltage was 0.15 Hz. When an input voltage of −3 to 0 V was applied, the output voltage corresponded to the inverter operation and varied from 0 to −1 V, respectively. The low inverting frequency could be attributed to the intrinsically slow ion migration property of the ion gel 45 . Subsequently, the elastomeric load-type inverters were subjected to a mechanical strain of up to 50% along and perpendicular to the channel length, as shown in Fig. 3e, f, respectively. The performance remained nearly constant when the device was subjected to mechanical strain, and the gain values were found to exceed 2 for all cases. Figure 3g shows the exploded schematic illustration, corresponding optical photograph, and circuit diagram of the zero-V GS load inverter developed using the methods discussed in the Materials and methods section. The zero-V GS load inverter was composed of a drive transistor (T D ) and a load transistor (T L ) with a channel width ratio of 1:5 (K L /K D = 5). The elastomeric zero-V GS load inverter was subjected to the same performance characterization analysis as that conducted for the load-type inverter. The results of the static and dynamic operations of the elastomeric zero-V GS load inverter, presented in Fig. 3h-j, highlight the stable performance of the device for all V DD inputs and repetitive input voltage cycles. Furthermore, the elastomeric zero-V GS load inverter exhibited sustainable performance against a mechanical strain of up to 50% applied along and perpendicular to the channel length (Fig. 3k, l). Figure 4 shows the structures and the corresponding performance of the elastomeric NOR and NAND gates prepared by connecting two drive transistors in parallel and series to the load transistors, respectively. To apply digital input signals (i.e., (0, 0), (0, 1), (1, 0), and (1, 1)) to the logic gates, two input voltages V IN,A and V IN,B with an amplitude of −3 V were applied with different frequencies of the square pulses, as shown in Fig. 4c-f. Input voltage signals V INA,B of 0 and −3 V were considered as logic states 0 and 1, respectively. The Boolean logic function characteristics of the elastomeric NOR and NAND were evaluated by obtaining V OUT during the application of a constant V DD of −1 V. The output voltages V OUT of 0 and −1 V were regarded as 0 and 1, respectively. The truth table for the elastomeric NOR and NAND logic gates is presented in Fig. S13 (Supplementary Information). Figure 4c, e show the output curves of the NOR gates, and Fig. 4d, f show the output curves of the NAND gates when a mechanical strain of up to 50% was applied along and perpendicular to the channel direction, respectively. Even when 50% mechanical stretching was implemented in both directions, normal NOR and NAND logic gate operations proceeded with no substantial change in performance. Overall, successful implementation of elastomeric inverters and logic electronics (i.e., NOR and NAND) can promote the realization of fully soft electronics, especially when integrated with a variety of functional sensors.

Elastomeric transistor array and soft robotic applications
In general, an array of functional sensors integrated with a transistor array can capture the dynamic responses to stimuli signals over a large area. Thus, it is essential to develop an elastomeric transistor array with reliable performance to facilitate its application in soft electronics. Figure 5a shows a photograph and expanded schematic illustration of the developed elastomeric transistor array. The array consisted of two electrode layers (i.e., the first S/D layer and second gate layer) connected through an EGaIn via-hole. The patterned array of P3NF/PDMS semiconducting and ion-gel layers were sequentially layered onto each channel. Finally, the encapsulation layer was placed on the array to ensure stable performance under various types of mechanical stimuli. Figure 5b presents the photograph and magnified images of the array to present the detailed structure of the transistor array. The electrodes of the array involved a common source as the data line, eight gates as the scan line, and eight drains. The gate electrodes were extended through the EGaIn via-hole to be in contact with the ion gel, as illustrated in the crosssectional image. Figure 5c indicates the field-effect mobility of all the arrayed transistors at the initial state and a 30% mechanical strain applied perpendicular to the channel length. The measurement was conducted using a custombuilt terminal board equipped with a mechanical stretcher, as presented in Fig. S2 (Supplementary (see figure on previous page) Fig. 3 Performance characterization of the elastomeric inverters. a Exploded schematic and photograph (upper) and circuit diagram (bottom) of the resistive load-type inverter. b VTCs and c corresponding gain characteristics of the resistive load-type inverter with different V DD values. d Dynamic VTC response of V OUT (black) of the resistive load-type inverter at V DD = 1 V subjected to square wave V IN pulses ranging from 0 to −3 V with frequencies of 0.15 Hz (blue). VTC response and gain of the resistive load-type inverter subjected to different levels of mechanical strain e along and f perpendicular to the channel length directions. g Expanded schematic and photograph (upper) and circuit diagram (bottom) of the zero-V GS inverter. h VTCs and i corresponding gain characteristics of the zero-V GS inverter with different V DD . j Dynamic VTC response of V OUT (black) of the zero-V GS inverter at V DD = 1 V subjected to square wave V IN pulses ranging from 0 to −3 V with frequencies of 0.15 Hz (blue). VTC response and gain of the zero-V GS inverter subjected to different levels of mechanical strain k along and l perpendicular to the channel length directions. Information). The average field-effect mobility at the initial state and 30% mechanical strain was 14.7 ± 0.63 and 11.7 ± 0.67 cm 2 /V s, respectively. (Fig. S14, Supplementary  Information). The values were slightly lower than those shown in Fig. 2 owing to the inevitable increase in the resistance of the array of electrodes.
To further validate the mechanical sustainability of the array, the ON current of all transistors was obtained in real-time under various mechanical stimuli. Figure 5d shows the applied mechanical stimuli and corresponding ON current map acquired in real-time (see Video S2, Supplementary Information). The measurement was conducted by sequentially applying −3 V gate and −1 V drain voltages to scan the 64 transistors. Note that the continuous scans were conducted 20 times while the elastomeric array was being deformed. All transistors maintained their ON current at more than 5e − 4 A regardless of the mechanical stimuli, thus successfully demonstrating an elastomeric transistor array with mechanical integrity.
To verify the feasibility of manufacturing the elastomeric devices and their functionality under possible elongation during soft robot gripping motions, various elastomeric electronic devices (i.e., transistors, NOR, and NAND) were integrated into a custom-made soft robot. The soft robot consisted of four soft fingers that could be pneumatically actuated using pumped air to grip a ball, as presented in Fig. 5e, f. The detailed manufacturing process is presented in the Materials and methods section and Fig. S15 (Supplementary Information). As shown in the sequential photographs in Fig. 5f, the soft robot performed five motions, namely, initial state-grip-lift-touchdown-release, to grip and release the blue ball. The electrical signals of the elastomeric electronic devices were monitored in real-time, as shown in Fig. 5f. Notably, the soft gripper is capable of gripping a variety of shapes and weights of balls, including a crystal ball, a water balloon, a bouncy ball, and soft dice, with no noticeable damage or failure, as presented in Fig. S16 (Supplementary Information). All the devices retained their characteristics, similar to the findings presented in the previous section (see Video S3, Supplementary  Information). These findings, when combined with appropriate detection sensors, contribute to the realization of sophisticated and intelligent motions of soft robots.

Conclusions
We developed high-performance mechanically resilient integrated electronics based on interconnected 2D AuNS elastomeric electrodes. Specifically, the intrinsic electrical conductivity of the AuNS was enhanced via hot pressing and the formation of a percolated network of AuNSs embedded in the PDMS elastomer, and thus, a highperformance elastomeric electrode was achieved. The highperformance AuNS elastomeric electrodes could be patterned via a simple manufacturing process. Thus, several elastomeric electronic devices could be prepared that operated stably under various types of mechanical stimuli. The interfacial contact resistance issue owing to the work function mismatch between the semiconductor and electrode was alleviated using the inert characteristics of Au, leading to high field-effect mobility of 19.8 cm 2 /V s. Moreover, we successfully prepared transistor arrays and demonstrated the integration of the integrated electronics onto a soft robot to highlight the feasibility of scaling up the field of soft electronics by implementing an active matrix with multifunctional sensor integration. Upon continuous and various mechanical deformations, all the devices exhibited outstanding dynamic performance with no observable variation in performance. The developed AuNS elastomeric electrodes and mechanically resilient integrated electronics provide novel opportunities for potential application in future soft electronics.