All Direct Ink Writing of 3D Compliant Carbon Thermoelectric Generators for High‐Energy Conversion Efficiency

Compliant thermoelectric generators (TEGs) can fully exploit their energy conversion efficiency by establishing conformal interfaces on arbitrarily shaped 3D heat sources. Although additive manufacturing processes allow scalable fabrication with flexibility and customizability, most printable TEGs are fabricated as planar‐type devices that harvest heat only in the in‐plane direction. Herein, 3D‐compliant TEGs fabricated solely using direct ink writing, which enables thermal‐transfer optimization for efficient through‐plane heat‐to‐electricity conversion owing to the out‐of‐plane printing of viscoelastic thermoelectric (TE) inks and unique device design is proposed. The rheological properties of carbon nanotube (CNT) TE inks are engineered to ensure conformal printing along directly written vertical thermal insulators. The ink TE properties are enhanced by the fine‐tuned incorporation of p‐ and n‐type dopants, where the electrical conductivity is further facilitated by nozzle‐induced CNT packing to achieve high‐power factors. To minimize the parasitic thermal loss from heat sources, an ultra‐thin bottom substrate is directly printed with polydimethylsiloxane, thereby realizing compliant 3D TEGs for heat harvesting in the out‐of‐plane direction. The TEG exhibits the highest normalized open‐circuit voltage (0.28 mV K−1 cm−2) among the additively manufactured TEGs and retains remarkable mechanical reliability against repetitive deformation, promising its potential as body heat harvesters or temperature sensors.


Introduction
Along with the performance improvements of thermoelectric (TE) materials, it is also becoming increasingly essential to DOI: 10.1002/aenm.202204171 flawlessly harness such enhanced energy conversion efficiency via the appropriate design of thermoelectric generators (TEGs) with outstanding mechanical reliability. [1][2][3][4][5][6][7][8] To achieve highly efficient heat harvesting, TEGs need to establish conformal interfaces on arbitrarily shaped or shape-changing 3D heat sources, such as the human body, to minimize heat loss through undesirable air gaps and facilitate heat conduction to the TE legs. [1,[9][10][11][12][13][14][15][16] Simultaneously, TEGs are required to ensure stable operation under deformation incurred by bending or stretching without significant degradation of the TE performance under any circumstances.
To accomplish such conformal contact on 3D heat sources, compliant and flexible TEGs have been predominantly prepared by depositing inherently flexible TE materials, which are also lightweight and processable at low temperatures, on soft platforms. [4,[17][18][19][20][21] In particular, their solution processability enables additive manufacturing processes via solution-based bottom-up fabrication (e.g., blade-casting, spray printing, and inkjet printing) and thus offers tremendous opportunities to achieve low-cost and large-area energy harvesting system. Among others, printing technologies allow scalable and high-density arrays of TE legs (i.e., a high fill factor) with a high degree of design freedom on flexible substrates. [18,[22][23][24][25] Nevertheless, most reported printable TEGs have been prepared by depositing the TE materials in the form of planar-type legs that lie flat and parallel to the substrate plane, thereby constraining the resulting device to harvest heat only in the in-plane direction. [20,[25][26][27] In real applications, temperature gradients are primarily imposed in the direction perpendicular to planar-type TEGs; therefore, it is essential to construct an array of TE legs standing orthogonal to the TEGs to realize thermalenergy harvesting in the out-of-plane direction. [28,29] Among additive manufacturing processes, direct ink writing (DIW), which is a class of omnidirectional printing, is one of the most promising fabrication technologies and offers high customizability to realize directly printable TEGs with 3D arbitrary shapes and structures. [30][31][32][33][34] In addition, DIW enables the printing of complex 3D structures using a broad set of materials for nozzle extrusion, ranging from inorganic TE materials to conductive polymers, by regulating their rheological properties. [32,[34][35][36][37] Therefore, DIW technology presents a breakthrough to overcome the limitations of conventional additively manufactured TEGs by directly printing 3D TE legs that transfer heat in the throughplane direction. [38] To enhance the energy conversion efficiency of TEGs, printable TE materials are required to simultaneously exhibit outstanding TE properties and mechanical stability against deformation for conformal contact with arbitrary heat sources and reliable heat harvesting. [20,39] Although Bi 2 TE 3 -based rigid TE materials possess high TE performance, complex hightemperature processes are required to prepare printable TE inks from such brittle materials. In addition, their inherent rigidity limits the conformal contact of TEGs with arbitrarily shaped heat sources as well as their mechanical stability under external stresses. In this regard, carbon nanotubes (CNTs) are promising candidates for TE materials owing to their excellent TE properties and mechanical flexibility. [40][41][42][43] Most importantly, CNTs can be homogeneously dispersed into highly concentrated inks with a broad window of adjustable viscoelastic properties such as viscosity and shear modulus to provide a good platform for realizing 3D-structured TEGs using DIW. [38] In addition, CNTs provide the advantage of easily tunable Seebeck coefficients between p-and ntype by directly incorporating organic dopants during the dispersion process without requiring additional post-doping after TE leg printing. [20,38] Furthermore, the viscoelasticity and printability of CNT ink allow direct writing on vertical standing printed polymers to optimize heat transfer and ultimately implement alldirect-written 3D-compliant TEGs.
Herein, we report highly integrated 3D-compliant TEGs whose entire components are printed exclusively via DIW using pre-doped CNT inks and polydimethylsiloxane (PDMS). Highperformance viscoelastic p-and n-type TE inks were prepared by ball-milling CNTs with organic dopants, and their rheological properties were systematically engineered to simultaneously enable high-resolution (<100 μm) nozzle dispensing and conformal printing without yielding on 1 mm-high 3D thermal insulators. Based on the low thermal conductivity of PDMS insulators and ultrathin elastic substrates, the resulting TEG can efficiently harvest electricity from temperature gradients imposed in the out-of-plane direction to generate an output voltage of 0.28 mV K −1 cm −2 , which is the highest TE performance among the additively manufactured TEGs. Moreover, our TEGs, fabricated solely using inherently flexible materials, can seamlessly conform to arbitrarily shaped 3D heat sources for uncompromised heat harvesting and exhibit remarkable reliability against stretching and bending. Finally, we demonstrate the potential of wearable body heat harvesters enduring deformation induced by body motion, and temperature sensors with fast responses.

Structural Design and Fabrication of DIW 3D-Compliant TEGs
The schematic in Figure 1a illustrates the design concept of the proposed TEG and its fabrication process. Most previously reported printable TEGs were fabricated as sheet-type devices that harvest heat in the in-plane direction, thereby limiting their functionality. Although 3D TEGs such as structurally deformable or textile-integrated types have been proposed to introduce a temperature difference across TE legs, low integration density, limited applications, and energy loss from thick substrates have impeded the maximization of their energyconversion efficiency. [41,42,50,54] To realize all directly written 3D TEGs that can harvest electricity from temperature gradients imposed in the through-plane direction, viscoelastic TE ink is a prerequisite for conformal printing along the curved surfaces of vertically standing 3D supports. For preparing the highperformance viscoelastic TE inks pre-doped as p-and n-type, single-walled carbon nanotubes (SWCNTs) were dispersed in diethylene glycol (DEG) with the p-and n-dopants, respectively, by homogenizing in planetary ball milling as shown in Figure 1b.
The alternate printing arrangement of p-and n-type CNT legs is beneficial to achieve maximized output power density. Figure 1c shows schematics and photographs of the sequential manufacturing processes of 3D TEGs whose entire components are directly written with tailored viscoelastic materials. Ultrathin soft substrates are printed using PDMS on a supporting glass to minimize heat loss from the heat source to the TEG. Thermal-energy harvesting in the out-of-plane direction requires an array of TE legs to stand perpendicular to the TEG and parallel to the imposed temperature difference. Therefore, as shown in Figure 1d, PDMS thermal insulators are introduced via direct printing on an ultra-thin substrate to provide vertical supports for the TE legs. The reasonably low thermal conductivity (≈0.16 W m −1 K −1 ) of PDMS provides the additional advantage of restricting heat conduction from the substrate to the top cold zone across the insulators. Subsequently, p-and n-type TE legs (1 mm wide and 4 mm tall) are alternately printed with SWCNT inks doped with poly(acrylic acid) (PAA) and poly(ethylenimine) (PEI), respectively, along the thermal insulators. The choice of SWCNT over MWCNT was primarily based on the thermoelectric properties of each carbon nanotube type after p-and ntype doping and the electrical conductivity enhancement enabled by dispenser printing owing to the facilitated carbon nanotube packing by the confined nozzle opening. The undoped SWCNT electrodes are printed to electrically connect the p-and n-type legs in series. It should be noted that the directly written undoped SWCNT electrodes exhibit low contact electrical resistance and firmly adhere to the underlying CNT TE legs. Finally, the fabricated 3D TEG is also encapsulated by printed PDMS to protect the TEGs from TE performance degradation owing to changes in the external environment (details in Experimental Section). Using DIW, 3D structurally compliant TEGs were fabricated in an area of 3 × 4.5 cm 2 (Figure 1e). The forked finger structure was suitable to achieve high-power density and highenergy conversion efficiency by increasing the surface area on the hot and cold sides of TE legs.

Rheological Property Optimization of CNT Inks
The viscoelastic properties of TE inks need to be fine-tuned to ensure unhindered continuous extrusion from nozzles and enable dispensing along curved surfaces in the out-of-plane direction without the inks undergoing shape deformation by gravity. Highenergy planetary ball milling in highly viscous diethylene glycol (DEG, ≈35.7 mPa s) can be used to prepare homogenously dispersed CNT inks of high concentrations. Rheological measurements demonstrated that the viscosity and complex shear modulus of the CNT ink can be facilely engineered by adjusting its concentration (see Experimental Section for details). The ballmilled TE ink exhibits decreasing dynamic viscosity with applied shear rates (shear-thinning behavior), whereas a rise in the CNT concentration from 2.4 to 14.4 mg mL −1 in DEG always results in increasingly viscous ink in all ranges (Figure 2a). Similarly, the measured storage modulus (G′) progressively rises with the CNT concentration, and the TE ink displays more solid-like behavior over a wide shear stress range of 10 −1 -10 2 Pa (Figure 2b). Consequently, the resulting shear yield stress ( y ) of the CNT ink can differ by three orders of magnitude, which suggests that SWCNT can offer a wide range of tunable rheological properties for DIW ( Figure 2c). Thus, the jettability and stability of the printed CNT ink exhibit disparate trends depending on its concentration and resulting rheological properties.
At a low concentration of 2.4 mg mL −1 (Figure 2c, inset), the ink viscosity and yield stress are too low to print clear patterns without ink spreading. In contrast, at higher (≥9.6 mg mL −1 ) concentrations, the viscosity of the ink is excessively high to induce nozzle clogging during printing. For that reason, we chose a CNT concentration within the intermediate range from 4.8 to 7.2 mg mL −1 , and the CNT ink could be printed at high resolution (< 300 μm) without nozzle clogging, as displayed in the optical microscope image in Figure 2d. To support the TE legs along the 3D thermal insulator, the CNT inks are required to maintain the printed pattern prior to the curing process without overflowing or spreading. Therefore, we printed CNT ink with concentrations of 2.4 and 7.2 mg mL −1 on curved surfaces using DIW and monitored any deformation of the printed pattern. As shown in Figure 2e,f, the printed ink was subjected to deformation and finally slid down the curvatures, at the CNT concentration of 2.4 mg mL −1 , although the CNT ink could be clearly printed on a flat substrate. On the other hand, a concentration of 7.2 mg mL −1 maintained the printed pattern after the curing process without the ink flowing along the curvatures. Finally, we optimized the concentration of the CNT ink in the DEG solvent to 7.2 mg mL −1 .

Thermoelectric Properties of p-and n-Type CNT Inks
Highly ameliorated thermoelectric properties of p-and n-type TE materials are indispensable as well as the temperature difference across TE legs to maximize the generated output power and energy conversion efficiency at a given temperature difference, as follows, where 0 , , S, , T H , ΔT TE , and Q TE are the energy-conversion efficiency, electrical conductivity, Seebeck coefficient, thermal conductivity, hot-side temperature, temperature difference across the TE legs, and heat flow through the TE legs, respectively. [1] The undoped CNT ink exhibited p-type characteristics owing to the presence of absorbed moisture and oxygen from ambient air, where the electrical conductivity and the Seebeck coefficient were almost invariable throughout the CNT concentration from 2.4 to 14.4 mg mL −1 ( Figure S1, Supporting Information). Although the pristine CNT ink itself possesses reasonable TE properties (electrical conductivity of 474 S cm −1 and Seebeck coefficient of 39 μV K −1 , as shown in Figure 3a), p-and n-doping of the CNT ink are required to further improve the TE properties of p-type CNT inks and convert the CNT ink to n-type, respectively, since the output power of the TEGs is determined by the sum of the Seebeck voltages of each type. Furthermore, polymer-based p-and ndopants can act as binders to enhance ink viscosity to improve the mechanical stability of the printed CNT ink. Therefore, PAA and PEI were selected as organic p-and n-type dopants, respectively, owing to their reasonable solubility in DEG and outstanding doping performance, and were respectively added to a 7.2 mg mL −1 CNT ink in DEG during ball milling. [38] To characterize and tune the TE properties, CNT inks were prepared at different dopant concentrations and blade-cast into 2 cm × 1 cm thin films, followed by vacuum drying (see Experimental Section). A customdesigned four-point measurement system was used to measure the TE performance of the prepared CNT films in the in-plane direction. With increasing PAA concentration, the electrical conductivity increased because more charge carriers were introduced from the water and moisture absorbed by the p-type dopants. [46] The Seebeck coefficient exhibited a similar rising trend up to a PAA concentration of 18 wt.%, and then decreased owing to the increased carrier concentration, which is in accordance with the inversely correlated relationship between the Seebeck coefficient and carrier concentration, as follows: where k B , e, h, m*, T, and n represent the Boltzmann constant, elementary charge, Plank constant, carrier effective mass, absolute temperature, and charge-carrier concentration, respectively. [47,48] The optimized PAA concentration for the p-type CNT ink was 18 wt.%, which had the highest power factor of 200.17 μW m −1 K −2 (Figure 3a). Because PEI molecules induce charge-carrier injection from amine groups, the undoped p-type CNT ink was facilely converted to n-type with negative Seebeck coefficients (Figure 3b). For the n-type CNT ink, the optimized dopant concentration and highest power factor were achieved at 30 wt.% and 235.05 μW m −1 K −2 , respectively. The absolute value of Seebeck coefficient gradually increased with the further addition of PEI, which indicates complete conversion to n-type. However, >30 wt.%, introduction of PEI rather induced the Seebeck coefficient to decrease, since it is inversely proportional to the carrier concentration. Despite the incorporation of PAA and PEI, at the optimized concentration, to the CNT ink, the dynamic viscosity and storage modulus of the resulting ink only negligibly changed, suggesting that the printability would be barely affected by the polymeric dopants ( Figure S2, Supporting Information). Next, the optimized PAA-and PEI-doped CNT inks were printed on glass substrates using a nozzle dispenser to compare the TE properties of the printed films to those of the bladecast films. Interestingly, the electrical conductivity values of the printed p-and n-type CNT films were higher by ≈60% and 23%, respectively, compared to those of the blade-cast films, whereas the Seebeck coefficients barely changed, regardless of the filmfabrication process (Figure 3c,d). The facilitated electrical con-ductivity of the printed CNT films could be attributed to nozzleinduced effects, such as alignment or packing of the individual CNTs, because the viscoelastic CNT ink in a wide syringe was extruded through a super-narrow nozzle-based print head. The effect of CNT alignment can be induced by shear flow in the ink-discharge direction as the hairy-type CNT fibers are extruded through a narrow nozzle. [43,49] To validate this possibility within the CNT network, TE films were printed at different printing pressures and velocities so that the CNT alignments of different degrees could be induced. However, no significant change in the measured electrical conductivity was observed, thereby suggesting that CNT alignment by the nozzle-exerted shear flow was inconsiderable ( Figure S3, Supporting Information). Moreover, polarized Raman spectroscopy measurements further preclude the possibility of the directional alignment of CNTs (Table S1, Supporting Information). Rather, the electrical conductivity enhancement can be attributed to the densely packed CNT network by the extrusion of the hairy-type SWCNT ink through the confined nozzle opening. As the nozzle size was systematically decreased from 550 to 125 μm (or, from 21 to 31G), the resulting electrical conductivity of the printed CNT films consistently rose from 602.34 to 813.67 S cm −1 (Figure 3e), without compromising the Seebeck coefficient at all, to result in significant improvements in the power factor from 220.51 to 325.67 μW m −1 K −2 (Figure 3f). Therefore, we speculate that the hairy-type SWCNT fibers were densely packed by the narrow nozzle during extrusion to improve the carrier mobility with enhanced conduction pathways, leading to the rise in electrical conductivity as follows: = neu, where n and are the charge carrier density and mobility, respectively. To further verify the CNT packing effect, a printed p-type TE film was passed onto 50 cycles of rolling compression between a set of two parallel rollers to constrict the CNT fibers into closer bundles. Even though the compressed film thickness was nearly halved, its sheet resistance barely changed. Thus, the resulting electrical conductivity was improved by >60%, which suggests that tighter packing of the CNT fibers can be beneficial for enhancing TE performance ( Figure S4, Supporting Information).

Thermoelectric Performance of All-DIW 3D-Compliant TEGs
After optimizing the TE-property and nozzle-dispensing conditions for both the p-and n-type CNT inks, the design parameters for developing 3D TEGs were further explored. To print vertically standing PN pairs and impose temperature gradients for heat harvesting in the out-of-plane direction, parallel rows of thermal insulators with finite height were periodically printed on the bottom substrate (Figure 1a). Here, PDMS with a low intrinsic thermal conductivity (0.16 W m −1 K −1 ) was adopted as the insulator material to curtail heat conduction across the insulators and thermally isolate the top region (cold zone) from the bottom (hot zone). According to Equation (1), increasing the effective temperature difference across the TE legs is important for achieving high-performance TEGs. Therefore, a 3D finite element analysis (FEA) simulation was performed on a model PDMS insulator with a single PN pair to predict the heat transfer and resulting temperature distributions across the TE legs. Figure 4a shows the FEA results of the temperature distribution at different thermal insulator heights. The maximum temperature difference between the hot and cool zones of the TE legs increased from 11.48 to 13.89 K after thermal equilibrium as the height of the thermal insulator was raised from 0.5 to 2 mm (Figure 4a). Consequently, the calculated output voltage of the single-pair TEG rose with the growing temperature difference imposed by the thermal insulator heights. It should be noted that the temperature difference (ΔT) and output voltage drastically increased as the insulator height rose from 0.5 to 1 mm, whereas the surge in ΔT was not as significant as the insulator was further heightened from 1 to 2 mm (Figure 4b). In other words, at a given temperature difference, ∆T across the low insulators rises with the increased height by the thermal resistance. However, the thermal resistance effect gradually decreases with increasing insulator height, and ∆T ultimately saturates. The calculated temperature differences with an increase in height using only PDMS were analogous to the results of the TEGs as shown in Figure S5 (Supporting Information). To deposit the vertically standing soft thermal insulator, PDMS, which was prepared by mixing with a curing agent in a weight ratio of 2:1, was printed on the substrate at 120°C. For thermal insulators of relatively low height from 0.5 to 1 mm, the printed PDMS was immediately cured owing to its high curing agent ratio and the heated substrate surface, without incurring any change in the initially intended insulator width (4 mm) due to overflowing. However, when printing insulators taller than 1 mm, the as-printed PDMS slid down along the structure and overflowed before completely curing, thereby occupying a larger area than that originally projected. As a result, the density of the PN pairs to be printed per unit area on the substrate should be negatively affected and the TE performance of the printed device can be compromised. Therefore, we designed TEGs to maximize the power density by considering the dimensions of the printed thermal insulators and a full-scale model. As a result, the height of the 1 mm PDMS structure was introduced for the thermal insulator to highly integrate the TE legs.
Then, FEA was performed on a 35 PN-pair TEG with a temperature difference of 15 K applied in the through-plane direction and the calculated ΔT across the TEG was 13 K, which generated an output voltage of 41.25 mV (Figure 4c). In addition, the simulated ΔT across the 35 PN-pair TEG was consistent with that of the single-pair TEG (Figure 4a), and the calculated output voltage was proportional to the number of connected PN pairs (Figure 4b). The 35 PN-pair TEG was fabricated by all-DIW processes as described above in Figure 1a,c, and the TE performance was measured at a temperature difference from 5 to 15 K. Notably, the TEG exhibited an open-circuit voltage of 39.18 mV at ∆T of 15 K, which is ≈95% of the FEA results (Figure 4c), and the generated power was 288.33 nW (Figure 4d). Figure 4e shows the timeresolved voltage of the TEGs attached to the bottom of a bowl when hot water (≈70°C) was poured into it to verify the effect of substrate thickness on TE performance. The TEG with a smaller substrate thickness of 70 μm exhibited a faster response to the applied temperature and ultimately achieved a higher ∆T across the device, compared to that with a thicker substrate (1 mm), by minimizing the parasitic heat loss across the substrate. Consequently, the TEGs with a thinner substrate (70 μm) enabled by the printing process generated a higher output voltage, which was in agreement with the FEA results.
According to Equation (1), the maximum output power scales linearly with the number of PN pairs. Relying on the highperformance TE inks with tailored rheological properties for nozzle dispensing and highly automated conformal printing process, we fabricated large-area 3D structural CNT TEGs with 140 PN pairs in an area of 6 cm × 7 cm to demonstrate the scalability of our DIW-fabrication strategy and augment their TE performance (Figure 4f). Our DIW process with optimized printing conditions enables reliable automated fabrication of scalable ultra-thin substrate, encapsulation, and highly integrated PN pairs and promises the reproducibility of large-area 3D-compliant TEGs with excellent yields. The fabricated 140 PN-pair 3D TEGs generated a maximum output voltage and power of 188.08 mV and 1.68 μW, respectively, at a temperature difference of 20 K (Figure 4g). Figure 4h and Table S2 (Supporting Information) illustrate the normalized output performance for comparison to the TEGs fabricated using additive manufacturing. By exploiting the enhanced TE properties of the PAAand PEI-doped CNT inks and high fill factor of the serially connected PN-legs enabled by micrometer-scale resolution printing, our highly integrated 3D TEG exhibits the highest normalized Seebeck voltage per unit area of 0.28 mV K −1 cm −2 among the additively manufactured TEGs. [20,[25][26][27][28]38,39,[50][51][52][53][54][55][56][57][58] Moreover, our proposed TEG also marks one of the highest normalized power density (1.24 × 10 −4 μW K −2 cm −2 ) when compared to TEGs based on organic TE materials or CNTs, which demonstrate the efficacy of heat regulation by 3D-printed PDMS thermal insulators and ultra-thin substrates. [18,20,27,38,39,54,55,57] Although a few studies have proposed the feasibility of printable TEGs, most of them are fabricated on thick commercial substrates, which are not printed, and they harvest heat only in the direction parallel to the device plane. Such a device design induces immense heat dissipation across the substrates and prevents heat harvesting from the temperature gradient applied across the TE legs standing perpendicular to the TEG, respectively. [39,55,56] Although some of them can harvest heat in the out-of-plane direction, they still suffer from low conformability on 3D heat sources because of their low device-component stretchability, such as TE legs and electrodes of high rigidity and bulky shapes. [44,45] On the other hand, our 3D TEGs were printed on an ultra-thin soft substrate to minimize parasitic heat loss, and they can be attached to various heat sources with good conformability owing to their flexibility. Furthermore, our fully printed TEG, from substrates to device encapsulation, has the potential to be cost-effective and mass-producible using a continuous process through all-DIW.

Mechanical Reliability of All-DIW 3D TEGs
For TEGs to efficiently harvest energy from heat sources of variable shapes and dimensions such as human skin, they are required to not only form conformal contact with arbitrarily shaped surfaces but also ensure stable operation without the degradation of TE performance even under drastic environmental changes or applied external stress. To examine the mechanical reliability of our fully printed 3D TEGs, the changes in electrical resistance and TE output performance relative to the initial values were measured under bending and stretching. During the bending test, the electrical resistance of the 3D TEG remained nearly unchanged (R/R 0 ≈ 1), even when the bending radius (r) in the x-and y-axis were as small as 23.12 and 13.51 mm, respectively (Figure 5a; Figure S6a, Supporting Information). As shown in Figure 5b and Figure S6b (Supporting Information), the electrical resistance barely changed (<1%) even after 1000 cycles of bending along both the x-and y-axis at r = 23.12 and 13.51 mm, respectively, which suggests that our 3D-compliant TEG is expected to seamlessly conform to uneven or warped surfaces without experiencing parasitic heat loss. Simultaneously, the open-circuit voltage and output power changes at ΔT = 10 K also remained <10% during the cyclic bending test to demonstrate exceptional reliability against the repetitive loading of our TEG, whose entire components are assembled by direct writing of inherently flexible CNTs and PDMS only (Figure 5c; Figure S6c, Supporting Information).
Although R/R 0 gradually increased due to the tearing of the CNT modules with an increase in tensile strain, the 3D TEGs retained an R/R 0 value <5% for small, applied strains up to 15% and excellent stability during 1000 cyclic stretching test at 5% strain (Figure 5d,e). Specifically, the elastomer encapsulating the TE legs can infiltrate into the CNT network to enable fiber reorientation under deformation, so that individual CNTs can accommodate the applied strains without compromising the conduction network. [42,59,60] Furthermore, it was difficult to identify any noticeable open-circuit voltage drop at higher tensile strains up to 15%, despite the power degradation due to the rising electrical resistance under stretching (Figure 5f). We also monitored the changes in electrical resistance relative to the initial values under twisting and pinching to investigate the mechanical stability of our TEGs. During the twisting tests, the electrical resistance of TEG barely changed (<4%) even under a continuous change in twisting angles from −90°to 90°( Figure S7a, Supporting Information). As shown in Figure S7b,c (Supporting Information), our TEG retained an R/R O value <1% even after pressing by the finger at the middle of the TEG, or after placing weights at three different spots on the TEG top surface. These results indicate that our compliant TEG can steadily convert thermal energy to electrical voltage even under repeated external deformation.
Harsh environmental conditions such as high temperature and humidity could also degrade TEG performance. In particular, the TE performance of n-type legs can be adversely affected by the adsorption of moisture from the surrounding environment, even at room temperature and moderate humidity, which could induce more p-type carriers in the CNTs to offset the n-doping effect by PEI molecules. [46] Therefore, to prevent TE performance degradation by unfavorable operation environments and to protect the TE legs and electrodes from external damages, we passivated the TEGs by directly printing PDMS encapsulating layers of the matching Young's modulus as the bottom substrate. [1,42] We conducted an accelerated stress test at a high temperature of 85°C and relative humidity of 85% to investigate the long-term tolerance of TEGs with and without PDMS passivation. The performance changes with respect to the initial value (V OC /V OC,0 and P max /P max,0 ) at a temperature difference of 5 K with and without the encapsulation of TEGs were measured over time. While the output performance of the TEGs without encapsulation was unstable and finally underwent a significant drop, the encapsulated TEGs exhibited outstanding performance stability for long-term operation under harsh temperature and humidity conditions for up to 556 h (Figure 5g,h).

Potential Applications of 3D-Compliant TEGs as Wearable Heat Harvesters and Sensors
Our 3D-compliant TEGs were attached to or worn on various heat sources of arbitrary shapes to demonstrate their potential for thermal energy harvesting and temperature sensing. As shown in Figure 6a, the large-area 3D-compliant TEG with 140 PN pairs was directly worn on the human body to harvest thermal energy under ambient conditions. Owing to the minimization of the heat loss from the ultra-thin substrate, the TEG generated an output voltage of 61.4 mV at ∆T = 5.1 K, which is ≈95% of the theoretical output voltage, by forming conformal contact on the complex forearm surface (Figure 6b). In addition, the TE output performance measured from the dynamic human body was in excellent agreement with the values acquired from the flat-plate measurement system at the same ∆T ( Figure S8, Supporting Information).
To investigate the temperature response of our 3D-compliant TEG, its open-circuit voltage was monitored over time as the device was subjected to thermal contact of varying durations. As shown in Figure 6c, the 140 PN-pair TEG attached to the curved surface of an aluminum cup filled with cold water (≈4.5°C) was put into close contact with a human palm. As soon as the hand touched the TEG, the output voltage was immediately generated, and it continuously increased with the contact time (Figure 6d). The maximum output voltage was 134.11 mV at a contact time of ≈7 s, after which the generated voltage gradually declined as thermal equilibrium was reached to lower the final effective temperature difference across the TEG. To further explore its temperature sensing capability, the TEG attached to a human palm was brought into contact with heat sources at different temperatures (20-80°C), and the time-resolved open-circuit voltage was measured (Figure 6e,f). As the TEG was brought into contact with targets of a higher temperature, the resulting output voltage increased correspondingly. At the same time, the TEG directly responded in less than tens of milliseconds owing to the ultra-thin substrate and encapsulation layer ( Figure S9, Supporting Information). It should be noted that a negative output voltage was measured when the target temperature was lower than that of the body (Figure 6f). These results demonstrate the possibility of utilizing our 3D-compliant printed TEGs as wearable highresolution temperature sensors with fast responses.
The 35 PN-pair TEG was worn on the joint part of the human wrist, where localized strains and distortions are expected to be imposed by body movements. The TEGs conformed to the curved human wrist, relying on its outstanding flexibility, and the TE performance from the body-air temperature difference was measured while the wrist was incrementally bent to steeper angles (Figure 6g). Owing to the excellent conformability and mechanical reliability of our 3D-compliant TEG, the changes in the measured normalized Seebeck voltage were maintained <10% under a continuous change in wrist angles from 0°to 50°at ΔT = 1 K (after thermal equilibrium state) between the skin and ambient air (Figure 6h). Furthermore, when the wrist was bent at angles that changed with incremental steps of 10°, the open-circuit voltage and output power remained nearly unchanged (Figure 6i; Figure S7, Supporting Information). In other words, the 3D TEG maintained conformal contact on an arbitrarily shaped surface, even when the human wrist underwent substantial distortion at a large bending angle (50°) and the device was subjected to considerable deformation.

Conclusion
We have demonstrated all directly written 3D-compliant TEGs with outstanding performance via thermal transfer design optimization, improvement of p-and n-type TE properties by CNT packing, and PN-pair density by high integration of TE legs. For high-performance viscoelastic TE inks, we carefully optimized their rheological properties by adjusting the CNT concentration in the solvent, which enabled direct ink printing along the 3D supporting structure. In addition, selective chemical doping of p-and n-type inks provided optimal TE properties, and the electrical conductivity was further enhanced by the printingnozzle-induced CNT packing effect to achieve high power factors of 200.17 and 235.05 μW m −1 K −2 for each type, respectively. DIW provides controllable shapes and thicknesses from one dimension to three dimensions using omnidirectional printing. The ultra-thin soft substrate fabricated by directly printing PDMS minimized the parasitic heat loss from the substrate. Furthermore, to deliver the temperature difference across the device, the vertical PDMS thermal insulators were printed on an ultrathin substrate. These soft PDMS substrates and vertical insulators led to conformal contact with arbitrary heat sources and thermal-energy harvesting in the out-of-plane direction of the printed TEGs. Our highly integrated 3D-compliant TEGs fabricated by DIW process exhibited an exceptional normalized Seebeck voltage of 0.28 mV K −1 cm −2 and an excellent normalized power density of 1.24 × 10 −4 μW K −2 cm −2 compared to those of additive-manufactured TEGs. Furthermore, the passivation layer of PDMS allows the remarkable long-term stability of TEGs against mechanical deformation and high-temperature humid environments. With enhanced mechanical reliability against deformation and high-energy conversion efficiency, our 3Dcompliant TEGs demonstrated the potential for thermal energy harvesting and sensing. We believe that our results pave a promising pathway to realize highly efficient 3D TEGs with a high degree of design freedom for self-powered flexible and/or wearable applications.
Preparation of p-and n-Type CNT Inks: SWCNTs were dispersed in a DEG solvent at varying concentrations, from 2.4 to 14.4 mg mL −1 , to optimize rheological properties and printing conditions, as shown in Figure 1h-k. To tune the CNT ink thermoelectric properties, PAA and PEI were added to a fixed CNT concentration in the solvent of 7.2 mg mL −1 as a function of p-or n-dopant concentrations of 5-30 wt.% and 10-50 wt.%, respectively. Planetary ball milling (Pulverisette 6, Fritsch) was carried out at 550 rpm for 2 h using a zirconia milling pot and balls to homogeneously disperse the CNTs and each dopant.
Fabrication of All-DIW 3D-Compliant TEG: All fabrication processes for the 3D structural CNT TEGs were conducted using a high precision fluid dispenser (ML-808GX, Musashi Eng.) with omnidirectional printable DIW equipment (SHOT mini 200Sx, Musashi Eng.). Before fabrication, the supporting glass was exposed to O 2 plasma (50 sccm, 50 mTorr, 100 W for 2 min, PlasmaPro 800 RIE, Oxford Instruments), after which a surface treatment was conducted with vapor-deposited FOTS for 90 min to provide sufficiently hydrophobic surface properties to ensure detachment of the fabricated TEGs from the supporting glass. For ultrathin soft substrates, a PDMS substrate with a mixed curing agent with a 10:1 weight ratio was printed on the prepared supporting glass using a 21-gauge needle with a pressure of 30 kPa, and then cured on a 100°C hot plate for 20 min. Printing of soft thermal insulators was carried out to generate the temperature distribution on the TE legs in the out-of-plane direction. To deposit the thermal insulators in the Z-axis with a thickness of 1 mm, the PDMS that mixed curing agent with 2:1 in a weight ratio was printed on the ultra-thin substrate. The printing conditions were optimized with a 21-gauge needle, pressure of 40 kPa, printing velocity of 20 mm s −1 , and substrate temperature of 120°C during 5-pass printing. For the p-and n-type TE legs, DIW of the prepared CNT inks was conducted along the thermal insulators with a 31-gauge needle at a pressure of 250 kPa and printing velocity of 5 mm s −1 at room temperature. The p-type CNT inks were first printed and dried at 80°C in a vacuum for 3 h. And then, the ntype CNT inks were printed and dried at 50°C for 5 h. The undoped-CNT inks were printed under the same printing conditions and dried at 80°C for 3 h as the interconnects between the p-and n-type legs in series. Finally, encapsulation with PDMS (curing agent ratio of 10:1) was conducted using DIW with a 21-gauge needle, printing velocity of 10 mm s −1 , pressure of 400 kPa, and subsequent curing at 100°C for 30 min.
Characterization: Rheological characterization of the CNT inks was carried out using a rotational rheometer (HAAKE MARS, Thermo Scientific) with parallel disks. CNT inks of different concentrations were mounted on the bottom disk and topped by a rotating disk with a fixed gap of 1 mm to measure rheological properties such as dynamic viscosity and shear storage modulus. The dynamic viscosity was measured with a logarithmic sweep of shear rates from 10 −2 to 10 3 s −1 . The shear storage modulus (G′) and loss modulus (G″) were measured in the shear stress range from 10 −1 to 10 3 Pa via oscillation tests with a fixed frequency of 1 Hz. All measurements were performed at room temperature. To characterize the in-plane TE properties, p-and n-type CNT films with dimensions of 2 cm × 1 cm were blade-casted and printed on a glass substrate, and dried under the same curing conditions mentioned above. The thicknesses of the CNT films were measured using a stylus-based surface profiler (Alpha-Step IQ, KLA Tencor Co.). The electrical conductivity and Seebeck coefficient of the CNT films were measured simultaneously using a four-point probe TE measurement system (TEP 6000, Seepel Instruments). To measure the Seebeck coefficient precisely, the probe measured the voltage changes at the two ends of the films where temperature differences of ±0.5, ±1.5, and ±2.5 K were given, and the linear correlation (R 2 ) of the measured voltage differences was then calculated (linearity > 0.999). The output performance of the 3D structural TEGs was evaluated using a homemade system consisting of two Peltier modules covered with thermal pads that were attached to heat sinks to control the temperature difference between the TEGs, and a Digital Multimeter (Keithley 2700). The temperatures of the hot and cool zones were monitored using a thermometer with a thermocouple series placed at the top and bottom of the TEGs. The output voltage and current were measured after reaching thermal equilibrium. Finite element analyses of heat transfers and TE effects were performed using COMSOL Multiphysics (COMSOL Inc.). Mechanical-reliability tests under bending and stretching stresses were conducted using a custom-built automated stretching machine with a linearized motor (TS-100-M, Namil Optical Components, Republic of Korea). Along with the performance improvements of TE materials, it is becoming increasingly essential to flawlessly harness such enhanced energy conversion efficiency via the appropriate design of TEGs with outstanding mechanical reliability. Images of the printing resolution and nozzle diameter were captured using an optical microscope (OM, BX53M, OLYMPUS). Infrared thermal images were captured by a thermal camera (FLIR E40, FLIR Systems, Inc.). The experiments of wearable thermoelectric generators were conducted with the consent of the human volunteers: the volunteers were informed about all relevant risks associated with the experiments and agreed to them. Also, the volunteers were aware that all data collected from the experiments could be disclosed in the published paper.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.