The overall process for the TE painting in the current study is shown in Fig. 2. The prepared TE paints with the Sb 2 Te 3 ChaM sintering aid are painted on a curved substrate and sintered at elevated temperatures (Fig. 2a–c), eventually, producing the curved painted TE device exhibiting high power generating performances (Fig. 2d). The resulting n- and p-type painted materials in the TE generators exhibit the ZT values competing those of bulk Bi 2 Te 3 -based materials (Fig. 2e). The detailed results and the related discussion on the each steps are described below.

Figure 2: Schematic illustrating for the fabrication of painted TE devices with Bi 2 Te 3 -based inorganic TE paints. (a) Photographs of the Sb 2 Te 3 ChaM solution and the ball-milled TE particle. (b) Photographs for the fabricated TE paint and the painting process on an alumina hemisphere. (c) Scheme for the sintering of ball-milled particles assisted by the Sb 2 Te 3 ChaM. The molecular Sb 2 Te 3 ChaM ions act as a sintering aid to fill up the void space among ball-milled particles and promote the grain growth and densification. The yellow and black particles indicate the ChaM molecules and ball-milled particles, respectively. (d) Photograph of the fabricated hemispherical TE device. (e) Comparison of the peak ZT values among the painted n- and p-type materials in the current study, the typical bulk Bi 2 Te 3 -based materials (denoted as n-bulk and p-bulk) and the printed materials reported in the literature (denoted as n-paste and p-paste)2,23. Full size image

Bi 2 Te 3 -based inorganic TE paints

The Sb 2 Te 3 -based ChaM was synthesized by dissolving bulk elemental Sb and Te in a thiol–diamine mixture34,35,36 instead of the widely used a N 2 H 4 solvent25,26,27,28,37,38,39,40,41 due to its high-level toxicity. Sb 3d3/2, Sb 3d5/2 and Te 3d5/2 peaks corresponding to metallic bonding peaks are identified in the X-ray photoelectron spectra (Supplementary Fig. 1), indicating the formation of an ionic Sb 2 Te 4 phase from elements42. We observed that this soluble compound decomposes into rhombohedral Sb 2 Te 3 and hexagonal Te on mild heat treatment above 100 °C, as confirmed by X-ray diffraction (XRD) analysis in Supplementary Fig. 2. It is seen that the peaks corresponding to Sb 2 Te 3 and Te phases in the XRD pattern (Supplementary Fig. 2) become sharper with increasing temperatures, suggesting the suitability as a sintering aid. The absence of peak representing the decomposition of the ChaM in thermogravimetric analysis (TGA) of the Sb 2 Te 3 ChaM dried at room temperature (Supplementary Fig. 3) implies that it was completely decomposed during drying process27.

The Sb 2 Te 3 ChaM can be dispersed in various polar solvents as long as their dielectric constant (ɛ, F m−1) ranges from 10 to 50 for example, dimethyl sulfoxide (ɛ≈47), dimethylformamide (ɛ≈36), ethylenediamine (ɛ≈13) and viscous polar solvents of ethylene glycol (ɛ≈37) and glycerol (ɛ≈43; Supplementary Fig. 4). This provides a room for tuning the dielectric constant, solvent viscosity and evaporation temperature of the TE paints. We dispersed the Sb 2 Te 3 ChaM (20 wt% of TE particles) in a mixed viscous solvent of glycerol and ethylene glycol containing n-type Bi 2.0 Te 2.7 Se 0.3 (BTS) or p-type Bi 0.4 Sb 1.6 Te 3.0 (BST) TE microparticles (Fig. 2a). The viscosity and evaporation temperature for the TE paints were both adjusted by controlling the ratio of glycerol (viscosity at room temperature≈934 mP s, boiling point≈290 °C) to ethylene glycol (viscosity at room temperature≈62 mP s, boiling point≈197 °C). We found that the suspension was stable against phase separation and precipitation for more than a week (Supplementary Fig. 5).

Sb 2 Te 3 ChaM as a sintering aid

To fully understand the sintering behaviour of the TE paints, both n- and p-type paints, repeatedly painted and dried, were sintered at various temperatures >350 °C, with all producing mechanically robust TE samples several hundred micrometres in thickness. Figure 3a–d compare the microstructure of n-type BTS and p-type BST TE materials sintered at 450 °C with and without the Sb 2 Te 3 ChaM. It is noted that a suspension of TE particles without the ChaM painted and sintered under the same conditions resulted in at most 60–70 % of the density achieved with the ChaM (Fig. 3e), regardless of the sintering temperature. As shown in Fig. 3e, the presence of the ChaM effectively increases the initial density of the TE materials by filling up pores, promoting the grain growth and densification of the ensemble of particles. As a whole, the evidences demonstrate the effectiveness of the Sb 2 Te 3 ChaM as a sintering aid.

Figure 3: Characterization of the painted TE materials. SEM images of the painted n-type materials (a) with and (b) without the ChaM, and the p-type materials (c) with and (d) without the ChaM. All scale bars are 5 μm (a–d). Comparison of (e) density and (f) electrical conductivity between the materials with and without the ChaM. Temperature-dependent TE properties of n- and p-type painted materials: (g) ZT value (h) electrical conductivity (i) absolute Seebeck coefficient and (j) thermal conductivity. Error bars represent the s.e. of the mean values of ZT, electrical conductivity, Seebeck coefficient and thermal conductivity obtained by the measurement of three different samples. Full size image

While the density of sintered materials kept increasing with temperature, asymptotically approaching 3.9 g cm−3 (n-type) and 3.6 g cm−3 (p-type) above 400 °C (Fig. 3e and Supplementary Fig. 6); however, a TGA profile in Supplementary Fig. 7 revealed that a weight loss occurs above 450 °C due to the evaporation of liquid Te, which is known to result in a slight degradation of properties via the formation of the Te vacancy defect43. Therefore, the optimum sintering temperature for the current study was taken at 450 °C.

As manifested from the microstructures (Fig. 3a–d), the grain morphology clearly dictates that the grain growth took place in a layer-by-layer mode, which requires two-dimensional nucleation event from a liquid medium as a prerequisite44. The scanning electron microscope (SEM) image of the fractured surface (Supplementary Fig. 8) shows the stereotypical microstructure formed by a nucleation and lateral growth44. This implies that the added sintering aid formed a liquid phase at the sintering temperature, which provides a diffusion path for grain growth. As evidenced by the differential scanning calorimetry curves of n-type and p-type paints (Supplementary Fig. 7), the Te phase formed from the Sb 2 Te 3 ChaM sintering aid is melted at ∼420 °C, lower than the sintering temperature of 450 °C. It means that the liquefied Te can contribute to the liquid-phase sintering on heat treatment. A possible contribution from the viscous flow mechanism during the initial stage of the liquid-phase sintering was ruled out based on an analysis on a time-dependent shrinkage measurement as shown in Supplementary Fig. 9, where the time exponent of 0.08 is determined to be much smaller than the theoretically expected one. It is noted that the viscous flow mechanism during liquid-phase sintering is often represented as the following relation45: Δl/l∝t1+y, where l and t denote a linear dimension of the sample and sintering time, respectively. Here, the exponent 1+y is slightly larger than unity due to increasing driving force with decreasing pore size during the process.

The temperature-dependent XRD patterns (Supplementary Figs 10 and 11) demonstrate that the Sb 2 Te 3 ChaM was completely integrated into the host phase, suggesting that the Sb 2 Te 3 ChaM should be compositionally compatible with the growth unit of the host phases. It is more pronounced in n-type materials. The XRD patterns (Supplementary Fig. 10) shows the peak shift to lower angle with increasing the sintering temperature, signifying the increase of Te stoichiometric ratio in a Bi 2 (Te,Se) 3 phase due to the integration of the Sb 2 Te 3 ChaM into the host phase. The significance of the improved sinterability is best-reflected in the electrical charge transport property, which is an order of magnitude higher electrical conductivity at 650–750 S cm−1 than those of the materials without the ChaM (Fig. 3f).

TE properties of the painted materials

Excellent TE properties are achieved in both the n- and p-type painted TE samples over the temperature range from 25 °C to 125 °C. The room-temperature ZT values of the n- and p-type samples marked 0.51 and 0.97, respectively (Fig. 3g), where the maximum values reached 0.67 for the n-type sample and 1.21 for the p-type sample at 100 °C (Fig. 3g). Note that these maxima are higher than those obtained with typical Bi 2 Te 3 -based bulk ingots (ZT≈0.8–1.0)1,2,3 and are close to the recently reported nanostructured TE materials (ZT≈1.1–1.9)46,47,48. Furthermore, these values are highest among the reported TE materials based on TE inks or pastes, and 3–4 times greater than anything that has been previously reported for printed TE materials (Fig. 2e)23.

These promising ZT values of the painted samples originate in high electrical conductivities and ultra-low thermal conductivities. The electrical conductivities of the n- and p-type samples (Fig. 3h) are 650–750 S cm−1 at room temperature, decreasing with increasing temperature. These high electrical conductivities result from the moderately high carrier mobilities of 149 cm2 V−1 s−1 for the n-type and 141 cm2 V−1 s−1 for the p-type materials. The Seebeck coefficient of the n-type samples (Fig. 3i) is 114 μV °C−1 at room temperature with a peak value of 134 μV °C−1 at 102 °C, and that of the p-type samples is 170–190 μV °C−1 over the entire measurement temperature range (Fig. 3i). These relatively low-Seebeck coefficients are caused by the high carrier concentrations of 3.0 × 1019 cm−3 for the n-type samples and 2.9 × 1019 cm−3 for the p-type samples, since the Seebeck coefficient and the carrier concentration are reciprocally proportional2,3.

The most significant effect of molecular ChaM-assisted sintering is seen in the great reduction in the thermal conductivities of the n- and p-type samples (Fig. 3j), that is, 0.5–0.6 W m−1 K−1 in comparison with the 1.5–2.5 W m−1 K−1 of bulk Bi 2 Te 3 -based materials2. The calculated lattice thermal conductivities were as low as 0.19 W m−1 K−1 for n-type and 0.20 W m−1 K−1 for p-type painted materials (Supplementary Fig. 12). These values are lower or comparable than the predicted minimum lattice thermal conductivities of 0.31 W m−1 K−1 in n-type Bi 2 Te 3 and 0.20 W m−1 K−1 and p-type (Bi,Sb) 2 Te 3 , which is calculated using the Debye–Callaway model with the assumption of full densities49. One possible explanation for the ultra-low lattice thermal conductivity is the porosity of materials. Although the Sb 2 Te 3 ChaM promotes the sintering of TE particles, their densities are still lower than the bulk values of 6.5–7.5 g cm−3. The analysis of porosity with N 2 adsorption measurement and SEM of these materials (Supplementary Figs 13 and 14) reveal the existence of both nano-scale and micro-scale pores. These multi-scale pores can significantly reduce the thermal conductivity by phonon scattering with a broad range of wavelength at pore sites. To further quantitatively estimate the porosity effect on the thermal transport, the lattice thermal conductivities of painted samples were corrected by using the modified formulation of the effective medium theory suggested by Lee et al.50: , where κ h and Φ are the lattice thermal conductivity of host materials and the porosity, respectively. The overall porosities of the painted samples were estimated by the direct method of comparing the sample density to the theoretical density of bulk materials with identical compositions. Using the bulk densities of BTS (7.55 g cm−3) for the n-type and BST (6.785 g cm−3) for the p-type materials, the calculated porosities of the painted samples were 0.47 for the n-type and 0.46 for the p-type samples. The calculated minimum lattice thermal conductivities of the n-type and p-type painted samples are 0.44 W m−1 K−1 and 0.47 W m−1 K−1, (Supplementary Fig. 12) respectively, which are comparable to those of typical nanostructured bulk materials prepared from ball-milled Bi 2 (Te,Se) 3 and (Bi,Sb) 2 Te 3 .

Generally, the porosity of solid materials strongly affects the charge carrier transport due to scattering of carriers at the pore sites51. A charge carrier passing near a pore is scattered due to the potential perturbation50, degrading the carrier mobility and eventually the electrical conductivity. The carrier-scattering effect on mobility can be qualitatively described by the Matthiessen’s rule52

Accordingly, the total scattering is the sum of the contribution of different carrier scattering mechanism. For example, μ bulk is the mobility induced solely by the carrier scattering with acoustic phonons. In the painted materials, considering no additional impurity element except Bi, Sb and Te, μ boundary and μ pore should be the critical factors to determine the overall mobility. Lee et al.50 suggested that the porosity effect on electrical properties become weaker for larger grains. Since the material with larger grains necessarily has larger pores with the lower number density under the same porosity, the scattering rate is reduced and mobility is enhanced for larger grain sizes. The fact that the grain size is in the range of several micrometres (Fig. 3a,c) and the pores are mainly macro-scale in the painted materials (<3% of micro-pores in volume) suggests that the moderately high mobility is attributed to the lower number density of the pore.

Another important factor to determine the electrical conductivity is the carrier concentration. To overcome the lower mobility of the painted samples than those of bulk, we chose the composition of BST (p-type) and BTS (n-type) for host matrix materials. The materials with such compositions are known to exhibit high carrier concentration by the formation of Sb Te antisite defect to provide hole in p-type and Se vacancy defect to provide electron in n-type. In fact, the carrier concentrations of the painted samples were two or threefold higher than 1∼2 cm−3 of typically used Bi 2 Te 3 -based materials2. Although these high carrier concentrations decreased the Seebeck coefficients, the electrical conductivities were significantly increased up to 650–750 S cm−1 at room temperature, close to bulk values. Consequently, in spite of high porosity, the high carrier concentration, the low number density of pores and bulk-scale grains can result in the high electrical conductivity of the painted materials.

All-painted TE generating devices on flat surfaces

The outstanding TE properties and painting processability of these TE paints make it possible to design highly efficient TE generating devices geometrically compatible with heat sources. As the first attempt, n- and p-type TE paints were applied with a brush to a flexible polyimide substrate, and then sintered at 450 °C for 10 min (Fig. 4a). These painted layers formed continuously uniform films with the thickness of about 50 μm (Fig. 4b). It means that the sintering condition is enough for the system to reach the final stage of sintering, where the coarsening process becomes stagnant with a narrow size distribution. Ag paste was painted in a way that the TE device consists of 5 couples of n- and p-type legs with lateral dimensions of 5 mm × 10 mm and an average thickness of ∼50 μm (Fig. 4a). The internal resistance of this device was 25.8 Ω, higher than the expected resistance in reference to the electrical properties, suggesting that the contact resistance between the Ag electrode and the TE leg is considerably high. We measured the contact resistance between the Ag electrode and the painted TE leg by the transmission line method (Supplementary Fig. 15). The measured contact resistance is quite high at 4.8 × 10−2 Ω cm2, which is three or four orders of magnitude higher than the contact resistance observed in conventional module composed of Bi 2 Te 3 -based TE legs53 and can be responsible for the internal resistance of the painted TE generator. To ensure reliable evaluation of an output power of this device, only the temperature of the hot side was modulated, while the cold side was kept at a constant temperature of 20±0.5 °C (Supplementary Fig. 16).

Figure 4: Output characteristics of in-plane TE devices painted on flat substrates. (a) Scheme and photograph of an in-plane type TE device composed of painted legs and silver electrodes on a polyimide substrate. (b) Cross-sectional SEM image of painted TE layer. Scale bar, 500 μm. (c) Output voltage and power, and (d) output power density of the painted TE device on a polyimide substrate. (e) Output voltage and power, and (f) output power density of the painted TE device on a glass substrate (The inset shows a photograph of the actual TE device). Scale bar in (a) and the inset of (f) is 20 mm. Error bars represent the s.e. of the mean values of output voltage, power and output power density obtained by repeatedly measuring three times. Solid and dashed lines in c,d,e and f indicate the guide for the measured values. Full size image

The TE device painted onto the polyimide substrate achieved an output voltage of 79.4 mV and an output power of 60.8 μW under the temperature difference of 50 °C (Fig. 4c). The output power density reached as high as 2.43 mW cm−2 (Fig. 4d), which doubles the best reported value for in-plane type TE devices33. The mW-level output power density is highly potential for the wearable TE energy harvester. Another TE device was prepared by painting onto a glass substrate under the same preparation conditions. This achieved the internal resistance of 26.3 Ω, the output voltage of 79.4 mV, the output power of 60.7 μW and the output power density of 2.43 mW cm−2 (Fig. 4e,f). The fact that these values are almost identical to the TE device painted onto a polyimide substrate suggests that the fabrication process can be consistently applied to a range of different substrates.

All-painted TE devices on curved surfaces

The versatility of the TE paints was best-demonstrated by TE devices directly realized onto curved surfaces such as onto the concave and convex surfaces of a glass hemi-cylinder, as depicted in Fig. 5. The resulting device has 5 couples of n- and p-type layers with the dimension of 5 mm × 10 mm × ∼50 μm (Fig. 5a,d). The internal resistances of the TE devices on convex and concave surfaces were almost identical at 23–25 Ω, which is consistent with the TE devices painted on flat substrates. Under the temperature difference of 30 °C, these devices produced an output voltage of 34–36 mV and output power of 17–18 μW, leading to a comparable power density (0.70–0.71 mW cm−2) to the TE devices painted on flat glass substrates (Fig. 5b,c for the concave device, and Fig. 5e,f for the convex device). The fact that the output power density of the TE devices painted on flat and curved substrates with the same dimension of TE legs merges into the same line (Supplementary Fig. 17) validates the applicability of the TE paints to any shaped surfaces.

Figure 5: Output characteristics of in-plane TE devices painted on curved substrates. (a,d,g) Photographs of the painted TE devices on concave and convex surfaces of a hemi-cylinder and a hemisphere (the insets of a and d show schemes of the TE devices). Scale bars in (a), (d) and (g) are 10, 10 and 50 mm, respectively. (b,e,h) Linear and curved lines indicate output voltages and powers, and (c,f,i) output power densities of the painted TE devices on concave and convex surfaces of a hemi-cylinder, and a hemisphere. Error bars represent the s.e. of the mean values of output voltage, power and output power density obtained by repeatedly measuring three times. Solid and dashed lines in b,c,e,f,h and i indicate the guide for the measured values and the predicted properties via extrapolations. Full size image

To further demonstrate the processability of TE painting onto large-sized curved surfaces with a full coverage, TE device was fabricated on a hemispherical alumina substrate with the diameter of ∼70 mm (Fig. 5g). We introduced 5.5 couples of triangular TE layers with 15 mm at the base and ∼25 mm in height and obtained the internal resistance of 40.2 Ω, which is expected for the enlarged TE layers (67% higher aspect ratio). To minimize radiation or convection factor from a heat source, the planar heat source was fully covered with a glass fabric and the apex of the hemispherical generator was thermally connected by thermal pads (Supplementary Fig. 18). Exposed to a temperature difference of 20.1 °C, this device produced the output voltage of 22.5 mV, the output power of 3.0 μW and the output power density of 0.073 mW cm−2 (Fig. 5h,i), which are significantly lower than those of the other devices. It is understood that this low output power density can originate in the longer TE legs which increase the internal resistance since the output power density is inversely proportional to the leg length under same temperature difference54. Assuming the identical dimension of the TE legs to those of other devices, the plotted output power density approached towards the others (Supplementary Fig. 17). As evidenced by the lower output voltage, small deviation in the graph (Supplementary Fig. 17) can be due to the heat loss from a thermally conducting alumina substrate, which forces the external temperatures to be different from the actual temperature applied to the TE legs.

Comparison with conventional TE module

To show how the painted TE generator on a curved surface is effective, we performed the comparative simulation study on the power output of the painted TE generator and the conventional module on a hemispherical curved heat source, based on a three-dimensional TE finite element model (FEM). The heat loss in the FEM was considered by including the convective heat transfer. To simulate the natural convection over all the surfaces that are exposed to air, the convection heat transfer coefficient was 10 W m−2 K−1 with an ambient temperature of 25 °C (ref. 55). The simulation details are described in the Supplementary Information. The temperatures across the apex and the bottom of an alumina hemisphere were kept at 45 and 25 °C (Supplementary Fig. 19). In the conventional module, since the contact area (d) with a hemisphere is small, the temperature distribution in the module is greatly non-uniform (Supplementary Fig. 20), which results in a significantly low output voltage of 13.3 mV for d=1 mm and 4.5 mV for d=0.1 mm. Thus, conventional module generates the output power of 76.9 μW (the output power density of 15 μW cm−2) when d=1 mm, and the output power of 8.6 μW (the output power density of 1.7 μW cm−2) when d=0.1 mm, which are greatly reduced values compared with the reported values of 4–10 mW cm−2 obtained on a flat heat source5. On the other hand, the uniform temperature distribution and electrical potential field on the painted generator (Supplementary Fig. 21) result in an order of magnitude higher output power density of 205 μW cm−2.

To further validate the practicability of the painting technology against the conventional module, we propose two designs of power generation systems based on the painting technology. First, the TE leg length in the painted TE generator was controllably varied to obtain the higher power output density, since the power output density can be maximized by the optimum TE leg length5,54. As shown in Supplementary Fig. 22, with the decrease of the leg length, the resistance linearly decreases and the output power increases as expected. The highest output power per unit area of 4.0 mW cm−2 was achieved by the generator with the leg length of 5 mm under the temperature difference of 50 °C. Furthermore, the predicted power output density based on the fitted function with the data points reached 11.0 mW cm−2 in the generator with the leg length of 1.4 mm, which is comparable to 30–50 mW cm−2 obtained from the conventional module with TE legs with an identical length on a flat heat source5.

In addition, we fabricated the through-plane TE generator using the moulded disks prepared from the TE paints. The details of the moulding experiments are described in the Supplementary Information (Supplementary Fig. 23). Two pairs of n-type and p-type moulded disks with the diameter of 4.0 mm and thickness of 1.0 mm were assembled by soldering with a Bi–Sn solder to Cu foil electrodes on an alumina hemisphere (Fig. 6a,b). The internal resistance was as low as 0.014 Ω, comparable to that of the conventional module. Under the temperature difference of 14 °C, this generator produced an output voltage of 8.0 mV, output power of 1.1 mW and output power density of 2.3 mW cm−2 (Fig. 6c). Furthermore, the predicted power output density on the fitted function with the data points is as high as 26.3 mW cm−2 under the temperature difference of 50 °C, which competes on par with the conventional module5. These results clearly demonstrate the practicability of the painting technology in terms of the TE performance as well as the processability.