High-temperature thin-film strain sensors with low temperature coefficient of resistance and high sensitivity via direct ink writing

High-temperature strain sensors are crucial for monitoring stress and strain in extreme environments.^1–3 However, traditional patch-type high-temperature strain sensors are very limited in that they are prone to detaching when exposed to high temperatures and are challenging to apply on complex curved surfaces.^4,5 Fiber-optic high-temperature strain sensors encounter similar issues, including low mechanical strength and poor environmental adaptability.^6,7 These sensors are highly susceptible to external stress and temperature fluctuations, which can lead to sensor failure, increased transmission loss, and compromised measurement accuracy and stability.

In contrast, high-temperature thin-film strain sensors offer distinct advantages. Because of their micrometer-scale thickness, these sensors can be integrated seamlessly with the components they are measuring, circumventing the need for high-temperature adhesives and the difficulty of conforming to complex surfaces.^8–10 This integration enhances their performance and reliability in extreme environments, but despite these advantages, high-temperature thin-film strain sensors still face challenges. A major issue is the coupling of strain signals with temperature signals in environments involving high and fluctuating temperatures. This coupling effect can obscure the true strain signal, making it extremely difficult to achieve precise strain measurements under such conditions.^11–14 Consequently, this limitation hampers their broader application in practical applications. Overcoming this coupling problem is essential to advancing the practical utility of high-temperature thin-film strain sensors. By overcoming this challenge, these sensors can fulfill their potential to provide accurate and reliable strain measurements in extreme environments and their applicability in various high-temperature applications.

To overcome these challenges, one approach is to introduce temperature-compensation circuits or algorithms. By measuring the ambient temperature in real time and correcting the strain signals accordingly, the impact of temperature variations on strain measurements can be minimized.^15,16 This method can enhance measurement accuracy but requires sophisticated electronic circuits and algorithmic support. Another approach is to use composite materials that combine those with positive and negative temperature coefficients to counteract the temperature effects on strain measurements.¹⁷ This combination can significantly reduce the overall temperature coefficient of the sensor. Currently, carbon-based materials are being used to develop strain sensors with low temperature coefficients,^18,19 but they face issues such as oxidation at high temperature and limited temperature resistance (typically not exceeding 300 °C) along with low sensitivity. Alternatively, forming composite thin films via co-sputtering of indium tin oxide and platinum can achieve high temperature resistance and high sensitivity.¹⁷ However, this manufacturing process is constrained by the limitations of the magnetron sputtering chamber and the complexity of the process, resulting in high costs and difficulty in applying it to large and complex curved surfaces.

However, inkjet printing technology is emerging as a novel deposition method to address the limitations of traditional physical vapor deposition processes.^20–22 Therefore, developing inks that can achieve a low temperature coefficient of resistance (TCR) and high sensitivity in high-temperature environments has become a focal point of research. Pb₂Ru₂O₆ and TiB₂ have emerged as ideal candidate materials because of their respective positive²³ and negative²⁴ TCRs. Combining these two materials not only significantly reduces the overall TCR of the composite film but also maintains high sensitivity in high-temperature environments. This innovative approach holds promise for developing high-performance and high-temperature strain sensors.

In this study, we used polysilazane (PSZ) as a matrix to combine Pb₂Ru₂O₆ and TiB₂, formulating a composite ink.²⁵ Using direct ink writing (DIW) technology, we fabricated PSZ/Pb₂Ru₂O₆/TiB₂ thin films. After annealing at 800 °C in air, the PSZ transformed into an amorphous ceramic, enhancing the film’s density and high-temperature performance. The resulting thin film exhibited excellent performance over a wide temperature range from 100 °C to 700 °C, with a TCR as low as 281 ppm/°C and a sensitivity approaching 19.8. Experimental results demonstrated that the PSZ/Pb₂Ru₂O₆/TiB₂ film could output stable strain signals even under varying temperature conditions. The performance improvement is attributed mainly to the complementary TCR characteristics of Pb₂Ru₂O₆ and TiB₂, which effectively reduce the overall TCR of the composite film. This study proposes a cost-effective solution, offering new insights into the design and fabrication of high-temperature, high-sensitivity, and low-TCR thin-film strain sensors. The findings showcase the significant application potential of these sensors in high-temperature strain measurements.

The TiB₂ powder used in this study had an average particle size of 1 μm and was purchased from Chaowei New Materials Co., Ltd., Shanghai, China. With an average particle size of 200 nm, the Pb₂Ru₂O₆ powder was obtained from Hehe Nano Tech Co., Ltd., Chengdu, China. PSZ was sourced from Qingci New Material Technology Co., Ltd., Hangzhou, China, with a curing temperature of 300 °C and labeled as TC-P03. The high-temperature electrode material was AgPd paste, acquired from Sayer Electronic Paste Co., Ltd., Shenzhen, China.

To prepare the printable PSZ/Pb₂Ru₂O₆/TiB₂ composite ink, PSZ, TiB₂ powder, and Pb₂Ru₂O₆ powder were mixed in a 1:1:1 weight ratio and stirred thoroughly using a mixer for over 1 h. For comparison, PSZ/TiB₂ ink was prepared by mixing PSZ and TiB2 powder in a 1:2 weight ratio, and PSZ/Pb₂Ru₂O₆ ink was prepared by mixing PSZ and Pb₂Ru₂O₆ in a 1:2 weight ratio.

The uniformly mixed slurries were printed onto ceramic substrates using a custom-built micro-scale Weissenberg-effect-based printing platform.²⁶ The printing patterns were designed using computer-aided-design software. The designed sensor chip had the dimensions of 5 mm in length and 7 mm in width, featuring six longitudinal grids, each with a width of ∼0.7 mm. During printing, a micrometer-sized needle with a diameter of 160 µm was used, the motor speed was set to 1000 rpm, and the printing-platform speed was 1 mm/s. The prepared samples were then annealed in a tube furnace in air with a heating rate of 10 °C/min, held at the target temperature for 1 h, and then allowed to cool naturally.

SEM imaging and energy dispersive spectroscopy (EDS) analyses were conducted using a Zeiss Sigma 300 scanning electron microscope operating at an accelerating voltage of 20 kV. XRD measurements were performed using a Shimadzu XRD-6100. The electrical resistance of the PSZ/Pb₂Ru₂O₆/TiB₂ films was measured using a Keysight 34972A data acquisition system within the tube furnace. Temperature was recorded using a commercial K-type thermocouple.

The resistance–temperature (R–T) testing system consisted of a quartz tube furnace (OTF-1200X; MTI KJ GROUP, China), a data acquisition device (Keysight 34972A), and a K-type thermocouple (KPS-K, China). The thermocouple and the PSZ/Pb₂Ru₂O₆/TiB₂ composite sensitive film were placed in the constant-temperature zone of the tube furnace, and both thermocouple signals and film resistance were recorded simultaneously. The strain testing system used a cantilever-beam deflection method. One end of the sample was clamped and placed in the constant-temperature zone of the quartz tube furnace, with the furnace temperature controlling the strain test temperature. Strain was applied by displacing the free end, controlled precisely by a high-precision stepper motor with a resolution of 1 μm and a maximum speed of 40 mm/s.

The design and fabrication process of the low-TCR high-temperature functional thin films using 3D printing technology is shown schematically in Fig. 1. The first step involves preparing the printing ink [Fig. 1(a)]. To mitigate significant resistance changes caused by temperature variations, we used a composite of high-temperature-resistant positive-TCR Pb₂Ru₂O₆ and negative-TCR TiB₂ particles to lower the overall TCR of the composite. The solvent used in the ink formulation was PSZ, which upon high-temperature annealing converts into an amorphous ceramic phase. This transformation enhances the film’s density, promoting tight connections between Pb₂Ru₂O₆ and TiB₂ particles and ensuring stability at high temperatures, making it an effective high-temperature ink solvent. The prepared ink is used in DIW technology to achieve patterned printing on an insulating substrate [Fig. 1(b)]. After printing, the film undergoes annealing at 800 °C in air for 1 h, followed by natural cooling. Once the electrodes are connected, the fabrication of the thin-film sensor is complete. Given that the materials used are semiconductors, they exhibit higher strain sensitivity compared to traditional metal materials.²⁷ Also, using complementary TCR materials (both positive and negative) minimizes the sensor’s sensitivity to temperature variations. This composite ink printing method is particularly well suited for developing high-temperature strain sensors.

The microstructure and performance of the thin films are closely related to the annealing temperature. We annealed the PSZ/Pb₂Ru₂O₆/TiB₂ thin films at various temperatures and observed significant differences in the surface microstructure at different temperatures [Figs. 2(a)–2(d)]. After annealing at 800 °C, the film exhibited the most compact and smooth surface. XRD analysis revealed that annealing at 800 °C resulted in the formation of new phases, including PbRuO₃ and RuO₂, which also exhibited positive TCR.¹¹ TiB₂ was partially converted to TiO₂ and B₂O₃,²⁸ but being amorphous, B₂O₃ was not detectable by XRD.^24,29,30 The presence of the glassy phase (B₂O₃) reduced the oxidation of TiB₂, preventing its complete transformation into TiO₂, as further evidenced by Figs. 2(i) and 3. TiO₂ also exhibits negative TCR.³¹ At 900 °C, the film surface began to show more microstructures, increased roughness, and higher porosity, likely due to the high-temperature volatilization of B₂O₃ and RuO₂.^11,24,32 Films annealed at 700 °C had even-higher porosity and surface roughness compared to those annealed at 800 °C. Thus, 800 °C was determined to be the optimal annealing temperature.

High-magnification SEM analysis further confirmed the film’s density as shown in Fig. 2(e). EDS analysis [Fig. 2(f)] of the PSZ/Pb₂Ru₂O₆/TiB₂ film annealed at 800 °C showed that the primary elements present were Ru, Pb, Si, Ti, C, and O, with trace amounts of Al likely originating from the alumina substrate. These elements matched the composition of the original materials. Besides oxygen, Pb was the most abundant element, followed by Ti and Ru, all of which showed an interspersed distribution. This distribution is beneficial for neutralizing the TCR. The Si and C originating from the PSZ form an amorphous SiO₂/SiCO ceramic phase after being exposed to high-temperature oxidative environments,^33,34 as evidenced by the XRD and EDS results. The XRD results show no characteristic peaks for substances composed of Si and C, while the EDS results reveal a significant presence of Si and O along with a small amount of C. This indicates that the material formed from Si, C, and O is in an amorphous state. The uniform distribution of Si in the EDS mapping indicates that the SiO₂/SiCO ceramic was effective in filling voids and enhancing the density. This was further supported by the observation that pure PSZ pyrolyzed at 800 °C in air resulted in a smooth, dense, and void-free surface as shown in Fig. 2(g). However, using PSZ alone does not achieve the same level of densification as that of the PSZ/Pb₂Ru₂O₆/TiB₂ composite film. The surface morphology of films made solely from PSZ and either Pb₂Ru₂O₆ or TiB₂ showed more cracks and higher porosity [Figs. 2(h) and 2(i)]. Therefore, the synergistic effect of incorporating PSZ and TiB₂ in the composite material improved the densification of the PSZ/Pb₂Ru₂O₆/TiB₂ film, filling the voids formed during the annealing process and reducing the high-temperature oxidation behavior of TiB₂. Furthermore, TiB₂ played a crucial role in lowering the TCR of the PSZ/Pb₂Ru₂O₆/TiB₂ film.

Further analysis of the cross section of the PSZ/Pb₂Ru₂O₆/TiB₂ film annealed at 800 °C as shown in Fig. 4(a) revealed a thickness of ∼5 μm and a highly dense structure. EDS results showed an interspersed distribution of Ru and Ti, with Ru and Pb exhibiting similar intensity distributions. This confirmed our hypothesis that the random mixing of Pb₂Ru₂O₆ and TiB₂ in the PSZ matrix would have a synergistic effect on the TCR of the composite film. Moreover, the film exhibited excellent thermal-expansion compatibility with the alumina substrate, with a tightly bonded interface, which is crucial for high-temperature applications. Based on the above analysis, we use the simple schematic shown in Fig. 4(b) to describe the annealing process of the film at high temperature. Although new substances such as PbRuO₃, RuO₂, TiO₂, and B₂O₃ are formed, these do not alter the TCR properties of the original materials. Therefore, the strategy of positive and negative compensation does not fundamentally change after high-temperature annealing.

The R–T characteristics of the PSZ/Pb₂Ru₂O₆/TiB₂ thin films are crucial for their applications in high-temperature environments. First, we compare the R–T curves of PSZ/TiB₂, PSZ/Pb₂Ru₂O₆, and PSZ/TiB2/Pb₂Ru₂O₆ inks after annealing at 800 °C for 1 h. Figure 5(a) shows the R–T curve of the PSZ/TiB₂ film, where the resistance decreases with increasing temperature, exhibiting a clear negative TCR with an average value of ∼−1245 ppm/°C. On the other hand, the PSZ/Pb₂Ru₂O₆ film shows an increase in resistance with temperature, displaying a nearly linear positive TCR, with an average TCR of 591 ppm/°C as shown in Fig. 5(b). Notably, the PSZ/Pb₂Ru₂O₆ film exhibits non-monotonic behavior beyond 750 °C, limiting its application at higher temperatures. The application temperature of the PSZ/Pb₂Ru₂O₆/TiB₂ film is similarly constrained by the intrinsic properties of Pb₂Ru₂O₆. Testing the PSZ/Pb₂Ru₂O₆/TiB₂ film at temperatures up to 700 °C shows a nearly linear positive TCR, but with a significantly reduced average TCR of ∼281 ppm/°C as shown in Fig. 5(c). This indicates clearly that TiB₂ plays a crucial role in lowering the TCR in the PSZ/Pb₂Ru₂O₆/TiB₂ composite film, thereby providing a promising approach for printing low-TCR sensitive films.

To further verify the high-temperature stability of the PSZ/Pb₂Ru₂O₆/TiB₂ film, we recorded the resistance change over time at different temperature steps starting from room temperature, i.e., 339 °C, 534 °C, and 725 °C, each maintained for 1 h. Simultaneously, temperature data were collected using a thermocouple as shown in Fig. 5(d). The results show that the resistance of the PSZ/Pb₂Ru₂O₆/TiB₂ film and the temperature measured by the thermocouple were synchronous and exhibited the same trend across all temperature platforms, with no lag observed. The resistance drift rate at each temperature platform was less than 0.2%, demonstrating excellent thermal stability. Finally, to validate the high-temperature durability, we conducted a constant-temperature test at 728 °C for 30 h, where the resistance change rate of the PSZ/Pb₂Ru₂O₆/TiB₂ film was only 5% as shown in Fig. 5(e). This represents the first report of a 3D-printed high-temperature thin film with both low TCR and high thermal stability across a wide temperature range from 100 °C to 700 °C.^{11,24,35–38}

In summary, the PSZ/Pb₂Ru₂O₆/TiB₂ film demonstrates high linearity, excellent strain sensitivity, low resistance drift rate at high temperature, strong high-temperature durability, and low TCR. These outstanding comprehensive performance characteristics underscore its significant potential for applications in high-temperature strain sensors.

Figure 6(e) shows the strain response curves of the TFSG at different loading rates (100 με/s, 200 με/s, 300 με/s) for a constant strain amplitude of 300 με. The results indicate that the peak values of the response curves remained consistent across different loading rates, confirming the TFSG’s stability and consistency in response to varying loading rates. Finally, a linear fit of the relationship between strain amplitude and resistance change rate was performed, revealing that the sensor exhibited high linearity (R² = 0.991) and a high gauge factor (19.81) as shown in Fig. 6(f). These results highlight the potential of the PSZ/Pb₂Ru₂O₆/TiB₂ thin-film strain sensor for high-precision strain measurements in high-temperature environments.

To demonstrate the performance of the PSZ/Pb₂Ru₂O₆/TiB₂ TFSG [shown in Fig. 7(e)] in high-temperature environments, we conducted constant-amplitude cyclic strain tests at ∼400 °C, 500 °C, 600 °C, and 700 °C as shown in Figs. 7(a)–7(d). At the same strain amplitude, the resistance change rate tends to decrease with increasing temperature, particularly at 700 °C, indicating that the gauge factor of the thin film decreases gradually with increasing temperature. Nevertheless, the strain response exhibits good consistency. To further validate the strain response characteristics of the PSZ/Pb₂Ru₂O₆/TiB₂ TFSG at high and varying temperature, we applied a strain amplitude of 300 με and conducted 30 cycles of testing. The results shown in Fig. 7(f) indicate that over ∼70 s, the furnace temperature dropped from ∼633 °C to 624 °C. Correspondingly, the sensor output generally showed a downward trend with decreasing temperature. However, the magnitude of the resistance change remained significant and was comparable to the constant-temperature values, demonstrating good adaptability to the varying temperature. These test analyses show that the PSZ/Pb₂Ru₂O₆/TiB₂ film has considerable potential in high-temperature strain testing, effectively reducing the impact of temperature variations on strain signal measurement.

In summary, we have developed a novel approach for fabricating high-temperature thin-film strain sensors with low TCR and high sensitivity, using a composite ink based on PSZ as the solvent, combined with positive-TCR Pb₂Ru₂O₆ particles and negative-TCR TiB₂ particles. This composite ink was used to manufacture the thin films via 3D printing in ambient air. Using PSZ as a solvent—which transforms into a dense amorphous ceramic phase after high-temperature annealing—along with the B₂O₃ glass phase generated from TiB₂ collectively enhances the densification of the composite film and the bonding among particles in the film. Also, the amorphous glass phase provides excellent wetting properties and tight interfacial bonding with the alumina substrate, demonstrating high thermal-expansion compatibility. Although new substances such as RuO₂ and TiO₂ are formed from Pb₂Ru₂O₆ and TiB₂ at high temperatures, these do not alter the TCR characteristics or affect the high-temperature stability of the film. Consequently, the PSZ/Pb₂Ru₂O₆/TiB₂ film exhibits excellent high-temperature performance. High-temperature testing showed that the PSZ/Pb₂Ru₂O₆/TiB₂ film has a low TCR of only 281 ppm/°C over a wide temperature range from 100 °C to 700 °C, which is more than double the reduction compared to the PSZ/Pb₂Ru₂O₆ film. Also, the film maintains a high sensitivity with a gauge factor of nearly 19.8. These improvements are attributed to the complementary TCR properties of Pb₂Ru₂O₆ and TiB₂ and the enhanced piezoresistive properties of the semiconductor components, which collectively reduce the overall TCR of the composite film and surpass the sensitivity of most existing high-temperature strain sensors. Also, the film exhibited significant signal output even under low strain and variable temperature, further demonstrating its practicality. The PSZ/Pb₂Ru₂O₆/TiB₂ ink offers a flexible and efficient method for in situ rapid printing of high-temperature-resistance, low-TCR, and high-sensitivity thin-film strain sensors on structural components operating in harsh environments.

The authors acknowledge the National Key Research and Development Program of China (Grant No. 2021YFB2012100), the Major Science and Technology Projects in Fujian Province (Grant No. 2023HZ021005), the Open Project Program of Fujian Key Laboratory of Special Intelligent Equipment Measurement and Control (Grant No. FJIES2023KF06), and the Industry-University-Research Co-operation Fund of the Eighth Research Institute of China Aerospace Science and Technology Corporation (Grant No. SAST2023-061).

The authors have no conflicts to disclose.

L.X. and F.Z. contributed equally to this work.

The data that support the findings of this study are available from the corresponding authors upon reasonable request.