Introduction

SAW RFID systems have garnered considerable research attention in sensing1,2, localization3,4, and identification5,6 applications due to their advantages of passive operation7,8, working in extreme environment9, and multi-parameter sensing10 capabilities. As illustrated in Fig. 1a, a typical SAW RFID system comprises reflective delay line type SAW RFID tags and a reader unit. When attached to a target object, the SAW RFID tag transduces physical parameters into measurable signals that can be remotely acquired by the reader11,12. The reader transmits a radio frequency interrogation signal to the SAW sensor’s antenna. The received signal is then converted into acoustic waves by an interdigital transducer (IDT) and propagates along the crystal substrate surface. A portion of the acoustic waves is reflected by the reflectors back to the IDT, reconverted to radio frequency signals, and retransmitted to the reader. The received signal encodes both the identity information and monitored physical properties such as pressure13, temperature14, or gas concentration15.

Fig. 1: Schematics of the wireless SAW RFID system, the 3-dB MSC, and the RMSC.
figure 1

a Schematic of the wireless SAW RFID system. b Schematic of a 3-dB multistrip coupler, where φ1 represents the phase shift caused by the strips. c Schematic of the RMSC

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The maximum wireless readout distance, a critical performance metric, directly determines deployment feasibility in extended-range applications. Since a 12 dB reduction in energy loss doubles the readout distance16, mitigating the high energy loss of SAW RFID tags (which often exceeds 18 dB7,10,17,18) is essential for range enhancement. Conventional SAW RFID reflectors consist of Bragg-conditioned strips that reflect incident waves through impedance discontinuities19. Due to the low per-strip reflectivity (usually less than 2%20,21), achieving high reflectance requires hundreds of strips. This configuration inevitably reduces operational bandwidth and induces significant energy trapping within the reflector due to strong internal resonance. The trapped energy gradually leaks out, manifesting as temporal roll-off in the time-domain response peak22,23. Consequently, although increasing the strip number theoretically enables near-total reflection, this approach yields limited enhancement in the time-domain peak amplitude while severely degrading coding capacity due to the narrow bandwidth and temporal roll-off. These fundamental limitations render Bragg grating-based reflectors impractical for extremely low-loss applications.

This paper presents an innovative SAW RFID architecture employing RMSCs for enhanced energy reflection. The proposed RMSC achieves wavefront redirection through energy redistribution between strips, fundamentally differing from conventional electrical and mechanical reflection reflectors. Theoretical analysis confirms its broadband near-total reflection capability, enabling significant energy loss reduction in RMSC-based SAW RFID. Through the finite element simulations, the parasitic resistance and capacitance effects on RMSC performance were analyzed. A prototype implementing this novel architecture was successfully fabricated and experimentally validated, demonstrating an extremely high amplitude of the reflected signal.

Marshall et al. demonstrated RMSC’s capability for near-total reflection24. This structure evolves from the multistrip coupler (MSC), which consists of an array of periodic metallic strips perpendicular to the SAW propagation direction25,26. The MSC’s operating mechanism is illustrated in Fig. 1b. An incident wave (IW in Fig. 1b) in track A can be decomposed into two partial waves of equal amplitude that span the full aperture of the MSC: the symmetric wave (SW in Fig. 1b) and the antisymmetric wave (AW in Fig. 1b). For the symmetric partial wave, which exhibits identical acoustic potentials on both tracks, the MSC acts as an open-circuited gating. However, the antisymmetric partial wave generates potentials with the same amplitude and opposite phases on the two tracks, for which the MSC presents a short-circuited gating. The symmetric and the AWs propagate through the MSC with different phase velocities vOC and vSC, where vOC and vSC represent the SAW phase velocities on the open-circuited gating and the short-circuited gating, respectively. The interference of these two partial waves results in a periodic energy change between track A and track B27,28,29. The phase of the antisymmetric in track A and that of track B maintain a 180° difference. When the phase of the SW in track A leads the phase of the AW by 90° after propagating through the MSC, the phase of the SW in track B lags the phase of the AW by 90°. The transmitted wave (TW in Fig. 1b), which is the sum of the two waves, exhibits equal intensity on both tracks with the phase on track B leading that on track A by 90°. This configuration of the MSC is commonly referred to as a 3-dB coupler.

By bending the strips at the upper track of the 3-dB coupler by 180°, an RMSC is formed. When a SAW with amplitude A and phase 0° is incident on port 1 of the RMSC, two SAWs emerge on ports 2 and 3, as shown in Fig. 1c. The SAW appearing on port 2, referred to as SAW 1, propagates to port 3 and subsequently generates SAWs on ports 1 and 4. Similarly, SAW 2 also induces SAWs on ports 1 and 4. On port 4, the components SAW 1-1 and 2-2 have a phase difference of 180°, resulting in destructive interference. On port 1, SAW 1-2 and 2-1 are in phase, resulting in constructive interference. While theoretical models predict near-total reflection for RMSC configurations, practical implementations necessitate connecting strips between corresponding electrodes. These structural features introduce parasitic effects, resulting in additional energy loss and a shift in the number of electrodes corresponding to maximum reflectivity30. Conventional RMSC analytic models often fail to adequately account for these parasitic phenomena, thereby failing to explain the discrepancies between simulated predictions and experimental measurements in fabricated devices.

Results and discussion

SAW RFID for wireless temperature measurement

The peak width of an SAW RFID device in the time domain is inversely proportional to its bandwidth in the frequency domain, as the time-bandwidth product of the device is fixed. A narrow peak width facilitates a large coding capacity, while a wide bandwidth enhances measurement accuracy. The electromechanical coupling factor k2 of the SAW substrate determines the upper limit of the achievable bandwidth. Consequently, selecting a SAW mode with a high k2 is advantageous for designing high-performance SAW RFID devices. Shear-horizontal (SH) modes on single-crystal substrates such as 32°YX-LiTaO3, 41°YX-LiNbO3, and 64°YX-LiNbO3 exhibit large k2 values but a leaky nature on free surfaces. SAW RFID devices for wireless sensing applications typically require long acoustic propagation paths (often exceeding 1 μs) to generate sufficient time delay for coordination with the reader. A significant portion of the SAW energy dissipates during propagation on the free surface. Although the k2 of Rayleigh modes on YZ-LiNbO3 and 128°YX-LiNbO3 is considerably lower than that of SH modes, they are more suitable for wireless applications due to their non-leaky nature. Additionally, Rayleigh modes on YZ-LiNbO3 and 128°YX-LiNbO3 have a large and stable temperature coefficient of time delay. Thus, the time delays and phases of SAW RFID devices on these substrates have high and linear sensitivities to temperature, which is an outstanding characteristic for accurate temperature measurement. The SAW RFID device on 128°YX-LiNbO3 has a larger critical dimension than one on YZ-LiNbO3 operating at the same frequency, because the phase velocity of the Rayleigh wave on 128°YX-LiNbO3 (approximately 4000 m/s) is faster than that on YZ-LiNbO3 (approximately 3500 m/s). The 128°YX-LiNbO3 substrate was selected in this study to reduce the fabrication difficulty.

Aluminum is widely employed in SAW RFID devices for its high electrical conductivity and low density. These properties enable aluminum electrodes to achieve relatively low ohmic loss and to excite high-frequency SAWs. The normalized thickness (ratio of electrode thickness to wavelength, h/λ) of aluminum electrodes in SAW RFID devices typically ranges from 0.63 to 3.7%13,15,17,31,32. A normalized aluminum thickness of 1.67% was selected in this study, which falls within the common range. The aluminum electrode used in this work was doped with 2 wt% copper to enhance its conductivity.

RMSC reflector with high reflectivity

It is essential to avoid mechanical reflection during the design of the RMSC reflector, as it causes undesired reflected peaks in the time domain. This reflection is primarily influenced by the pitch of the RMSC structure. To identify a suitable pitch, the reflection characteristics of RMSC reflectors with varying pitches were simulated using the model illustrated in Fig. 1S. The results indicate that when the RMSC pitch exceeds half the wavelength, strong impedance mismatch leads to high-amplitude reflection peaks at both edges of the RMSC, which can degrade the amplitude of the main peak and coding capacity of the device. When the RMSC pitch equals half the wavelength (satisfying the Bragg condition), the acoustic wave is trapped within the RMSC strips owning to the strong internal reflection. The trapped energy gradually leaks out, leading to a roll-off in the time domain. Conversely, for pitches smaller than half the wavelength, the impedance mismatch is weak, resulting in weak reflection. Moreover, a shorter pitch of the RMSC strip reduces the total width of the RMSC, causing the left and right reflectors to merge with the main peak. Narrower electrodes in RMSC designs produce weaker reflections caused by acoustic impedance discontinuities, thereby enhancing device performance. However, reducing the electrode width increases ohmic loss and introduces fabrication challenges due to the smaller critical dimension. After balancing ohmic loss, manufacturing constraints, and reflection suppression requirements, an RMSC electrode pitch of 3/8 wavelength was selected as the optimal compromise.

The performances for RMSCs with an aperture of 70 wavelengths were simulated as a function of strip number using the structural parameters shown in Table 1. The RMSC pitch is set to 3/8 wavelength to avoid Bragg reflection, and the gap between port 2 and port 3 is set to half of its pitch to minimize resistance and possible bulk wave conversion, while maintaining a consistent critical dimension, as shown in Fig. 2a. The parasitic effects imposed by strip resistance and capacitance between connection strips were included in the simulation. The simulation results of average transmittance, reflectance, and loss for Type1 RMSCs across 413–453 MHz were calculated, as shown in Fig. 2b. For ideal RMSCs, where neither capacitance effects nor resistance effects are included in the numerical simulations, the energy loss is minimal and independent of the strip number. The strip number only determines the ratio of reflected to transmitted energy. The maximum reflectance and minimum transmittance occur simultaneously when the strip number is 40. The RMSC with this optimal strip number achieves near-total reflection over a wide frequency range, with only 0.04 dB of SAW energy being lost or transmitted.

Fig. 2: Schematic and simulated performance of the RMSCs on 128°YX-LiNbO3.
figure 2

a Schematic of Type1 and Type2 RMSCs. b Simulated average transmittance, reflectance, and loss for Type1 RMSCs as a function of strip number. c Simulated average reflectance for RMSCs with different connecting strip types as a function of strip number. d Simulated average reflectance for RMSCs with different apertures as a function of strip number. e Measured transmittance, reflectance, and loss of the RMSC with optimal strip number as a function of frequency compared to the ideal model and the model considering the parasitic elements

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Table 1 Structural parameters of the RMSCs
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The ideal RMSC can achieve near-total reflection. However, the ohmic loss and stored charges damage its performance. Ohmic loss occurs when SAWs propagate through the RMSC reflector, as currents induced in the metal electrodes are dissipated due to the inherent resistance. This phenomenon was simulated by incorporating parasitic resistances into the finite element model in this manuscript. After being excited by the incident wave, the induced charges distribute across the entire metal strips, including the connecting segments. Charges on the connecting strips generate SAWs with wavevectors perpendicular to these strips. However, the wavenumber of these SAWs differs from that of the incident wave because the phase velocity of acoustic waves varies with the propagation direction. The resulting wavelength mismatch with the periodic metal strip pitch prevents these weak SAWs from constructively interfering and amplifying. Only a small fraction of the charges on the connecting strips regenerate SAWs, while most are stored due to capacitances between adjacent connecting strips. This phenomenon is simulated by incorporating parasitic capacitances into the finite element model in this manuscript.

The parasitic resistances of strips and parasitic capacitances between connecting strips have a significant impact on the performance of RMSCs. The ohmic loss power for an acoustic wave is proportional to the acoustic wave power and total resistance. When the RMSC satisfies the interference condition, the entire incident wave is converted into a reflected wave, with no excited transmitted wave. If the RMSC reflector has slightly fewer strips than required for perfect constructive interference, the amplitude of the reflected wave is weaker. Consequently, the ohmic loss power of the reflected wave decreases due to the reduced induced current and lower associated parasitic resistance. For the RMSC suffer from large ohmic loss, this reduction in ohmic loss may outweigh the decline in the excitation efficiency of the reflected wave caused by the deviation from optimal interference. This trade-off can potentially reduce the number of strips needed to achieve maximum reflectance. In contrast, parasitic resistances do not significantly influence the strip number required for minimum transmittance. This is because any transmitted wave resulting from a deviation from perfect constructive interference cannot be fully attenuated by ohmic loss. The storage charges reduce the electro-acoustic conversion efficiency of the RMSC, which is equivalent to a decrease in the electromechanical coupling coefficient k2 of the SAW substrate near the RMSC region. The reduction in k2 caused by the parasitic capacitances narrows the phase velocity difference between SW and the AW. As a result, additional strips are needed to provide sufficient propagation length for achieving a 90° phase difference between the modes. Therefore, parasitic capacitances increase the strip number required to meet the interference condition. Affected by both factors, the reflectance of the practical RMSC is less sensitive to variations in the strip number compared to the ideal RMSC. Moreover, the maximum reflectance and minimum transmittance no longer always occur together. The lowest transmittance is observed at a strip number of 50, whereas the highest reflectance occurs at a strip number of 40, with the combined lost and transmitted energy reaching 1.84 dB.

To reduce parasitic capacitances and SAW generation due to the connecting strips, the connection strips were alternately placed, one at the top and one at the bottom (Type2 RMSC in Fig. 2a). The distances between connection strips in Type2 RMSC are greater than those in Type1 RMSC, resulting in lower connection strip capacitances. The maximum simulated reflectance increases from 65.4% for Type1 RMSC to 69.3% for Type2 RMSC, as shown in Fig. 2c. The simulated average reflectance for type2 RMSCs with apertures of 40 wavelengths, 70 wavelengths, and 100 wavelengths was calculated, as shown in Fig. 2d. The RMSC with a short aperture has smaller RMSC strip capacitance and is susceptible to parasitic capacitances from connection strips, requiring more strips to achieve the highest reflectance. Additionally, the RMSC with a shorter aperture has smaller ohmic loss and higher maximum reflectance. The RMSC with an aperture of 40 wavelengths achieves a maximum reflectance of 83.3% at 45 strips. Further shortening the aperture improves reflectance but may introduce significant diffraction loss in SAW RFID.

A Type2 RMSC with 45 strips and an aperture of 40 wavelengths was fabricated for experimental validation, with its transmittance, reflectance, and loss spectra shown in Fig. 2e. The near-zero measured transmittance aligns closely with simulations of the parasitic-inclusive model. However, a 0.33 dB discrepancy in energy loss was experimentally observed, potentially attributable to SAW radiation from connection strips, fabrication-induced and environment-induced errors, and bulk wave conversion. As discussed previously, the charges distributed on connecting strips excite weak SAWs. This phenomenon is not included in the simulation and could contribute to the discrepancy. Additionally, the electrode thickness deposited via electron-beam evaporation was non-uniform across the wafer, leading to slight variations in ohmic loss among devices. Exposure to airborne dust and moisture during testing changed the propagation loss of surface acoustic waves on the free surface. Therefore, fabrication-induced and environment-induced errors are potential factors for the observed discrepancy. Moreover, bulk wave conversion occurring at the left and right edges of the RMSC strips cannot be fully captured in the simulation, which could also contribute to the discrepancy. The simulation results of the ideal model deviate from experimental data, rendering this model unsuitable for RMSC design optimization. Crucially, the RMSC maintains approximately 77.8% average reflectance across 393 to 473 MHz, resulting in only 1 dB of energy loss. The high reflectance effectively reduces the energy loss of the device and enhances the interrogation distance of the wireless SAW RFID system. Additionally, the wide frequency range contributes to reducing the peak width of the time domain response, thereby expanding coding capacity and increasing measurement accuracy. These characteristics make the RMSC suitable for application as an SAW RFID reflector.

To compare the performance of RMSC with traditional reflectors, time domain responses of open-circuited (OC) and SC reflectors with varying electrode numbers were simulated using the models shown in Fig. 2S. The results demonstrated that when the electrode number exceeded 20 for the OC reflector or 40 for the SC reflector, strong internal reflection between electrodes occurred. Further increase in the electrode count did not significantly enhance the peak amplitude. The reflectances of the SC reflector with 20 electrodes and the OC reflector with 40 electrodes were both below 21%, a value significantly lower than the reflectance achieved by the RMSC reflector.

SAW RFID using RMSCs with maximum reflectivity

A novel SAW RFID architecture employing RMSC technology (referred to as RMSC SAW RFID) is proposed in this section. Two optimized RMSCs, serving as high-performance reflectors, are positioned on both sides of a single-electrode-type bidirectional IDT, as illustrated in Fig. 3a, b. The IDT with 8 electrode pairs operating at the fundamental harmonic frequency can achieve an available bandwidth of more than 80 MHz. The designed SAW RFID exhibits three distinct high-amplitude peaks in the time domain. SAWs excited by the IDT propagate toward RMSCs and are then reflected back to the IDT. A portion of the reflected signals is converted into electrical signals, forming the first and second peaks with propagation distances of 2L1 and 2L2, respectively. The remaining waves propagate and are reflected by another reflector, generating the third peak with a propagation distance of 2L1 + 2L2.

Fig. 3: Layout, photo, impedance matching circuit, and comparison of the performance of the fabricated SAW RFID with optimized RMSCs with simulation results.
figure 3

a Schematic layout of the SAW RFID with RMSC reflectors. b Photo of the fabricated chip. c Schematic of impedance matching circuit for the SAW RFID. d Measured Smith chart of the unmatched and matched SAW RFIDs. e Measured frequency domain response of the unmatched and matched SAW RFIDs. f Measured time domain response of the unmatched and matched SAW RFIDs

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The impedance mismatch between the IDT and the 50 Ω system is another critical factor contributing to energy loss. Increasing the number of IDT finger pairs helps align the IDT impedance closer to 50 Ω. However, a larger number of finger pairs significantly reduces the device’s bandwidth. Additionally, this increase leads to higher internal reflections, potentially altering the peak shape in the time domain. To address this issue, an impedance matching circuit is implemented to eliminate the impedance mismatch at the IDT interface, as shown in Fig. 3c. The matched IDT exhibits an impedance closer to 50 Ω, with a wide operational bandwidth, as shown in Fig. 3d, e. This circuit reduces the input reflection at the IDT to 50 Ω system interface by approximately 20 dB, evidenced by the reduced peak amplitude at time t = 0 in matched versus unmatched devices in Fig. 3f. The bandwidth of SAW RFID is over 80 MHz. However, the relative bandwidth of commonly used compact antennas is typically less than 10%. In practical wireless measurements, the available bandwidth of SAW RFID systems is often constrained by antenna limitations. To assess performance under real-world conditions, the operational bandwidth was set to 40 MHz in this study. The peak amplitudes in the time domain corresponding to a 40 MHz operational bandwidth are listed in Table 2. The peak amplitude in the time domain employed in this study aligns conceptually with the negative value of insertion loss referenced in prior work7. Insertion loss is a frequency-domain parameter that quantifies signal energy attenuation. However, its effects are directly observable in time domain waveforms due to the Fourier relationship between domains. In SAW RFID systems, insertion loss is often used to characterize the peak amplitude in the time domain. In this manuscript, we utilize the peak amplitude in the time domain instead of insertion loss to reduce ambiguity. Impedance matching enhances the amplitude of the first and second peaks by approximately 7.4 dB. Concurrently, matching reduces the unconverted components in RMSC-reflected SAW echoes, resulting in diminished improvement for the third peak amplitude (3.4 dB). There is a spurious signal between the 2nd and 3rd peaks due to a wave running twice the distance L1.

Table 2 The peak amplitudes of the RMSC SAW RFID in the time domain
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A comparison between our work and state-of-the-art SAW RFID devices with high peak amplitudes is provided in Table 3. Short-circuited (SC) gratings satisfying Bragg conditions are widely applied in conventional SAW RFID designs. The reported maximum peak amplitude for the SAW RFID with SC gating reflectors and a bidirectional IDT is around -30 dB. The peak amplitude of this type of SAW RFID can be further improved by replacing the bidirectional IDT with a single-phase unidirectional transducer. However, this reduces the relative bandwidth to 2.13%, which compromises the coding capacity and measurement accuracy. Another SAW RFID structure, termed the connected IDT (CIDT) SAW RFID, achieves low energy loss as reflectors are unnecessary in this structure. The reported maximum peak amplitude for the CIDT SAW RFID is around −18 dB. The RMSC-based SAW RFID developed in this work achieves a peak amplitude of −10.6 dB, which is at least 7.4 dB higher than that of conventional SAW RFID devices. Consequently, wireless SAW RFID systems utilizing the proposed RMSC structure can achieve a reading range at least 1.53 times greater than the same systems employing other types of SAW RFID, as a 12 dB reduction in energy loss doubles the readout distance.

Table 3 Comparison between our work and SAW RFID devices with high peak amplitudes
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The temperature characterization of the fabricated RMSC SAW RFID was measured. Time delay combinations and phase combinations extracted from the three reflected peaks are plotted as a function of temperature from −20 to 90 °C in Fig 4a. Here, τi and φi (i = 1,2, or 3) are the time delays and phases of the three reflectors. τ31 denotes τ3−τ1, φ31 represents φ3−φ1, and φ3221 is defined as (φ3−φ2)−(φ2−φ1). Substrate thermal expansion and temperature dependence of crystal stiffness constants induce a linear increase in propagation length and decrease in the phase velocity with rising temperature, consequently increasing time delays linearly. Both time delays and unwrapped phases exhibit linear thermal dependencies (ordinary determination coefficients R2 > 0.9999). The scattering loss of SAW arises from thermal lattice vibrations that intensify with temperature, thereby reducing the reflected peak amplitude. Longer propagation paths exhibit higher susceptibility to this effect. As temperature increases from −20 to 90 °C, the first, second, and third peak amplitudes decrease by 1.3, 1.7, and 2.9 dB, respectively, as shown in Fig 4b.

Fig. 4: Results of temperature measurements on RMSC SAW RFIDs.
figure 4

a Measured τ31, φ3221, and φ31 as a function of temperature from −20 to 90 °C. b Measured amplitudes of first, second, and third peaks in the time domain. c Fluctuation of the temperature signal calculated from the unaveraged measured signals τ31, φ3221, and φ31 of the SAW RFID, and PT100 under 0, 30, and 60 °C temperature load

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Figure 4c compares temperatures determined by RMSC SAW RFID against PT100 reference values. Testing at 0 °C, 30 °C, and 60 °C yielded 500 datasets per temperature under low signal-to-noise ratio conditions. Despite exceeding the unambiguity measuring range of φ3221 and φ31, the 2π phase ambiguities were effectively eliminated by a multistep evaluation scheme33, as evidenced by error-free measurements. The 6σ uncertainties of the temperature measurements are summarized in Table 4. Experimental results indicate that phase estimations exhibit significantly higher precision than time delay estimations. Chamber temperature fluctuations dominate the internal temperature uncertainty of φ31, making φ31’s intrinsic error negligible. Consequently, the temperature uncertainty of φ31 matches the PT00 reference. Omission of higher-order terms in the estimation model introduced minor bias (defined as the average deviation between estimated and PT100 reference temperature).

Table 4 The 6σ uncertainties of the temperature results
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The observed characteristics of high linearity, low loss across a wide temperature range, and closed experimental-simulation matching demonstrate the excellent suitability of RMSC SAW RFID technology for temperature measurement.

Materials and methods

Numerical analysis

Two-dimensional finite element models were developed to evaluate the RMSC performance, with the RMSC positioned midway between the IDTs, as illustrated in Fig. 5a. The S21 parameters from the delay line model in Fig. 5b eliminated the IDT influence. The reflectance (R), transmittance (T), and loss (L) of the RMSC were calculated by:

$$\left\{\begin{array}{l}R={|{S}_{11,\mathrm{RMSC}}/{S}_{21,\mathrm{DL}}|}^{2}\\ T={|{S}_{21,\mathrm{RMSC}}/{S}_{21,\mathrm{DL}}|}^{2}\\ L=1-{|{S}_{11,\mathrm{RMSC}}/{S}_{21,\mathrm{DL}}|}^{2}-{|{S}_{21,\mathrm{RMSC}}/{S}_{21,\mathrm{DL}}|}^{2}\end{array}\right.$$
(1)

where Sij,RMSC represents the S parameter of the RMSC model, and S21,IDT denotes the reference delay line S21. Time-domain window functions suppressed triple reflection interference23,34,35.

Fig. 5: Simulation models and parasitic parameters.
figure 5

a The simulation models of the delay line with the RMSC (type2) for calculating its reflectance, transmittance, and loss. b The simulation model of the delay line without the RMSC for reference. c The photo and measured resistances for different normalized strip lengths (the length of the aluminum strip line divided by its width). d The simulation model and simulated parasitic capacitances between adjacent connection strips for different capacitor identities

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Distributed resistors (RIDT for IDT finger, Ri for strips) and capacitors (Ci for adjacent connection strips) modeled parasitic effects. Aluminum strip resistances were measured employing four-terminal Kelvin sensing with a Keysight 34461A multimeter, as shown in Fig. 5c. Direct current resistance data showed linear correlation with normalized strip length (length/width ratio), yielding an experimental sheet resistance of 0.29 Ω/square. For the applied aluminum electrodes operating at 433 MHz, the calculated skin depth is approximately 3.9 µm. Since the physical thickness of the electrode (0.15 µm) is significantly less than the skin depth, the skin effect is negligible. The alternating current does not have sufficient space to be confined to a thin surface layer and instead distributes relatively uniformly across the entire cross-section. Consequently, the radio frequency resistance of the aluminum electrode remains close to its direct current resistance. Three-dimensional finite element simulations quantified parasitic capacitances on 128°YX-LiNbO3, applying potentials to adjacent strips and extracting capacitances from charge values, as shown in Fig. 5d.

Fabrication procession

The designed SAW devices in this study were fabricated using the standard photolithography and lift-off technique, as shown in Fig. 6. Initially, a positive photoresist (S1805, Resemi) was spin-coated onto the surface of the 128°Y cut LiNbO3 and baked to enhance adhesion. Subsequently, the chip pattern was transferred from the photomask to the wafer through photolithography (NSR-2005i9C, Nikon), followed by development. Thereafter, a 3 nm titanium adhesion layer and 150 nm aluminum (with 2 wt% copper) layer were sequentially deposited on the wafer using an electron-beam evaporator (Ohmiker 50B, Cello Technology). Finally, the wafer was immersed in N-methyl-2-pyrrolidone (NMP) to complete the lift-off process.

Fig. 6: Schematic diagram of the RMSC SAW RFID fabrication procession.
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The devices were fabricated by wafer spin coating, photolithography, development, deposition, asn lift-off in sequence

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Experimental setup and measurement

To eliminate the impedance mismatch between the IDT and the 50 Ω system, an impedance matching circuit was designed. The measured impedance of the SAW RFID deviates from the intrinsic impedance of the IDT due to signal reflections between the reflectors and the IDT. To determine the actual IDT impedance, silicone rubber was applied between the reflectors and the IDT to absorb the excited SAWs, as depicted in Fig. 7a. The SAW devices were mounted on a printed circuit board for S parameter measurements, with impedance matching circuits integrated prior to the PCB pad, as illustrated in Fig. 7b. A microstrip line section was connected between the PCB pad and the coaxial cable. The port extension method was implemented after calibrating the vector network analyzer and the cable to compensate for phase shifts induced by the microstrip line and SMA connector in the measured impedance. Following port extension, the impedance at 433 MHz was corrected from 18.5246 - j66.3539 Ω to 78.1648 - j149.1173 Ω, corresponding to a shift from point a to point b in Fig. 7c. A shunt capacitor of 0.5 pF was introduced to transition the impedance at the center frequency from point b to point c. Subsequently, a series inductor of 47 nH was added to adjust the impedance from point c to point d (50 Ω).

Fig. 7: Experimental setup for impedance matching procession and temperature measurement.
figure 7

a SAW device configuration for IDTimpedance measurement. b Test fixture setup for characterizing SAW RFID properties. c Measured impedances before and afterport extension. d Schematic of the experimental setup for the RMSC SAW RFID temperature measurement. e Schematic diagramof the multistep evaluation scheme

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For temperature characterization, the RMSC SAW RFID was mounted in a high-precision chamber (Espec GSH-24V). A vector network analyzer (Keysight E5071C) monitored S11 parameters continuously, synchronized with platinum resistance temperature detector recordings (Heraeus PT100 1/3B connected to Keysight 34461A). A 20 dB attenuator emulated low SNR conditions, as schematically shown in Fig. 7d. Temperature was determined from signal delay time (τ) and phase (φ). Although temperature estimations using phases offer higher precision for sensing applications compared to estimations using delay times36, their measurement range is limited by the 2π phase ambiguity. The extracted phase estimation may correspond to multiple temperature solutions if the temperature measuring range exceeds a range corresponding to more than 2π phase variation37. This challenge can be effectively addressed through the implementation of a multistep evaluation scheme without compromising phase precision31. For the designed RMSC SAW RFID, the scheme is τ31 → φ3221 → φ31. Initial temperature Tτ31 from τ31 locates the period where the phase φ3221 resides. A higher-precision temperature, Tφ3221, is obtained from φ3221. Then, Tφ3221 determines φ31 period and calculates the temperature Tφ31, which exhibits much higher precious than the Tτ31, as illustrated in Fig. 6e. The wireless measured time delays τi and phases φi of the first, second, and third peaks vary with temperature T and the readout distance between the SAW RFID tag and transceiver d:

$$\left\{\begin{array}{l}{\tau }_{i}={\tau }_{i,0}(1+\mathrm{TCD}(T-{T}_{0}))+2d/c\\ {\varphi }_{i}=2\pi {f}_{0}{\tau }_{i}\\ {\tau }_{i,0}=2{L}_{i}/{v}_{0}\\ {\tau }_{3,0}={\tau }_{1,0}+{\tau }_{2,0}\end{array}\right.$$
(2)

where τi,0 represents the time delay of the SAW RFID under temperature T0, v0 is SAW velocity, c is the speed of light, f0 is operating frequency, and TCD (temperature coefficient of time delay) shows the SAW’s sensitivity to temperature variations. Measurement errors induced by the readout distance d variation are eliminated through differential signal processing.

Conclusion

In this article, a novel SAW RFID-type temperature sensor using reflective MSC as reflectors is proposed. The SAW RFID has a low energy loss due to the high reflectance of the reflectors. The performance of the reflective MSC was predicted by incorporating the parasitic effects into the simulation model. The optimal RMSC strip number with the highest reflectance was found based on the improved simulation model. The fabricated RMSC shows good consistency with the simulation result of the practical model, with a high energy reflectivity of 77.8%. A SAW RFID based on RMSC was designed, fabricated, and tested. The fabricated 128°YX-LiNbO3 RMSC SAW RFID shows extremely high peak amplitude over a wide temperature range. The peak amplitudes of the first, second, and third peaks are −10.63 dB, −11.30 dB, and −13.67 dB. The experiments show that the device performs excellently as a temperature sensor. The R2 of the estimation-temperature relationship is over 0.9999, and the temperature resolution is better than 0.07 °C.

The current RMSC SAW RFID structure can be further improved. The required strip number of the RMSC reflector is inversely related to the electromechanical coupling coefficients of the acoustic wave mode. Using a substrate with a high electromechanical coupling coefficient enables the RMSC to achieve higher reflectance for the ohmic loss, as fewer strips cause lower ohmic loss. Rayleigh modes on YZ-LiNbO3 and 128°YX-LiNbO3 single-crystal substrates are widely employed in the SAW RFID device. However, their electromechanical coupling coefficients rarely exceed 6%. Heterostructure multilayer substrates may serve as better alternatives; they can excite SAWs with significantly higher electromechanical coupling coefficients. Additionally, the current IDT design exhibits strong reflectivity to incident SAWs, particularly after impedance matching. This induces the multiple transit reflections, which reduce the coding capacity. This issue can be mitigated through IDT design modifications. For example, employing a split-finger electrode configuration can effectively reduce the IDT reflectivity, as this design inherently suppresses mechanical reflections. However, this approach requires a finer critical dimension for the electrodes. Reducing the electrode thickness is another method to lower IDT reflectivity. It may adversely affect the performance of RMSC reflectors by increasing ohmic loss, unless advanced alignment techniques are incorporated during fabrication to achieve two different electrode thicknesses in a single device.