Bimorph material/structure designs for high sensitivity flexible surface acoustic wave temperature sensors

A fundamental challenge for surface acoustic wave (SAW) temperature sensors is the detection of small temperature changes on non-planar, often curved, surfaces. In this work, we present a new design methodology for SAW devices based on flexible substrate and bimorph material/structures, which can maximize the temperature coefficient of frequency (TCF). We performed finite element analysis simulations and obtained theoretical TCF values for SAW sensors made of ZnO thin films (~5 μm thick) coated aluminum (Al) foil and Al plate substrates with thicknesses varied from 1 to 1600 μm. Based on the simulation results, SAW devices with selected Al foil or plate thicknesses were fabricated. The experimentally measured TCF values were in excellent agreements with the simulation results. A normalized wavelength parameter (e.g., the ratio between wavelength and sample thickness, λ/h) was applied to successfully describe changes in the TCF values, and the TCF readings of the ZnO/Al SAW devices showed dramatic increases when the normalized wavelength λ/h was larger than 1. Using this design approach, we obtained the highest reported TCF value of −760 ppm/K for a SAW device made of ZnO thin film coated on Al foils (50 μm thick), thereby enabling low cost temperature sensor applications to be realized on flexible substrates.


Introduction
Temperature monitoring is essential for electrical equipment and mechanical systems; thus various temperature sensors, such as semiconductor oxide sensors, optical fiber sensors and infrared sensors, have been widely used in industry [1][2][3][4] . However, current temperature sensing technologies have serious limitations associated with power supply and data transmission. Passive operation and wireless interrogation are often required in many hazardous environments, such as moving machinery, contaminated areas, chemical or vacuum chambers and high voltage plants. In these applications, acoustic waves, especially surface acoustic wave (SAW) based sensors have significant advantages as they provide capabilities of wireless readout, battery-free operation, real-time and remote data communication [5][6][7][8][9][10] . They also have other merits including high accuracy, low or no maintenance, light weight, reliability and robustness.
In order to use an acoustic wave (for example, SAW) sensor for temperature sensing, one of the key parameters is the temperature coefficient of frequency (TCF), defined as rate of frequency change with temperature relative to a resonant frequency. The TCF values of SAW devices are linked with their thermal stability 9,11 . Most materials have negative TCFs, which means the frequency of the SAW device decreases with an increase in temperature. However, for most sensing applications, such as those for gas, pressure, humidity, chemicals and biosensing, thermal stability is highly desired.
Therefore, most researchers use techniques to reduce the TCF values or achieve a temperature compensation during sensing. This can be easily implemented using an additional compensation layer such as silicon dioxide [12][13][14][15] or alumina 16,17 , both of which have positive TCFs. In contrast, for temperature sensing applications, a large absolute value of the TCF with a good linearity is desired. However, so far, there are few reports on how to maximize the TCF values by choosing different materials and/or designing various multilayer structures.
Based on literature, the TCF values of SAW devices made from common piezoelectric materials such as LiNbO3, ZnO, AlN, and GaN generally range from -18 ppm/K to -75 ppm/K 10,18-21 . Therefore, in order to increase temperature sensitivity, most researchers increased the resonant frequencies of SAW devices (up to hundreds of MHz and GHz), which will increase the responses for sensing but dramatically increase the fabrication costs and complexity of process/measurement. An alternative approach is to maximize the TCF values of SAW devices by choosing suitable low-cost materials and/or multilayer designs, without the need for significant increase in resonant frequencies.
A further essential challenge in temperature sensing is to detect or monitor changes on a curved or bendable surface, such as those for healthcare applications, and for this purpose, a temperature sensor needs to be mechanically flexible or bendable. High TCF readings have previously been reported for ZnO film based SAW devices fabricated onto polymer (such as polyimide), which are flexible substrates [22][23][24]

Principle and design methodology for achieving high TCFs
The TCF of a layered SAW structure depends on both the temperature variation of acoustic properties and temperature expansion coefficient (TEC) of each material. The theoretical TCF is defined by the following equation 9 : where f, T, vp, λ and α' are frequency, temperature, phase velocity, designed wavelength and TEC of the multi-layer structure, respectively. For Al, the TEC value is about 23.6 ppm/K, which is quite large among the most commonly used metals and ceramic materials. Apart from the TEC values, there are two other factors which are critical for the TCF values of the SAW devices, and thus will be discussed as follows.

a. Deformation of bi-layer from thermal expansion
The interfaces between the substrate (such as Al foil or thin plate) and ZnO thin film are assumed to be perfectly bonded during heating/cooling from room temperature to 150 o C, where strain due to lattice mismatch is neglected in the analysis. As the temperature increases, the differences in the TECs of ZnO and Al substrate result in the bending of the layered structure. This deformation will also contribute to the strain values due to thermal expansion of two layers, which can be expressed as: where α, F, w, h, and E are the TEC, force, width, thickness and Young's modulus of each layer respectively, whilst 1⁄ is the curvature of the bending structure. We assume that during heating/cooling, there is an equilibrium of moments and no slippage, therefore, From Eqs. (2) and (4) By defining a factor b where ℎ = • ℎ , the strain in the ZnO layer is: Therefore, the design wavelength λ is no longer a constant during the temperature change, i.e., The TEC of the Al is much larger than that of ZnO, and also is larger than ∆ , thus ′ > . As the Al layer expands and deforms more easily than ZnO, it will contribute more to the frequency shift due to the thermal expansion.

b. Temperature coefficient of moduli
If the substrate is thick enough compared to the wavelength, Rayleigh based SAWs will be dominant. However, due to thin nature of Al foils and plates, Lamb waves will be generated if the thickness of Al is of similar order to the ZnO film 9 . The phase velocities vp of the A0 mode wave (vpA) and S0 mode lamb wave (vpS) propagating in a homogeneous and isotropic plate are given by 26 : , ν is Poisson's ratio and ρ is the density of the composite.
For both of these Lamb wave modes, we have, Unlike those of the polymers, the temperature coefficients of density for metals and ceramics are quite small from room temperature up to 100 o C (the range used in the experimental measurement). Therefore, the densities of both ZnO and Al are assumed to be constant values in this study, whereas the moduli of the materials could be slightly changed with temperature, which could be one of the factors for changes of TCF values. There were previous reports that the temperature moduli coefficients (TMCs) of micro-size of Al wires were much larger than that of the bulk Al 27,28 .
When the Al foil or plate becomes much thinner, the Al material below each interdigital transducer (IDT) finger would be within micro sizes (both in thickness and in-plane size). Therefore, it is expected that the elastic properties of thin Al foils would contribute significantly to the device's TCF. Accordingly, we have designed different SAW devices with various Al substrates thicknesses and various wavelengths of IDTs to measure the TCF values.  Table 1.  Figs. 1b and 1c). However, with further increase of Al substrate thickness, the changing trends of the TCF values are different. Fig. 1d    The changes of wave modes can also be understood as their dependence on the ratio between the designed wavelength and the thickness of the device (λ0 / h). As the ratio of λ0 / h is much larger than 1, the device excites Lamb waves; whereas the device excites Rayleigh and Sezawa modes when the ratio is much smaller than 1.

Results and discussion
Accordingly, a Rayleigh-Lamb hybrid wave is excited when the ratio is roughly equal to 1 for this study. The wave modes of all the devices were verified from both experimental measurements of reflection spectra S11 and FEA modeling of surface vibration modes; with examples shown in Fig. 2. further larger value of λ will occupy a large special area on the device surface, and the frequency will be down to a few MHz, which is not good for precision sensing application. Whereas if the Al foil is too thin, the lithography process will become difficult. If the Al substrate is thicker, the film stress generated during the deposition process (due to the ion bombardment during sputtering, and the lattice mismatch and the thermal expansion coefficient mismatch between the ZnO film and Al substrate) causes the increased curling of the ZnO/Al film, which increases the difficulty for lithography process. Besides the absolute values of the TCF readings, a good linearity is also critical for a precision temperature sensor. The S11 frequency signals for SAW devices on all the Al substrates generally show highly linear frequency shifts as a function of temperature.

Conclusion
In summary, we have presented an approach to designing layered SAW structures based on ZnO/Al foils and plates to maximize the TCF readings for flexible-substrate temperature sensing applications. Theoretical and FEM simulation were used to optimize the bimorph ZnO/Al structures and achieve high TCF values of the ZnO/Al SAW devices. Example devices were fabricated on ZnO coated Al foil and plates with various thicknesses. A normalized wavelength ℎ ⁄ was chosen to describe the changes of the TCF values, and the TCF readings of the ZnO/Al SAW devices show dramatic differences when the normalized wavelength of ℎ ⁄ is larger than unity.
Results showed that an Al foil (50 μm thick) with 400 μm wavelength achieved the highest TCF reading (-760 ppm/K) ever reported, which is promising for a low cost flexible-substrate temperature sensor applications.

a. Experimental methods
ZnO films were selected as the piezoelectric layer and were deposited on Al foil (50 5 μm), thin (200 μm) and thick (600 μm and 1.6 mm) Al plate using direct-current (DC) magnetron sputtering deposition. During the deposition process, a zinc target with 99.99% purity was used, with an Ar/O2 flow ratio of 6/13 sccm, DC target power of 420 W, and a gas pressure of 6 × 10 -4 mbar. The distance between the target and the sample holder was 100 mm, and the holder was rotated during the deposition to improve the uniformity of thin films. The thicknesses of all ZnO thin films were ~5 μm controlled by the deposition time at a rate of ~5.6 nm/min. X-Ray Diffraction (XRD, SIEMENS D5000) was used to obtain the crystalline phases of ZnO thin films and results showed that the film texture is highly c-axis oriented, i.e., with a strong (0002) crystal orientation (see Supplementary Information).
The IDTs composed of 20 nm Cr and 100 nm Au were prepared using a conventional photolithography and lift-off process. The IDTs had wavelength λ0 values from 64 μm up to 800 μm, with 30 pairs of fingers and an aperture of 5 mm. During the TCF measurement, the temperature was changed from room temperature to around 100 ºC within an oven and verified with a temperature sensor fixed on top of the acoustic wave device (more details can be seen from Supplementary Information)., and the resonant frequency of the device was recorded using a network analyzer (Keysight HP8753A).

b. Data availability
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.