Thermomechanical and Creep Behaviors of Multilayered Metallization Systems Developed for High‐Temperature Surface Acoustic Wave Sensors

The structural stability and durability of a sensing device at high‐temperatures (HT) have important effects on its functionality and reliability. This becomes more critical in the devices that work based on the surface acoustic waves (SAW). In this study, the thermomechanical and creep behaviors of the metallization systems, RuAl, MoLa, and Mo suggested for the electrodes of HT‐SAW sensors are investigated. Several experiments are designed to obtain the state and the value of stress in the films deposited on a Si [100] substrate caused by the fabrication process and the operational conditions. Results show that after the film deposition, the intrinsic compressive stress in the MoLa film is significantly lower than the other films. However, after annealing the samples, the lowest residual stress is reached in the Mo. Linear stress variations during the thermal cycling of the annealed samples are obtained for all metallizations. To study the durability of the films at HT, the creep behavior of the samples is investigated by keeping them at a temperature of 600 °C for 10 h. The creep rate and its constitutive equation for the films are obtained. It is observed that the creep rate of MoLa and Mo films is much lower than RuAl.


Introduction
Thin films consisting of pure molybdenum (Mo), molybdenumlanthanum oxide (MoLa), and ruthenium-aluminum (RuAl) are suggested metal films for electrodes of high-temperature (HT) surface acoustic wave (SAW) sensors based on our recent extensive researches on different multilayered thin film systems. [1][2][3][4][5][6][7][8][9][10] Despite the high performance temperature of the metallization systems made of these metals, they have characteristics such as low electrical resistivity and corrosion resistance, which make them a suitable choice for SAW sensor electrodes. [2,11,12] DOI: 10.1002/admt.202201979 HT-SAW sensors can be used for wireless sensing of temperature, pressure, and detection of gases, in turbine rotors, furnaces, ovens, etc., without any batteries or high sources of energy. A very high reliable sensing operation at different high temperatures between 300°C to 900°C is expected for a HT-SAW sensor, which depends on the stability and durability of the electrodes (such as interdigital transducers (IDTs)) and the substrate materials. However, defects caused by stresses due to the deposition process, thermal variations, and creep such as damages in the form of cracking, buckling, or blistering in the film or at the film-substrate interface, affect the operation of a SAW sensor. The residual stress in the film due to the deposition and annealing processes has a significant influence on the adhesion, the thermomechanical behavior of thin films, [13][14][15] and their electrical resistivity. [16] Therefore, an investigation of stress variations in the thin films caused by the fabrication process, as well as due to the operational conditions is important for the design, processing, and lifetime performance of HT-SAW sensor components.
Most studies on the metal films with HT applications have only focused on the material aspects for the development of a stable metallization system at high temperatures, such as the investigation of functional cover and barrier layers, tailoring a multilayer metal film for special applications, deposition, and stabilization process. [2,[10][11][12]17] So far, very little attention has been paid to the intrinsic stress due to the deposition process, as well as the thermomechanical and creep behaviors of these films. [2] Moreover, the comparison of the metallization systems' behaviors with each other would give some significant insights into the effectiveness of each film.
A conventional method for studying the stress in films is to measure the curvature variations of the film-substrate samples. In 1909, Stoney proposed an equation for the calculation of the stress in films based on curvature variations of the filmsubstrate samples. [18] Later, this equation was modified by other researchers to calculate the biaxial stress in a film deposited on a substrate. [19][20][21][22] www.advancedsciencenews.com www.advmattechnol.de There are several methods for the curvature measurement of a film-substrate sample. Using a stylus with physical contact to the sample surface is a very common method to measure the film curvature. However, this method can have an impact on the measurement caused by contact force and is not applicable for the in situ curvature measurement during the film deposition or at high temperatures. Indeed, the results of curvature measurements are sensitive to environmental noises. Measuring film strain using X-ray diffraction is another method that is suitable for a single-layer film and needs much time and expertise. [23,24] The curvature measurement with optical interferometry is another method that is suitable in the case that the curvature is large enough, and when special measurement equipment is not available. [21] Scanning the film surface with an optical laser beam and measuring the reflected beam deflections is a solution for the above-mentioned limitations which gives an accurate in situ measurement of the film-substrate curvature during the deposition and at high temperatures. [21] A multibeam optical laser can be used to reduce the measurement time and to measure continuously the biaxial curvature variations of the film-substrate sample without moving optical components. [25] A cluster of an in situ multibeam optical sensor (MOS) system on an ultrahigh vacuum (UHV) pressure chamber equipped with an automated heating system was developed for such a low-noise measurement, which is used in this study.
In this paper, a comparative study was done to investigate the stress variations due to the deposition and annealing, as well as during the typical temperature changes for sensor applications including thermal cycling and isothermal heating in Mo, MoLa, and RuAl films proposed for HT SAW sensor electrodes. Besides, the behavior of these unstructured films during 10 h of isothermal heating has been studied, which is important for the creep characterization of the sensor components. In addition, the constitutive equations of an established creep model for thin metal films are obtained from the experiment results and discussed.

Specimen Preparation
Four sample systems made of three different thin metal films of Mo, MoLa, and RuAl were deposited on a double-sided polished single crystalline silicon (Si) substrate with [100] orientation. The thickness of the Si substrate was 200 μm with a layer of 1 μm thermally grown SiO 2 on both sides to prevent the reaction of the Si with air. Before depositing the metal film, the Si wafer was cut into square samples with a length of 15 mm. Then, a barrier layer of AlN, as well as SiO 2 with 20 nm thickness each, were deposited on the substrate to prevent a chemical reaction between the metal film and the substrate at high temperatures. Despite the fact that the AlN layers contained 16 at% of oxygen, they are denoted as AlN in this paper. The same layers were also deposited on top of the films as cover layers to prevent the oxidation of the metal films in the real application. These barrier and cover layers were used for all samples. More descriptions about the reasons for the selection of such barrier and cover layers systems are available in the previous studies. [1,2,5,8,12,26] The schematic views of the metallization systems used in this study are shown in Figure 1. It is worth mentioning that the Si substrate is not used in the real application and the reason for using it as a substrate in this study is the isotropic behavior of the Si [100] in the wafer plane (cubic anisotropy) which is more convenient for the strain-stress and creep calculations compared to an anisotropic piezoelectric material which is required to fabricate SAW sensors. Moreover, the barrier layer between the metal film and substrate prevents the chemical interactions between the metal and the substrate significantly. Therefore, extended films on a cubic anisotropic Si substrate serve as a model system to perform the first straightforward experiments to study the fundamental thermomechanical and creep behavior of the thin film systems suggested for HT applications.
All deposition processes were done in a high vacuum chamber (Creamet 400 CI3, CREAVAC GmbH, Germany) with an average vacuum pressure of 10 −6 mbar, equipped with a rotating holder for spinning the substrate during the deposition for having a homogeneous film deposition. The AlN layers were deposited at room temperature by reactive active RF magnetron sputtering while a mixture of Ar and N 2 gasses with a ratio of 40:8 was applied. The SiO 2 layers were deposited by the same method at the substrate temperature of 180°C using Ar and O 2 gasses with a ratio of 6:1.
To prepare the samples of Mo metallization, a layer of Mo with a thickness of 100 nm was deposited at the substrate temperature of 400°C by DC magnetron sputtering (Figure 1a). In the other group of samples, a multilayer film consisting of Mo and oxidized Lanthanum (La 2 O 3 ) was deposited using a stepwise process. For the preparation of this film, a layer of Mo with a thickness of 11 nm was deposited, then a layer of La with 0.125 nm nominal thickness was sputtered on its top, and then O 2 gas was applied to the sample to form La 2 O 3 . This process was repeated eight times and at the end, a layer of Mo with 11 nm thickness was applied to get a total film thickness of 100 nm (Figure 1b).
The RuAl samples were deposited as a multilayer system, starting with 7 nm of sputtered pure Al, followed by 55 nm of cosputtered RuAl, then again 7 nm of pure Al, 55 nm of RuAl, and as the uppermost layer, again 7 nm of pure Al were added, resulting in a total nominal thickness of 131 nm (denoted as RuAl-131, Figure 1c). In some applications, for example, SAW sensors operating at GHz frequency ranges, electrodes with less metal thickness have some advantages. Therefore, only one layer of RuAl and two layers of Al with the same thickness as the previous RuAl stacks were deposited to make samples with a nominal metal layer thickness of 69 nm (denoted as RuAl-69, Figure 1d). Details of the deposition of the films were described in. [2,11,12]

Specimen Curvature Measurement
The variations of stress in the films were obtained by measuring the changes in the sample curvature using a multibeam optical sensor (MOS) (K-Space Associates Inc., USA). The MOS was installed on an UHV chamber (Creamet 400 CI3, CREAVAC GmbH, Germany) with an average vacuum pressure of 10 −9 mbar equipped with a radiation heater below the sample holder (Figure 2a). The laser source of the MOS device produces a laser beam which is divided into two sets of perpendicular beams by x and y etalons, creating an array of 3 by 3 laser spots on the sample surface. A high-speed camera records the spaces between the spots on the sample, which are used for the calculation of the curvature variations. [25] Using this method, the curvature of the sample is measured in two directions perpendicular to each other, which results in a more precise value of the sample curvature as compared to a single-direction measurement.
The stress in the film ( f ) is calculated by substituting the measured sample curvature and some material parameters in the modified Stoney's equation; [18,22] where R is the curvature radius of the sample measured by MOS, h f and h s are the thicknesses of the film and the substrate, respectively, and M s is the biaxial modulus of the substrate which in Si [100] is obtained by: where E s and s are the elastic modulus and poison's ratio of Si [100] which are equal to 130 GPa and 0.28, respectively. [27] The modified Stoney's equation (Equation (1)) gives the average biaxial elastic stress throughout the film thickness if the substrate is thick compared to the film, while it is thin enough to bend due to the film stress. The substrate should bend only because of the stress in the film, thus it should be free with no constraints. Therefore, a sample holder was designed as shown in Figure 2a, in which the sample is only in contact with three small ceramic balls with a very smooth surface and small contact area to the sample to minimize the friction force that could influence free bending.
The curvature radius of the substrate was measured before the film deposition as a reference curvature (R ref ). After deposition of the film system, the curvature of the same sample with identical adjustment on the sample holder was measured again (R). These two curvatures were subtracted to obtain the curvature variations of the sample due to the film deposition. Then, the average residual stress in the film system after the deposition, which is called as-deposited stress, was calculated by substituting the sample curvature variations in Equation (1). The stress variations in the film system were also obtained during the annealing, thermal cycling, and isothermal heating using the MOS system and Equation (1) as described.

Specimen Thermal Treatment Procedure
In the first step, after the deposition of the whole layer stack (i.e. barrier layers, metal film, and cover layers), the samples were annealed to stabilize the film microstructure. This was done at 900°C for 10 h in the UHV chamber with an average vacuum pressure of 10 −9 mbar. Figure 3a shows the temperature changes with time used for the annealing of Mo, MoLa, and RuAl samples.
Thermal cyclings between room temperature and 600°C, 700°C, as well as 800°C, respectively, were applied to the www.advancedsciencenews.com www.advmattechnol.de annealed samples with a heating and cooling rate of 2 K min −1 in the UHV chamber. The first two thermal cycling procedures were performed consecutive, as shown in Figure 3b. However, the thermal cycling at 800°C was performed as a separate cycle (Figure 3c). Subsequently, the samples were subjected to isothermal heating at 600°C for 10 h at the UHV condition to investigate the creep behavior of the films. For this purpose, the samples were heated up to 800°C with a rate of 2 K min −1 , then cooled down to 600°C, kept at this temperature for 10 h, and, finally, cooled down to room temperature (Figure 3d).

Specimen Microstructure Characterization
The morphology of the films in the annealed samples was determined by scanning transmission electron microscopy (STEM, Tecnai F30, FEI company, Hillsboro, OR, USA) and by scanning electron microscopy (SEM, Helios 5 CX, Thermo Fisher Scientific, Waltham, MA, USA) of cross-sections of the films. From the images obtained with a mode described in Figure 6, which is sensitive to the orientation contrast, the grain size distribution was evaluated.

Results and Discussions
The variations of stress in the film after deposition and during annealing, thermal cycling, as well as isothermal heating were investigated for all metallization systems and are discussed in the following subsections.

Film Stress Before and After Annealing
After the deposition of a metallization system, including metal film layer(s), as well as the barrier and cover layers, the film experienced a kind of residual stress which is categorized as intrinsic stress. This intrinsic stress which is caused by the manufacturing (i.e. deposition) process cannot be quantified easily during the sample preparation. Besides, there is no specific equation to calculate the intrinsic stress in the film due to the deposition. This is generally because different known and unknown factors affect the intrinsic stress in a film. In the sputter deposition process, the striking particle energy, the substrate temperature, the microstructure of the film, as well as the process parameters such as gas pressure, gas ratio, and power may have some effects on the value and the type of the intrinsic stress within the deposited film on the substrate. [28][29][30][31][32] The average residual stress throughout the thickness of the film system after the deposition process, which is called "asdeposited stress", was calculated using Equation (1) for the four metallization systems, and is presented in Table 1. According to this table, different values of stress remain in the films after deposition on the Si substrate, while the type of as-deposited Table 1. The calculated residual stress in the film systems (metal film + barrier and cover layers) after deposition (as-deposited) and after annealing (annealed). stress in all of the metallization systems is compressive. The minimum value of as-deposited stress was obtained for the MoLa film, while the maximum value was acquired for RuAl-131. The development of stress in the films during annealing was obtained and is shown as a graph with respect to the temperature variations in Figure 4. For the RuAl and MoLa samples, by increasing the temperature of the specimen from room temperature to 900°C, the compressive residual stress decreases to zero at a certain temperature value depending on the metallization, and subsequently, the film experiences tensile stress. In contrast to this, in the Mo sample, the compressive stress reduces to zero by increasing the temperature during isothermal heating up to 900°C, and then tensile stress occurs during cooling down to room temperature. This can be interpreted by grain growth in the films accompanied by the annihilation of defects formed during the deposition process. [21,33] Furthermore, the thermal expansion coefficient (CTE) of the Si substrate is lower than that of the metal film materials. These mismatches contribute to the high tensile stress during the cooling. Furthermore, the mismatched thermal expansion coefficient between the film and the substrate generates high tensile stress during the cooling because the CTE of the Si substrate is lower than that of the metal film materials. The value of the thermal expansion coefficient of bulk Si is equal to 2.6 × 10 −6 K −1 [34] at room temperature, while for bulk Mo and RuAl this value is equal to 4.8 × 10 −6 K −1 [35] and 5.5 × 10 −6 K −1 , [36] respectively. Thus, at the end of annealing, a high tensile residual stress remains in the film, which has different values for each metallization. The residual stress in the film at the end of annealing, named "annealed stress," for each metallization was presented in Table 1. The maximum stress remains in the annealed RuAl-69 film, while in the annealed Mo and MoLa films the amount of residual stress is much smaller. The lower the tensile residual stress in the film, causes the higher mechanical stability and longer lifetime of the electrodes of the HT SAW sensors.

Film Stress During Thermal Cycling
The stress variations during the thermal cycling between room temperature and high temperatures were investigated to determine the stability and consistency of the film during the typical temperature changes in the operational conditions. The results of film stress versus temperature during the thermal cycling experiment are shown in Figure 5. As shown in this figure, the variations of stress with temperature during the thermal cycling are almost linear in all films and without any abrupt changes, which is important for the calibration of temperature sensors. Besides, the annealed films exhibit stable stress behavior, as the value of stress at a certain temperature is the same for the thermal cyclings up to the different temperatures. To measure the temperature with a SAW sensor, the reflected signal of the sensor is calibrated based on temperature; therefore, the stable behavior of the metal system is important to rely on the pure effect of temperature on the shift in the signal peak frequency. At the beginning of the heating process, a sharp drop in the stress-temperature curves is observed in all of the graphs, which is due to the delay in the measurement of the temperature once the heating starts. However, the temperature measurement system becomes stable very soon, thus it doesn't affect the results. In addition, the cooling process occurs smoothly from the maximum temperature to room temperature, and no sharp variations were observed in the stress-temperature curve. Therefore, the results of the cooling curve were used for further investigations of the ratio of stress variations with temperature.
According to Figure 5, the value of residual stress in the films did not change at the end of each thermal cycling, and the same stress values as at the initiation of the thermal cycling were obtained for each film. Therefore, it seems that all films experienced elastic or quasi-elastic strains even at high temperatures during thermal cycling. However, such a conclusion has to be made carefully, as the recovery of plastic strain is a common phenomenon in nanocrystalline metals and thin films. [37][38][39] Previous studies [38,40] have shown that in thin metal films with an average grain dimension below 100 nm, the plastic strain recovers in the same way that the elastic strain recovery happens in bulk metals by releasing the load. This means that the total deformation in the material is recovered to its reference or initial value after releasing the load. However, the mechanism of plastic strain recovery in nanocrystalline metals is related to the deformations of grain boundaries rather than grains. The reason for this behavior is that in these metals, the volume fraction of the grain boundaries increases to the order of the volume fraction of grains. Therefore, the grain boundary deformation mechanisms become important for the descriptions of the thin metal film behavior with nanoscale grains. According to the cross-section morphology of the STEM images shown in Figure 6, the width and heights of the grains in the films are equal or less than 100 nm. Moreover, in our researches which has been published in, [2,6,11,12,41,42] a morphology investigation of the metal films in the same metallization systems was done through an extensive SEM analysis of the surfaces of the samples, STEM investigations of cross-sections and XRD analysis in Bragg-Brentano geometry, supported by X-ray pole figure investigation, which showed globular grains with the same dimension normal to the plane of the STEM images, meaning that the grains have comparable width and length. Since the dimensions of grains in three perpendicular directions are less than 100 nm in the investigated metals, they can be considered nanocrystalline metal films.
The stress variations with respect to the temperature were obtained for each metallization system from the slope of the stressdisplacement curve during the cooling (Figure 5), and the values are shown in Table 2. Comparing the results of different metallization systems revealed various ratios of stress variations between the minimum and maximum temperatures during the thermal cycling. In case of the Mo and MoLa sample, there was a constant slope of the stress curves during cooling down from 900°C to RT. In contrast to this, in case of both RuAl films, a kink in the stress curves was observed at about 600°C with a smaller slope at higher temperatures. The highest ratio of stress variations was obtained for the RuAl-131 film (equal to 1.25 MPa K −1 for temperatures below 600°C), while this ratio was much smaller in the Mo and MoLa samples (0.50 MPa K −1 in the case of Mo and 0.54 MPa K −1 in the case of MoLa). The stress variations in Mo and MoLa films are very similar because their coefficients of thermal expansion are comparable. [33] www.advancedsciencenews.com www.advmattechnol.de  According to Table 2, the ratio of stress variations with temperature in the thin RuAl film is significantly lower than in the thick RuAl film. The barrier and cover layers with their physical properties and their individual CTE also influence the temperaturedependent behavior of the films. Therefore, the difference in the ratio of the RuAl layer thickness to the total cover and barrier layers thickness in the two RuAl samples may affect the variations of the average stress in the film system. The considerable reduction of the stress variation ratio of the RuAl films at temperatures higher than 600°C could be related to the integration of inelastic strains in the RuAl film at higher temperatures. However, since the stress in the film recovers completely at the end of the cool-ing process and the mechanism of the plastic strain recovery in nanocrystalline materials is not clear yet, this would not be a robust conclusion. Although, it should be noted that, no signs of microdamage or other defects were observed in the STEM images of the RuAl films after thermal treatments (Figure 6a,b).

Creep Behavior of Films
The variations of stress during 10 h of isothermal heating at 600°C for the four metallization systems are illustrated in Figure 7a. The value of stress in the films at the initiation of the isothermal heating was deducted from the total stress at each measurement point, therefore the curves in Figure 7a show the stress variations due to a constant sample temperature of 600°C. The lowest variations of stress were obtained in the MoLa samples, in which the stress-time curve becomes almost a plateau in less than one hour. However, the stress in the RuAl-131 film varies continuously with time during the isothermal heating and the stress variations don't reach a constant value within the observed time period. The variations of strain in each film were obtained by dividing the stress values by the biaxial modulus of each metal calculated using Equation (2) with the material properties extracted from, [43] then the stain variations versus the isothermal heating time are displayed in Figure 7b. According to Figure 7, at the beginning of the isothermal heating, the relaxation occurs at a very high rate, called primary creep, which is an unstable process. [40,44] However, after a few minutes, the variations of stress-strain become much slower, called secondary creep, and these results are used for the creep characterization. The mechanism of creep in nanocrystalline thin films is different from that observed in bulk materials. [40,[44][45][46][47][48] The relaxation mechanism in these thin films is based on the transformation of material rather than the dislocation motion which is a dominant mechanism in bulk polycrystalline metals. [40,45,46] Nabarro-Herring and Coble creep models are suggested for the description of the stress-strain relaxation mechanism in nanocrystalline thin films. [44,47,48] The Nabarro-Herring model is explaining the relaxation mechanism by the transformation or diffusion of matter through the grain boundaries, while the Coble model is dealing with the material flow along the grain boundaries.
To describe these two mechanisms in a constrained thin film with a stabilized microstructure (i.e. an annealed film), a single constrained grain of a thin metal film on a substrate is shown in Figure 8a. It was found from the cross-section images ( Figure 6) that in the case of the RuAl-69 and Mo layer, all grains in the annealed films are extended throughout the thickness of the metal layer. In the MoLa film, there are also columnar grains which are additionally constrained by the layers of tiny La 2 O 3 pins. These particles strongly affect the grain growth, which is visible from the greatly different grain morphology of the Mo and MoLa sample in Figure 6c,d. Therefore, the La 2 O 3 particles will also influence the free deformation of the grains during stress relaxation. In the case of the RuAl-131 film, there are some globular grains with a size of about half of the film thickness, and some grains are also extended throughout the thickness of the film. Although the film morphology is not identical in the four film systems, for the first approximation considered in this paper, the samples are evaluated using the same model assuming that the individual grain is constrained between the cover and barrier layers, as shown in Figure 8b, which shows the same grain depicted in Figure 8a with some selected lattice planes perpendicular to the film plane indicated with the black lines. Biaxial tensile stresses in the form of intrinsic and thermal stresses are applied to the annealed film during the temperature changes, which are assumed to be normal to the grain boundaries because of the negligible thickness of the film compared to its lateral dimensions (Figure 8c). When the temperature is kept constant at a relatively high value (i.e. 600°C ) in comparison with the melting point of the film material, the stress-strain in the film initiates to relax. The cover and barrier layer constraints prevent changing the grain dimensions at their top and bottom interfaces. Thus, according to the Nabarro-Herring creep model, the relaxation could only occur by the mass transformation and atoms vibration within the grain, while the grain boundaries will not deform in the constrained film. This is illustrated in Figure 8d by the deformation of the lattice planes. This mechanism may cause the reduction of strain (and therefore stress) at the grain boundaries, while high-stress values remain within the interior of the grains (Figure 8d). The schematic picture of a single grain for the description of the relaxation behavior based on the Nabarro-Herring creep model in a thin film constrained by a substrate was used firstly by Jackson and  Li. [44] It was shown that the diffusion of matter through the grain boundaries cannot completely relax the stress in the constrained thin films. They suggested local plastic deformation as the dominant relaxation mechanism in the constrained films, which is quantified by the Coble creep model. [44,48] Based on this model, the relaxation could occur by the flow of matter along the grain boundaries which may cause the local thickening/thinning of the grains in the constrained film [44,46] (Figure 8e), undeformed lattice planes and deformed grain boundaries). Therefore, the Coble creep model is used for the quantification of the creep mechanism of the metal films in this study.
It is worth mentioning that, in the metallization system studied here, there is no interdiffusion between the film and the substrate, because the barrier layer eliminates this process significantly. [2,8,11,12] In addition, reference measurements of the barrier layers on the substrate revealed a negligible creep rate of these layers. Therefore, we can conclude that the relaxation within the metallic layer was the dominant effect on the relaxation of the average stress in the film during the isothermal heating.
The Coble creep model is described by the following equation [48] : wherėis the creep rate, is the initial stress, is the atomic volume, K is the Boltzmann constant, T is the temperature, d is the grain diameter, and is a constant related to the grain shape. D is the combined grain boundary diffusion parameter, which consists of , the grain boundary thickness, and D, the grain boundary diffusivity. The creep rate of each film was calculated from the slope of the strain-time curves in Figure 7b at the secondary creep phase where the strain varies slowly with time, which was then recorded in Table 2. In the Mo and MoLa samples, the strain curves were approximated with one linear function, while the strain curve of the RuAl films was divided into two segments, which were fitted with a linear function individually. The D was calculated for each metal by substituting the values oḟ, , and T from the experiments in Equation (3) while considering K = 1.38 × 10 −23 J K −1 and = 1. [49] Besides, the average atomic volumes of RuAl, MoLa, and Mo were obtained equal to 0.909 × 10 −29 , 1.28 × 10 −29 , and 1.28 × 10 −29 m 3 , respectively. [36,50] The average grain diameter of each metal was approximated from the STEM images (Figure 7), which are obtained 70 nm for RuAl-131, 40 nm for RuAl-69, 25 nm for MoLa, and 90 nm for Mo. A minimum deviation of 10% in the measurement of the grain size is expected for all films. The calculated values of Ds were recorded in Table 2.
It was observed that the MoLa metallization has the lowest creep rate among the studied metallization systems for HT SAW sensors which makes it a suitable material system from this aspect for having a reliable sensor through a long lifetime. However, a measurement on the real SAW substrate is also needed for the confirmation this result. In the RuAl metallization, the creep rate decreases significantly after keeping the sample at a high temperature for a certain time (i.e. 4 h for RuAL-131 and 6 h for RuAl-69). The reason for such a change is not clear in these complicated film systems, and it needs an extensive investigation of the films' microstructure by an advanced defect detecting method. However, according to the previous studies, [44,46] the formation and evolution of hillocks in the constrained film under biaxial tensile stress could be a reason for this change in the creep rate.
According to Table 2, the thin RuAl film (i.e. RuAl-69) has a significantly lower creep rate compared to the thick film (RuAl-131). The value of creep rate in the MoLa film is slightly lower than that of Mo, however, the value of D in MoLa has been calculated two orders of magnitude lower than the value of this parameter in the Mo film, which could be due to the existence of columnar www.advancedsciencenews.com www.advmattechnol.de grains and La 2 O 3 pins in MoLa that reduces the possibility of the local grain deformation. Since the grain boundary thickness is assumed to be identical in the Mo and MoLa samples, the lower value of D in MoLa indicates a lower grain boundary diffusivity, which also could be explained by the presence of the La 2 O 3 particles.
Regarding these results, one has to have in mind that the different films experienced different stresses at the beginning of the isothermal annealing, which emerged during the deposition and the subsequent heat treatments. Besides, the ratio of the isothermal heating temperature with respect to the melting temperature of the materials is lower for Mo (2623°C [35] ) compared to RuAl (2300°C [36] ), which also affects the creep rate.
In addition, the calculation just considers the Coble creep model. However, the different samples don't equally fulfill the preconditions for the application of the Coble model, and in addition to the creep relaxation itself, further relaxation processes might take place in the films, which contribute to the observed relaxation. However, these results represent the first reference point for the description of the relaxation of the investigated hightemperature materials.
A predictable and stable stress variations behavior is required for the metallization of electrodes in HT SAW sensors. To achieve a predictable behavior, linear, and reproducible variations of stress with temperature are required, which were acquired for all metallization systems investigated in this study. For the stable stress behavior, a film with the minimum stress-strain variations rate (almost zero) during isothermal heating or the lowest creep rate is desired to obtain a consistent response from the temperature sensor at a constant temperature. In this study, on the extended films on Si reference substrates, the lowest stress and the lowest creep rate were obtained for the MoLa and Mo metallization systems during isothermal heating at 600°C for 10 h in UHV conditions. To transfer the results to HT SAW devices, the same procedure investigated in this study can be used for further investigations of the films on the piezoelectric substrate.

Conclusion
The thermomechanical and relaxation behaviors of the sputtered metallization systems suggested for HT SAW sensors, i.e. RuAl, MoLa, and Mo, on a Si [100] substrate were investigated. These films on Si substrates served as straightforward model systems for the preliminary fundamental investigations toward the understanding of the relaxation behavior of the metallization systems.
It was observed that: • compressive residual stress remained in all films after the deposition, while tensile residual stress remained in the annealed films. The lowest value of tensile stress was attained in the annealed MoLa sample. • the annealed samples of all metallizations showed linear and reproducible variations of stress with temperature during the thermal cycling, which makes them promising candidates for application in a high-temperature sensor. • for these samples on Si, the lowest residual stress was measured for the Mo and MoLa films. These samples also showed the lowest creep rate.
In the end, the constitutive equations for the creep behavior description of the studied metal films, as constrained nanocrystalline films, were acquired based on the Coble creep model. Although this creep model does not cover all processes, which might take place in these thin films, the results serve as the first step toward the prediction of the long-term relaxation behavior of these metallization systems on Si substrates. Based on these results, further investigations of the film on single crystallin bulk piezoelectric substrates, which are mainly used as the substrate of HT SAW sensors (e.g. LGS or CTGS) and are trigonal or full anisotropic materials, are required to transfer the results to application.