In Situ Synchrotron XRD Characterization of Piezoelectric Al1−xScxN Thin Films for MEMS Applications

Aluminum scandium nitride (Al1−xScxN) film has drawn considerable attention owing to its enhanced piezoelectric response for micro-electromechanical system (MEMS) applications. Understanding the fundamentals of piezoelectricity would require a precise characterization of the piezoelectric coefficient, which is also crucial for MEMS device design. In this study, we proposed an in situ method based on a synchrotron X-ray diffraction (XRD) system to characterize the longitudinal piezoelectric constant d33 of Al1−xScxN film. The measurement results quantitatively demonstrated the piezoelectric effect of Al1−xScxN films by lattice spacing variation upon applied external voltage. The as-extracted d33 had a reasonable accuracy compared with the conventional high over-tone bulk acoustic resonators (HBAR) devices and Berlincourt methods. It was also found that the substrate clamping effect, leading to underestimation of d33 from in situ synchrotron XRD measurement while overestimation using Berlincourt method, should be thoroughly corrected in the data extraction process. The d33 of AlN and Al0.9Sc0.1N obtained by synchronous XRD method were 4.76 pC/N and 7.79 pC/N, respectively, matching well with traditional HBAR and Berlincourt methods. Our findings prove the in situ synchrotron XRD measurement as an effective method for precise piezoelectric coefficient d33 characterization.


Introduction
Recently, aluminum nitride (AlN) piezoelectric film has attracted great attention due to wireless communication technology experiencing rapid development from 2-4G to 5G [1]. Bulk acoustic wave (BAW) filters based on AlN piezoelectric film exhibit significant advantages in terms of compact size, high performance and high compatibility with the standard complementary metal-oxide-semiconductor (CMOS) process [2][3][4]. However, limited by the relatively low intrinsic longitudinal piezoelectric coefficient d 33 , the bandwidths of BAW filters based on AlN piezoelectric film are generally less than 3% [5,6]. There is an urgent need to seek breakthroughs in AlN materials. Rare earth element doping, including scandium (Sc) [7][8][9], yttrium (Y) [10] and tantalum (Ta) [11], has been proven to be an effective method to improve the piezoelectric properties of AlN materials. Among them, scandium doping is regarded as the most efficient method, since Akiyama M demonstrated a~400% piezoelectric response increase in 2009 [7]. With the help of first-principle calculations, Tasnadi F [12] revealed that the increased intrinsic sensitivity of axial strain induced by large elastic softening leads to the anomalous enhancement of piezoelectric response by Sc introduction. For example, when the scandium concentration is 20%, the piezoelectric coefficient d 33 of Al 0.8 Sc 0.2 N film can increase from 5.38 pC/N to 11.19 pC/N, leading to a 9% relative bandwidth of the corresponding filters [13].
It is evident that the piezoelectric response of Al 1−x Sc x N film is a key parameter for the design and optimization of high-frequency acoustic resonators and filters. At present, Al 1−x Sc x N growth methods include magnetron sputtering, molecular beam epitaxy (MBE) [14] and metal-organic chemical vapor deposition (MOCVD) [15]. Among them, magnetron sputtering is still the most commonly used method for Al 1−x Sc x N piezoelectric material deposition due to its high compatibility with traditional device fabrication processes and relatively low manufacturing costs. Although the piezoelectric response of Al 1−x Sc x N film can be predicted by theoretical calculations [12,16], the values of fabricated films often deviate from the theoretical ones, due to the deterioration of crystalline quality, intrinsic stress and calculation accuracy. In particular, with the increase in Sc concentration to around 30%, the crystal quality of Al 1−x Sc x N film may significantly deteriorate because of abnormal oriented grains (AOG) formation. When Sc concentration is higher than 50%, the non-polar cubic structure is more stable than the polar wurtzite structure [16], which has adverse effects on its piezoelectric response [9,[17][18][19]. Therefore, it is crucial to develop an effective and accurate experimental method for the evaluation of Al 1−x Sc x N film piezoelectric property.
At present, the methods commonly used for piezoelectric characterization include PiezoMeter [8], double-beam laser interferometry (DBLI) [20], piezoresponse force microscopy (PFM) [21] and acoustic resonators [22]. d 33 values ranging from 3.2 pC/N to 4.53 pC/N were reported by using above methods [21,23,24], while slightly higher values ranging from 4.9 pC/N to 5.1 pC/N were obtained after measurement system calibration [25,26]. However, since the piezoelectric coefficient of Al 1−x Sc x N film is only tens of pC/N, about an order of magnitude smaller than barium titanate (BaTiO 3 ) [27] and zirconate titanate (PZT) [28], it is very challenging to characterize Al 1−x Sc x N film using these methods. Synchrotron radiation is an advanced collimated light source with a high intensity and a wide spectrum. X-ray diffraction (XRD) with an extremely powerful X-ray source produced by synchrotron radiation facilities offers a puissant and special technique by which to characterize the structure of materials on the atomic or molecular scales [29]. It provides greater accuracy to investigate material properties such as phase composition, crystallite size, strain and defect [30]. It also allows time-resolved in situ characterization with a significantly reduced measurement time and a much higher resolution, exhibiting particular advantages in structure characterization on sub-nanometer scales. For example, Shiomi et al. investigated the piezoelectric coefficient of Al 0.2 Ga 0.8 N film based on synchrotron XRD, verifying the feasibility of this method to characterize the piezoelectric response at the picometer scale [31].
Herein, in the present work, we developed an in situ measurement system based on the synchrotron radiation-powered XRD technique to characterize the piezoelectric coefficient d 33 of Al 1−x Sc x N films. The measured results quantitatively demonstrated the lattice spacing variation of Al 1−x Sc x N films induced by piezoelectric effect upon applied external voltage. Longitudinal piezoelectric coefficients d 33 of Al 1−x Sc x N film with different Sc concentrations were successfully obtained and compared with traditional measurement methods. Moreover, by implementing substrate clamping effect calibration, the d 33 deviation between synchrotron XRD and other methods was significantly reduced, indicating the validity of synchrotron XRD characterization for precise d 33 measurement.

Synchrotron XRD Measurement System Setup
Figure 1a-c illustrates the brief fabrication process of Al 1−x Sc x N samples with x = 0, 10% and 20%. Firstly, 200 nm Mo/850 nm Al 1−x Sc x N/150 nm Mo sandwiched stacks were deposited by magnetron reactive sputtering on high-resistivity Si substrate with a 30 nm AlN seed layer. Those three layers were continuously deposited without a vacuum break to avoid particle or photoresist residual contamination. Highly crystalline AlN film with (0002) the full width at half maximum (FWHM) of 1.40 • was observed on controlled samples, while FWHM slightly increased to 1.76 • and 2.90 • for Al 0.9 Sc 0.1 N and Al 0.8 Sc 0.2 N film due to the deterioration of crystallinity caused by Sc introduction, as shown in Figure 2. Then, the top Mo layer was patterned using the ion beam etching (IBE) process and acted as a hard mask for subsequent Al 1−x Sc x N-selective etching. Anisotropic etching of Al 1−x Sc x N films with different Sc contents was carried out by tetramethylammonium hydroxide (TMAH) for bottom mesa formation. Finally, top electrode Mo was patterned by IBE process for external voltage connection.
10% and 20%. Firstly, 200 nm Mo/850 nm Al1−xScxN/150 nm Mo sandwiched stacks were deposited by magnetron reactive sputtering on high-resistivity Si substrate with a 30 nm AlN seed layer. Those three layers were continuously deposited without a vacuum break to avoid particle or photoresist residual contamination. Highly crystalline AlN film with (0002) the full width at half maximum (FWHM) of 1.40° was observed on controlled samples, while FWHM slightly increased to 1.76° and 2.90° for Al0.9Sc0.1N and Al0.8Sc0.2N film due to the deterioration of crystallinity caused by Sc introduction, as shown in Figure 2. Then, the top Mo layer was patterned using the ion beam etching (IBE) process and acted as a hard mask for subsequent Al1−xScxN-selective etching. Anisotropic etching of Al1−xScxN films with different Sc contents was carried out by tetramethylammonium hydroxide (TMAH) for bottom mesa formation. Finally, top electrode Mo was patterned by IBE process for external voltage connection.
The schematic of the in situ synchrotron XRD measurement system is shown in Figure 1d. It consists of a high-intensity X-ray source and detector, a printed circuit board and a voltage source. The previously fabricated Al1−xScxN samples were mounted on the PCB board. The top and bottom electrodes were connected to the voltage source through lead bonding, which could effectively avoid the accidental penetration of piezoelectric film in the testing process. The X-ray beam was incident at the center of the top electrode to obtain symmetric diffraction as external voltage was applied to the top electrodes of samples. The shift in synchrotron XRD curves could be observed by applying different voltages. Synchrotron XRD characterization was carried out at the Shanghai Synchrotron Radiation Light Source. The line stations used were BL14B1 and BL02U2, both of which can provide X-rays with an energy of 10 keV and support the in situ piezoelectric characterization of Al1−xScxN samples.

High Overtone Bulk Acoustic Resonators Fabrication
High overtone bulk acoustic resonator (HBAR) devices, without the requirement of a suspended film structure, are widely used to estimate the piezoelectric response and electromechanical coupling coefficient with the advantage of a simplified fabrication process [32]. The fabrication process of Al1−xScxN HBAR devices with x = 0 and 10% is shown in Figure 3. The essential piezoelectric stacks of an HBAR device, consisting of 200 nm Mo/850 nm Al1−xScxN/150 nm Mo sandwiched film stack, were continuously deposited on high-resistivity Si substrate with a 30 nm AlN seed layer, as shown in Figure 3a. The top Mo and Al1−xScxN layers were etched by IBE and TMAH, respectively, as shown in Figure  3b. Benefiting from the highly selective and anisotropic TMAH etching, smooth and clean The schematic of the in situ synchrotron XRD measurement system is shown in Figure 1d. It consists of a high-intensity X-ray source and detector, a printed circuit board and a voltage source. The previously fabricated Al 1−x Sc x N samples were mounted on the PCB board. The top and bottom electrodes were connected to the voltage source through lead bonding, which could effectively avoid the accidental penetration of piezoelectric film in the testing process. The X-ray beam was incident at the center of the top electrode to obtain symmetric diffraction as external voltage was applied to the top electrodes of samples. The shift in synchrotron XRD curves could be observed by applying different voltages. Synchrotron XRD characterization was carried out at the Shanghai Synchrotron Radiation Light Source. The line stations used were BL14B1 and BL02U2, both of which can provide X-rays with an energy of 10 keV and support the in situ piezoelectric characterization of Al 1−x Sc x N samples.

High Overtone Bulk Acoustic Resonators Fabrication
High overtone bulk acoustic resonator (HBAR) devices, without the requirement of a suspended film structure, are widely used to estimate the piezoelectric response and electromechanical coupling coefficient with the advantage of a simplified fabrication process [32]. The fabrication process of Al 1−x Sc x N HBAR devices with x = 0 and 10% is shown in Figure 3. The essential piezoelectric stacks of an HBAR device, consisting of 200 nm Mo/850 nm Al 1−x Sc x N/150 nm Mo sandwiched film stack, were continuously deposited on high-resistivity Si substrate with a 30 nm AlN seed layer, as shown in Figure 3a. The top Mo and Al 1−x Sc x N layers were etched by IBE and TMAH, respectively, as shown in Figure 3b. Benefiting from the highly selective and anisotropic TMAH etching, smooth and clean Al 1−x Sc x N sidewalls with a 50-60 • etching profile were obtained, as shown in Figure 4. Due to the lower etching rate of Al 0.9 Sc 0.1 N compared with pure AlN film, the sidewall angle of Al 0.9 Sc 0.1 N was~10 • smaller with a tapered etching profile. It should be noted that the Al 1−x Sc x N film underneath the signal terminal of the top electrode should also be removed to avoid parasitic HBAR structure. Then, an oxide sidewall was formed at the boundary of the Al 1−x Sc x N etching area to avoid potential short circuit risk between the top and bottom electrodes (Figure 3c). Then, 20 nm Ti/300 nm Au was deposited and accordingly patterned for pad formation. Finally, the pentagonal-shaped top electrode was patterned to define the critical piezoelectric resonance area, as shown in Figure 3e. The frequency characteristics of the reflection coefficient (S 11 ) were carried out by a network analyzer KEYSIGHT E5071C.

d33 Measurement by Synchrotron XRD Method
The in situ synchrotron XRD curves of AlN, Al0.9Sc0.1N and Al0.8Sc0.2N films under different applied voltages are shown in Figure 5. In general, the diffraction peaks of the Al1−xScxN (0002) plane, reflecting the c-plane lattice spacing with different Sc concentrations and applied electric field, are located between 28.5° to 28.9°. As shown in Figure 5a, without external voltage, a distinct peak corresponding to AlN (0002) is located at 28.85°. A clear peak shift of 0.013° to lower angles was observed when a negative voltage of −100 V was applied; while an opposite 0.010° shift to higher angles was observed upon the application of positive 85 V. Synchrotron XRD curves of Al1−xScxN films with Sc concentrations of 10% and 20% exhibit similar phenomena, with peak shifts of 0.010° and 0.015° for Al0.9Sc0.1N and Al0.8Sc0.2N films under applied voltages of 60 V and 40 V separately, as shown in Figure 5b,c. It should be emphasized that thanks to the high resolution of the synchrotron radiation-powered X-ray source, diffraction peak shifts as small as 0.001° can be clearly distinguished. This behavior corresponds to the inverse piezoelectric effect of piezoelectric film, and can in turn be used to calculate the piezoelectric coefficient. By applying a longitudinal electric field E on the piezoelectric films and calculating the change rate of (0002) interplanar spacing (dE-d0) / d0, the longitudinal strain S and the piezoelectric coefficient d33 of piezoelectric films can be obtained according to Equation (1) [33]:

d 33 Measurement by Synchrotron XRD Method
The in situ synchrotron XRD curves of AlN, Al 0.9 Sc 0.1 N and Al 0.8 Sc 0.2 N films under different applied voltages are shown in Figure 5. In general, the diffraction peaks of the Al 1−x Sc x N (0002) plane, reflecting the c-plane lattice spacing with different Sc concentrations and applied electric field, are located between 28.5 • to 28.9 • . As shown in Figure 5a, without external voltage, a distinct peak corresponding to AlN (0002) is located at 28.85 • . A clear peak shift of 0.013 • to lower angles was observed when a negative voltage of −100 V was applied; while an opposite 0.010 • shift to higher angles was observed upon the application of positive 85 V. Synchrotron XRD curves of Al 1−x Sc x N films with Sc concentrations of 10% and 20% exhibit similar phenomena, with peak shifts of 0.010 • and 0.015 • for Al 0.9 Sc 0.1 N and Al 0.8 Sc 0.2 N films under applied voltages of 60 V and 40 V separately, as shown in Figure 5b,c. It should be emphasized that thanks to the high resolution of the synchrotron radiation-powered X-ray source, diffraction peak shifts as small as 0.001 • can be clearly distinguished. This behavior corresponds to the inverse piezoelectric effect of piezoelectric film, and can in turn be used to calculate the piezoelectric coefficient. By applying a longitudinal electric field E on the piezoelectric films and calculating the change rate of (0002) interplanar spacing (d E-d 0 )/d 0 , the longitudinal strain S and the piezoelectric coefficient d 33 of piezoelectric films can be obtained according to Equation (1) [33]: where d E and d 0 are interplanar spacing with and without applied voltage. The interplanar spacing d is obtained by the classic Bragg formula λ = 2dsinθ, where θ is the position of the diffraction peak. The energy of the synchrotron radiation-powered X-ray in the work is 10 keV, corresponding to a wavelength of 0.124 nm. The obtained XRD curves were fitted using Gaussian functions to extract the 2θ values for the peaks, and the c-plane lattice spacing d = λ/2sinθ and longitudinal lattice strain S = (d E -d 0 )/d 0 were derived on the basis of the above equations. The applied electrical field dependence of the Al 1−x Sc x N strain is shown in Figure 5d-f. It is worth noting that the linear relationship between the applied external voltage and the lattice strain was observed, matching very well with the theoretical piezoelectric effect of Al 1−x Sc x N films. The d 33 can be obtained by extracting the slop from the strain-electrical field correlations. The d 33 of pure AlN film is extracted at 3.54 pm/V. When the scandium concentration increases to 10% and 20%, the d 33 increases to 5.58 pm/V and 9.48 pm/V, corresponding to a 57.6% and a 168% improvement, respectively. dependence of the Al1−xScxN strain is shown in Figure 5d-f. It is worth noting that the linear relationship between the applied external voltage and the lattice strain was observed, matching very well with the theoretical piezoelectric effect of Al1−xScxN films. The d33 can be obtained by extracting the slop from the strain-electrical field correlations. The d33 of pure AlN film is extracted at 3.54 pm/V. When the scandium concentration increases to 10% and 20%, the d33 increases to 5.58 pm/V and 9.48 pm/V, corresponding to a 57.6% and a 168% improvement, respectively.

d33 Measurement by HBAR Method
As a comparison, we also adopted the commonly used acoustic resonators for d33 characterization. Figure 6a shows the top-view SEM image of the fabricated Al1−xScxN HBAR device with a pentagon-shaped resonant area. As shown in Figure 6b, the S11 curves of Al1−xScxN HBAR devices with Sc concentrations of 0% and 10% exhibit multiple resonance modes in the measured frequency range. The strongest resonance frequency is located around 3.00 GHz and 2.58 GHz, with 10.04 MHz and 9.90 MHz frequencies splitting between adjacent modes for AlN and Al0.9Sc0.1N films, respectively.

d 33 Measurement by HBAR Method
As a comparison, we also adopted the commonly used acoustic resonators for d 33 characterization. Figure 6a shows the top-view SEM image of the fabricated Al 1−x Sc x N HBAR device with a pentagon-shaped resonant area. As shown in Figure 6b, the S 11 curves of Al 1−x Sc x N HBAR devices with Sc concentrations of 0% and 10% exhibit multiple resonance modes in the measured frequency range. The strongest resonance frequency is located around 3.00 GHz and 2.58 GHz, with 10.04 MHz and 9.90 MHz frequencies splitting between adjacent modes for AlN and Al 0.9 Sc 0.1 N films, respectively. Mason models incorporated with measured scattering curves are commonly adopted for material parameter extraction [34]. The equivalent circuit of a Mason model for Al1−xScxN HBAR devices, consisting of an Si substrate, a bottom electrode, a piezoelectric layer and a top electrode, is shown in Figure 7; where Z, γ, C0 are acoustic impedance, phase shift and static capacitance, respectively. h = e/ε S , where e is the relevant components Mason models incorporated with measured scattering curves are commonly adopted for material parameter extraction [34]. The equivalent circuit of a Mason model for Al 1−x Sc x N HBAR devices, consisting of an Si substrate, a bottom electrode, a piezoelectric layer and a top electrode, is shown in Figure 7; where Z, γ, C 0 are acoustic impedance, phase shift and static capacitance, respectively. h = e/ε S , where e is the relevant components of the piezoelectric matrix, and ε S is the permittivity of piezoelectric materials. As shown in Figure 6c  Mason models incorporated with measured scattering curves are commonly adopted for material parameter extraction [34]. The equivalent circuit of a Mason model for Al1−xScxN HBAR devices, consisting of an Si substrate, a bottom electrode, a piezoelectric layer and a top electrode, is shown in Figure 7; where Z, γ, C0 are acoustic impedance, phase shift and static capacitance, respectively. h = e/ε S , where e is the relevant components of the piezoelectric matrix, and ε S is the permittivity of piezoelectric materials. As shown in Figure 6c Figure 8a illustrates d33 measurements using the Berlincourt method PIEZOTEST PM300 [35,36]. Al1−xScxN piezoelectric samples were clamped between two contact probes and subjected to a low frequency force. Electrical signals generated from Al1−xScxN film  Figure 8a illustrates d 33 measurements using the Berlincourt method PIEZOTEST PM300 [35,36]. Al 1−x Sc x N piezoelectric samples were clamped between two contact probes and subjected to a low frequency force. Electrical signals generated from Al 1−x Sc x N film were collected and compared with a built-in reference, and thus d 33 values with polarization direction could be directly given by the system. As for Al 1−x Sc x N sample preparation, 900 nm Al 1−x Sc x N films with x = 0% and 10% were directly deposited on low resistivity Si substrates. Then, a 250 nm Au top electrode was deposited and patterned for top electrical connection, as shown in Figure 8b. The d 33 values of AlN and Al 0.9 Sc 0.1 N films measured by PIEZOTEST PM300 were 6.33 pC/N and 8.96 pC/N, respectively. were collected and compared with a built-in reference, and thus d33 values with polarization direction could be directly given by the system. As for Al1−xScxN sample preparation, 900 nm Al1−xScxN films with x = 0% and 10% were directly deposited on low resistivity Si substrates. Then, a 250 nm Au top electrode was deposited and patterned for top electrical connection, as shown in Figure 8b. The d33 values of AlN and Al0.9Sc0.1N films measured by PIEZOTEST PM300 were 6.33 pC/N and 8.96 pC/N, respectively.

d33 Discussion
The piezoelectric coefficient d33 of AlN and Al0.9Sc0.1N films measured by Synchrotron XRD, HBAR and PIEZOTEST PM300, together with theoretical calculated values, are summarized in Table 1. The theoretical calculations were performed using the Vienna Ab ini-

d 33 Discussion
The piezoelectric coefficient d 33 of AlN and Al 0.9 Sc 0.1 N films measured by Synchrotron XRD, HBAR and PIEZOTEST PM300, together with theoretical calculated values, are summarized in Table 1. The theoretical calculations were performed using the Vienna Ab initio Simulation Package (VASP) [37][38][39]. It is observed that the d 33 measured by synchrotron XRD are about 40% lower compared to that measured by PM300, while the d 33 values obtained by synchrotron XRD and HBAR are much closer (~10%). Moreover, compared with theoretical values, the measured results from synchrotron XRD and HBAR are 22-34% smaller, while that of PM300 are 14-18% larger. One possible reason for the above deviations may come from measurement system errors, fabrication process variations and crystalline quality differences in the piezoelectric film. However, this alone is not reasonable to explain such consistently large deviations introduced by each method, and needs to be carefully considered. Since the deformation amount of Al 1−x Sc x N piezoelectric film is relatively small (only tens of picometers/voltage), the influence of the rigid substrate clamped to the piezoelectric film cannot be ignored during d 33 measurement. Referring to Lefki et al. [40], the interference of the substrate during d 33 measurement is quantitatively analyzed below.
The following equations can be deduced from the classic piezoelectric equation based on the symmetry of Al 1−x Sc x N materials [40]: where D 3 is the longitudinal electrical displacement of the piezoelectric film, S 1 , S 2 , S 3 and T 1 , T 2 , T 3 are the strain and stress of the film in the in-plane x, y and out-of-plane z directions, respectively, d 31 is the transverse piezoelectric coefficient, ε T 33 is the dielectric constant of the film in the longitudinal direction, and s E 11 , s E 12 , s E 13 , s E 33 are the mechanical compliances of the piezoelectric film.
As described above, synchrotron XRD uses the inverse piezoelectric effect for d 33 measurement. Ideally, the piezoelectric film would deform both in the longitudinal and in-plane directions when the voltage is applied. However, due to the restrictions from the substrate, the in-plane strains of piezoelectric film in the x and y direction S 1 and S 2 are assumed as zero. Since the longitudinal stress T 3 = 0, the in-plain stress can be deduced from Equations (3) and (4) as: The calibrated longitudinal piezoelectric coefficient d 33,i considering inverse piezoelectric effect can be expressed as: where d 33,XRD is the experimental result measured by synchrotron XRD. By using theoretical values of s E 11 , s E 12 , s E 13 and d 31 for a rough evaluation, the measured d 33,XRD from synchrotron XRD is underestimated because of the deformation constraint by the substrate. The d 33 value of AlN and Al 0.9 Sc 0.1 N films obtained by synchronous XRD is revised to 4.76 pC/N and 7.79 pC/N according to above the correction, which is 34% and 40% larger than the originals.
The d 33 extracted using the HBAR device also uses the inverse piezoelectric effect, which is similar to synchrotron XRD. The calibrated d 33,r can be expressed by replacing the flexibility coefficient s E ij and piezoelectric strain coefficient d ij in Equation (7) with the stiffness coefficient C E ij and piezoelectric stress coefficient e ij , as shown below: d 33,r extracted from HBAR devices can be expressed as: According to the above, the d 33,r of the AlN and Al 0.9 Sc 0.1 N films is revised to 5.43 pC/N and 8.25 pC/N, leading to a 29% and 37% increase from the originals. It is observed that the revised piezoelectric coefficient d 33 obtained by HBAR devices is consistent with that from synchrotron XRD.
Although the Berlincourt method is the most convenient and fast way for piezoelectric coefficient measurement, the substrate would deform in-plane alongside Al 1−x Sc x N film due to the Poisson effect, introducing additional in-plane strain in piezoelectric films. The relationship between strain, Poisson's ratio µ and Young's modulus of substrate Y can be expressed as: Then, the in-plane stress is straightforwardly calculated from the strain-stress equation as follows: The calibrated longitudinal piezoelectric coefficient d 33,d considering the substraterestricted direct piezoelectric effect can be expressed as: in Equation (16) is negative for Al 1−x Sc x N film due to additional in-plane stress, leading to an overestimated d 33,PM300 measurement results. The d 33 of AlN and Al 0.9 Sc 0.1 N films obtained by PM300 is thus revised to 4.29 pC/N and 7.03 pC/N from 6.33 pC/N and 8.96 pC/N. It should be noted that the actual measurement process is much more complex due to the influence of the substrate's resistivity, quasi-static external force and fixed clamping force during PM300 measurement. Table 1 summarizes the d 33 results of synchrotron XRD, PM300 and HBAR before and after substrate-related calibration. The revised d 33 value of synchrotron XRD is 34-40% higher, while the value of PM300 is 22-32% lower compared with the original values. As a result, the deviation obtained by these two methods is reduced from up to 70% to about 10%. The deviation between the synchrotron XRD and HBAR results is within 15%, and the deviation between synchrotron XRD and theoretical values is within 13%, which is believed to be caused by the crystalline quality, sample structure and measurement configurations [41]. Moreover, the d 33 value of Al 0.9 Sc 0.1 N films is consistent in the range of 7.03 pC/N to 8.25 pC/N obtained by different methods, which is always 52-64% higher than pure AlN. This is consistent with previous reports [8,16,42], indicating that Sc introduction can significantly improve the intrinsic piezoelectric property of AlN film. The d 33 values obtained using the synchrotron XRD method are also in good agreement with previously reported results, as shown in Table 2. The above results demonstrate the feasibility and effectiveness of the synchrotron XRD method and the applicability of the proposed revised models. The Berlincourt method is predominantly used for d 33 measurement due to its simple and quick measurement process. However, it is very difficult to produce a homogeneous uniaxial stress on the piezoelectric film, and the results may be affected by the sample clamping situation and electrode size; therefore, the method is usually suggested for d 33 relative comparison [48]. The HBAR method can be not only used for d 33 measurement, but also for a complete set of material parameters, such as the dielectric constant, sound velocity and density [49]. However, it requires a complete fabrication process of acoustic devices, and the results strongly depend on the accuracy of the resonance frequencies and the fitting precision of a large group of material parameters. Compared with the HBAR method, the sample fabrication process of synchrotron XRD is much simpler. What is more, though a few theoretical parameters are used during substrate clamping effect calibration, the d 33 is directly extracted from the strain-electric field correlation without the involvement of material parameters, and the accuracy of the obtained results can also be roughly verified by the linearity of the strain-electric field relation.

Conclusions
In summary, synchrotron XRD, together with HBAR devices and a PM300 PiezoMeter, was adopted to accurately characterize the longitudinal piezoelectric coefficient (d 33 ) of Al 1−x Sc x N films in this paper. By considering the substrate clamping effect, more reliable and consistent d 33 results were obtained, exhibiting the indispensability of the correction metlongitudinal piezoelectric coefficient hod for piezoelectric characterization, especially for materials with a small piezoelectric coefficient, such as the Al 1−x Sc x N system. Moreover, synchrotron XRD was proven as an effective method by which to evaluate the accuracy of d 33 extracted from PIEZOTEST PM300 and HBAR, providing a feasible, precise and alternative technique for piezoelectric response characterization.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest.