In Situ Synchrotron XRD Characterization of Piezoelectric Al_1−xSc_xN Thin Films for MEMS Applications

Abstract

Aluminum scandium nitride (Al_1−xSc_xN) 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 Al_1−xSc_xN film. The measurement results quantitatively demonstrated the piezoelectric effect of Al_1−xSc_xN 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 Al_0.9Sc_0.1N 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.

1. 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 d₃₃, 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 d₃₃ of Al_0.8Sc_0.2N 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−xSc_xN film is a key parameter for the design and optimization of high-frequency acoustic resonators and filters. At present, Al_1−xSc_xN 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−xSc_xN 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−xSc_xN 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−xSc_xN 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−xSc_xN 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]. d₃₃ 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−xSc_xN film is only tens of pC/N, about an order of magnitude smaller than barium titanate (BaTiO₃) [27] and zirconate titanate (PZT) [28], it is very challenging to characterize Al_1−xSc_xN 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_0.2Ga_0.8N 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 d₃₃ of Al_1−xSc_xN films. The measured results quantitatively demonstrated the lattice spacing variation of Al_1−xSc_xN films induced by piezoelectric effect upon applied external voltage. Longitudinal piezoelectric coefficients d₃₃ of Al_1−xSc_xN film with different Sc concentrations were successfully obtained and compared with traditional measurement methods. Moreover, by implementing substrate clamping effect calibration, the d₃₃ deviation between synchrotron XRD and other methods was significantly reduced, indicating the validity of synchrotron XRD characterization for precise d₃₃ measurement.

2. Materials and Methods

2.1. Synchrotron XRD Measurement System Setup

Figure 1a–c illustrates the brief fabrication process of Al_1−xSc_xN samples with x = 0, 10% and 20%. Firstly, 200 nm Mo/850 nm Al_1−xSc_xN/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_0.9Sc_0.1N and Al_0.8Sc_0.2N 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 Al_1−xSc_xN-selective etching. Anisotropic etching of Al_1−xSc_xN 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.

Figure 1.

(a) Mo/Al_1−xSc_xN/Mo piezoelectric stack deposition; (b) Top Mo/Al_1−xSc_xN etching; (c) Top electrode Mo patterning; (d) Schematic of the measurement setup for the in situ synchrotron XRD characterization under static voltage supply.

Figure 2.

The XRD rocking curves of (0002) plane for AlN, Al_0.9Sc_0.1N and Al_0.8Sc_0.2N.

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−xSc_xN 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−xSc_xN samples.

2.2. 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−xSc_xN 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−xSc_xN/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−xSc_xN 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−xSc_xN sidewalls with a 50–60° etching profile were obtained, as shown in Figure 4. Due to the lower etching rate of Al_0.9Sc_0.1N compared with pure AlN film, the sidewall angle of Al_0.9Sc_0.1N was ~10° smaller with a tapered etching profile. It should be noted that the Al_1−xSc_xN 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−xSc_xN 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 (S₁₁) were carried out by a network analyzer KEYSIGHT E5071C.

Figure 3.

The fabrication process of Al_1−xSc_xN HBAR devices. (a) Mo/Al_1−xSc_xN/Mo piezoelectric stack deposition, (b) Top Mo/Al_1−xSc_xN patterning, (c) SiO₂ isolation layer deposition and patterning, (d) Au contact layer deposition and patterning, (e) Top electrode Mo patterning.

Figure 4.

Cross-section SEM images of (a) AlN and (b) Al_0.9Sc_0.1N piezoelectric stacks.

3. Results and Discussion

3.1. d₃₃ Measurement by Synchrotron XRD Method

The in situ synchrotron XRD curves of AlN, Al_0.9Sc_0.1N and Al_0.8Sc_0.2N films under different applied voltages are shown in Figure 5. In general, the diffraction peaks of the Al_1−xSc_xN (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−xSc_xN films with Sc concentrations of 10% and 20% exhibit similar phenomena, with peak shifts of 0.010° and 0.015° for Al_0.9Sc_0.1N and Al_0.8Sc_0.2N 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 (d_E–d₀)/d₀, the longitudinal strain S and the piezoelectric coefficient d₃₃ of piezoelectric films can be obtained according to Equation (1) [33]:

$$d_{33}={\left(\frac{\partial S_3}{\partial E_3}\right)}^T=\frac{\left(d_E-d_0\right)}{d_0}\cdot \frac{1}{E},$$ (1)

where d_E and d₀ 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.

Figure 5.

Synchrotron XRD curves of (a) AlN, (b) Al_0.9Sc_0.1N, (c) Al_0.8Sc_0.2N under different applied voltages V; Electric field E dependence of longitudinal strains of (d) AlN, (e) Al_0.9Sc_0.1N, (f) Al_0.8Sc_0.2N derived from synchrotron XRD peaks. The data from the standard PDF cards for AlN (No. 00-025-1133) are referred.

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–d₀)/d₀ were derived on the basis of the above equations. The applied electrical field dependence of the Al_1−xSc_xN 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−xSc_xN 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.

3.2. 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 Al_1−xSc_xN HBAR device with a pentagon-shaped resonant area. As shown in Figure 6b, the S₁₁ curves of Al_1−xSc_xN 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_0.9Sc_0.1N films, respectively.

Figure 6.

(a) Top-view SEM image of Al_1−xSc_xN HBAR device; (b) S₁₁ response of HBAR devices with AlN and Al_0.9Sc_0.1N films; Mason equivalent circuit fitting of (c) AlN and (d) Al_0.9Sc_0.1N on a 200 MHz span.

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−xSc_xN 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,d, the simulated results of the Mason model are in good agreement with the measured S₁₁ curves. The d₃₃ of AlN and Al_0.9Sc_0.1N films extracted using the Mason model are 4.22 pC/N and 6.04 pC/N, respectively.

Figure 7.

Equivalent circuit of the Mason model for Al_1−xSc_xN HBAR device.

3.3. d₃₃ Measurement by PM300 Method

Figure 8a illustrates d₃₃ measurements using the Berlincourt method PIEZOTEST PM300 [35,36]. Al_1−xSc_xN piezoelectric samples were clamped between two contact probes and subjected to a low frequency force. Electrical signals generated from Al_1−xSc_xN film 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 Al_1−xSc_xN sample preparation, 900 nm Al_1−xSc_xN 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 Al_0.9Sc_0.1N films measured by PIEZOTEST PM300 were 6.33 pC/N and 8.96 pC/N, respectively.

Figure 8.

(a) Schematic of d₃₃ measurement by PIEZOTEST PM300 [36]; (b) Cross-section SEM image of piezoelectric sample.

3.4. d₃₃ Discussion

The piezoelectric coefficient d₃₃ of AlN and Al_0.9Sc_0.1N 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 initio Simulation Package (VASP) [37,38,39]. It is observed that the d₃₃ measured by synchrotron XRD are about 40% lower compared to that measured by PM300, while the d₃₃ 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.

Table 1.

The measured and corrected d₃₃ of AlN and Al_0.9Sc_0.1N films from synchrotron XRD, PM300, HBAR and theoretical calculation.

Material	Method	Measured d33 (pC/N)	Corrected d33 (pC/N)	Theoretical Calculated d33 (pC/N)
AlN	Synchrotron XRD	3.54	4.76	5.38
	PM300	6.33	4.29
	HBAR	4.22	5.43
Al0.9Sc0.1N	Synchrotron XRD	5.58	7.79	7.89
	PM300	8.96	7.03
	HBAR	6.04	8.25

Since the deformation amount of Al_1−xSc_xN 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 d₃₃ measurement. Referring to Lefki et al. [40], the interference of the substrate during d₃₃ measurement is quantitatively analyzed below.

The following equations can be deduced from the classic piezoelectric equation based on the symmetry of Al_1−xSc_xN materials [40]:

$$D_3=d_{31}·\left(T_1+T_2\right)+d_{33}·T_3+{\epsilon }_{33}^T·E_3,$$ (2)

$$S_1=s_{11}^E·T_1+s_{12}^E·T_2+s_{13}^E·T_3+d_{31}·E_3,$$ (3)

$$S_2=s_{12}^E·T_1+s_{11}^E·T_2+s_{13}^E·T_3+d_{31}·E_3,$$ (4)

$$S_3=s_{13}^E·T_1+s_{13}^E·T_2+s_{33}^E·T_3+d_{33}·E_3,$$ (5)

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, d₃₁ is the transverse piezoelectric coefficient, ${\epsilon }_{33}^T$ is the dielectric constant of the film in the longitudinal direction, and $s_{11}^E, s_{12}^E, s_{13}^E, s_{33}^E$ are the mechanical compliances of the piezoelectric film.

As described above, synchrotron XRD uses the inverse piezoelectric effect for d₃₃ 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 S₁ and S₂ are assumed as zero. Since the longitudinal stress T₃ = 0, the in-plain stress can be deduced from Equations (3) and (4) as:

$$T_1=T_2=\frac{-d_{31}{E}_3}{s_{11}^E+s_{12}^E}$$ (6)

The calibrated longitudinal piezoelectric coefficient d_33,i considering inverse piezoelectric effect can be expressed as:

$$d_{33,i}=\frac{\Delta l}{V}=\frac{S_3}{E_3}=d_{33,\mathrm{XRD}}+\frac{2s_{13}^E{d}_{31}}{s_{11}^E+s_{12}^E}$$ (7)

where d_33,XRD is the experimental result measured by synchrotron XRD. By using theoretical values of $s_{11}^E,s_{12}^E,s_{13}^E$ and d₃₁ for a rough evaluation, the measured d_33,XRD from synchrotron XRD is underestimated because of the deformation constraint by the substrate. The d₃₃ value of AlN and Al_0.9Sc_0.1N 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 d₃₃ 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 $s_{ij}^E$ and piezoelectric strain coefficient $d_{ij}$ in Equation (7) with the stiffness coefficient $C_{ij}^E$ and piezoelectric stress coefficient $e_{ij}$, as shown below:

$$s_{11}^E=\frac{C_{11}^E{C}_{33}^E-C_{13}^E{}^2}{\left(C_{11}^E-C_{12}^E\right)\left[c_{33}^E\left(C_{11}^E+C_{12}^E\right)-2C_{13}^E{}^2\right]},$$ (8)

$$s_{12}^E=-\frac{C_{12}^E{C}_{33}^E-C_{13}^E{}^2}{\left(C_{11}^E-C_{12}^E\right)\left[c_{33}^E\left(C_{11}^E+C_{12}^E\right)-2C_{13}^E{}^2\right]},$$ (9)

$$s_{13}^E=-\frac{C_{13}^E}{c_{33}^E\left(C_{11}^E+C_{12}^E\right)-2C_{13}^E{}^2},$$ (10)

$$d_{31}=\frac{e_{31}{C}_{33}^E-e_{33}{C}_{13}^E}{\left(C_{11}^E+C_{12}^E\right)C_{33}^E-2C_{12}^E{}^2},$$ (11)

$$d_{33}=\frac{e_{33}\left(C_{11}^E+C_{12}^E\right)-2e_{31}{C}_{13}^E}{\left(C_{11}^E+C_{12}^E\right)C_{33}^E-2C_{13}^E{}^2}.$$ (12)

d_33,r extracted from HBAR devices can be expressed as:

$$d_{33,r}=\frac{e_{33}}{C_{33}^E}.$$ (13)

According to the above, the d_33,r of the AlN and Al_0.9Sc_0.1N 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 d₃₃ 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−xSc_xN 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:

$$S_1=S_2=-\frac{\mu T_3}{Y}$$ (14)

Then, the in-plane stress is straightforwardly calculated from the strain-stress equation as follows:

$$T_1=T_2=\frac{-\frac{\mu T_3}{Y}-d_{31}{E}_3-s_{13}^E{T}_3}{s_{11}^E+s_{12}^E}$$ (15)

The calibrated longitudinal piezoelectric coefficient d_33,d considering the substrate-restricted direct piezoelectric effect can be expressed as:

$$d_{33,d}=\frac{Q}{F_3}=\frac{D_3}{T_3}=d_{33,\mathrm{PM}300}+2d_{31}\frac{\frac{\mu }{Y}+s_{13}^E}{s_{11}^E+s_{12}^E},$$ (16)

where d_33,PM300 is the experimental result measured by PM300. $2d_{31}\frac{\frac{\mu }{Y}+s_{13}^E}{s_{11}^E+s_{12}^E}$ in Equation (16) is negative for Al_1−xSc_xN film due to additional in-plane stress, leading to an overestimated d_33,PM300 measurement results. The d₃₃ of AlN and Al_0.9Sc_0.1N 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 d₃₃ results of synchrotron XRD, PM300 and HBAR before and after substrate-related calibration. The revised d₃₃ 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 d₃₃ value of Al_0.9Sc_0.1N 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 d₃₃ 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.

Table 2.

d₃₃ comparison with other reports.

Material	d33 (pC/N)	Reference	Material	d33 (pC/N)	Reference
AlN	4.53	[24]	Al0.9Sc0.1N	7.5	[8]
AlN	4.76	Our work	Al0.9Sc0.1N	7.79	Our work
AlN	4.9	[25]	Al0.88Sc0.12N	7.9	[43]
AlN *	5.0	[44]	Al0.85Sc0.15N	7.92	[22]
AlN	5.1	[26]	Al0.83Sc0.17N	9.5	[43]
AlN *	5.1	[45]	Al0.8Sc0.2N	11.5	[8]
AlN	5.53	[46]	Al0.75Sc0.25N	13.2	[47]

* Obtained by theoretical calculations.

The Berlincourt method is predominantly used for d₃₃ 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 d₃₃ relative comparison [48]. The HBAR method can be not only used for d₃₃ 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 d₃₃ 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.

4. Conclusions

In summary, synchrotron XRD, together with HBAR devices and a PM300 PiezoMeter, was adopted to accurately characterize the longitudinal piezoelectric coefficient (d₃₃) of Al_1−xSc_xN films in this paper. By considering the substrate clamping effect, more reliable and consistent d₃₃ 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−xSc_xN system. Moreover, synchrotron XRD was proven as an effective method by which to evaluate the accuracy of d₃₃ extracted from PIEZOTEST PM300 and HBAR, providing a feasible, precise and alternative technique for piezoelectric response characterization.

Author Contributions

Data curation, W.J., L.Z., L.C. and X.Y.; Formal analysis, W.J.; Funding acquisition, L.Z. and Z.M.; Investigation, W.J.; Project administration, L.Z.; Resources, X.L.; Software, X.Y.; Supervision, W.Y.; Validation, Z.M. and W.Y.; Writing—original draft, W.J.; Writing—review and editing, Y.Y. and Z.M. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

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.

Funding Statement

This research was funded by the National Natural Science Foundation of China, grant No. 62274171, the Natural Science Foundation of Shanghai, grant No. 21ZR1474500 and Shanghai Technology Innovation Project, grant Nos. 20DZ1100603 and 22501100700.