A method for extracting sole mechanical properties of Bragg reflector by GHz ultrasonic pulse-echo technique

A solidly mounted resonator (SMR)¹ allows acoustic isolation of the piezoelectric layer from the substrate with the acoustic Bragg reflector acting as an airgap in a free-standing film bulk acoustic resonator (FBAR). The acoustic Bragg reflector is fabricated by alternating deposition of high and low acoustic impedance layers on the substrate. In contrast to the airgap type FBAR, SMR is promising for high frequency and high-power handling in the RF filter applications because the heat generation caused by dielectric and mechanical losses can be dissipated into the supported substrate. Ivira et al. reported that the FBAR structures are far more prone to heat than SMRs.² On the other hand, ScAlN has recently received attention for use in commercial bulk acoustic wave (BAW) filters because of the large electromechanical coupling. However, compared to AlN, ScAlN possesses lower intrinsic mechanical Q_m,³ higher tan δ, and lower thermal conductivity,⁴ making heat accumulation problematic. The thermal conductivity of ScAlN films (3–8 W m⁻¹ K⁻¹)⁴ is reported to be orders of magnitude lower than that of AlN films. High power-tolerant SMR structures will be increasingly important as operating frequency and Sc concentrations increase.

Resonator Q is highly dependent on the acoustic properties of the Bragg reflector, and separate evaluation of the acoustic properties of piezoelectric layer part and the reflector part is difficult in a common electric impedance characterization.

In this study, an experimental method for extracting sole reflector properties by employing ultrasonic pulse-echo measurement in the GHz ranges is reported. The simulation results of the mechanical reflector properties, which this study aims to extract experimentally, are shown in Figs. 1(a) and 1(b). The transmission loss indicates the degree of acoustic isolation between the substrate and the piezoelectric layer. For example, the W/SiO₂ reflector exhibit higher reflectance and wider bandwidth than those of Mo/SiO₂ one owing to larger acoustic impedance difference in W/SiO₂. A large transmission loss valley results in higher reflectance of the Bragg reflector and higher Q resonance of the piezoelectric layer. As can be seen, the effective Q of SMR (blue plot) degrades from the input intrinsic Q value of 3000 with decreasing reflectance (increasing transmittance) of the Bragg reflector.

In a preliminary experiment, we employed a standard ultrasonic microscope system, which uses acoustic echo signals from the surface of the reflector.⁵ However, in such a reflectance method, the difference between the echo signals from the reflector surface and that from the reference standard plate were too weak to detect experimentally.⁵ Therefore, we here propose a transmittance method using the echo reflected from the back side of the substrate. The echo signals include the information of round-trip transmittance of the reflector.

There have been many studies addressing a transmittance measurement in order to evaluate phononic crystal bandgap. Most experimental transmission measurement in phononic crystals are centered on Lamb wave⁶ or SAW devices.⁷ Although BAW measurements in the kHz–MHz ranges^8–10 or laser ultrasonic techniques in the subterahertz ranges¹¹ have been reported, there is few studies on the ultrasonic pulse-echo method or ultrasonic microscope method in the GHz range.

The measurement procedure is shown in Fig. 2. First, as shown in Fig. 3, time domain responses of (1) the ultrasonic transducer alone and (2) the ultrasonic transducer/salol coupler/Bragg reflector structure are measured, as shown in Fig. 3. Next, the echoes (1) and (2) of the time domain response of A₁ and C in Fig. 3, respectively, are gated and Fourier transformed to obtain the frequency response [Fig. 4(a)]. (4) Round-trip transmittance for infinite length of the salol/reflector structure is obtained by subtracting (1) transducer insertion loss, (3) the salol propagation loss, and the transmission loss TL of transducer/coupler boundary from (2). TL of the transducer/coupler boundary can be calculated by the following equation:

where Z_c and Z_b are the acoustic impedance of coupler and buffer rod, respectively. By substituting acoustic impedance of the salol coupler and sapphire buffer rod in Eq. (1), TL is estimated to be 5.8 dB. The TL should be also subtracted from Eq. (1).

The propagation loss of salol can be easily estimated in a preparatory experiment using a salol coupler on a reference material structure. Actual thickness of the salol coupler can be determined from the multiple refection delay time of the salol layer and acoustic velocity of 2700 m/s.¹² Finally, assuming that the Bragg reflector is vertically symmetric, (5) a halfway transmittance of infinite length of the salol/reflector structure [Fig. 4(b)] shown as black solid line is obtained by dividing (4) by 2.

To assess the validity of the present procedure, the theoretical simulation was used to compare the mechanical transmittance of the Bragg reflector part simply calculated by a mechanical equivalent circuit model and that acquired by the present procedure. As shown in Fig. 5, the simulation for the present procedure was conducted using the Mason's equivalent circuit model.^13,14 Elastic constants include a small imaginary component in the model to avoid an aliasing effect in the inverse Fourier transform process. As shown in Fig. 4(b), transmission loss of the Bragg reflector alone simulated by the present procedure is in completely agreement with that calculated using a simple mechanical circuit model. This result indicates that mechanical properties of the Bragg reflector part can be experimentally extracted by the present method.

In the experiment, Sc_0.40Al_0.60N film ultrasonic transducers were prepared by the RF magnetron sputtering technique.¹⁵ The Sc_0.40Al_0.60N film with 1.8 μm thickness was grown on the Pt bottom electrode (100 nm)/sapphire buffer rod (1.3 mm thickness). After the growth of Sc_0.40Al_0.60N films, Au films were deposited as a top electrode. Experimental impulse response of transducer in the time domain was acquired from inverse Fourier transform of S₁₁ measured by network analyzer (Keysight Technologies, P9370A). The experimental insertion loss curves of transducer were obtained by Fourier transform of the first echo reflected from the back side of the buffer rod in the time domain impulse response.¹⁶ Experimental and simulated longitudinal wave insertion loss curves of the ScAlN film are shown in Fig. 6(a). Theoretical curves were simulated by the Mason's equivalent circuit model including the electrode, as shown in Fig. 5. By comparing experimental (black solid plot) and theoretical curves (green solid line),^17,18 electromechanical coupling coefficient k_t² of the Sc_0.4Al_0.6N piezoelectric layer part was estimated to be 15.8%. Insertion loss of the ScAlN film transducer was measured to be 7.0 dB at 1.2 GHz and fractional bandwidth was 77%.

A water coupler is commonly used in the ordinary pulse-echo measurement system. In the previous study, however, the attenuation of the water coupler between the buffer rod and the Bragg reflector in the GHz range was too large to detect the apparent echo signal.² We also suffered a mis-alignment of acoustic axis between the buffer rod surface and Bragg reflector surface.⁵ Therefore, in this study, the salol coupler was employed to reduce propagation loss. Sputter-deposited SiO₂ film spacers as shown in Fig. 2 were employed in order to avoid the mis-alignment.

Three Mo/SiO₂ Bragg reflectors with one, two, and three pairs of Mo and SiO₂ films were fabricated. Mo and SiO₂ films were deposited on the silica glass substrate alternatively by the sputtering technique. In the all reflector, the thickness of each layer was adjusted so that the band center of Bragg reflectors was 1.5 GHz. Thicknesses of Mo and SiO₂ were targeted at 1030 nm and 930 nm, respectively. The actual thickness of each layer determined from cross-sectional scanning electron microscope (SEM) images is summarized in Table I.

(1) The experimental longitudinal wave insertion loss curve of the Sc_0.4Al_0.6N transducer (black solid plot) and (2) the first echo signal reflected from the backside of the Bragg reflector substrate (red plot) are shown in Fig. 6. The blue and yellow lines are the salol coupler propagation loss and the refection loss of the salol coupler/sapphire buffer rod boundary, respectively. The transmission loss of the Bragg reflector calculated by a mechanical equivalent circuit model and that experimentally obtained by proposed procedure are shown in Figs. 7(a)–7(c). These figures are the same representation as Fig. 1. A large dip in the transmission loss means higher reflectance of the Bragg reflector and leads higher Q resonance of the piezoelectric layer. The actual film-thickness of Mo and SiO₂ determined from cross-sectional SEM image (Table I) was used in the theoretical simulation of transmission loss of the sole Mo/SiO₂ reflector as shown by the blue line. For density and acoustic velocity constants of Mo and SiO₂, the values reported for the bulk materials^19,20 were used. As shown in Fig. 7(b), a discrepancy is observed between the theoretical result (blue line) and the experimental result (red plot). This is due to the difference in the density and acoustic velocity constants between bulk materials and thin films. Therefore, the actual density and acoustic velocity constants of Mo and SiO₂ for thin films were estimated by comparing the theoretical curve with the experimental curve. The theoretical curve (green line) calculated using 0.7 times the density of bulk SiO₂ (silica glass), as shown in green line, shows a good agreement with experimental curve (red plot). As shown in Fig. 7(c), around the 2 GHz region, a discrepancy between the theoretical curve (blue line) and the experimental plot was observed. This is because the signal less than −25 dB could not be detected due a noise floor in the present measurement. Therefore, we could not draw the fitting curve (green line). However, except the 2 GHz region, the experimental plots agreed well with the theoretical curve (blue line). A dominant factor in determining the limitation of reflectance and frequency is the sound attenuation in the salol coupler. The use of a low loss solid bonding coupler improves the reflectance and frequency measurement limits.

In conclusion, the GHz pulse-echo technique was used to experimentally evaluate mechanical properties of Bragg reflectors. The experimental curves agree well with the theoretical curves when the transmission loss is greater than −25 dB. This method with the solid salol coupler can be applied for a shear wave reflectance measurement by using a shear wave transducer based on c-axis tilted ZnO^21,22 or ScAlN films.²³ Shear wave reflectance is important to obtain a high Q resonator even for the longitudinal wave Bragg reflector.²⁴ This method is promising for the design and experimental evaluation of Bragg reflector wafers.

This work was supported by JST CREST (No. JPMJCR20Q1), JST FOREST, and KAKENHI (Grant-in-Aid for Scientific Research B, Nos. 19H02202 and 21K18734).