Bulk acoustic wave transformer based on the combination of the high-ε epitaxial PbTiO₃ and low-ε ScAlN thin films

Wireless power transfer has attracted much attention for charging the batteries of miniature electronic devices such as radio frequency identifier and sensors.¹ The energy from electromagnetic waves is usually extracted by a rectifying antenna (called a rectenna) that converts RF energies to direct currents. However, a weak RF signal cannot bias the diode sufficiently in a rectenna with low input impedance. Impedance transformation of a standard 50 Ω antenna enables high-voltage operation of the diode.² 

GHz voltage transformers operating in Lamb wave mode^3–5 or Lamé-mode⁶ have been fabricated using interdigital transducers (IDTs), but in GHz ranges, the power tolerance of IDTs is lowered by the sub-micrometer width of the electrode on the substrate. Bulk acoustic wave (BAW)-type polarization-inverted transformers are expected to boost the power handling capability⁷ because their acceptable power is determined by the entire thickness of the polarization-inverted layer. In addition, the transformation ratio of a BAW-type transformer can be increased merely by increasing the number of layers, thus realizing small-size surface-mounted devices. In contrast, the size of an IDT-type transformer generally increases with the transformation ratio. We previously reported a BAW-type transformer based on quasi-shear mode in a zigzag ScAlN polarization-inverted layer.⁸ In this device, impedance transformation by the input and output layers was achieved by exploiting the capacitance difference between the thick zigzag layer and thin monolayer with the same resonant frequency.

In this study, we fabricated thickness-extensional mode BAW transformers by combining two thin films with different dielectric constants ε (see Fig. 1). The capacitive impedance Z_C of the BAW resonators is calculated as

where d is the film thickness, f is the resonant frequency, ε is the dielectric constant, and S is the electrode area. From Eq. (1), the capacitive impedance of a BAW resonator is inversely proportional to its dielectric constant ε. Impedance transformations occur between an input high-ε layer and a low-ε output layer. Therefore, by combining a high- and low-ε layer, we can expect to achieve a voltage transformer. Tetragonal lead titanate (PbTiO₃: PTO) epitaxial films have the highest electromechanical coupling coefficient k_t² among the high-ε piezoelectric materials such as barium strontium titanate (BST) and potassium sodium niobate (KNN). In contrast, the k_t of ScAlN films is the highest in low-ε piezoelectric materials such as AlN, ZnO, and SiO₂. Therefore, we considered that a combination of epitaxial Pb(Zr,Ti)O₃ and ScAlN films would maximize the voltage gain and efficiency of the transformer.

The theoretical voltage gain of the BAW piezoelectric transformers was computed using the electromechanical transmission line model (Mason's equivalent circuit model).⁹ The voltage gain vs k²Q is plotted for different ratios of ε_in to ε_out (where ε_in and ε_out denote the dielectric constants of the input and outer layers, respectively) in Fig. 2.

Assuming that the resonant frequency of the input layer matches that of the output layer, Eqs. (2) and (3) describe the theoretical operating frequency f_o and voltage gain G_V of the BAW piezoelectric transformers, respectively. These parameters can predict the transformer performance without requiring equivalent circuit models,

where d_in and d_out are the thicknesses of the input and output piezoelectric layers, respectively, v_in (v_out) (m/s) are the input (output) acoustic velocities, ρ_in (ρ_out) (kg/m³) are the input (output) densities, Z_in (Z_out) (kg/m²/s) are the input (output) acoustic impedances, k_in (k_out) are the input (output) electromechanical coupling coefficients, and ε_in (ε_out) (F/m) are the input (output) dielectric constants. Q_m is the mechanical quality factor. From these formulas, the operating frequency f_o (Hz) and voltage gain G_V were calculated to be within ±0.1% and ±1% of the precise electromechanical transmission line model (Mason's equivalent circuit model), respectively (see Fig. 2). For a free-standing film structure, intrinsic k_t² should be substituted in Eqs. (2) and (3) when thin electrode layers are ignored. In the case of a high overtone bulk acoustic wave resonator (HBAR) structure which includes a thick substrate, overall effective electromechanical coupling coefficients k_eff² should be substituted in Eqs. (2) and (3) instead of intrinsic k_t². The overall k_eff² can be roughly estimated from the intrinsic k_t² by means of the relation k_eff²/k_t² = M_p/M where M_p is the mass of piezoelectric active layer and M is that of an overall resonator, respectively. On the other hand, the overall k_eff² also can be experimentally determined from resonant and anti-resonant frequencies of overtone multiple resonant peaks of HBAR using the following equation:

where f_s and f_p are the peak frequencies of the real part of admittance and impedance in the vicinity of thickness extensional mode resonant frequency, respectively. Note that Mason's equivalent circuit model provides more accurate predictions of the device voltage gain.

To boost the voltage gain, a high electromechanical coupling coefficient k_t of the thickness-extensional mode and a large ε_in/ε_out are required (Fig. 2). Epitaxial PTO films are expected to possess high k_t and high ε, whereas ScAlN films possess high k_t but low ε. A BAW transformer with a high-ε sputter-epitaxial PTO film and a low-ε ScAlN film (shown in Fig. 1) should provide a high voltage gain. We previously reported a high k_t² of 28.1% of PbTiO₃ (PTO)¹⁰ and 17.6% of Pb(Zr,Ti)O₃ sputter-epitaxial films.¹¹ Shortly after Akiyama et al. newly reported an increased piezoelectric constant d₃₃ in ScAlN films,¹² we reported the first fabrication of ScAlN film bulk acoustic resonator (FBAR).¹³ The experimental k_t² of ScAlN film was 12%.¹⁴ 

The lattice constants of lanthanum-doped (100) strontium titanate (La-STO) conductive single-crystal substrates are similar to those of the PTO. We prepared two types of BAW transformers operating in different frequency ranges: 50 MHz and 400 MHz. As the high-ε layers of the BAW transformers operated in the 50- and 400-MHz ranges, we prepared tetragonal lead titanate (PbTiO₃: PTO) sputter epitaxial films. Epitaxial PTO films (17.5 μm for 50 MHz and 1.25 μm for 400 MHz) for the input layers were grown on the La-STO substrates (0.3 mm) by RF magnetron sputtering with a powder target. After growing the PTO films, the substrates were turned over, and the output Sc_0.4Al_0.6N layers (56 μm for 50 MHz and 5.2 μm for 400 MHz) were grown on their reverse sides by RF magnetron sputtering with a ScAl alloy (Sc: 43 at. %) target.

The crystal orientations of the films were determined by x-ray diffraction (X'Pert PRO, PANalytical). FWHM values of the ω-scan rocking curves of the 50-MHz PTO film, 50-MHz ScAlN film, 400-MHz PTO film, and 400-MHz ScAlN film were determined as 1.5°, 2.2°, 0.08°, and 1.8°, respectively, indicating good crystalline orientation (Fig. 3).

The k_t² provides the material intrinsic electromechanical coupling of the layer. To evaluate k_t², conversion loss (CL), voltage gain, and transmission loss (S₂₁) of the BAW piezoelectric transformer were measured by a network analyzer (E5071C, Agilent Technologies). Comparing the experimental CL curves with the theoretical CL curves, the k_t² of the input PTO and output ScAlN films of the BAW transformer operating in the 50 MHz range was determined as 22% and 16%, respectively (see Fig. 4).¹⁴ 

On the other hand, overall k_eff², including a thick substrate, determines the transformer performance. Using Eq. (4), k_eff² of PbTiO₃ and ScAlN layers was determined to be 1.3% and 7.7% for the 50 MHz transformer, respectively. Of course, the overall k_eff² in the HBAR structure decreases compared with an intrinsic k_t² in the free standing structure because of the large mass of the non-piezoelectric SrTiO₃ substrate in HBAR. Overall Q_m values (Q_entire) for the 50 MHz transformer were found to be 250 for PTO and 100 for ScAlN, respectively. Experimental k_eff² and Q_entire products, which determine the transformer performance, were 7.9 for the PTO layer and 3.1 for the ScAlN layer in the 50 MHz transformer, respectively.

As shown in Fig. 5(a), the raw experimental S₂₁ is found to be −6.1 dB, which is measured by a network analyzer where input and output impedances are 50 Ω. Because the input and output of the present transformer are different from 50 Ω, the S₂₁ is degraded due to the impedance mismatch. Therefore, ideal S₂₁, when the input and output characteristic impedance is intentionally adjusted to match to the input and output impedance of the transformer using inductance, is calculated from raw experimental S₂₁. As a result, the ideal S₂₁ reached −1.8 dB. The information of the inserted component is summarized in Table I. The open circuit voltage gain in the 50 MHz range was 12.3 [see Fig. 5(b)]. The gain of 25.0 was obtained in the impedance matching condition when the series inductance is inserted. The theoretical S₂₁, considering for a 50 Ω system, and the open circuit voltage gain simulated by Mason's equivalent circuit model show good agreement with the experimental results.

As shown in Fig. 6, k_t² of the input PTO and the output ScAlN film of the BAW transformer operating in 400 MHz range was determined to be 34% and 17%, respectively, comparing the experimental CL curves with the theoretical CL curves. Using Eq. (4), overall k_eff² of PbTiO₃ and ScAlN layer was determined to be 0.4% and 0.1% for the 400 MHz transformer, respectively. Overall Q_m values (Q_entire) for the 400 MHz transformer were found to be 2500 for PTO and 2700 for ScAlN, respectively. Experimental k_eff² and Q_entire products, which determine the transformer performance, were 5.6 for the PTO layer and 6.1 for the ScAlN layer in the 400 MHz transformer, respectively.

The information of the inserted component is also summarized in Table I. The raw experimental S₂₁ and impedance matched ideal experimental S₂₁ were found to be −6.0 dB and −0.91 dB, respectively, as shown in Fig. 7(a). The voltage gain with open circuit and inductance insertion are obtained to be 40.9 and 49.8 [Fig. 7(b)]. Large difference in impedance between input PTO and output ScAlN in Fig. 7(c) shows apparent impedance conversion.

In conclusion, the BAW piezoelectric transformer with combination of high and low ε thin films is fabricated by RF magnetron sputtering. Sputter-epitaxial PbTiO₃ and ScAlN films were selected as the input high ε layers and the output low ε layers, respectively. The properties of ScAlN and PbTiO₃ layers—rocking curve FWHM, ε_r, k_t², k_eff², Q_entire, and k_eff² Q_entire product—are summarized in Table II. The open circuit voltage gain of 12.3 in the 50 MHz range and 40.9 in the 400 MHz range was experimentally demonstrated. Figure 8 shows the comparison of the voltage gain in the previously reported piezoelectric transformers with that in this study. The BAW type transformers in this study showed an increase in the performance when compared with state-of-the-art piezoelectric transformers. This transformer appears promising for use in a voltage transformer in the rectenna.

This work was supported by the JST CREST (No. JPMJCR20Q1) and KAKENHI (Grant-in-Aid for Scientific Research Nos. 19H02202 and 18K19037).