Theoretical and experimental study of shear mode bulk acoustic wave transformer based on c-axis zigzag ScAlN multilayer for rectenna application

A miniature electric source by RF–DC conversion can satisfy the increasing demand of wireless sensors for the internet of things (IoT). A rectifying antenna (called rectenna) is generally used for RF–DC conversion. A weak RF signal degrades conversion efficiency because of the insufficient activation of the diode in the rectenna. A Dickson charge pump¹ is a device used to amplify the RF voltage.^2,3 However, charge pumps are large and suffer from low efficiency and poor impedance matching.⁴ In order to overcome these problems, MHz piezoelectric transformers by means of the thickness extensional mode of PZT plates⁵ or lateral extensional mode of AlN films⁶ were reported for rectenna applications. Several experimental and theoretical approaches for the GHz transformers have been studied.^6–9 These devices operate in the Lamb wave mode^7–9 or Lamé-mode¹⁰ using an interdigital transducer (IDT). Bulk acoustic wave (BAW) transformers are attractive for rectenna applications as they are small and have high power handling capability¹¹ compared with IDT-type transformers. However, fabrication of the BAW transformer in the GHz ranges has not been achieved because it is difficult to grow a thin-film polarization-inverted layer. In this study, we propose the free-standing polarization-inverted BAW transformers based on c-axis zigzag ScAlN multilayers operating in the low GHz range as shown in Fig. 1.

In previous studies, a complex behavior in the mechanical part of the transformer has been generally predicted by employing a finite element method (FEM).^5–10 Therefore, the theoretical simulation of the entire performance of the rectenna comprising the antenna, transformer, and rectifier using a common circuit simulator is not straightforward. Here, we report a simple formula predicting the voltage gain and simple equivalent circuit model, which can be easily implemented in a circuit simulator in contrast to the FEM.

The BAW transformer combines an input standard monolayer piezoelectric film and an output polarization-inverted multilayer film as shown in Fig. 1. Here, we developed the c-axis zigzag structures for the polarization-inverted multilayer. In this structure, the c-axes of the films are symmetrically tilted with the same thickness. The thickness extensional mode is excited as the fundamental mode, whereas the thickness shear mode is excited as the overtone mode (see Fig. 1). A higher overtone mode can be excited by increasing the number of ScAlN layers in the stack. The resonant frequencies of the resonators based on n-layer polarization-inverted multilayer piezoelectric films are the same as those of monolayer resonators.

The capacitive impedance Z_C of the c-axis zigzag n-layers is given by the following equation:

where d is the thickness of each piezoelectric layer, f_r is the resonant frequency of the c-axis zigzag stack resonator, ε is the dielectric constant, and S is the electrode area. Equation (1) indicates that the capacitive impedance of an n-layer c-axis zigzag resonator is n times larger than that of a monolayer resonator when the thickness shear mode is excited. Voltage transformations can be achieved between the input monolayer and output multilayer because of impedance transformations. We previously reported various thin-film polarization-inverted structures such as (0001)/$(0001¯)$ ScAlN films,¹² (11$2¯$0)/(⁠$1¯1¯$20) ZnO films,¹³ c-axis zigzag ZnO,¹⁴ and Pb(Zr,Ti)O₃(PZT)/PbTiO₃(PTO).¹⁵ Vorobiev and Gevorgian also reported (001)/(00$1¯$⁠) (Ba, Sr) TiO₃ structures.¹⁶ 

The piezoelectricity of AlN was greatly improved by Sc doping less than Sc/(Sc + Al) of 43% where is the phase transition point.¹⁷ We previously reported a high electromechanical coupling coefficient, $kt2$⁠, of 12% for thickness extensional mode excitation in a c-axis-oriented ScAlN film.¹⁸ Quasi-thickness shear mode piezoelectric constant $e′35$ for the c-axis tilted film is enhanced with increasing pure thickness extensional mode e₃₃, whereas pure thickness shear mode e₁₅ rather reduces $e′35$ in the θ >45°, where θ is the c-axis tilt angle from the substrate normal, as shown in the following equation:¹⁹ 

The calculated electromechanical coupling coefficients of quasi-thickness extensional mode $k′35$ and that of quasi-thickness shear mode $k′35$ in ScAlN and AlN as a function of the c-axis tilt angle are shown in Fig. 2. The elastic and piezoelectric constants of Sc_xAl_1−xN predicted by a density functional theory (DFT)²⁰ were used in the calculation. As shown in Fig. 2, the maximum $k′35$² in Sc_0.45Al_0.55N is much larger than that of AlN. $k′35$ increases and undesired $k′33$ decreases with the c-axis tilt angle increase up to 35°.

The theoretical voltage gain and transmission loss S₂₁ of the BAW piezoelectric transformers were simulated by the electromechanical transmission line model (Mason's equivalent circuit model)²¹ considering polarization-inversions²² as illustrated in Fig. 3. The voltage gain increases with k²Q_m or the number of layers n in the output multilayer, as shown in Fig. 4.

Although the electromechanical transmission line model mentioned above is valid at any frequency, it is difficult to be implemented in a common electric circuit simulator because the complex mechanical circuit cannot be described by simple RLC components. In order to simulate easily the entire performance of the rectenna including an antenna, the BAW piezoelectric transformer, and a rectifier, using the electric circuit simulator, the simpler circuit model describing the free-standing BAW piezoelectric transformer was derived as illustrated in Fig. 5. This model is precise only in the vicinity of the operating frequency. As shown in Fig. 6, this model is in good agreement with the accurate electromechanical transmission line model (Mason's equivalent circuit model) in the vicinity of the operating frequency. In the vicinity of the operating frequency, the curves of the simpler model agreed with that of the exact Mason's equivalent circuit model with ±8% for S₂₁ and ±5% for voltage gain, respectively.

Simple formulas [Eqs. (3) and (4)] describing the theoretical operating frequency and voltage gain of the BAW piezoelectric transformers were also derived in order to calculate the expected characteristics without using any equivalent circuit models. When the resonant frequency of the input layer is the same as that of the output layer, the theoretical operating frequency f and the theoretical voltage gain G_V are given by

where d_in and d_out are the thicknesses of each piezoelectric layer, v_in and v_out are the acoustic velocities, ρ_in and ρ_out are the densities, k_in and k_out are the electromechanical coupling coefficients, ε_in and ε_out are the dielectric constants of the input and output layers, Q_m is the mechanical quality factor, and n is the number of layers in the output layer. The voltage gain is proportional to Q_mk_ink_out following Eq. (4). From these formulas, the operating frequency and voltage gain can be calculated within the accuracy of ±1% and ±15% of the precise electromechanical transmission line model (Mason's equivalent circuit model), respectively (see Fig. 4).

In the experiment, the c-axis four-layer zigzag ScAlN output film was grown on sacrificial layers/Pyrex glass substrate by glancing angle RF-magnetron sputtering with a Sc_0.43Al_0.57 alloy target. The substrate inclination from the target surface was 70° to obtain the c-axis titled by approximately 25°–45° with respect to the substrate normal. In order to grow the c-axis zigzag multilayer film, the substrate was rotated by 180° after the growth of each layer. The four-layer c-axis zigzag structure was obtained by repeating this process three times. A c-axis tilted ScAlN monolayer film for the input layer was grown after the deposition of the intermediate electrode film on the c-axis zigzag four-layer. After the growth of ScAlN films, the substrate was removed by wet etching of the sacrificial layer. Al and Au thin films were used for the sacrificial layers removed using an iodine-based etchant. Top and bottom electrodes were deposited on both sides of the ScAlN stack by taking care of the alignment between the top and bottom electrodes.

The cross-sectional scanning electron microscopy (SEM) images of the developed free-standing BAW piezoelectric transformer are shown in Figs. 7(a) and 7(b). The c-axis zigzag structure without the substrate was clearly observed. ψ-scan XRD curves were measured (X'Pert PRO, PANalytical) to obtain quantitative information on the out-of-plane orientation of the film. The c-axis tilt angles of the even and odd layers of the stack were ψ = 33° and ψ  = 25°, respectively. The FWHM values of the ψ-scan curves indicating the out-of-plane orientations of the even and odd layers were determined to be 7.8° and 3.8°, respectively.

The transmission loss S₂₁ and voltage gain of the free-standing BAW piezoelectric transformer were measured using a network analyzer (E5071C, Agilent Technologies) with RF probes (|Z| probe, Z10-GS-500, Form Factor). A voltage gain of +10 dB in the 0.5 GHz range was observed (Fig. 8). The voltage gain bandwidth was 12 MHz, corresponding to a relative bandwidth of 2.2%. The effective electromechanical coupling coefficients k_eff² for the fifth overtone mode of the input monolayer and output four-layer estimated using the resonance/antiresonance method²³ were 4.8% and 4.4%, respectively. Additionally, the theoretical voltage gain was simulated using the electromechanical transmission line model (Mason's equivalent circuit model) considering fourth polarization-inversions. The experimental k_eff² were used in the simulation. The experimental results are in good agreement with the theoretical prediction where the experimental k_eff² were used. In the vicinity of the operating frequency, the experimental curves agreed with simulated curves with ±10%.

In conclusion, the free-standing BAW piezoelectric transformer based on the c-axis zigzag ScAlN multilayer was experimentally and theoretically demonstrated. The theoretical voltage gain of the transformer was simulated using the electromechanical transmission line model (Mason's equivalent circuit model) by considering the polarization-inversions increase with k²Q_m. The simple circuit model describing the free-standing BAW piezoelectric transformer was derived, which is only precise in the vicinity of the operating frequency, to simulate the entire performance of the rectenna including an antenna, the BAW piezoelectric transformer, and a rectifier easily. Simple formulas describing the theoretical operating frequency and voltage gain of the BAW piezoelectric transformers were also derived to predict the performance without using any equivalent circuit models or FEM. An experimental voltage gain of +10 dB with a relative bandwidth of 2.2% was achieved in the transformer based on a four-layer c-axis zigzag ScAlN film. This voltage transformer looks promising for rectennas of wireless sensors.

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