This paper investigates the issues on acoustic energy reflection of flexible film bulk acoustic resonators (FBARs). The flexible FBAR was fabricated with an air cavity in the polymer substrate, which endowed the resonator with efficient acoustic reflection and high electrical performance. The acoustic wave propagation and reflection in FBAR were first analyzed by Mason model, and then flexible FBARs of 2.66 GHz series resonance in different configurations were fabricated. To validate efficient acoustic reflection of flexible resonators, FBARs were transferred onto different polymer substrates without air cavities. Experimental results indicate that efficient acoustic reflection can be efficiently predicted by Mason model. Flexible FBARs with air cavities exhibit a higher figure of merit (FOM). Our demonstration provides a feasible solution to flexible MEMS devices with highly efficient acoustic reflection (i.e. energy preserving) and free-moving cavities, achieving both high flexibility and high electrical performance.

With their small sizes, high frequencies and high performance, film bulk acoustic resonators (FBARs) are widely applied in communication systems and sensing fields.1,2 Meanwhile, flexible electronics, such as flexible displays, e-skins and wearable health care develop rapidly in recent decades, attracting intensive research attention.3–5 However, research on flexible FBARs is less studied. One of the immediate problems is to match components to the flexible application and functionality. In general, these components are not compatible with existing manufacturing processes for flexible electronics. As for flexible radio-frequency (RF)FBARs and thin-film piezoelectric devices, processes like removal of sacrificial materials in corrosive liquid or gaseous environment may bring damage to flexible materials, hindering the development of high-performance flexible devices to some extent. Therefore, attention should be focused on the fabrication of flexible RF devices like FBARs. In 2006, Akiyama and his co-workers6 deposited piezoelectric aluminum nitride (AlN) films on flexible polyethylene terephthalate (PET) substrates and measured pulse signals from fingertip. Jin et al7 deposited zinc oxide films on polyimide (PI) for flexible microfluidic systems. Chen et al8 reported a bulk acoustic resonator with aluminum electrodes and zinc oxide piezoelectric layer on PI in 2015.

As mentioned above, some previous exploratory studies on flexible FBARs have been reported but overall their performances are still limited due to the acoustic energy leakage. While achieving flexibility, it is of great significance to construct an effective acoustic reflection structure to improve the electrical performance of the resonator. Air-gap type structure is more feasible when performing flexible film bulk acoustic wave device design and still retains high electrical performance.9–11 In this paper, we demonstrated an air-gap type flexible FBAR in the flexible PI substrate using transfer printing technology and investigated the issue on acoustic reflection of flexible FBARs.

FBARs are thin-film piezoelectric devices in the form of a sandwiched structure. A typical configuration of FBARs is shown in Fig. 1. When RF voltage is applied on the electrodes, the piezoelectric layer converts electrical energy into mechanical energy and vice versa. Mechanical resonance is generated in the FBAR stack, leading to mass displacements associated with longitudinal (thickness direction) bulk acoustic waves.

The generated bulk acoustic waves propagate and reflect in the FBAR stack, forming a standing wave. The reflection occurs at the interface between layers with different acoustic impedance. Reflection coefficient Γ can be defined as (assuming the wave propagates from Z1 to Z2):

Γ=Z2Z1Z2+Z12
(1)

where Z is the material acoustic impedance.

Eq. (1) reveals that Γ is determined by Z1 and Z2, and a high reflectivity can be achieved by maximizing the difference between Z1 and Z2. Information on approximate acoustic impedance level of different materials is shown in Table 1.

High-performance resonators are expected to have small energy loss when resonating. For acoustic resonators, the loss of acoustic energy takes a large portion of total energy loss. In general, there are two reasons for the acoustic loss. One is acoustic loss inside the resonant body (e.g. material loss), and the other one is acoustic energy leakage outside the resonant body. Therefore, we preferentially chose low-loss materials and an efficient reflective structure to prevent acoustic energy leakage.

FBARs’ electrical performance is characterized by FOM, defined as the product of quality factor Q and effective coupling coefficient keff2.12Q is a measure of loss in the system calculated using Q=Qs2+Qp2 in this paper.

The electrical performance of FBARs can be roughly predicted by Mason model, especially on the trend of performance influenced by various design parameters (e.g. material parameters and thicknesses of layers in the acoustic stack). Fig. 2 illustrates a simplified Mason model of air-gap type FBARs. In Mason model, the non-piezoelectric layer is equivalent to a complex-impedance two-port network while piezoelectric layer can be equivalent to a three-port network with output ports particularly.

Assuming that an efficient reflective interface is formed and the acoustic wave propagates only in the sandwiched stack, each layer in Mason model can be considered as a uniform transmission line and can be described by the ABCD transmission matrix which is expressed as:

ABCD=ckljZskljsklZckl
(2)

where k is the wave propagation constant, l is the length of transmission line (thickness of a layer in FBAR stack), and Z is the surface impedance which can be calculated based on material properties and design dimensions. The ABCD transmission matrix promotes the calculation of Mason model.

In our previous work, similar technology has been applied in the fabrication of flexible resonators.9,10 Silicon oxide layer was first deposited as sacrificial layer and patterned by wet etching. Then similar procedures were implemented for the depositing and patterning of FBAR stack and Au layer on electrode extensions. Finally, the sacrificial layer was removed in diluted hydrofluoric acid solution for hours. The photo of the fabricated FBAR is shown in Fig. 3 (a).

After the removal of the sacrificial layer, the FBAR stack detached from the silicon wafer except the anchor zone. In addition, the connecting portion in the anchor zone was patterned with small circles, reducing the connection force between the FBAR and the wafer, which will facilitate the subsequent transferring process. With the aid of a soft polydimethylsiloxane (PDMS) stamp, robust and high yield transferring was realized with a succession of 100% in ten transferring processes.9,10,13 During the transferring process, FBARs were first separated from the silicon wafer and attached to the stamp. Then FBARs were transferred onto the target substrates with stamp. With a slow and appropriate releasing rate, FBARs combined with the target substrates and separated from the stamp. The transferring printing process operated under an optical microscope.

This work focuses on the influence of acoustic reflection on electrical performance of flexible FBARs. The simulation results of the FBAR based on Mason model was first compared with the fabricated one on an air cavity. Parameter S11 of the latter was measured by a vector network analyzer (VNA, Agilent Technologies, E8363B) using a 150 μm-pitch GSG RF probe (Allstron). Their impedance diagrams are shown in Fig. 4 (a), revealing a good agreement. Note that the cavity provides an efficient reflective layer that greatly reduces acoustic energy leakage. For the measured FBAR on a cavity, the calculated Q, keff2 and FOM are 993, 5.04 % and 50, respectively, which is comparable with FBARs on rigid substrates.14 This experiment also proves the correctness of Mason model and its parameters, facilitating further simulation and design work.

Besides, substrate materials with different acoustic impedance levels and acoustic loss coefficients were simulated by Mason model. The simulation reveals a divergence in their resonance performance as shown in Fig. 4 (b). By changing the real part and the imaginary part of acoustic complex impedance, the magnitude of impedance was attenuated. In fact, the real part of acoustic impedance weighs the sound energy loss inside, while the imaginary part reflects the storage capacity of the material for the sound energy, and it has a certain effect on the impedance curve.15 

The resonator performance on different substrates without cavities was also investigated. In this section, FBARs were transferred onto PDMS, UV film, PI and silicon wafer, respectively. And the scheme of scattering parameter S11 and Smith charts are shown in Fig. 5.

In Fig. 5(a), the curve of FBAR on an air cavity as a whole is closest to zero, verifying the minimal acoustic energy leakage. It can be inferred that acoustic energy is perfectly reflected at the high-efficiency acoustic reflection layer provided by the air cavity. Then spurious modes of the FBAR on silicon are due to multiple reflection in the low acoustic attenuation silicon. PI polymer substrate has a higher energy loss peak because of higher acoustic attenuation. Since PDMS and UV film have strong viscoelasticity, they are the top two in energy loss. The Smith charts shown in Fig. 5 (b) also reveal the best performance with an air cavity and the inferior performance with PDMS, PI and UV film as the reflection layers. The air-gap type FBAR (on cavity) exhibits excellent performance due to its near-1 high-efficiency acoustic reflection. Obviously, the measured results are consistent with the conclusion from Table 1. The greater difference in acoustic impedance, the better they are to suppress acoustic energy leakage. Finally, their FOMs were calculated and shown in Table 2. As expected, flexible FBAR on an air cavity has a higher FOM than others, which is consistent with the simulation result mentioned earlier.

In this paper, flexible air-gap type FBARs with efficient acoustic reflection were achieved. Thanks to the free-moving cavities, FBAR on an air cavity exhibits high FOM of 50 which is much higher than the control group. This demonstration provides a useful exploration for high-performance MEMS devices used in diverse scenes such as flexible sensing systems, wearable devices and so on.

This work was supported by National Natural Science Foundation of China (Grant No. 51375341), the National High Technology Research and Development Program of China (“863” Program, Grant No. 2015AA042603), and the 111 Project (Grant No. B07014).

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