# A polymer-based MEMS loudspeaker featuring a partially stiffened membrane actuated by a PZT thin film

Romain Liechti, Christel Dieppedale, Timothée Rotrou, Gwenael Le Rhun

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## To cite this version:

Romain Liechti, Christel Dieppedale, Timothée Rotrou, Gwenael Le Rhun. A polymer-based MEMS loudspeaker featuring a partially stiffened membrane actuated by a PZT thin film. Communications Engineering, 2025, 4, pp.98. 10.1038/s44172-025-00438-x. cea-05204507

HAL Id: cea-05204507

https://cea.hal.science/cea-05204507v1

Submitted on 8 Aug 2025

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# A polymer-based MEMS loudspeaker featuring a partially stiffened membrane actuated by a PZT thin film

Romain Liechti<sup>a</sup>, Christel Dieppedale<sup>a</sup>, Timothée Rotrou<sup>a</sup>, Gwenaël Le Rhun<sup>a</sup>

<sup>a</sup>Univ. Grenoble Alpes, CEA, Leti, F-38000 Grenoble, France

## Abstract

This study focuses on the design and performance of a polymer-based MEMS loudspeaker featuring a partially stiffened membrane actuated by a lead zirconate titanate (PZT) thin film. The flexible polymer reduces the stiffness of the structure, while the stiffened regions broaden the frequency response. The PZT thin film, known for its excellent piezoelectric properties, drives the membrane to produce sound. To integrate the PZT thin film onto the polymer membrane, a transfer-based manufacturing process, described in previous work, is utilized. Key performance metrics such as sound pressure level (SPL), resonance frequencies, and total harmonic distortion (THD) were analyzed through experiments for both free field and in-ear applications. The results demonstrate that this hybrid membrane design, paired with the PZT actuator, achieves decent efficiency and sound quality while showcasing the robustness of the manufacturing process. Additionally, the transfer process can be adapted to integrate transparent piezoelectric actuators, enabling the creation of fully transparent loudspeakers for innovative applications in audio and display technologies.

## Introduction

Loudspeakers are electro-acoustic transducers that convert electrical signals into acoustic signals. To reproduce the entire audio spectrum, they must cover a frequency range from 20 Hz to 20 kHz. To achieve this broad range, loudspeakers designed for domestic use often employ multiple transducers: larger and heavier ones for low frequencies, and smaller, lighter ones for higher frequencies. In contrast, smaller devices like smartphones and laptops must reproduce the full audio range using a single transducer due to size constraints, which introduces additional physical limitations and compromises sound quality. Conventional loudspeakers rely on mechanical movement to generate sound waves, typically via a diaphragm attached to a coil within a magnetic field. While effective, these designs tend to be bulky due to the permanent magnet, making them unsuitable for miniaturized electronic devices. To meet the growing demand for smaller and more efficient audio components, Micro-Electro-Mechanical Systems (MEMS) loudspeakers have emerged as a promising alternative [1, 2]. MEMS technology enables the fabrication of micro-scale devices, integrating mechanical and electrical components into compact structures. In

recent years, MEMS loudspeakers using electrodynamic [3], piezoelectric [4–6] and electrostatic transduction [7, 8] have been presented.

The difficulty of achieving low frequencies with MEMS technology arises from the physical constraints of miniaturization. Generating low-frequency sound waves requires the acceleration of a large volume of air at a low frequency, which results in a low resonance frequency and a large diaphragm displacement—both difficult to attain on a micro-scale. Additionally, the stiffness of commonly used MEMS materials, such as silicon, limits the flexibility needed for effective low-frequency sound reproduction. To compensate for the stiffer material, multiple compliant structures, using the advantage of the viscosity of air were presented [9–15]. More recently, similar structures were sealed using PDMS [13, 16–18]. Therefore, there is a growing need for alternative materials that can overcome these limitations while preserving the benefits of MEMS technology. Polymers, with their lower Young’s modulus offer a promising solution to the low-frequency performance challenges in MEMS loudspeakers. These materials allow for larger diaphragm movements, improving sound reproduction at lower frequencies. However, polymers also have significant drawbacks, particularly their low thermal budget, which

<footnote>Email address: romain.liechti@cea.fr (Romain Liechti)</footnote>
makes them incompatible with traditional piezoelectric thin-film manufacturing processes that typically require high temperatures. To address this issue, a layer transfer method is a pertinent approach to integrate piezoelectric thin films onto polymer substrates [19]. In this method, the PZT stack is initially grown on a suitable substrate and then transferred to a host substrate using various techniques, such as grinding the donor substrate [20], etching a sacrificial layer between the PZT and the growth substrate [21–24], or laser lift-off [25]. More details on low temperature processes for PZT integration are given in [26]. Through a thin-film transfer process, it becomes possible to combine soft polymers materials with the high piezoelectric coefficient of thin film PZT. This approach helps to address the thermal budget limitations and contributes to the development of MEMS loudspeakers with the potential to deliver high-quality sound across a wide frequency range.

This article begins with the design of the polymer-based MEMS loudspeakers, using Computer Assisted Design (CAD) tools and a lumped element model to conduct a preliminary, qualitative study. This approach helps identify key parameters that need to be adjusted—whether increased or decreased—to optimize performance. Unlike most MEMS loudspeakers, the presented design achieves pistonic motion over a wide frequency range, resulting in a flat frequency response and low harmonic distortion. The article then details the manufacturing process, focusing on the integration of piezoelectric thin films onto polymer substrates. Finally, electrical, mechanical, and acoustic measurements of the device are presented, highlighting its potential for use in compact audio systems.

# Results

## Design and modeling

The loudspeaker is designed to achieve pistonic motion across a wide frequency range, similarly to a conventional macroscopic loudspeaker. To function effectively as a second-order oscillator over a broad frequency range, the loudspeaker must closely approximate a distributed element system. This requires the apparent stiffness of the spring element to be significantly smaller than that of the mass and radiating element. In traditional macroscopic loudspeakers, the suspension’s apparent stiffness is typically several orders of magnitude higher. For an uniform clamped membrane, the second axisymmetric mode occurs at 2.3 times the frequency of the fundamental drum mode [27], yielding a bandwidth

slightly exceeding one octave. While this architecture is commonly adopted in MEMS loudspeakers [5, 6], it is primarily suited for reproducing narrow-band sounds such as alarms or sirens. To overcome these limitations, alternative architectures have been proposed to enable wider frequency-range pistonic motion [4, 28, 29]. These designs are closer to the ideal loudspeaker, offering an extended frequency range. Figure 1a presents a 3D partial section view of the loudspeaker, showing the silicon bulk with etched central stiffeners. The polymer membrane is separated from the bulk by an oxide layer, and on top of the membrane, an annular piezoelectric actuator comprises three consecutive layers. The outer radius of this actuator is larger than the back opening, while the inner radius lies approximately halfway between the clamping edge and the stiffeners, near the inflection point, expected due to the clamped-guided shape of the deformed membrane. More details regarding the materials are provided in Section a. Figure 1b illustrates a half cross-sectional view of the deformed loudspeaker (electrodes omitted). A potential difference between the top and bottom electrodes generates an electric field across the piezoelectric layer, inducing radial stress in the annular actuators. This stress bends the polymer membrane due to the boundary conditions of the thin piezoelectric film. The suspended annular section of the membrane bends symmetrically, with a cross-sectional shape resembling a clamped-guided beam, exhibiting an inflection point where the curvature transitions from concave above to convex below. In this configuration, the loudspeaker behaves as a second-order forced oscillator, with its electrical equivalent circuit depicted in Figure 1c. From the electrical equivalent circuit, the velocity $v$ can be determined by calculating the ratio between the input force $F_{in}$ and the total mechanical impedance $Z_m$ of the loudspeaker. The mechanical impedance of the loudspeaker writes

$$Z_m = R_m + j\omega M_m + \frac{1}{j\omega C_m} + 2Z_r S_{d'}^2 \quad (1)$$

where $\omega$ is the pulsation, $R_m$ the equivalent resistor due to the viscous damping, $C_m$ is the apparent compliance of the membrane, $M_m$ is the equivalent mass of the membrane, $S_{d'}$ is the effective radiating surface of the loudspeaker and $Z_r$ the radiation impedance of a rigid circular piston flush-mounted into an infinite baffle expressed as

$$Z_r = \frac{\rho_0 c_0}{S_{d'}} \left( 1 - \frac{J_1(2k_0 a)}{k_0 a} + j \frac{H_1(2k_0 a)}{k_0 a} \right), \quad (2)$$

where $J_1$ is the Bessel function of first order and first
kind, $H_1$ is the Struve function of the first kind, $a$ is the radius of the equivalent radiating surface $S_d$ and $k_0$ is the wave number [30].

Deriving the input force $F_{in}$ analytically for such a structure is challenging, particularly due to the significant influence of residual stress. However, $F_{in}$ is proportional to the total force $F$ generated by the annular piezoelectric layer. This total force is determined by integrating the stress induced by the piezoelectric effect, which arises from the applied voltage across the piezoelectric layer, as expressed by

$$F = 2\pi e_{31,f} E \left( \frac{r_o^2 - r_i^2}{2} \right) \quad (3)$$

where $r_o$ is the outer radius of the piezoelectric layer, $r_i$ is the internal radius of the piezoelectric layer, and $e_{31,f}$ is the reduced effective piezoelectric coefficient for thin films and is calculated using

$$e_{31,f} = \frac{d_{31}}{s_{11}^E + s_{12}^E} \quad (4)$$

The radiated pressure can then be determined by integrating the radiated power, which simplifies to the Rayleigh integral for a flat surface [31]. The resulting pressure at $(r, \theta, \omega)$ is then expressed as

$$p(r, \theta, \omega) = -j\omega\rho_0 S_d v \frac{2J_1(k_0 a \sin \theta)}{k_0 \sin \theta} \frac{e^{jk_0 r}}{2\pi r}, \quad (5)$$

where $\theta$ is the angle from the normal to the undeformed membrane plane with the line from the center of the membrane to the evaluation point, $\rho_0$ is the density of air, $v$ is the harmonic velocity of the membrane, and $r$ is the distance between the center of the membrane and the evaluation point. From this equation, it is easy to see that the pressure is proportional to the velocity $v$ multiplied by $j\omega$ which corresponds to the acceleration of the membrane. The bandwidth of the loudspeaker in free field is thus bounded by the resonance frequency created by $C_{ms}$ and $M_{ms}$ expressed as

$$f_s = \frac{1}{2\pi\sqrt{M_m C_m}} \quad (6)$$

at which the restoring force due to the membrane and the inertia due to the mass are canceled, and at which the impedance is dominated by the viscous resistance $R_m$.

Figure 1d illustrates the pressure radiated by a vibrating piston flush-mounted in an infinite baffle, normalized to the flat-bandwidth pressure and its resonance frequency. The plot demonstrates that, as

predicted by equations 5 and 1, the pressure follows the behaviour of an under-damped high-pass filter. Reducing the mass shifts the resonance frequency to higher values, which decreases the bandwidth. Conversely, reducing the mass increases the loudspeaker's sensitivity. Increasing the compliance $C_m$ lowers the resonance frequency $f_s$ and broadens the bandwidth of the loudspeaker. However, unlike electrodynamic loudspeakers—where the force is nearly independent of mechanical parameters $M_m$ and $C_m$—the force $F_{in}$ generated by the piezoelectric layer is inversely proportional to the apparent compliance $C_m$ of the assembly, which in this case includes the actuator and the passive layer (the membrane). This additional relationship introduces a further constraint to the optimization problem. The optimization of the loudspeaker thus requires balancing a reasonably low resonance frequency to extend the bandwidth with maintaining a low mass $M_m$ to ensure good sensitivity. Alternatively, increasing the input force $F_{in}$ increases the sound pressure level without affecting the shape of the frequency response. An increase of the input force can be obtained by optimizing the geometry and the piezoelectric material, to increase the mechanical transduction factor $\gamma$ and the piezoelectric coefficient $e_{31,f}$.
a

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b

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c

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d

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**Fig. 1:** Working principle and 3D representation of the loudspeaker a 3D CAD drawing of the loudspeaker with partial opening, depicting the multiple layers of the membrane and of the piezoelectric annular actuator. Thicknesses are not to scale. b Half cross section view of the deflected membrane, thicknesses are not to scale. c Electrical equivalent circuit describing the behavior of the loudspeaker: The resistor $R_g$ represents the electrical resistance of the connectors and metal traces. The capacitor $C_p$ arises from the permittivity of the piezoelectric material between the top and bottom electrodes. The parameters $M_m, C_m$, and $R_m$ represent, respectively, the equivalent mass, the apparent compliance, and the viscous damping of the second-order oscillator formed by the membrane. $F_{in}$ is the force generated by the assembly of the piezoelectric layer on the membrane. The impedance $Z_r$ accounts for the effect of the fluid on the membrane. The electrical, mechanical, and acoustical domains are interconnected via transformers with ratios $\gamma$ and $S_d$, representing, respectively, the transduction ratio of the piezoelectric actuator on the membrane and the effective radiating area. d Pressure generated by a circular piston flush-mounted in an infinite baffle as a function of frequency, neglecting the radiation impedance and normalized to the flat bandwidth pressure at $10f_s$ and to the resonance frequency of the reference curve (black), for different relative values of $M_m, C_m$, and $F_{in}$.

## Process

The technological process is detailed in Figure 2. A high-quality PZT film, 1 µm thick with a Zr/Ti ratio of 52/48, is first grown on a platinized Si wafer by chemical solution deposition (CSD) using a commercial PZT sol-gel solution provided by Mitsubishi Materials Corporation. More details about the deposition process can be found in references [32, 33]. Note that the Pt bottom electrode layer is directly sputter deposited on SiO₂ without the use of adhesion layers like TiO₂ or ZrO₂. The low energy density interface (approximately 1 J m⁻²) between Pt and SiO₂ is key for detaching the PZT stack from the donor wafer by mechanical separation later in the process. An electrode made of 5 nm of ruthenium and 100 nm of platinum is deposited by sputtering to form the Metal Insulator Metal (MIM) capacitor. The thin Ru layer enhances the adhesion of Pt on the PZT film. Finally, 20 nm of an adhesion Ti layer, followed by 100 nm of

SiO₂ film, are deposited on top of the electrode. The SiO₂ layer serves as a stop layer when etching the bottom electrode, preventing the etch from reaching the polymer. The resulting stack is depicted in Figure 2a. In parallel (Figure 2b), an Si receiver wafer is prepared, starting with the realization of a hard mask for the final deep Si etching at the end of the fabrication. A 5 µm thick SiO₂ layer is deposited and patterned on the backside of the wafer (Figure 2c). The front side of the Si wafer is covered with an 1 µm thick SiO₂ layer, which will serve as a stop layer during the final Deep Reactive Ion Etching (DRIE) step. A 30 µm thick polyimide, referred to as LTC, is then spin-coated and reticulated at 300 °C for 1 h under N₂ (Figure 2d). The resulting LTC polymer layer first serves as glue for bonding both wafers and will eventually function as the elastic membrane of the micro-loudspeaker devices. The bonded wafers are annealed at 300 °C for 30 min under 10 kN of pres-

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<figure><img src="image_7.png" /><figcaption>**Fig. 2:** Schematic representation of the manufacturing process used for the loudspeakers. a High-quality PZT film (1 µm thick, 52/48 Zr/Ti ratio) grown on platinized donor Si wafer via chemical solution deposition. The Pt electrode was sputtered directly on SiO₂, facilitating subsequent detachment. b Deposition of a frontside SiO₂ stop layer (1 µm) on a receiver wafer. c Preparation of a backside hard mask (5 µm SiO₂) for deep Si etching. d Spin-coating and reticulation of a 30 µm polyimide (LTC) layer, serving as glue and elastic membrane. e Wafer bonding using LTC. f Transfer of the PZT MIM capacitor stack onto the host wafer via separation via Pt/SiO₂ interface. g Top electrode, PZT layer, and bottom electrode patterned and etched by RIE. h Membrane released by cavity etching in Si using DRIE.</figcaption></figure>

sure (Figure 2e). Then, by inserting a thin blade between the bonded wafers, a sharp separation occurs between the Pt and SiO₂ layers, as explained previously and illustrated in a previous paper [34]. The PZT MIM capacitor stack is thus transferred onto the host wafer, directly onto the polymer layer (Figure 2f). Note that the donor wafer can be recycled. The layer transfer process used here has previously shown its potential for other piezoelectric MEMS applications [34–37]. The piezoelectric actuator is subsequently formed by successively patterning the top electrode, the piezoelectric PZT layer, and the bottom electrode, using three distinct photolithography masks (Figure 2g). All three layers are etched by the RIE process. Finally, the membrane is released by etching a cavity in the Si bulk through the DRIE process (Figure 2h).

## Characterization

The quality of the bonding was monitored by scanning acoustic microscopy (SAM) as illustrated in Figure 3a. The image shows mainly dark contrast meaning that the wafers are well bonded. Clear contrasts, sign of non-bonded areas, can be seen on the periphery only. Pictures of the donor and receiver wafers after layer transfer are shown in Figures 3b and 3c, respectively. We clearly see the SiO₂ layer on the donor and the Pt layer on the receiver. However, the separation was not exclusively occurring at the Pt-SiO₂ interface but also very locally at the Pt/PZT interface. XRD analysis was performed on the PZT film as shown in Figure 3d. It reveals that PZT exhibits a pure perovskite phase with a strong (100)

preferred orientation. The latter is highly desired for PZT at morphotropic phase boundary (MPB) as it is known to promote highest transverse piezoelectric coefficient $e_{31,f}$. Scanning Electron Microscope (SEM) observations were performed to check the integrity of the piezoelectric actuator on the LTC polymer membrane after the layer transfer process. Figures 3e and 3f show SEM images of a Focused ion Beam (FIB) cut, focusing on the PZT MIM capacitor and the PZT stack on LTC, respectively. On the first image, we see the 1 µm thick PZT layer in between electrodes, without apparent damage, and with clear and sharp interfaces. On the second image, we can observe the PZT MIM capacitor that top the 16 µm thick LTC membrane. Here as well, the interfaces between all the layers composing the device stack appear clean and well-defined. The dielectric, ferroelectric and piezoelectric properties of the PZT were assessed on both test capacitors and MEMS devices using the TF2000 Analyzer from aixACCT. Polarization and dielectric permittivity curves, shown respectively in Figures 3g and 3h, were obtained on PZT actuators that are used to actuate MEMS loudspeakers. The P-V loop measured at 200 Hz with triangular waveform signal shows typical hysteresis shape of a ferroelectric material. The maximum polarization reaches 38 µC m⁻² for an applied electric voltage of 30 V, while the remnant polarization $2P_r$ is 24 µC m⁻². The capacitance, measured to calculate the dielectric constant, was recorded by sweeping DC voltage between –20 V and 20 V while applying an AC excitation signal (1 kHz, 150 mV). A butterfly
shape curve, characteristic of ferroelectric materials, is observed. The maximum relative permittivity is close to 1500 and the dielectric losses (not shown) are below 10%. The mechanical displacement of the PZT film under applied voltage was measured using a double beam laser interferometer (DBLI) coupled with the TF 2000 measurement system. It allows extracting the longitudinal piezoelectric coefficient $d_{33,f}$ from the slopes of the hysteresis loop, which is a good indicator of the piezoelectric performance. Figure 3i shows the displacement curved recorded at various voltages on 1 mm² test capacitor. More interestingly, by measuring the $d_{33,f}$ on capacitors of different sizes (in our case for sizes of 0.25, 0.56 and 1 mm²), one can extract the transverse piezoelectric coefficient $e_{31,f}$ thanks to a finite element model detailed in reference [38]. In addition, it is possible to extract the true $d_{33,f}$ coefficient, since the latter varies with the ratio $r$ between the size of the capacitors and the thickness of the substrate [39]. The $d_{33,f}$ and $e_{31,f}$ coefficient values extracted from the model are 125 pm V⁻¹ and 17 C m⁻², respectively. These values are comparable to the best values reported in literature for standard PZT films deposited on Pt/Si substrate [38]. Figure 3j shows a photograph of a wafer at end of process gathering various designs of loudspeakers with different sizes. A micro-speaker device is also pictured in Figure 3k. We can see the transparent polymer based membrane, with etched central stiffeners underneath, surrounded by annular shaped piezoelectric actuator. At last, the deformation of a loudspeaker membrane, 12 mm wide, at equilibrium was measured by Digital Holographic Microscopy (DHM). The scan presented in Figure 3l shows a deformation of 3 µm at the stiffened center of the membrane, due to various residual stress in the layers.
<figure><img src="image_8.png" /><figcaption>b</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>c</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>d</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>e</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>f</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>g</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>h</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>i</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>j</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>k</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>l</figcaption></figure>

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**Fig. 3: Material and mechanical characterization**
**a** Scanning acoustic microscopy image of the bonding interface between the donor and the receiver wafer at the step depicted in Figure 2e. The image was acquired in reflection mode at 10 MHz. Dark regions indicate well-bonded areas, while light regions represent voids or delaminations. **b** and **c** show photos of the donor and receiver wafers after debonding. The region labeled as 1, which appears purple on the donor wafer and gray on the receiver wafer, corresponds to the SiO₂ and platinum layers respectively, as illustrated in Figure 2f. The region labeled as 2 indicates areas where the platinum electrode remained attached to the donor wafer. **d** XRD measurement of the piezoelectric stack showing the desired orientation (100) of the PZT film. **e** Scanning Electron Microscopy (SEM) image of the piezoelectric actuators on the manufactured devices, highlighting the thicknesses: 100 nm of platinum at the top and bottom, and 1 µm of PZT. **f** SEM picture of the membrane, indicating a thickness of 16 µm for LTC, 1 µm for SiO₂, and a 1 µm piezoelectric actuator on top. **g** Polarization loop of the fabricated PZT at the fabrication step represented in Figure 2d, for 3 different voltages corresponding to an electric field of 5 MV m⁻¹, 15 MV m⁻¹ and 30 MV m⁻¹ respectively. **h** Dielectric permittivity curve obtained for PZT actuators used in MEMS loudspeakers. **i** Displacement recorded at various voltages on 1 mm² test capacitor. **j** Picture of a finished wafer, depicting different design of loudspeakers with different diameters. **k** Binocular loupe picture of a device on the wafer before dicing, revealing the transparency of the membrane. **l** Digital Holography Microscopy (DHM) scan showing the static deformation of the membrane after the release etching, with a deformation of 3 µm at the stiffened center.
Free Field

The loudspeaker is tested in a GRAS anechoic
chamber under free-field conditions. After dicing
and bonding it onto a custom-designed printed cir-
cuit board (PCB) with a 12 mm hole, it is mounted
on a 200 × 200 mm² aluminum baffle to minimize
acoustic short-circuiting within the frequency range
of interest. Figure 4a presents a top-view image of
the loudspeaker mounted on the custom PCB, while
Figure 4b shows a cross-sectional view of a halved
loudspeaker, emphasizing the thickness of the sili-
con stiffening structure and the thinness and trans-
parency of the polymer membrane. During acoustic
measurements, the loudspeaker operates without a
back acoustic load. The microphone is positioned
10 mm from the membrane surface, as illustrated
in Figure 4c, which shows the measurement setup
within the GRAS AL0030 anechoic chamber. The
measured pressure response, recorded at 15 VDC ±
6 VAC and 10 mm from the membrane, is presented
in Figure 4d. The response exhibits characteristics
typical of a pistonic-motion loudspeaker, resembling
a high-pass filter with its cut-off frequency deter-
mined by the resonance frequency. The resonance
frequency is measured at 3043 Hz. At higher fre-
quencies, a higher-order mode generates a secondary
peak in the pressure response around 14 kHz. Figure
4e shows the total harmonic distortion (THD) mea-
surement at an actuation voltage of 15 VDC ± 1.5 VAC,
corresponding to a pressure response approximately
12 dB lower than that shown in Figure 4d. Below
the resonance frequency, harmonic components are
amplified, resulting in elevated THD levels. At reso-
nance, the fundamental frequency is amplified, while
harmonic components are not, resulting in very low
THD. Above resonance, in the pseudo-flat response
range, the THD remains relatively low, at approxi-
mately 1%. Figures 4f and 4e provide two differ-
ent representations of the pressure measured at var-
ious angles relative to the normal of the loudspeaker
plane. The pressure response is measured at a con-
stant distance for angles ranging from -70° to 70°
in 2° increments. According to Equation 5, and due
to the dimensions of the loudspeaker relative to the
wavelength of the highest audible frequencies, the
frequency response remains nearly uniform across all
angles. Figure 4g illustrates the radiation pattern of
the loudspeaker at 100 Hz, 3 kHz, 5 kHz, and 10 kHz.
At 100 Hz, the pressure level is low, and the response
is influenced by background noise in the room; how-
ever, the average pressure is angle-independent. At
3 kHz and 5 kHz, the radiation pattern forms a per-
fect arc of a circle. At 10 kHz, a slight decrease in
pressure with increasing angle is observed. Figures

4h to 4k depict a reconstruction of the axisymmet-
ric modal shape of the loudspeaker at four different
frequencies. The displacement of the loudspeaker is
measured along its radius, and the modal shape is
digitally reconstructed. At low frequencies, such as
100 Hz and 2.9 kHz, the modal shape is similar to the
one of a vibrating piston, with the stiffened center
moving as a rigid body. At higher frequencies, a sec-
ond axisymmetric modal shape emerges, character-
ized by a maximum displacement in the unstiffened
section of the membrane. This mode shape could be
responsible for the pressure peak in the frequency
response, despite the suspension and the stiffened
membrane appearing out of phase.

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<figure><img src="image_20.png" /></figure>

In-Ear

In order to characterize acoustically the loud-
speaker for in-ear applications, a GRAS RA0045 ear-
occluded coupler is used. To accommodate the shape
of the loudspeaker to the circular aperture of the ear-
occluded coupler, a 3D-printed adapter is designed.
The adapter features a threaded hole to accommo-

date the coupler and guarantee a sealed cavity. On
the other side of the adapter, a square cavity con-
fines the loudspeaker. Figure 5a depicts a cross-
sectional view of the assembly of the loudspeaker,
the PCB, the adapter, and the ear-occluded coupler.
The printed circuit board, on which the loudspeaker
is glued and bonded, features a 12 mm opening to

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430
accommodate the rear acoustic radiation of the loud-
speaker and ensure an unchanged back acoustic ra-
diation impedance in the frequency range of inter-
est. Figure 5b depicts a picture of the measurement
setup. The microphone of the coupler is plugged
into a GRAS 26AC preamplifier and a GRAS 12AK
power supply and signal conditioner. Similarly to
the free-field measurement setup, the signal is sam-
pled at 44.1 kHz and acquired using a PXI 4461 data
acquisition device. Figure 5c depicts the frequency
response measured at 15 VDC ±1.5 VAC inside the ear-
occluded coupler. Due to a resistive air leak, the pres-
sure response of the loudspeaker is degraded com-
pared to the measurement in the very low frequen-
cies. This effect is studied in more detail in [40]. Be-
low 100 Hz, the pressure decreases to approximately
86 dB SPL due to leakage. Above 200 Hz, the effect of
leakage becomes minimal, and the pressure stabilizes
at 100 dB SPL. Beyond 300 Hz, the pressure response
remains reasonably flat as expected, until the reso-
nance of the loudspeaker inside the coupler, occur-
ring at approximately 3 kHz, begins to increase the
pressure. Unlike softer loudspeakers, the resonance
frequency is not significantly affected by the addi-
tional acoustic stiffness created by the cavity. Figure
5d presents the total harmonic distortion (THD) gen-
erated by the loudspeaker under the same measure-
ment conditions. Due to the lower sound pressure
level and noise below 100 Hz, the THD appears high
and reaches 100 %. Above 100 Hz, within the almost
flat frequency range, the THD reduces to 1 % or lower.
At higher frequencies, the resonance frequency of
the loudspeaker inside the coupler creates subhar-
monic peaks at approximately 600 Hz, 930 Hz, and
1450 Hz. Further, the dip in the frequency response
is responsible for the peak in the total harmonic dis-
tortion at the corresponding frequency. The loud-
speaker's high sensitivity of 98.6 ± 3, dB SPL V⁻¹ in the
190 Hz to 1000 Hz range, attributed to its large radi-
ating area and high piezoelectric coefficient, enables
the generation of substantial pressure across a broad
frequency band with a reasonable actuation voltage.
This makes it particularly suitable for portable in-ear
applications.
<figure><img src="image_21.png" /><figcaption>a</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>c</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>b</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>d</figcaption></figure>

<caption>**Fig. 5:** In-ear measurement setup and measurement results a Cross sectional view of the measurement setup including the loudspeaker, the printed circuit board, the adapter and the ear-occluded coupler b Picture of the measurement setup. c Pressure response measured with the measurement setup of Figure 5b with an actuation voltage of 15 V<sub>DC</sub> ± 3 V<sub>AC</sub>. d Total Harmonic distortion (THD) measured in the measurement setup of Figure 5b, at an actuation voltage of 15 V<sub>DC</sub> ± 1.5 V<sub>AC</sub>.</caption>

## Conclusion & Outlook

The integration of high-performance thin-film piezoelectric material on a suspended soft membrane with a stiffened center is successfully demonstrated through the design and fabrication of a loudspeaker, highlighting the feasibility of this approach for innovative transducer applications. On the device and due to a large emitting area, a sound pressure level of 110 dB<sub>SPL</sub> at 3032 Hz is measured. In a ear-occluded coupler, the loudspeaker demonstrates a sound pressure level of 100 dB<sub>SPL</sub> in a wide bandwidth and at an actuation of voltage of 15 V<sub>DC</sub> ± 1.5 V<sub>AC</sub>. To decrease the resonance frequency of the loudspeaker, the design could focus on innovative structures that minimize the influence of stress in both the polymer and PZT layers on its behavior, for example, by integrating additional degrees of freedom. Optimizing the stiffening structure could also help reduce the moving mass, further enhancing sensitivity. For in-ear applications, a specific design featuring multiple membranes with higher resonance frequencies could improve the frequency response, along with optimizing the sealing of the experimental measure-

ment setup. This work represents a significant step forward in enabling the integration of piezoelectric actuators onto polymer surfaces that are otherwise incompatible with the high crystallization temperatures required for PZT. By overcoming this limitation, the proposed process opens up a range of possibilities for functionalizing polymer membranes in applications where traditional fabrication techniques would fall short. For instance, when combined with a transparent piezoelectric stack, similar to the one developed in [37], this technique could enable the realization of transducers for transparent devices, such as those used in anti-fouling applications [41] optics [42], loudspeakers [43], microfluidics sensors [44], and bio-engineering [45]. The process offers compatibility with low-temperature substrates, making it particularly promising for the integration of piezoelectric actuators into flexible electronics, wearable devices, and other emerging technologies that rely on polymer-based systems. Future research on the manufacturing process will aim to optimize the adhesion layer to improve reliability and scalability while also evaluating device performance under various
environmental conditions. Addressing these challenges could lead to the development of new multifunctional devices that integrate piezoelectric action with transparency and flexibility, enabling their use in a wide range of innovative applications.

### Acknowledgement

This work was supported by the Carnot Institute, France. We thank Catherine Brunet-Manquat for sample preparation and SEM analysis, Pierre Montméat and Pierre Perreau for bonding and debonding, and Frédéric Ritton and Alain Campo for patterning (etching, stripping) steps.

### Author contribution

R.L. conceptualized the device, performed simulations, carried out experiments and investigations, conducted formal analysis, realized the results visualization, and wrote the original draft. C.D. fabricated the device, carried out experiments and investigations, and reviewed and edited the manuscript. T.R. carried out experiments and investigations and reviewed and edited the manuscript. G.L.R. acquired funding, provided resources, managed the project, carried out experiments and investigations, and wrote the original draft.

### Conflict of interest

The authors declare no competing interests.

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