Applied Physics A

, Volume 107, Issue 3, pp 621–629

Fluoroethylenepropylene ferroelectrets with patterned microstructure and high, thermally stable piezoelectricity

Authors

  • X. Zhang
    • Institute for Telecommunications Technology
    • Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology & Department of PhysicsTongji University
  • J. Hillenbrand
    • Institute for Telecommunications Technology
    • Institute for Telecommunications Technology
  • S. Haberzettl
    • Institute for Telecommunications Technology
  • K. Lou
    • Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology & Department of PhysicsTongji University
Invited paper

DOI: 10.1007/s00339-012-6840-7

Cite this article as:
Zhang, X., Hillenbrand, J., Sessler, G.M. et al. Appl. Phys. A (2012) 107: 621. doi:10.1007/s00339-012-6840-7

Abstract

Layered fluoroethylenepropylene (FEP) ferroelectret films were prepared from sheets of FEP films by template-patterning followed by a fusion-bonding process and contact charging. The layered ferroelectret films show consistency and regularity in their void structures and good bonding of the layers. For films composed of two 12.5 μm thick FEP layers and a typical void of 60 μm height, the critical voltage necessary for the built-up of the “macro-dipoles” in the inner voids is approximately 800 V. At room temperature, Young’s modulus in the thickness direction, determined from dielectric resonance spectra of the fabricated films with a typical thickness of 85 μm, is about 0.21 MPa. Initial quasistatic piezoelectric d33 coefficients of samples contact charged at a peak voltage of 1500 V are in the range of 1000–3000 pC/N. From these, ferroelectrets with high quasistatic and dynamic (up to 20 kHz) d33 coefficients of up to 1000 pC/N and 400 pC/N, respectively, which are thermally stable at 120°C, can be obtained by proper annealing treatment. This constitutes a significant improvement compared to previous results.

1 Introduction

Some non-polar space-charge electrets based on polymer foams exhibit a significant piezoelectric effect. These foams are now named ferroelectrets or piezoelectrets [13]. Since the first such films, made of polypropylene (PP), were developed in Finland about 15 years ago [4], the polarization, charge storage, mechanical properties, and piezoelectricity have been intensively investigated. Owing to their unique features, such as large piezoelectric d33 coefficients, flexibility, light weight, and low cost, many applications have been suggested [19]. Some devices based on PP ferroelectret films, such as movement monitors and non contact vital monitors [5], are commercially available right now. Many other applications, such as microphones [6], ultrasonic transducers [7], flexible ferroelectret field-effect transistors [8], and ferroelectret accelerometers [9] are being developed in some laboratories. Unfortunately, the relatively poor stability of d33 in PP ferroelectret films, with working temperatures normally lower than 60°C, limits their applications when the devices are required to work at elevated temperatures.

Recently, the development of thermally stable ferroelectrets has been pursued in several laboratories and much progress has been made. Since the thermal stability of d33 in ferroelectrets is dependent on the retention of the internal space charges, two approaches are possible to achieve this goal. One is the development of new ferroelectrets based on thermally stable electret materials, such as cross-linked PP (XPP) [10], cycloolefines (COC) [11], polyethylene-terephthalate (PET) [12], polyethylene-naphthalate (PEN) [13], and fluorocarbon polymers [1425]; the other is chemical modification, such as surface modification of cellular PP by using fluorination [26]. Of these two approaches, the former one, in particular the one using fluorocarbon films, has shown the most promise. For instance, the very recently developed fabrication process for ferroelectrets based on thermally stable fluorocarbon polymers with tailored void structure is very attractive. Particularly, template-based methods allow one to control the microstructure of the films. In addition, the thermal stability can be optimized by controlling the charge distribution during charging [22].

In this article, an improved process for preparing mechanically stable fluoroethylenepropylene (FEP) ferroelectrets with highly regular, patterned microstructure and good bonding of the layers is described. This process also leads to piezoelectric d33 coefficients which are of equal magnitude, but thermally more stable, than the best results [18] reported before. The thermal stability, pressure dependence, and spatial dependence of piezoelectric d33 coefficients in such FEP ferroelectret films will be discussed.

2 Experimental details

2.1 Sample preparation

The polymer layers used were 12.5 μm thick FEP films provided by the DuPont Company. The preparation process consisted of two steps: Patterning of the FEP layers by pressing at a given temperature and fusion bonding of the film stack.

Figure 1 shows schematically the preparation of a laminated film by using two metal templates. The templates have regularly spaced, hexagonally arranged, circular recesses obtained by drilling. Each recess has a diameter of 1 mm and a depth of about 500 μm, and the distance between the centers of neighboring recesses is 1.2 mm. In the patterning step, two FEP films and one soft rubber pad were arranged in an alternating sequence and sandwiched between the two templates, as shown in Fig. 1. The sandwich was hot pressed by a hydraulic press at an elevated temperature of 90°C for 60 s. Then the soft rubber pad between the FEP layers was removed, thus obtaining two film-template structures. In the following fusion-bonding step, the two film-template structures were clamped and the whole assembly was placed in an oven and exposed to a temperature of 290°C for 10 min. The assembly was removed from the oven and allowed to cool to room temperature before removing the templates. For three-layer sandwiches, a piece of flat FEP film was inserted between the patterned FEP films and the same fusion-bonding parameters were used. It is worth noting that this method can also be used to prepare voided films with a variety of other polymers, such as pure polytetrafluoroethylene (PTFE), PTFE/FEP, PET, and so on. In this paper, the discussion is focused on laminated films made of FEP layers.
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Fig. 1

Schematic of preparation process of laminated films

The scanning electron microscopy (SEM) images in Fig. 2 show the surface and a cross section of the fabricated films. The surface of the laminated film shows that the periodic structure of the template can be transferred from the template to the polymer layer by pressing (upper part of the figure). The cross sections of the laminated films with two and three-layers (middle and bottom parts of the figure) reveal ordered void structures with regular and consistent lateral dimensions but somewhat varying void thickness, and good bonding at the interface between the layers. Because of the varying depth of the voids, the thickness of the samples depends on location and is in the range from 60 to 200 μm for the two-layer samples.
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Fig. 2

Scanning-electron microscopy images of the surface of a laminated film (upper part) and cross sections of laminated films (middle and bottom parts)

Most of the experimental results have been obtained for two-layer samples. Therefore, in this paper only results for such samples will be discussed. However, three- and multi-layer samples are also of interest. Studies on such films will be continued and results will be reported in a later paper.

2.2 Charging process

In order to render the fabricated films piezoelectric, contact charging was performed on the films at room temperature. The samples were first metalized by evaporation on both sides with ∼100 nm thick aluminum electrodes. The electrodes have a diameter of 20 mm. A triangular-shaped voltage pulse of 20 ms duration (rising and falling parts 10 ms each) with peak amplitudes between 100 and 1500 V, supplied from a Radiant Precision Workstation Materials Analyzer was applied to the samples. The resulting electrode charge was measured and from these measurements the remanent charge on the interior walls of the voids was calculated (see Sect. 2.3). Charging can also be performed with pulses of longer duration, up to hundreds of seconds. In this case, higher remanent charges and thus higher d33 coefficients are observed. If the triangular voltage pulse is followed by another such pulse of opposite polarity, a hysteresis curve can be determined. This will be discussed in Sect. 3.1.

2.3 Calculation of remanent charge in the voids from the electrode charge

The charge density on the walls of the voids may be calculated from the charge density on the electrodes by considering the geometry of the voids and the thicknesses of the air and solid layers. A schematic cross section of a plane-parallel void covering the entire area of the sample is shown in Fig. 3(a). More realistic cross sections of voids covering the sample area only partially are depicted in Figs. 3(b) and 3(c). While the voids in Fig. 3(b) are also plane-parallel, those in Fig. 3(c) can be described by the volume enclosed by two spherical caps.
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Fig. 3

Various void geometries: (a) Plane-parallel void covering the entire sample area; (b) Plane-parallel voids covering regularly arranged circular areas of the sample surface; (c) Voids formed by two spherical caps; the voids are also regularly arranged over the sample surface

For the calculations we assume that the charge density on the walls of the voids is uniform and has the same magnitude σ0, but opposite sign, on the upper and lower walls. The denomination of the geometric dimensions and dielectric constants may be seen in Fig. 3(a). In the lateral plane, perpendicular to these cross sections, the voids are of circular shape with a radius r0. Then the induction charge σi on the upper electrode of the plane-parallel void shown in Fig. 3(a) may be calculated from Gauss’ law and Kirchhoff’s second law in a straightforward manner [27], yielding
$$ \sigma_i=\frac{\frac{\sigma_0}{\varepsilon_2}s_2+\frac{\sigma_0+\sigma^{\prime}_0}{\varepsilon_3}s_3}{\frac{1}{\varepsilon_1}s_1+\frac{1}{\varepsilon_2}s_2+\frac{1}{\varepsilon_3}s_3}$$
(1)
Taking s1=s3=12.5 μm, s2=60 μm, ε1=ε3=2.3, and ε2=1, corresponding to the actual values in the present experiments, and \(\sigma_{0}=-\sigma^{\prime}_{0}\), one obtains σ0=−1.18σi.

For the void structure shown in Fig. 3(b), there is no induction charge in the areas connecting adjacent voids. Therefore, a correction factor equal to the ratio of the total sample area to the area covered by the voids, which equals 1.53, has to be introduced. Thus σ0=−1.81σi.

Finally, for the more realistic void geometry of Fig. 3(c) the charge density on the outer electrodes is a function of the distance r from the void center. This can be taken into consideration by expressing the void height s2(r) as a function of r. One easily finds
$$ s_2(r)=2\Bigl(\sqrt{R^2-r^2}-\sqrt {R^2-r^2_0}\Bigr),$$
(2)
where R is the radius of the sphere from which the spherical caps are derived and r0 is the radius of the cap. Substitution of (2) into (1) yields a charge density σi(r) which has to be integrated over the void surface to obtain the charge Qi on this surface and thus the charge density \(\sigma_{i}=Q_{i}/\pi r^{2}_{0}\). The calculation yields with the above values, taking now s2(0)=60 μm,
$$ \sigma_0\approx-2.32\sigma_i,$$
(3)
where the correction for the area not covered by voids is already included. The result in (3) is approximate since s1 and s3 have been assumed to be independent of location which, due to the curvature of the spherical caps, is not exactly true.

These results for the charge density on the inner walls of the voids will be further discussed in Sect. 3.1.

2.4 Mechanical properties

For the determination of Young’s modulus in the thickness direction of the laminated ferroelectret films, dielectric resonance spectra were measured with a high-precision impedance analyzer (Agilent 4294 A). At the dielectric (or mechanical) resonance of the free thickness-extension mode, the anti-resonance frequency fa of the sample is given by [28, 29],
$$ f_\mathrm{a}=\frac{1}{2s}\sqrt{\frac{Y}{\rho}}$$
(4)
where ρ and s are the bulk density and the maximum thickness of the sample, respectively. Thus, once fa is obtained from the dielectric resonance spectrum and s is measured, the elastic modulus Y of the laminated ferroelectret films in the thickness direction can be determined.

2.5 Piezoelectric properties

2.5.1 Quasistatic measurements

The piezoelectric d33 coefficient can be determined by a variety of methods [18, 30]. Here, a quasistatic method for assessing the direct piezoelectric effect was used. The method consists of applying a positive or negative force F=mg to the sample by, respectively, putting a mass m on the sample surface or removing it. The d33 coefficient is given by [31]
$$ d_{33}=\frac{Q}{F}=\frac{\sigma}{p}$$
(5)
where Q refers to the amount of charge induced on the electrodes, σ is the induced charge density, and p=F/A is the pressure applied to the sample. Since the removal of force from the sample can be better controlled than application of force, the mass was first put on the sample for an extended period of time before it was removed and the amount of induced charge Q was measured and integrated over 10 s by means of an electrometer (Keithley 6514).

2.5.2 Acoustic measurements

Acoustic measurements with the ferroelectret film used as a piezoelectret microphone can be employed to determine the piezoelectric d33 coefficient from the microphone sensitivity [18]. In the present study, free-field measurements with a distance of 20 cm between loudspeaker and piezoelectret microphone were performed. For these measurements, circular film samples with an area of 3.14 cm2 and metalized on both sides are placed on a PCB-board and clamped to it by a contact spring. A junction field-effect transistor (JFET) and some other electronic components on the PCB-board serve as an impedance converter. A perforated metal housing, transparent for sound waves, shields the PCB-board and its components electrically. The output voltage V of the microphone is fed into the impedance converter. Its output is fed into a measuring amplifier (B&K 2610) whose output is recorded by a PC. A calibrated 1/2″-condensor microphone (B&K 4191) together with a preamplifier (B&K 2669) and the measuring amplifier (B&K 2610) were used to determine the reference free-field sound pressure p at the location of the ferroelectret microphone. As sound source an active dynamic loudspeaker, controlled by the PC, was utilized. From the acoustic free-field measurements the voltage sensitivity MV=V/p of the ferroelectret films can be directly obtained as a function of frequency. The piezoelectric d33 coefficient of a film may be calculated by the voltage sensitivity MV according to [18]
$$ d_{33}=M_V\cdot C_\mathrm{F}/A_\mathrm{F}$$
(6)
where AF is the area of the film and CF its capacitance.

2.5.3 Interferometric measurements

Interferometric measurements of the d33 coefficient were performed by utilizing the inverse piezoelectric effect. During the measurements the ferroelectret films are glued to a sample holder and are electrically excited by a sinusoidal AC-voltage. The resulting movement of the free surface of the film is detected by the laser beam of a Michelson interferometer (SIOS SP-S). AC-voltages of 20 Vpp are supplied by a PC-controlled function generator (M&R Systems WG-820). Since the interferometer utilizes a focused laser beam, the spatial resolution is in the 10 μm range. The exact measuring position x and the focus of the beam on the film sample can be manually adjusted by means of three micrometer screws, which are moving the sample holder.

The sinusoidal thickness vibration amplitude A(x) due to the applied AC-voltage V is superposed by unavoidable disturbing signals, e.g. vibrations of the sample holder and electronic noise. The raw data from the interferometer are transmitted to a PC. Subsequently phase sensitive lockin-amplifier-like filtering and conventional IIR-prefiltering are used to eliminate the disturbing signals and obtain the vibration amplitude A(x) at a certain location x on the sample. The d33 coefficient at the location x can then be calculated according to
$$ d_{33}(x)=A(x)/V.$$
(7)

2.6 Isothermal decay of the piezoelectric d33 coefficient

Measurements of the isothermal decay of the quasistatic piezoelectric d33 coefficient were carried out in order to investigate the thermal stability of the ferroelectrets. Samples were annealed at a temperature of 120°C for a specified amount of time before measurements of d33 were taken at room temperature. A sequence of such measurements on a sample yields an isothermal decay curve which characterizes the sample with respect to thermal stability.

3 Results and discussion

3.1 Electric polarization of laminated FEP-PTFE films

In order to investigate the built-up of the “macro-dipoles” in the inner air voids of the fabricated films, measurements of electrical hysteresis loops of the samples were taken with the impedance analyzer mentioned in Sect. 2.2. Figure 4(a) shows the electrode charge density vs. instantaneous applied voltage as complete cycles of triangular voltage pulses of various peak amplitudes were applied to a two-layer FEP film. Figure 4(b) indicates the corresponding relationship between the remanent electrode charge density and the peak voltage applied to the sample. No electric hysteresis loop can be recorded when the peak voltage is less than 800 V, suggesting that the electric field strength in the inner voids is not high enough to trigger air breakdown. Actually, the maximum voltage across the inner voids, obtained at the locations of maximum height of the voids, is equal to 677 V. Upon further increasing the peak voltage, the hysteresis loops become more prominent, resulting in the enhancement of the quasi-permanent charge density, as shown in Figs. 4(a) and (b). Similar results were obtained before by Lindner et al. [32]. The electrode charge density reaches 0.2 mC/m2 at an applied peak voltage of 1500 V. The charge densities on the internal walls of the voids may be calculated from (1) to (5) and are also plotted in Fig. 4(b). As found in Sect. 2.3, the charge densities on the walls of the voids are significantly higher (up to a factor of 2.3) than the charge densities on the electrodes. Although no direct measurements of such internal charge densities are reported in the literature, some indirect estimates do exist [3335]. Even though these are for PP ferroelectrets, the reported values of the order of 0.5 mC/m2 are in good agreement with the present data in Fig. 4(b).
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Fig. 4

Electric hysteresis loops (a) and quasi-permanent charge density (b) for a laminated FEP sample with a thickness of 85 μm. Void with geometry I: Plane-parallel void covering the entire sample area; Void with geometry II: Plane-parallel void covering regularly arranged circular areas of the sample surface; Void with geometry III: Void formed by two spherical caps and the voids are also regularly arranged over the sample surface

In order to evaluate the possible contributions of charge injection from the electrodes into the polymer and of interfacial polarization to the quasi-permanent trapping of charge [36], a reference experiment was performed on a single-layer FEP sample [23]. An electric field of 80 MV/m, which is much higher than that experienced by the FEP layers in the laminated films, was applied to the single-layer FEP sample in the reference experiment. A quasi-permanent charge density less than 0.01 mC/m2 was observed, much smaller than the value found in the two-layer sample. Therefore, under the given experimental conditions, charge injection and an interfacial polarization between electrodes and polymer surfaces are negligible, and the Paschen breakdown in the gas volume of the voids is the dominant charging mechanism [37, 38].

3.2 Mechanical properties of laminated FEP-PTFE films

Ferroelectrets are electromechanical materials in which both the mechanical and the electrical properties are equally relevant; therefore, Young’s modulus in the thickness direction of the fabricated films was determined from the dielectric resonance spectrum. Figure 5 shows the complex capacitance spectrum of a free (i.e. unclamped) laminated FEP sample, indicating the thickness-extension mode. The respective anti-resonance frequency was determined from the loss peak at 106 kHz. Taking the bulk density of 2.15×103 kg/m3 for FEP and a typical thickness of 85 μm for the fabricated film, an average bulk density of 630 kg/m3 is obtained for the laminated film. Equation (4) then yields a compressive elastic modulus of 0.21 MPa on the basis of the experimental results. Because of the above-mentioned thickness variation over the sample surface, Young’s modulus also depends on location.
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Fig. 5

Dielectric resonance spectrum of a laminated FEP film contact charged at a bias voltage of 1500 V. The thickness of the sample is 85 μm

3.3 Thermal stability of the piezoelectric d33 coefficients

The isothermal stability of the piezoelectric d33 coefficients of the laminated films was investigated by annealing the samples at a temperature of 120°C for given periods of time and measuring the quasistatic d33 values at room temperature. Results on the thermal stability of the d33 coefficient of the films, measured at an applied pressure of 3.1 kPa, are shown in Fig. 6. All samples were contact charged with an applied peak voltage of 1500 V at room temperature and the initial d33 value was obtained following storage of one day at room temperature. As seen from Fig. 6, the initial d33 values are larger for the thinner films (75 and 82 μm) and amount to 3650 pC/N, but are smaller for the thicker sample (191 μm). One reason for this phenomenon could be the charging voltage, since its maximum value of 1500 V is probably too small for optimally charging the thicker samples. Another reason might be the different mechanical properties of the samples of various thicknesses. Studies are under way to investigate this further. Figure 6 also indicates that the piezoelectric d33 coefficients of the samples exhibit a relatively fast initial decay at 120°C. After 500 min at this temperature, all samples exhibit fairly steady values. For one of the samples, the remaining quasistatic d33 coefficient is still above 1000 pC/N after annealing for 3000 min at 120°C. Therefore, thermally stable FEP ferroelectrets with very high d33 coefficients up to 1000 pC/N can be obtained by using the preparation method described above followed by proper annealing treatment. This is a significant improvement compared to previous results obtained in [18], where stable d33 values at 120°C are in the range of 500 to 600 pC/N.
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Fig. 6

Isothermal decay of the quasistatic piezoelectric d33 coefficients for laminated FEP films at a temperature of 120°C. The samples were contact charged at a bias voltage of 1500 V

3.4 Pressure dependence of d33

The pressure dependence of the piezoelectric d33 coefficients is of importance because it is not only a critical parameter for the applications of such piezoelectric materials, but it also reveals the structure of the laminated films [18, 30]. Results on the pressure dependence of d33 for four samples, with different thicknesses, are shown in Fig. 7. In order to examine the possible structural damage of the samples at high applied pressures, the pressures applied to the samples were first increased from low to a high value of 15.7 kPa, and then from the high value back to low values. The experimental results do not indicate a hysteresis; thus only the data obtained by increasing the pressure are plotted in Fig. 7. The d33 coefficients for all samples shown in Fig. 7 exhibit a small increase with increasing applied pressure up to 0.7 kPa and a stronger reduction as the applied pressure further increases to 15.7 kPa. The increase of the d33 coefficients in the small pressure range is probably due to the non-flat surface and varying thickness of the laminated films. Since the pressure was applied by pressing a rigid metal plate against the metalized samples, more and more bubbles were compressed with increasing pressure. This results in an enhancement of the d33 coefficients.
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Fig. 7

Quasistatic d33 coefficients for laminated FEP samples as a function of applied pressure

3.5 Local dependence of d33

In this and the following section, measurements of the d33 coefficient with two different methods, having either a very good or virtually no lateral resolution, are presented. These two methods are an interferometric and an acoustic method, respectively. Since the Michelson interferometer used in this work is based on a focused laser beam, lateral resolution of the inverse piezoelectric activity in the 10 μm range can be obtained. Four such interferometric measurements in the frequency range from 10 Hz to 300 kHz are shown in Fig. 8. The first two measurements were both performed near the center of the same bubble at a distance of about 20 μm. The third measurement was taken in the middle of another bubble, while the last measurement was carried out somewhere between bubbles. The measured vibration amplitudes of the sample surface are given on the left axis of the figure and the resulting d33 coefficients according to (7) are given on the right axis. The three measurements taken in the center of a bubble are similar to typical measurements made on conventional PP ferroelectrets: A slightly decreasing d33 coefficient with increasing frequency followed by the first resonance at a frequency in the 100 kHz range. All three measurements presented in Fig. 8, performed on a bubble, show a fundamental frequency at about 60 kHz and higher resonances at about 90 and 140 kHz. In the frequency range from 10 Hz down to 1 Hz the d33 coefficient of about 1000 pm/V=1000 pC/N is compatible with a quasistatic result of 2000 pC/N which was obtained for the same sample. Results shown in Fig. 8 obtained in the area between the bubbles indicate that the vibrations of the bubbles couple mechanically or acoustically into this area. As expected, the coupling is increasingly more damped toward higher frequencies, resulting in decreasing vibration amplitudes. The relatively soft fixation of the film samples on the sample holder by a double sided adhesive tape may contribute to this coupling.
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Fig. 8

Interferometrically determined frequency responses measured at four different positions on a laminated FEP film. The two ordinate scales are related by (7) and both scales apply to all curves. The sequence of curves from top to bottom at 1 kHz is indicated in the legend box

3.6 Acoustic measurements of d33

The main advantage of the acoustic method when measuring laminated films is the proper averaging of the d33 coefficients obtained [18], since the applied sound pressure is identical everywhere on the sample for low frequencies, i.e. when the wavelength of the sound is much larger than the sample. The acoustic method therefore supplements quasistatic and interferometric methods for the determination of d33.

In Fig. 9 voltage sensitivities of four different laminated FEP films, used as capacitive microphones, are shown. For low frequencies the sensitivities of the laminated FEP films are in the range from 0.65 to 1.1 mV/Pa, while typical PP ferroelectrets have a sensitivity of about 2 to 2.5 mV/Pa [6]. For frequencies above 1 kHz, for all films a significant increase of the sensitivity was found, followed by a maximum at about 6 kHz, with sensitivities roughly 2.5 times higher compared to the low frequency values. The origin of this behavior is the pressure built-up due to the reflected wave, well known in acoustic measurements, when the area of the microphone is comparable or larger than the square of the wavelength. For the measurements presented, the relevant area is the area of the PCB-board which was about five times larger than the area of the laminated FEP films. Since the pressure built-up is known for circular, quadratic and other simple geometries [39], its influence can be corrected.
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Fig. 9

Acoustically measured frequency responses of the voltage sensitivity of four laminated FEP films. The sequence of curves from top to bottom at 1 kHz is indicated in the legend box

With this correction and according to (6), the d33 coefficients of the four laminated FEP films used as microphones can be calculated from their voltage sensitivities presented in Fig. 9. The results are shown in Fig. 10. As expected, all frequency responses are relatively flat or slightly decreasing with increasing frequency. The values are between 300 and 400 pC/N and thus much smaller than quasistatic or on-bubble interferometric results. However, considering the increase of Young’s modulus with frequency and air streaming phenomena [18], and taking into account the reduced piezoelectric activity over part of the area of the laminated FEP films, the acoustically measured d33 coefficients are compatible with the quasistatic and interferometric values.
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Fig. 10

Frequency responses of the d33 coefficient calculated from the sensitivities of the four laminated FEP films shown in Fig. 9. The pressure built-up in Fig. 10 was corrected numerically. The sequence of curves from top to bottom at 100 Hz is indicated in the legend box

4 Summary

Fluorocarbon ferroelectrets with well-controlled microstructures were successfully fabricated from compact FEP layers by patterning with templates and subsequent fusion bonding. The ferroelectrets show consistency and regularity in their void structures and good bonding of the layers. The critical voltage across the laminated films, which leads to electrical breakdown in the inner voids, is around 800 V. At room temperature, Young’s modulus in the thickness direction of the fabricated films with a thickness of 85 μm, determined from the dielectric resonance spectra, is about 0.21 MPa. The typical initial quasistatic piezoelectric d33 coefficients of the ferroelectrets are in the range of 1000–3000 pC/N. By proper annealing samples with very high d33 coefficients (up to 1000 pC/N quasistatic and up to 400 pC/N in the audio range), thermally stable at 120°C, can be obtained. This constitutes a significant improvement compared to previous results [18].

Acknowledgements

The authors want to dedicate this article to Professor Reimund Gerhard at the occasion of his 60th birthday. In addition, the authors gratefully acknowledge financial support by the “Hessische Ministerium für Wissenschaft und Kunst”, the “Deutsche Forschungsgemeinschaft” (DFG), the Natural Science Foundation of China (NSFC, No. 50873078), and the State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University (EIPE11203).

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© Springer-Verlag 2012