# Pure longitudinal plate mode excited by poled domains transducers on LiNbO3

E. Courjon, J. Masson, D. Gachon, L. Gauthier-Manuel, N. Bodin, W.

Daniau, S. Ballandras, J. Hauden

► To cite this version:

E. Courjon, J. Masson, D. Gachon, L. Gauthier-Manuel, N. Bodin, et al. Pure longitudinal plate mode excited by poled domains transducers on LiNbO3. EFTF-FCS'07, 2007, Geneve, Switzerland. pp.1073-1076, 10.1109/FREQ.2007.4319244. hal-00194787

HAL Id: hal-00194787

https://hal.science/hal-00194787v1

Submitted on 20 Apr 2021

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Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
Pure longitudinal plate mode excited by poled domains
transducers on LiNbO3

E. Courjon, J. Masson, D. Gachon, L. Gauthier-Manuel, W.
Daniau, N. Bodin, S. Ballandras

Institut FEMTO-ST, UMR 6174 CNRS, UFC-ENSMM-UTBM
32 Ave. de l'Observatoire, 25044 Besançon Cedex, France
sylvain.ballandras@femto-st.fr

J. Hauden,

Photline Technologies
Besançon, France

Jerome.hauden@photline.com

*Abstract*—In this paper, we present new results on the development of piezoelectric transducers based on periodically poled ferroelectrics domains. The fabrication of test devices operating in the range 50 – 500 MHz has been achieved. Pure longitudinal modes are excited, yielding high frequency operation of test devices with easily achievable lithography process (20 and 10 µm periods). The dispersion analysis of our devices is reported and the capability of the proposed wave-guide to support pure longitudinal modes along the plate radial dimension is emphasized

I. INTRODUCTION

The possibility to manufacture elastic wave-guide based on
a thin ferroelectrics film deposited on a single crystal
substrate and periodically poled to enable the excitation of
surface acoustic wave has been demonstrated recently [1].
The so-called periodically poled piezoelectric inter-digital
transducer (PPT) simply consists in two electrically
conductive media embracing a periodically poled
ferroelectrics layer. It has been successfully implemented and
tested for the excitation of elliptically polarized waves in the
frequency range of 1-3 GHz.

In previous work, we have investigated the possibility to
develop PPTs on LiNbO₃ [2]. The first experiments have been
performed on optical grade 500 µm thick 3" Z-cut wafers.
We used optical - instead of acoustics - grade wafers because
of their tighter tolerances in terms of total thickness variation
and side parallelism. The fabrication of PPTs on such wafers
gives access to the excitation of symmetrical Lamb modes
with an operating frequency twice higher than those obtained
using standard inter-digital transducers.

In this paper, the fabrication of high frequency PPTs
exhibiting poling periods of 10, 20 and 40 µm have been
successfully realized (5, 10 and 20 µm line-width
respectively). Several millimeter long ferroelectrics gratings of
respectively 3960, 1980 and 990 periods have been tested and
the corresponding admittances have been measured.
Contributions corresponding to the elliptically polarized Lamb

waves already observed for lower frequency devices have
been identified, corresponding to a wave velocity close to
3800 m.s⁻¹ (near the Rayleigh wave velocity). Also clear
contributions corresponding to a higher phase velocity have
been observed. Simulations have been achieved using our
periodic finite element code, enabling to analyze the
experimental responses. It was found that the above-
mentioned contributions correspond to a pure longitudinal
wave homogeneously distributed along the whole thickness of
the plate and propagating near 6500 m.s⁻¹. Such a wave cannot
be excited using standard Inter-Digital Transducer (IDT).
Consequently, the capability of the poled transducer to excite
it allows for the implementation of very high frequency
devices thanks to the combination of a high phase velocity and
the natural operation of the transducer, doubling the operation
frequency compared to standard IDT for a given spatial
period. The paper reports on the theory/experiment assessment
and conclude on the applicability of such a solution for high
frequency signal processing.

II. PERIODICALLY POLED TRANSDUCER (PPT) PRINCIPLE

The PPT is fundamentally based on a periodically poled
piezoelectric medium. Each side of this medium is metallized,
then providing a capacitive dipole in which elastic waves can
be excited thanks to phase construction. Such a periodically
poled structure can be advantageously achieved on
ferroelectrics materials like PZT [1] because of the rather
small value of its coercitive electric field (the absolute value
of the electric field above which the ferroelectrics poling can
be controlled).

The principal advantages of PPTs compared to standard
periodic inter-digital electrode transducer (IDTs) deposited
atop piezoelectric materials are first the robustness of the
excitation versus defects or surface contamination (no
passivation is required to avoid short circuit as for standard
IDTs) and second the opportunity to excite waves exhibiting a
wavelength equal to the poling period, contrarily to standard
IDTs for which the wavelength is equal to twice the
mechanical period (Bragg condition). One can also note that

<footnote>This work has been funded by the European Community as the
InterReg III project DOMINOS.</footnote>
comparably to film bulk acoustic resonators (FBARs), it can
operate with large excitation powers as the electrodes are
separated by a bulk material layer. We have shown in [2] the
capability of the structure to excite elliptically polarized plate
waves (Lamb modes).

To improve the understanding of the device operation, the dispersion curves of Lamb modes on a Z-cut LiNbO₃ are plotted in fig.1, allowing us to point out the operating frequency of the excited modes for each of our sample configurations [2]. A simple geometric construction gives the operating frequencies for each excited Lamb mode [3]. For a given plate thickness *h*, the slope *m* of a straight line passing through the origin is equal to the wavelength-plate thickness ratio (*m*=*λ*/*h*). In our case, the thickness of the wafer is 500 µm, a standard value for commercially available material (e.g. Crystal Tech Inc.). We consider periods of our experimental setups (200 and 100 µm respectively) yielding values of *m* equal to 0.4 and 0.2 (our devices, the acoustic wavelength *λ* equals the poling period *p*). Projecting the corresponding lines on the Lamb wave dispersion curves allows for the prediction of the wave velocity and hence of the operating frequency for each mode.

<figure><img src="image_2.png" /><figcaption>Figure 1. Dispersion curve of Lamb waves on a Z-cut LiNbO₃ plate, frequency-thickness product ranging from 0 to 25 km.s⁻¹. The straight lines indicate the expected operating rules of the experimental PPT-based devices</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2. Coupling coefficients of the corresponding modes versus frequency.thickness product</figcaption></figure>

Since the values of *m* are always smaller than 1 (i.e. the frequency-thickness products corresponding to the test device are in the range 5-50 km.s⁻¹), we could not take advantage of the high velocity of the S₀ mode. As a consequence, the first coupled mode on our device should always exhibit a wave velocity close to 3750 m.s⁻¹, yielding operating frequencies respectively equal to about 19 and 38 MHz. This first order prediction nicely meets the experimental values. Note that the corresponding experimental coupling coefficient generally remains moderate, between 1% and 1‰, whereas theoretical values are found in the range 1-10%. This point needs more investigation to be clearly explained. More, note practical implementation only reveals the signature of symmetrical modes, assuming perfectly symmetrical transducer structures.

As previously presented [2], we have exploited a dedicated poling bench to control the poling of thick (500µm) Z-cut LiNbO₃ plates. It mainly consists in a high voltage amplifier used to apply an electric field to the LiNbO₃ wafer strong enough to invert the spontaneous polarization of the material. The domains to be poled are defined thanks to a photo-resist pattern on top of a plate surface. This yields a dielectric barrier strong enough to prevent any electric field to be located underneath the resist. The high poling voltage is applied to the plate following the sequence shown in fig. 3 and using liquid electrodes made with a saturated lithium chloride solution. This sequence is designed to favor the domain nucleation, to stabilize the inverted domains (i.e. to avoid back-switching of the domains) and to avoid electrical breakdowns [4]. The poling process is monitored thanks to the measurement of the electric current crossing the wafer during the sequence. The signature of a successful domain inversion corresponds to the current discharge observed in fig.3. The poling can be easily controlled by a simple optical post-observation, as it generates a contrast between at the edge of the poled domains (see fig. 4).

<figure><img src="image_4.png" /><figcaption>Figure 3. Domain inversion monitoring: probed high voltage applied on the wafer (green curve, poling sequence) and resulting crossing current (red curve). Voltage and current gain are respectively 1V/5000V and 1V/5mA. 1st step: the applied electric field is smaller than the coercitive limit, to prepare the sample for the nucleation step. 2nd step: the applied field overcomes the coercitive limit, yielding nucleation and consequently poling (this step lies between the 2 dashed cursors). 3rd step: linear decrease of the field to end-up the nucleation (self-termination step, exponential decrease of the current). 4th step: stabilization of the poling by applying a field smaller than the coercitive limit</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 4. Optical verification of the poling efficiency (a) case of a 100 µm period device, evidence of contrast changes between Z⁺ (native polarization) and Z⁻ (switched polarization) domains (b) evidence of contrast modification in the vicinity of the poled domain walls at the poled strip edge (the whole plate is Z⁺ oriented, the poled strips are Z⁻ oriented)</figcaption></figure>

### III. HIGH FREQUENCY DEVICES

Different devices have been achieved and presented in [2] operating in the frequency range 20-50 MHz, showing a good predictability of their electrical response using period FEA. In this work, we have pushed one step further the fabrication of PPT to demonstrate their capability to operate in the intermediate frequency range (50-500 MHz). In that matter, we have fabricated a new set of masks with poling periods (acoustic wavelengths) equal to 10, 20 and 40 µm. Only the devices corresponding to the two last periods have been found to operate and allowed for electrical measurements. Figure 5 shows the admittance of a 20 µm period PPT.

<figure><img src="image_6.png" /><figcaption>Figure 5. Experimental admittance of a 20 µm period PPT</figcaption></figure>

Although the response is somehow difficult to interpret (numerous parasitic bulk wave pollution), two strong contributions are pointed at 190 and 320 MHz respectively. The first one was actually expected in the vicinity of 200 MHz according to the above-presented first order analysis but we did not expect the one at 320 MHz from the dispersion curves, even if they are far to be comprehensive regarding the

operating conditions (wavelength-plate thickness ratio $m=0.04$). The same situation was pointed out for the 40 µm wavelength device. We then have computed the harmonic admittance of the corresponding PPT structure and superimposed the obtained theoretical predictions with experimental measurements. This is reported in fig.6 and 7 for the 20 µm and 40 µm period devices respectively.

<figure><img src="image_7.png" /><figcaption>Figure 6. Theory/experiment assessment for the 20 µm period PPT device</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 7. Theory/experiment assessment for the 40 µm period PPT device. Experimental curves have been focused on the useful part to improve the plot readability</figcaption></figure>

Even if the first modes are slightly shifted from theory to experiment, these plots point out the good agreement between both results. In a first order approximation, it is possible to calculate the equivalent phase velocity of each contribution, yielding values of 3800 and 6500 m.s⁻¹ respectively. Once again, the first value can be easily related to the asymptotic limit emphasized in fig.1 for the very first Lamb wave contribution (i.e. Rayleigh wave velocity) but the second one approaches the longitudinal bulk wave velocity along X axis that does not clearly appear on the dispersion curve. As a consequence, we have computed the equivalent of a dispersion curve using our periodic FEA code and superimposed the predicted modes (the most important ones in terms of response
amplitude for the sake of readability) with the Lamb wave dispersion curve of fig. 1. This is reported in fig. 8.

<figure><img src="image_9.png" /><figcaption>Figure 8. Superimposition of dispersion curves computed thanks to the Green's function approach and by periodic finite element analysis</figcaption></figure>

This plot shows that a clear contribution of a quasi-longitudinal mode propagating along the lateral direction of the plate arise for almost any frequency.thickness operating point. This contribution may be interpreted as the location where the high velocity Lamb waves strongly interacts, yielding significant changes in the group velocity between 6000 and 7000 m.s⁻¹. It can also be consider as a typical mode of the wave-guide, particularly favoured by the periodic poling of the plate. Note that such mode was not identified in previous work achieved on PZT [5] but it should certainly exist and should be emphasized along the same theoretical approach. Figure 9 shows the polarization of the mode near 165 MHz for the 40 µm period PPT device. Even if one can remark after a detailed analysis that the actual mode shape is a complex combination of shear, elliptical and piston-like displacements, the longitudinal polarization of the mode strongly predominates.

## IV. CONCLUSION

We have demonstrated the possibility to excite longitudinal modes using periodically poled transducer on LiNbO₃ Z-cut. The velocity of these mode approaches 6500 m.s⁻¹, allowing for easily access intermediate and high frequency range without lithography breakthrough for the definition of the periodic grating required to build the devices. Although the numerous modes of our PPT clearly is a drawback for signal processing, it sounds that reaching very small wavelength-plate thickness ratio favor the spectral

localization of those modes near asymptotical limits, corresponding to the Rayleigh wave and to the longitudinal mode along the plate surface. Although efforts have to be paid for improving the signal/noise ratio of the device response and to fully characterize the modes, these results encourage us to try and demonstrate the capability of PPT to actually achieve signal processing operations.

<figure><img src="image_10.png" /><figcaption>Figure 9. Sequence of dynamic vibration of the 40 µm period PPT operating near 165 MHz, iso values of displacement along the plate radial dimension (a) t=0 (b) t=1/(4.f) (c) t=1/(2.f) (d) t=3/(4.f)</figcaption></figure>

## REFERENCES

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[2] E. Courjon, N. Bodin, G. Lengaigne, L. Gauthier Manuel, W. Daniau, S. ballandras, Fabrication of periodically poled domain transducers on LiNbO₃, Proc. of the IEEE IFCS, 2006

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