Surface acoustic wave characterization of optical sol-gel thin layers

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Surface acoustic wave characterization of optical sol–gel thin layers Dame Fall a, François Compoint b, Marc Duquennoy a,⇑, Hervé Piombini b, Mohammadi Ouaftouh a, Frédéric Jenot a, Bogdan Piwakowski a, Philippe Belleville b, Chrystel Ambard b a IEMN-DOAE (UMR CNRS 8520), Institut d’Electronique, de Microélectronique et de Nanotechnologie, Département d’Opto-Acousto-Electronique, Université de Valenciennes, 59313 Valenciennes, France b CEA, DAM, Le Ripault, F-37260 Monts, France

a r t i c l e

i n f o

Article history: Received 17 December 2015 Received in revised form 5 February 2016 Accepted 8 February 2016 Available online xxxx Keywords: Surface acoustic wave Optical sol–gel layers IDT transducer SAW sensor Ultrasonic NDT

a b s t r a c t Controlling the thin film deposition and mechanical properties of materials is a major challenge in several fields of application. We are more particularly interested in the characterization of optical thin layers produced using sol–gel processes to reduce laser-induced damage. The mechanical properties of these coatings must be known to control and maintain optimal performance under various solicitations during their lifetime. It is therefore necessary to have means of characterization adapted to the scale and nature of the deposited materials. In this context, the dispersion of ultrasonic surface waves induced by a micrometric layer was studied on an amorphous substrate (fused silica) coated with a layer of ormosil using a sol–gel process. Our ormosil material is a silica–PDMS mixture with a variable polydimethylsiloxane (PDMS) content. The design and implementation of Surface Acoustic Wave InterDigital Transducers (SAW-IDT) have enabled quasi-monochromatic Rayleigh-type SAW to be generated and the dispersion phenomenon to be studied over a wide frequency range. Young’s modulus and Poisson’s ratio of coatings were estimated using an inverse method. Ó 2016 Published by Elsevier B.V.

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1. Introduction

44

High power lasers can damage optical components. Laser Induced Damage (LID) is characterized by craters of a few microns that appear mainly on the exit surface of the beam in fused silica when irradiated with a powerful laser beam, especially at 350 nm. The CEA (Atomic Energy and Alternative Energies Commission) suggests developing coatings on laser transmission optics to mitigate shock waves that can modify and increase the density of fused silica inducing an increase in absorption that explains the rapid increase in damage after repeated laser pulses [1,2]. To achieve this objective, a wide range of hybrid materials based on a mixture of silica and PDMS has been developed using sol–gel processes. These coatings have interesting optical and mechanical properties for the target application. Several formulations of these hybrid materials have been optimized to produce optical coatings for lasers. In order to classify these thin layers correctly, a novel technique was tested to determine the elastic properties (Young’s modulus and Poisson’s ratio) of these thin layers 1–2 lm thick. A surface wave dispersion technique will then be used to determine the mechanical properties of these thin layers. SAW-IDTs will be

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⇑ Corresponding author.

used over a wide frequency range from 10 to 60 MHz to effectively generate surface acoustic waves. Several techniques can be used to generate Rayleigh-type surface waves. Wedge sensors are traditionally used to generate surface waves, but above 10 MHz the losses and attenuations related to this sensor technology become too significant. Another interesting technique is laser-ultrasonics, which offers numerous advantages such as the possibility of non-contact generation and broadband generation [3,4]. In recent years, several publications have demonstrated the relevance of this method for the characterization of thin films [5–7]. However, depending on the nature of the materials, the suitability of this method of generation varies according to the penetration depth and/or fragility of the layers (problem of ablation). Finally, the acoustic signature is also an interesting technique enabling measurements to be carried out at very high frequency [8]. However, it is essential to work in immersion, which in some cases is not feasible in terms of the integrity of the structure or device to be controlled. In this study, we designed and implemented SAW transducer. This original solution is based on the development of interdigital transducers to generate quasi-monochromatic surface waves and obtain a rapid and accurate estimation of the phase velocity, key information for the characterization of the layers. Moreover, the use of SAW-IDTs allowed HF (High frequency) surface waves to

http://dx.doi.org/10.1016/j.ultras.2016.02.006 0041-624X/Ó 2016 Published by Elsevier B.V.

Please cite this article in press as: D. Fall et al., Surface acoustic wave characterization of optical sol–gel thin layers, Ultrasonics (2016), http://dx.doi.org/ 10.1016/j.ultras.2016.02.006

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be generated over a broad frequency range [9]. IDT are typically used in acousto-electronic signal processing devices such as surface wave filters, oscillators, and resonators. Today, most SAW applications are in the field of telecommunications and the frequencies used are typically very high and can reach several gigahertz [10]. Acoustic IDTs are used in NDT (Non Destructive Testing) applications, but are usually used at frequencies of a few megahertz [11]. It has already been shown that micrometer layers influence SAW propagation, although for frequencies in the range of megahertz, the SAW wavelengths are well above the micrometer [9,12]. In this study, we show that the micrometric sol–gel layers, with very low Young’s modulus compared to the silica, also influence (dispersion phenomenon) SAW propagation. Then, through the study of this dispersion, it was possible to determine, by inversion, some important characteristics such as elastic constants. One of the advantages of this ultrasonic technique is having SAW attenuation between 10 and 60 MHz that is not too significant. Thus, the SAW can propagate over several tens of millimeters and it is possible to characterize a large area of the sample. In addition, no specific sample preparation is required, and no metal layer is necessary, unlike with femtosecond-based techniques [13]. Therefore, samples can be tested directly with no specific preparation.

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2. Sol–gel coatings

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The sol–gel layers that have been developed are made with silica and PDMS elastomer. Those two materials have been chosen because of their high transparency especially around the UV wavelength [14], and for their high laser damage threshold. Indeed, silica is one of the best materials to resist to a high energy laser beam. PDMS is a silicon based inorganic polymer. It has a weak absorption coefficient (5
103 cm1) and some good heat resistance properties, which are very interesting properties to resist to the laser beam [15,16]. The two materials have similar refractive index (1.41 for PDMS and 1.45 for silica) [14], and PDMS can be associated with silica by a sol–gel synthesis. Indeed, the hybrid silica–PDMS solution is made from the silica precursor, the tetraethylortosilicate (TEOS) and a commercial PDMS solution supplied by Sigma–Aldrich with hydroxyl groups at the end of the polymer chains. The sol–gel reaction begins with the TEOS hydrolysis in which the ethyl groups that ended the TEOS species are switched with hydrogens elements to form silanols Si–OH species. A condensation of the hydrolyzed TEOS occurs under an acid catalysis. We used two types of acid to perform this reaction, the hydrochloric acid (HCl) and the trifluoromethansulfonic acid (TFS). With the hydrolysis and the condensation of the TEOS species, a silica network is formed. The PDMS chains react with the silanols Si–OH groups of the hydrolyzed TEOS or on the surface of the silica network. The two reactions occur simultaneously, but the PDMS reaction with the silica species is not always total. Indeed, when the PDMS amount increases, some PDMS chains remain free in the organic network, which give to the high PDMS loads some viscoelastic properties. Meanwhile, weaker, autonomous and reversible hydrogens bonds can be created between the silanols and the oxygen elements of the PDMS chains. Using those two elements, the viscoelastic properties and the reversible hydrogens bonds, we aim at giving to the layers some self-healing properties. Once the sol–gel reaction is made, a transparent and homogenous solution is obtained, and a maturing step of 4 days is made to wait for the stabilization of the species in solution. It is the maturing step used after synthesis. Indeed, after this step, the solution can be used to make coatings. The sol–gel solution has a very weak viscosity after the reaction (<5cP), but a gelling of the

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Fig. 1. Transmission spectra of a naked silica substrate and the same substrate with a silica–PDMS layer.

solutions occurs after 40 days of maturing. With a maturing time of 40 days after the synthesis, the solution tends to gelify. The solution is coated before gelling on silica polished substrates by dip or spin coating techniques. The used technique to make the materials used in this study is spin-coating, but dip coating is also possible to make silica–PPDM thin layer. Once the thin layer is obtained, the sample is dried and a heat treatment is made at 120 °C to activate the chemical bounds between the silanols surfaces groups of the substrate and the sol–gel species of the layer. A solid silica–PDMS hybrid thin coating with strong adhesion to the substrate is obtained. The transmission spectra show that the silica–PDMS coating give to the sample some higher transmission values, with the presence of Fresnel’s interference that is typical for antireflective layers properties (Fig. 1). The analysis of that interference is useful to determine the refractive index of the layer and the substrate with the Fresnel laws. Once the refractive index of the layer is known, the optical and real thickness can be calculated. Density values of the layers are necessary to find the mechanical properties by surface acoustic wave characterization. At first, we estimated the sol–gel layers density with a mixture model. The density is 970 kg/m3 for the PDMS [13] and 1920 kg/m3 for the polymeric silica [17] in which we considered the internal porosity. Meanwhile, the literature shows that for higher amount of PDMS in the material, the structure of the hybrid is coarser with a higher internal porosity [13]. Thus, there is an uncertainty on the density of the layer at high PDMS ratio (30–40%w) that has been detected by a variation of the refractive index values between two layers on its transmission spectra. The density characterization techniques on massive materials were not fit to measure thin layers material on its substrate. For this reason, secondly, we analyzed the layers with density values that have an uncertainty of 5% and 10%. The different parameters of the layer that have been analyzed are presented in Table 1. The unordered structure of polymeric silica confers its total isotropy and high homogeneity on a macroscopic scale. At ultrasound scale, glass appears homogenous and isotropic. The density of the silica is 2201 kg m3 and the polymeric silica porosity made by sol–gel is 12.9% [13] therefore its density was 1921 kg m3. The Young’s modulus E and Poisson’s ratio t are given in the Ref. [18] (E = 73GPa and t = 0.16).

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3. Dispersion of SAW in sol gel layer on substrate structure

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When a Rayleigh-type SAW propagates on the surface of a homogenous material its energy is concentrated within a thickness of about one wavelength beneath the surface. When this wave

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5 10 30 40

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Silica–PDMS layers obtained with HCl catalysis

Silica–PDMS layers obtained with TFS catalysis

Thickness (lm)

Density

Thickness (lm)

Density

/ / 3.7 4.6

/ / 1817 1700

0.62 0.67 2.6 2.6

1874 1826 1636 1541

propagates in a layer on substrate structure, the surface wave becomes dispersive [19–22]. The velocity of this wave partly depends on the characteristics of the layer. Its measurement thus allows the characteristics of the layer to be determined by means of an inverse method. The wave equation for the displacement in a perfect elastic medium with absence of piezoelectric effects and external forces is given by the following equation [23]:

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q

2

2

@ ub @ uc ¼ C abcd @xa @xd @t 2

ð1Þ

where ub are the displacement components, t is time, q and Cabcd are the mass density and the stiffness tensor of the medium concerned respectively. We consider the case of a thin isotropic and homogeneous layer deposited on a semi-infinite isotropic and homogeneous substrate (Fig. 2). In each medium, the solution of the wave equation satisfying the boundary condition of the free surface (x2 = h) is assumed to be linear combinations of partial waves of the form [19]:

212 214

ið~ k~ rxtÞ

uj ¼ Aje

¼ Aj eikbx2
eikðx1 vtÞ

ð2Þ

231

pffiffiffiffiffiffiffi where i = 1, k = 2p/k is the wave number, v = x/k is the phase velocity and Aj are the relative amplitudes of the different components of each partial wave. This solution describes the Rayleigh-like modes which propagate in the X1 direction and whose displacement components decay with depth. Therefore, the quantity b in each terms of the solution must be a purely imaginary constant. The substitution of Eqs. (2) into (1) leads to a linear system linking v, b and Aj in the medium considered The non-trivial solutions for this system lead to the secular equation for each medium which can be considered as algebraic equation in b. There are four partial waves in the layer (four roots for b) and two in the substrate (two roots for b). In each medium, the partial waves are combined linearly with amplitudes Aj chosen in order to satisfy the boundary conditions (free surface at x2 = 0 and continuity of displacement and stress components at the interface x2 = h). This resolution yields the dispersion relation:

232 234

det ½M ¼ 0

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ð3Þ

3

been calculated. To calculate the phase velocities of the surface modes, the silica substrate and the sol–gel layer were defined by their density and elastic constants. Since the materials are assumed isotropic and homogeneous, the Young’s modulus E and the Poisson’s ratios t are linked to elastic constants as following: E = C 11  2:C 212 =ðC 11 þ C 12 Þ and t = C 12 =ðC 11 þ C 12 Þ. In Fig. 3, the theoretical phase velocity of the first Rayleigh mode propagating on a layer on substrate structure is reported over a range of frequencies up to 100 MHz based on the initial data. It is very interesting to analyze this curve and to observe that the phase velocity of the surface wave decreases systematically in the presence of sol–gel coating. This coating can be called ‘‘loading” because it loads the substrate [20,21]. In this case, the velocity of SAW compared with the velocity of the surface wave which would propagate on an unstressed substrate is reduced by the presence of the sol–gel coating. This phenomenon is consistent with the fact that surface waves are slowed in the presence of a rubbery layer. SAW are dispersive on coated silica wafer and their phase velocities may decrease by around 400 m/s over a frequency range between 10 and 100 MHz. So, if it is possible to carry out measurements over this wide frequency range, it is possible to accurately characterize the mechanical properties, which is why we have chosen to use SAW to highlight this phenomenon on these structures. The main challenge was firstly to develop interdigital transducers to generate high frequency SAW over a wide frequency range and secondly to develop a signal processing method to obtain sufficiently accurate estimates of SAW propagation velocities. In general, these characterizations (elastic constants, thickness, residual stress,. . .) were obtained by measuring the phase velocities. Considering Rayleigh-like wave dispersion, the experimental determination of these phase velocities can be deduced from measurements of group velocities. This can be performed directly on the temporal signals, or indirectly using a Wavelet Transform [24] for example performed with signals corresponding to different propagation distances. The phase velocities can also be obtained using 2-DFFT (two-dimensional discrete Fourier transform) [25] with time signals recorded at uniformly spaced distances. The different modes can then be isolated and identified in the frequency– wavenumber representation. So, to obtain accurate estimates of phase velocities, a large number of measurements are required and the signal processing must be carried out with extreme rigor. This obviously necessitates a great deal of time in terms of measurements and calculations. To overcome these drawbacks, in this study we proposed narrowband SAW-IDTs which offer the possibility of generating quasi-monochromatic SAW. In these conditions, it is possible to implement techniques for SAW estimating phase velocities as with non-dispersive materials enabling. These techniques are generally more rapid and accurate.

where M is 6 by 6 matrix depending on k, v and on the characteristics of the layer (shear and longitudinal wave velocities, density and thickness) and those of the substrate. In order to check the dispersion of the first Rayleigh mode in sol gel coated silica wafer, the phase velocities versus frequency have

Layer

0 ρ 0 , cacbd

Substrate

ρ 1, c1acbd

X1

0 h X2

Fig. 2. Graded plate and coordinate system.

Fig. 3. Phase velocities of the first Rayleigh mode propagating on coated silica wafer in frequency up to 100 MHz.

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4. Generation and detection of SAW

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An interdigital-electrode transducer (SAW-IDT) consists of two overlapping metal comb-shaped electrodes with overlapping fingers. The electrodes are deposited on a piezoelectric substrate of lithium niobate (LiNbO3). When a voltage U is applied between the two electrodes there is an accumulation of charges the signs of which alternate from one finger to the other thus creating an electric field between each pair of electrodes. The combination of the piezoelectric effect of the substrate and the electric field generates expansions and compressions in the material thus creating movement. It is this movement that gives rise to surface waves perpendicular to the electrode fingers (Fig. 4). In this study, the piezoelectric sheet chosen is made of lithium niobate (128°YX) as this material has a very high electromechanical coupling coefficient (K2 = 5.3%) [26]. SAW-IDTs generate quasi-monochromatic surface waves and so several IDTs devices have been designed to cover a large range of frequencies. Given the velocity of SAW in LiNbO3 (around 4000 m/s) it was necessary to make IDT devices the electrodes of which are between 25 and 100 lm wide. To determine the optimal configuration for a correct response in terms of amplitude and bandwidth [10,27], several IDTs were developed by varying the overlapping length w of the comb fingers and the number of fingers N. These transducers were obtained using the lift-off process available at the IEMN’s technological center. This method allows the high-resolution deposition of electrodes (gold here) on niobate wafers. The main constraint was the aspect ratio between the width a and the aperture width Wa of the electrodes which was very high (12 < Wa/a < 150) and that any contact between two fingers would create a short-circuit and thus render the transducer unusable. The connection between the electrodes and the generator was provided by an ‘‘SMA end launch” connector. The piezoelectric wafer and plug were placed on an epoxy sheet and gold conductors, welded using a manual wire bonder, provided the electrical connection. The SAW-IDT MEMS were tested electrically and acoustically. Their bandwidths at different frequencies were tested using impedance probe measurements and their yields were estimated using emission-reception acoustic tests. The SAW-IDT MEMS used have 25 pairs of fingers (N = 50) and the ‘‘burst” is composed of 20 sinusoids. These two conditions allow quasi-monochromatic SAW to be obtained (Fig. 5). An outline of the setup for velocity measurements is presented in Fig. 6 and two photographs of this system are given in Fig. 7. The SAW-IDT is placed flat and maintained on the sample with a couplant. The transducer surface, on which the fingers are deposited, is in contact with the sample. The surface wave generated by the SAW-IDT MEMS propagates perpendicularly to the fingers along the surface of the piezoelectric LiNbO3 substrate on which the comb has been deposited. In the area where the piezoelectric substrate and the sample are in contact, the wave is transmitted and then propagates in the sample. This contact allowed us to carry out several sets of measurements at different points of detection

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Fig. 4. Sketch of SAW-IDT.

Fig. 5. Signal detection by the interferometer of normal displacements of SAW generated by an SAW-IDT operating at 20 MHz.

Fig. 6. Sketch of the set up for generation of surface acoustic waves with SAW-IDT and detection with interferometer.

Fig. 7. Photographs of experimental set up.

on the sample while maintaining the same coupling between the SAW-IDT MEMS and the sample. For SAW detection, a heterodyne interferometer UHF120 was used. Good detection levels, with good signal to noise ratios have been obtained thanks to the quality of the coupling which enabled the cross-correlation method to be used [9]. The level of displacement of the surface waves was good despite the low optical reflection coefficient of the glass. Although the bandwidth of the interferometer is very large (1.2 GHz) good results were obtained between 10 MHz and 60 MHz. Attenuation due to the presence of the coatings is high. We also note that this attenuation is directly related to the ratio of PDMS present in layers. The higher the amount of PDMS is, the stronger this attenuation becomes. This may be due to an increasing viscoelasticity in the material with a higher presence

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of ungrafted PDMS chains on silica, which causes a phenomenon of acoustic waves damping [28]. Up to 10% of PDMS, it is possible to perform measurements with frequencies up to 60 MHz. For 30% and 40% of PDMS, measurements are possible up to a frequency of 40 MHz. Fig. 5 shows an example of signals detected with the interferometer for a SAW-IDT operating at 20 MHz with a peak to peak electric pulse of 40 V and 20 sinusoids. For this example, the normal displacement due to SAW is around 8 nm peak-to-peak. The entire sample-IDT assembly is placed on a micrometric displacement table. For each position, the displacement caused by the surface wave is detected at the focal point of the spot laser interferometer. The electrical signal corresponding to the displacement as a function of time (A-scan) is then collected on the oscilloscope and recorded on a computer. An important advantage with this system is the reproducibility during measurement. Indeed, since the entire sample-IDT assembly is placed on a micrometric displacement table, the coupling between the sample and the IDT is the same for each measurement sequence and it is possible to maintain a usable signal throughout the experiment. Since the signal is quasi-monochromatic, the propagation velocity can be estimated using for example a cross-correlation method [9]. Knowing the values of the displacements of the interferometer detection point and the delays via the cross-correlation method, the velocities can be estimated. The distance between the IDT and the detection point of the interferometric receiver varied up to 10 mm in 500 lm increments. Each test enabled about ten times of flight to be measured from which an estimation of the phase velocity was obtained. This step was repeated about twenty times in order to obtain the average velocity associated with its dispersion. 5. Inverse problems & experimental characterization OF ‘‘layer on substrate’’ structures An example of the phase velocity measurements obtained for sample with 10% of PDMS is showed in Fig. 8. For each frequency tested, which corresponded to the SAW-IDT MEMS eigenfrequencies, about twenty velocities were estimated. A mean and a standard deviation were also calculated. The average phase velocities are represented by dots. The experimental curves of the phase velocities are accompanied by the theoretical dispersion curves obtained from the final data. The inverse method consists in looking for the combination of E and t for each of the 6 coatings so as to obtain theoretical propagation velocities as close as possible to those measured experimentally. A minimization routine was executed to find the E and t. The theoretical values of the phase velocities were calculated for each of the SAW-IDT MEMS eigenfrequencies over the entire range of working frequencies using the values of E and t. A least squares

Fig. 8. Theoretical dispersion curve and phase velocity measurements.

minimization was carried out. The processing algorithm then seeks to maximize the value of the coefficient of determination. This coefficient of determination is defined by:

P

407 408 409

410 2

ðy  f i Þ R2 ¼ 1  Pi i 2 i ðyi  yÞ

ð4Þ

 is mean where the values yi are measured values of velocities, y value of velocities and fi are the calculated values (predicted values) of velocities. For solving non-linear least squares problems, several minimization algorithms are used such as Gradient Descent method [29], Gauss–Newton algorithm [30], Livenberg–Marquardt algorithm [31] and simplex method [32]. In this study, iteratively, several depths and pairs of elastic coefficients were tested with a minimization routine developed in MatlabÒ. The minimization method is based on the dichotomy. It consists in an iterative method of bracketing the desired minimum. Starting from an initial bounded interval, which is guaranteed to contain a minimum, the scanning of the interval with different small constant steps allows the width of the bounded interval to be progressively reduced until the desired convergence threshold is reached, i.e. until the width of the bounded interval is sufficiently small with a desired tolerance. This inverse procedure was used on the 6 coated samples. With this routine developed in MATLABÒ, a large number of pairs (E, t) were tested. Large intervals for the thickness were voluntarily chosen to ensure an extremum of R2 was obtained. First, the Young’s modulus interval was set at 0.1 GPa and the Poison coefficient interval was set at 0.01 for a range of Young’s modulus from 1 to 60 GPa and Poison ratio from 0.01 to 0.5. The layers thickness is determined with the optical interference of Fresnel and the variation in peak to valley is less than 20 nm [33,34]. The density values are obtained with a mixture law and are given in Table1. The results are presented in Fig. 9 and in the Table 2. These results show that the percentage of PDMS strongly influences the Young’s modulus of the layers. For 5% and 10% PDMS in coatings, Young’s modulus is reduced by 35% (E = 32.5 GPa) and 50% (E = 24.6 GPa), respectively. Then, for values of 30% and 40% PDMS, SAW mitigation becomes much more significant and the values of Young’s modulus are 7.8 GPa and 5.4 GPa, corresponding to reductions of 84% and 89%, respectively. This is in good agreement with the results reported in the Ref. [35]. Those results fit with the mechanical properties trend that has been shown by Mackenzie and et al. [35] on massive silica–PDMS materials. Thus it is possible to obtain various mechanical properties by adjusting the chemical formulation of the sol–gel synthesis. The results between HCl and TFS catalysis are slightly different. The TFS catalysis is well-known to perform silicone materials, and is a stronger catalyzer than HCl for PDMS–silica hybrids syn-

Fig. 9. Young’s modulus versus PDMS percentage in coating (TFS catalysis).

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Table 2 Estimations of Young’s modulus. % PDMS

5 10 30 40

Silica–PDMS layers obtained with HCl catalysis

Silica–PDMS layers obtained with TFS catalysis

Thickness (lm)

E (GPa)

Thickness (lm)

E (GPa)

/ / 3.7 4.6

/ / 7.6 5.1

0.62 0.67 2.6 2.6

32.5 24.6 7.8 5.4

477

thesis [36]. It explains why the Young’s modulus is higher for the same%w PDMS amount with a TFS catalysis. Regarding the estimation of Poisson’s ratios, we obtained 0.26 and 0.27 for the 5% and 10% PDMS coatings, respectively. Then for the 30% and 40% PDMS layers, we had Poisson’s ratios of 0.3 and 0.32, respectively. To take the influence of the porosity into account, some density simulations were performed and the impact on Young’s moduli estimates checked. We considered that the porosity could have an effect and therefore reduce the density between 5% and 10%. Taking 1554 kg/m3 (5%) and 1472 kg/m3 (10%) for the densities corresponding to the 30% PDMS layer, and 1463 kg/m3 (5%) and 1387 kg/m3 (10%) corresponding to the densities in the 40% PDMS layer, respectively, the data inversions produced the following results. For coatings with 30% PDMS, the initial Young’s modulus of 7.8 GPa was reduced to 5.9 GPa and 4.1 GPa with decreases in density of 5% and 10%. Similarly, for 40% PDMS coatings, the initial Young’s modulus of 5.4 GPa was reduced to 3.6 GPa and 2.3 GPa for decreases in density of 5% and 10%. This reduction is consistent with the values reported in the literature. It is therefore quite likely that the porosity should be taken into account even if the latter is quite difficult to measure.

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6. Conclusion

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488

In this work, we studied the propagation of surface acoustic waves in a structure with a micrometric sol–gel layer. We have shown that the dispersion phenomenon of the surface wave in this type of structure is sufficient to consider the mechanical characterization of layers. The real interest of high frequency surface acoustic waves was shown, as well as the potential of SAW-IDT MEMS for the characterization of such structures up to frequencies of 60 MHz. By solving the inverse problem, we obtained good estimations of Young’s modulus and Poisson’s ratio for different PDMS percentages in sol–gel layers.

489

Acknowledgments

490 491

We would like to thank Nord-Pas-de-Calais (CPER funds) and the European Union (FEDER funds) for supporting our research.

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Please cite this article in press as: D. Fall et al., Surface acoustic wave characterization of optical sol–gel thin layers, Ultrasonics (2016), http://dx.doi.org/ 10.1016/j.ultras.2016.02.006

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