# Development of a Broadband (100–240 MHz) Surface Acoustic Wave Emitter Devoted to the Non-Destructive Characterization of Sub-Micrometric Thin Films

^{*}

## Abstract

**:**

_{3}is proposed. It is shown that this solution efficiently enables the generation of SAW (displacement level up to 1 nm) in a frequency range of between 100 and 240 MHz. The electrical characterization and a displacement field analysis of SAW by laser Doppler vibrometry are presented. The transducer’s significant unidirectionality is demonstrated. Finally, the characterization of two titanium thin films deposited on silicon is presented as an example. A meaningful SAW velocity dispersion (~10 m/s) is obtained, which allows for the precise estimation (5% of relative error) of the submicrometer thickness of the layers (20 and 50 nm).

## 1. Introduction

## 2. Broadband (100–240 MHz) Surface Acoustic Waves Emitter

_{3}. Interdigital transducers consist of comb-shaped metal electrodes (often made of gold or aluminum) composed of interlocking fingers with a finger overlap distance of W [20,21,22]. The IDT electrode structure is presented at the top of Figure 1a for an IDT with a constant electrode period. The electrodes are deposited on piezoelectric substrate so that, when an electrical voltage is applied between the two adjacent electrodes, an accumulation of charges is created, whose signs alternate from one finger to the other. This implies the creation of an electric field between each pair of fingers. The combination of the piezoelectric properties of the substrate and this field leads to expansions and compressions in the material, creating displacements [22]. When the applied electric voltage V

_{E}is sinusoidal, vibrations are constructively created only if the periodicity p is equal to half a wavelength of the Rayleigh wave λ, thus producing surface acoustic waves. In the case of the periodic structure, they are emitted on both sides of the transducer (SAW

_{±}in the IDT side, viewed at the bottom of Figure 1a). Thus, the frequency f

_{0}, which corresponds to this cumulative effect, is called the synchronous frequency or resonant frequency, defined as f

_{0}= V/2p. Here, V is equal to the propagation velocity of the SAW in the substrate and p is equal to the periodicity of the interdigital electrodes, and the acoustic wavelength λ is equal to double the value of the period λ = 2p. Due to the reciprocity of the piezoelectric field, it is possible to acquire the propagated wave in an electrical form using another interdigital transducer of the same type. The signal received in this way is delayed and attenuated in relation to the transmitted signal, and this type of configuration makes it possible, for example, to create filters or delay lines.

_{min}is equal to approximately 56, which prevents the diffraction of the emitted acoustic field at propagational distances large enough for the layer characterization. The final IDT, mounted on a PCB with its SMA connector plug, is shown in Figure 1c. The electrical connection with the IDT is assured by soldered gold microwires.

_{0-p}. The mentioned IDT length (1 mm) determines that the duration of the emitted chirped pulse is equal to around 2 µs, given that the Rayleigh velocity is 3878 m/s for LiNbO3-Y+128°. Thus, the time–frequency product (TFP, product of the pulse duration and signal bandwidth) is equal to approximately 280. Designing chirped transducers with a TFP in the range of 100–300 is practical regarding the need to ensure the minimization of the IDT dimensions and the level of Fresnel ripples in the emitted spectrum while maintaining a high emitting efficiency [24,25].

_{3}and possessing 200 nm-thick aluminum electrodes. The difference in the acoustic power, emanating in opposite directions, was demonstrated. However, all the frequency components were present in the forward- and backward-emitted SAW. At the same time, our experimental results show that the reflectivity of a gold electrode grating causes all the high-frequency components to be completely redirected in the direction of forward emission (Figure 4). Only a narrow band signal in the vicinity of 100 MHz is able to propagate in the backward direction. The spectrum energy ratio between the forward and backward emissions is about 7.8 dB.

## 3. Application to the Characterization of Thin Films

_{R}of Rayleigh waves as a function of frequency consists in calculating the maximum of the function A(V) at the output of a correlator that measures and compensates for the delays between the signals detected by the vibrometer at positions 1, 2 and N. In other words, a velocity band is defined such that V

_{min}< V

_{R}< V

_{max}, and then A(V) is determined. A(V) is a function of the velocity V; therefore, the velocity at which the function is at its maximum corresponds to the measured wave velocity for the frequency f

_{0}under consideration. The function A(V) is defined by [36]:

_{0}is the frequency, V

_{R}is the measured wave velocity, N is the number of measurement points, V is the wave velocity (considered as a variable) and S is the constant resulting from the cross-correlation of all the signals received.

_{p}using the experimental measurements of the velocity dispersion consisted in solving the inverse problem. The dispersion curves depend, in particular, on the thickness of the layers, as well as the Young’s modulus E and Poisson’s ratio ν of the layers and the substrate. For each coated wafer, an inversion method was used to identify the best of the layer thickness fit (the elastic coefficients of the layer and substrate are known). This enables dispersion curves of the theoretical and experimental velocities that are as close as possible to be obtained. First, the theoretical calculation was carried out using rounded values for the thicknesses. These theoretical phase velocity dispersion curves were calculated within the 100–240 MHz band. Then, a least squares minimization routine was performed to adjust the set of parameters, so that the theoretical velocities were as close as possible to the measured velocities. Thus, the inversion algorithm is based on the dichotomy principle and the minimization of the Pearson coefficient R

^{2}. The objective function R

^{2}must be as close to 1 as possible.

^{2}= 0.9964 and 0.9993, respectively. This is quite satisfactory, considering that there is always a difference between the set points imposed on the evaporation racks and the actual thicknesses deposited. These values were compared with those obtained using a profilometer and the differences were of the same order of magnitude (±2 nm). As the measurement errors are often estimated as being within a few percent, these results corroborate the relevance of the values obtained using ultrasound. It is also important to specify that thickness measurements using a profilometer can only be carried out for one step intentionally manufactured on the sample and their accuracy decreases if the measurement is made over a long distance, whereas ultrasonic measurements can be made over the entire surface of the wafer, including in the center of the sample

## 4. Conclusions

_{3}was presented. Implementing a piezoelectric material such as LiNbO

_{3}with an important electromechanical coupling coefficient [40] allowed us to obtain a high SAW displacement level (up to 1 nm) in the 100–240 MHz frequency range. Additionally, using relatively thick (450 nm) and highly reflective gold electrodes assures the high unidirectionality of the transducer, which efficiently enables the redirecting of the acoustic energy into the non-destructively tested sample (crossing of the transducer–sample interface by the wave) and obtain its propagation on the sample over a distance of a few millimeters. The presented SAW emitter, which is based on dispersive IDT, permitted us to estimate the thickness of the 20 and 50 nm Ti layers with a 5% relative error. Future research will involve further increasing the transducer frequency in order to obtain a better characterization precision. However, a comprehensive analysis of the limiting phenomena, such as the decreased SAW displacement level and increased attenuation, will be necessary.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) SAW emission principle with a constant-period IDT. (

**b**) Schematic image of the chirped IDT SAW emitter and locations of optical measurement points. (

**c**) Photo of the chirped IDT used for thin film characterization.

**Figure 3.**Optical measurement of SAW emission by the chirped IDT: (

**a**) A-scan, corresponding to the displacement of the surface wave in the time domain; (

**b**) spectrum of the same signal; (

**c**) longitudinal B-Scan, revealing bidirectional emission, multiple reflections and the formation of the temporal envelope of the emitted wave packet.

**Figure 4.**Optical measurement of the SAW emission by the chirped IDT: FFT of the longitudinal B-scan.

**Figure 5.**Optical measurement of the SAW emission by the chirped IDT: transversal B-scan showing the generated SAW packet.

**Figure 7.**Theoretical (dotted lines) and experimental (solid lines) dispersion curves for 20 and 50 nm of titanium on silicon in the [1$\overline{1}$0] direction, and the thickness E

_{p}inversion results. Dashed lines are theoretical curves corresponding to a ±5% thickness variation relative to the initial estimated value.

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**MDPI and ACS Style**

Duquennoy, M.; Smagin, N.; Kadi, T.; Ouaftouh, M.; Jenot, F. Development of a Broadband (100–240 MHz) Surface Acoustic Wave Emitter Devoted to the Non-Destructive Characterization of Sub-Micrometric Thin Films. *Sensors* **2022**, *22*, 7464.
https://doi.org/10.3390/s22197464

**AMA Style**

Duquennoy M, Smagin N, Kadi T, Ouaftouh M, Jenot F. Development of a Broadband (100–240 MHz) Surface Acoustic Wave Emitter Devoted to the Non-Destructive Characterization of Sub-Micrometric Thin Films. *Sensors*. 2022; 22(19):7464.
https://doi.org/10.3390/s22197464

**Chicago/Turabian Style**

Duquennoy, Marc, Nikolay Smagin, Tahar Kadi, Mohammadi Ouaftouh, and Frédéric Jenot. 2022. "Development of a Broadband (100–240 MHz) Surface Acoustic Wave Emitter Devoted to the Non-Destructive Characterization of Sub-Micrometric Thin Films" *Sensors* 22, no. 19: 7464.
https://doi.org/10.3390/s22197464