# Features of Electro-Induced Periodical Structures in LiTaO3 Single Crystal and Their Interaction with Surface Acoustic Wave

Authors: Siarhei D. Barsukou; Jun Kondoh; Sergei A. Khakhomov
Journal: Advances in Materials Science and Engineering
 (2019)

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## Abstract

In this research, the features of electro-induced periodical structures in the volume of LiTaO3 thin plate were theoretically and experimentally investigated. For the theoretical and experimental investigations, the calculations based on the finite element method and measuring of the surface acoustic wave (SAW) interaction were implemented simultaneously. The observed difference of the electro-induced structures provides a new opportunity to control of the acoustic wave propagation in a ferroelectric substrate. The volume-existed periodical structures were induced as different electric potentials were applied to the surface arranged electrodes. The features of the induced structure were theoretically investigated based on a developed theoretical unit cell model for different induced structure configurations. The properties of the acoustic wave interaction with the periodical structure were studied on the basis of a theoretical full 3D model of an SAW device. A novel controllable SAW device was fabricated and studied experimentally. The experimental results show significant differences in magnitude and phase of both reflected and transmitted signals depending on the induced structure configuration.


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## Body

## 1. Introduction

Phononic crystals (PCs) and acoustic metamaterials (AMs) have generated considerable recent research interests because they have been provided to observe and study variety of new ultrasound effects. Many years, researches on interaction of acoustic waves in solids with constant electric field [1–3], alternating electric field [4–6], and rotating electric field [7, 8] are conducted. The kind of the acoustic handmade materials allows the investigation of new effects of the acoustic nonlinear interaction in the advanced SAW device structures [9–12]. Presently, many papers have been focused on the controllable acoustic wave interaction with the PC and/or the AM structures [13–15]. Those are based on the volume- or surface-periodical increments, which are fitted in the normally homogeneous substrate [16–18]. Therefore, main features and potential of applications are determined by the conditions of the acoustic wave interaction. Unfortunately, most investigations of the AM and PC structures characterized the unchanged periodical element geometry and did not allow switchable acoustic wave interaction. Currently, a new kind of the controllable and periodical structures has simultaneously been attracting the widespread interest and growth in popularity [19–22]. The most important feature of the PCs with electro-induced structures is the possibility to manage the incident acoustic wave in real time [23–26]. The controllable induced structures have a good opportunity as the active part of the multifunctional SAW device, such as controllable delay lines, band-pass filters, and switchable acoustic multiplexors. The electro-induced structures in a thin plate LiTaO3 crystal, which behave like the PC structures, were discussed in [27, 28]. In this research, the possibility of switchable interaction with the shear horizontal (SH) SAW was proposed. Different electro-induced 2D structures were formed in the volume of a thin plate by varying of the electric potential applied to the top and bottom electrodes. The SH-SAW was used to observe the reflected signal. However, the features of the periodical structure formation for different configurations and the SH-SAW interaction were not discussed. The current research provides a new method for investigation of the periodical electro-induced structure based on the unit structure and the full wave model of the controllable SH-SAW device. The transmitted signal deviations on the periodical structure configurations were investigated. The scattering parameters of the transmitted SH-SAW were analysed and compared using the developed transmitted-type SH-SAW device.


## 2. Materials and Methods

The proposed transmitted type of the controllable SH-SAW device structure is shown in Figure1. The SH-SAW device was fabricated on the 36YX-LiTaO3 (LT) thin plate of 250 μm. The wave propagates in the X direction. The device structure includes the waveguide, transmitted interdigital transducer (IDT 1), received IDT 2, and the electro-induced structure region with the rectangular “ABCD.” The electro-induced structure region is formed by the four groups of the surface arranged electrodes of E1, E2, E3, and E4. Those are represented as the electrode structure (ES), hereafter. The pairs of the electrodes on the top and bottom surfaces of the crystal are mutually perpendicular. The IDTs and ESs were made from aluminium using a conventional lithography method. The parameters of the ESs depend on the SAW device application and its operating frequency. The SAW device was developed for the resonance frequency of 10 MHz. The wavelength λ is 420 μm. In the SAW device discussed, the distances between electrode fingers of IDTs and ESs, which are the parameters of t and d in Figure 1, respectively, were taken to obtain the matched SAW interaction condition and equal the half wavelength. The distance S between IDTs and ES was S = n · λ, where n is an integer.Figure 1
Structure and principle of the SAW device and main axes directions. E1, E2, E3, and E4 are the conductive electrodes.When the electric potentials were applied to the ES, the static displacement and piezoelectric polarization distributions were caused due to an electrostatic effect. The periodical structure of the static displacements is induced in the volume of the crystal. This structure is the same as the acoustic impedance structure. If the value of the electric field applied is smaller than the coercive field, the domain switching does not occur. The incident SH-SAW was generated from IDT 1. The transmitted and reflected interacted SAWs have been received by the IDT 2 and IDT 1, respectively. Due to the SH-SAW interaction with the electro-induced periodical structure, the incident wave has been divided into the transmitted and reflected waves. The interaction properties of the SAW depend on the induced structure configuration and electric field intensity. These parameters are switchable. However, the periodical structure formation is the complicated scientific task. It is defended by many parameters: the ferroelectric material was used, the ES configuration, thickness of the crystal, and the intensity of the electric field were applied.


## 3. Results and Discussion

### 3.1. Theoretical Investigations of the Periodical Structure Formation

To investigate of the electro-induced displacement distribution and possibility of periodical structure formation, the single structural unit cell, which was the rectangular “ABCD” in Figure1, was extracted for the detailed consideration. The configuration of a single unit is shown in Figure 2.Figure 2
The dimensions of the unit cell FEM model inμm.The finite element method (FEM) was used for the theoretical investigation. In the model, the classical descriptions of the electric and relative particle displacements were used. The quasi-static approximation was applied to describe the electric field of the SAW and an electric potential. The FEM model consists of the ferroelectric substrate and two pairs crossed electrodes of E1, E2 and E3, E4. The thicknesses of the platet were 50 and 250 μm. The periodical structure features were defined by the dimensions of the electrode structure and value of the electric field applied. All boundaries correspond to the electrical and mechanical potentials absence and the periodic boundary conditions to the lateral boundaries. To simplify the FEM model, the thickness and weight of the electrode fingers were not taken into account. As the phase velocity of the SH-SAW of the 36YX-LT is 4212 m/s, the wavelength was 420 μm and the electrode width was 105 μm. The dimensions of the structural unit are 420 × 420 μm2. The applied electric field was 1 MV/m. The parameters of the static particle displacements in the domain unit cell were measured along the X-direction and at the middle of the structure. The FEM model was solved in the time domain with a resolution of 1 ns. The results of the periodical structures were discussed for the moment of time of 1 μs. The results of the induced static displacements for the thin plate thickness of 50 μm, when the DC of 50 V is applied only to the top side electrodes, are shown in Figure 3. Figures 3(a) and 3(b) represent the calculated components of the static displacement dX (the black curve), dY (the red curve), and dZ (the blue curve) in the X, Y, and Z axes directions, respectively. The total static displacement (the dotted curve) due to the electrostatic effect was calculated as dtot=dX2+dY2+dZ2. Inspection of Figure 3(a) indicates that the total static displacement almost consists of the Z component. As the 36YX-LT was used, the results obtained are reasonable. Figure 3(b) shows the components of the static displacement distribution along the thickness of the thin plate. The particle displacement prevails in the Z direction. From Figure 3(b), the linearity of the components of static displacement along the thickness is found. The total static displacement distributions in the middle and along the thickness are, respectively, shown in Figures 3(c) and 3(d). The displacement induced in the volume clearly shows the periodic distribution with a maximum value of 1 nm.Figure 3
Static displacement distribution at a crystal thickness of 50μm measured in μm. The dX, dY, dZ, and dtot components of the static displacements measured (a) at the middle of the crystal along X-axis direction and (b) along thickness. Total static displacement measured (c) in the middle of the crystal and (d) along the thickness.
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(d)Figure4 represents the static displacements induced in the plate with a thickness of 250 μm and DC of 250 V is applied. In Figure 4(a), the periodic induced static displacement is observed. For the thick plate, the total displacement in the middle of the substrate was not zero. That is due to the components of the displacement distributions affect each other. Comparison of Figures 4(b) and 3(b) shows that the displacements distributed along the thickness for the thick plate is nonlinear with pronounced nonlinearity near the electrode region. At the far-field region from the electrodes, the displacement shows linearity. The total static displacement in the volume is shown in Figures 4(c) and 4(d). It is clearly seen that the maximum value locates near the electrode region and decreases along the volume. In the far-field region, the total displacement shows a multiplicative character. The periodical structure has been violated (Figure 4(d)). For the discussed structure and in case of the thick plate, the periodic structure has been induced almost near the surface region with a maximum value near the electrodes.Figure 4
Static displacement distribution at a crystal thickness of 250μm measured in μm. The dX, dY, dZ, and dtot components of the static displacements measured (a) at the middle of the crystal along X-axis direction and (b) along thickness. Total static displacement measured (c) in the middle of the crystal and (d) along the thickness.
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(d)The results for the induced structure, when the opposite DC potentials were applied to the top and bottom electrodes, are shown in Figure5. The electro-induced structure represents the four separated “domains” in the volume. The calculated parameters of the static displacement components are discussed in Figures 5(a) and 5(b). By inspecting Figure 5(a), the periodical displacement distribution is found. The value of the displacement in the middle of the thin plate is relatively low. The major contribution of the static displacement along the thickness is due to the dY component (red curve in Figure 5(b)), which has the same direction with the electric field action. The total static displacement achieves maximum near the electrode region and reduces to zero in the middle of the thin plate. The total static displacement in the volume is summarized in Figures 5(c) and 5(d). Here, Figure 5(c) shows the periodic acoustic impedance induced in the volume with a maximum value above 0.25 nm. The static displacement near the surface region had achieved a value of 1.7 nm.Figure 5
Static displacement distribution at a crystal thickness of 250μm measured in μm for the case of the apposite electric potentials applied to the top and bottom ESs. The dX, dY, dZ, and dtot components of the static displacements measured (a) at the middle of the crystal along X-axis direction and (b) along thickness. Total static displacement measured (c) in the middle of the crystal and (d) along the thickness.
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(d)The most complicated induced structure has been obtained in the case of the periodical structure shown in Figure6. As the opposite electrode potentials were applied to the top and bottom ESs simultaneously, the electric field was distributed in the volume and on the surface of the structure. Here, the two “domains” with opposite directions were induced in the volume of the structure. The calculated static displacement components are shown in Figures 6(a) and 6(b). Here, the main contribution to the periodical structure formation has been provided by the dY and dZ components. The results of the total static displacement have the two peaks: the first one, with an amplitude of 1.2 nm, corresponds to the between top and bottom electrode interaction. The second one, with an amplitude of 0.8 nm, is due to the effect of coalescence of the volume-distributed components of static displacement. Moreover, the static displacement has been induced between surface electrodes due to electrostatic interaction. From Figure 6(b), it is found that the static displacements have been achieved maximum near the surface region. However, the discussed structure is not symmetric. Thus, due to the nonlinearity of the component, the total static displacement had not achieved the zero value in the middle of the structure. To summarize, the total static displacement distribution is represented in Figures 6(c) and 6(d). Here, the induced periodic displacement distribution can be found. In both induced “domains,” the dY component has an opposite direction of polarization, which allows the propagated plate SAW polarization to be controlled. In addition, the results allow the prediction of the different features of the acoustic wave interaction with the periodical electro-induced structures, including the effects of polarization.Figure 6
Static displacement distribution at a crystal thickness of 250μm measured in μm for the case of the apposite electric potentials applied to the top and bottom ESs simultaneously. The dX, dY, dZ, and dtot components of the static displacements measured (a) at the middle of the crystal along X-axis direction and (b) along thickness. Total static displacement measured (c) in the middle of the crystal and (d) along the thickness.
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### 3.2. Full 3D Model and Acoustic Wave Interaction

To investigate the features of acoustic wave interaction with the electro-induced structure, the full model of the controllable SH-SAW device was developed and studied using the FEM. The theoretical model of the controllable device is shown in Figure7.Figure 7
The configuration and structure of the model of the SAW device with the controllable electro-induced periodical structure.The FEM model includes the ferroelectric substrate, two IDTs (IDT 1 and IDT 2), and the ES arranged on the top and bottom surfaces. The number of the electrode fingers of each IDT is 20 (=NE1). The ES consists of NE2 = 10 electrode fingers on the top and NE2 = 60 on the bottom surfaces. The distance between the IDTs and ES was 10λ. The total dimensions of the FEM model are 2000 × 1000 μm2. The thickness of the crystal was 50 μm. The electrical potential of 200 V was applied to the ESs to induce the periodical structure with configuration as was discussed in Figure 6. The SH-SAW propagates in the X-direction from IDT 1 to IDT 2. The FEM model was solved in the time domain, which allows the features of the induced periodical structure to be analysed. Moreover, the full wave model allows the effects of SH-SAW scattering on the periodical structure to be investigated. All results discussed were calculated for the time of 10 μs. In the model, all boundaries correspond to the electrical and mechanical potentials absence. The lateral boundaries correspond to the low reflection condition. First, the periodical structure formation was observed without the SH-SAW action. The results of the periodical structure formation are shown in Figures 8(a) and 8(b).Figure 8
Results of the theoretical investigations of the full 3D FEM model of the SAW device. (a) ThedX, dY, and dZ components of the induced static displacement distribution along the wave propagation direction, (b) the registered induced structure formation signal (the black curve) and spectra (the red curve), (c) results of the displacement at the SH-SAW interaction with the induced structure, and (d) the input signal spectra (the red curve) and the output signal and spectra (the black curve).
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(d)The induced static displacements ofdX, dY, and dZ components occurred due to the linear electrostatic effect and under external DC electric field action as plotted in Figure 8(a). The induced structure is located in the region from 8 to 10 mm. The expressed displacement component of dZ corresponds to the particle displacement in the Z direction. In the structure region, the displacements of dX and dY were also observed. However, in contrast to the expressed one, the dZ, the dX and dY components were smaller and almost unipolar. The occurred displacement distribution properties depend on the induced structure configuration and parameters of the model. When the DC is applied, due to particle displacement at the periodical structure induced region, the short SAWs generate from the ES and propagate in the IDT 1 and IDT 2 directions. This SAWs as the periodical structure formation signal was registered by IDTs. The periodical structure formation has been characterized via analysis of the registered signal spectra. The black curve in Figure 8(b) shows the registered signal by using the IDT. The short wave packet registered from 1 to 3 μs corresponds to the periodical structure formation, and the lower amplitude signal between 4 and 7 μs is the result of reflection of the SAW. The spectrum of the registered signal is the red curve in Figure 8(b). Two peaks at 9.6 and 12.8 MHz were observed: the first one corresponds to the resonance frequency of the IDT structure. The second maximum relates to the periodical structure formation in the volume of the substrate as the result of electrostatic interaction between top and bottom periodical ESs. Therefore, it depends on the actual electric field distribution in the volume of the electron-induced structure. The electric field distribution is mainly determined by the induced structure configuration, i.e., variety of applied electric potentials. The results of the acoustic wave interaction are shown in Figures 8(c) and 8(d). This process includes the SH-SAW transmission and the periodical structure formation simultaneously. Using the FEM model, the SH-SAW interaction was calculated for the time till 10 μs with a resolution of 1 ns. The propagated SH-SAW interacts with the induced periodical structure, and the results at 10 μs are plotted in Figure 8(c). Here, the dZ component of the particle displacement corresponds to the SH-SAW interaction with the electro-induced structure. Analysed results of the displacement distribution show that the propagated SH-SAW has been plotted the shape of the preinduced static displacement in the structure region (the matched interaction condition). Then, the acoustic energy redistribution in the volume of the crystal occurs. The transmitted SH-SAW amplitude was comparable with the incident SH-SAW. To analyse the acoustic wave interaction, the registered signal and spectra (the black curves) and applied signal spectra (the red curve) are compared in Figure 8(d). The registered output signal at the amplitude above 5 V shows the wave process in the SAW device. The signal consists of two parts: the short signal from 1 to 2.5 μs corresponds to the SAW propagation from the ES region as the induced structure formation signal and the second one is the result of the SH-SAW interaction. The SH-SAW interaction processes start at the time of 3 μs. The resonance frequency of the both signals at 10 MHz was found. The antiresonance frequency was observed at 12.8 MHz, which corresponds to the acoustic band gap caused due to the SH-SAW interaction on the periodical structure. Need to note that the volume-induced periodical structure has also been characterized by the same maximums. Thus, the developed full wave 3D model allows the periodical structure inducing in the volume of the thin plate to be described. The time-dependent analysis shows the result of the displacement distribution related to the SH-SAW interaction, and the acoustic band gap structure was observed.


### 3.3. Experimental Results of the SAW Interaction

The SAW device was fabricated on the 36YX-LT substrate with a thickness of 250μm. The SAW device consists of a thin plate, two IDTs, and ES. The parameters of the IDTs and ES were optimized for the centre frequency of 10 MHz using the SH-SAW phase velocity of 4212 m/s and the wavelength λ of 420 μm. The number of the electrode fingers of each IDT was 32. The ES was formed with 20 electrode fingers on the top and 116 on the bottom sides. All electrodes were made from the aluminium film with a thickness of ca. 100 nm. The distance between IDT and ES was 32λ.The response signal due to the DC applied is shown in Figure9(a). The applied DC was 200 V. The measurements were carried out using a digital oscilloscope (Keysight Technologies, DSO-X3102A). The response signal (the black curve) characterizes the short impulse of the damped oscillations occurred due to electrostatic effect between ESs and the SAWs propagating in the volume of the thin plate. The time delay around 3 μs was measured because it corresponded to the wave propagation time from ES to IDT. The spectra of the registered signal are shown in Figure 9(a) with the red curve. At list, four resonance frequencies of F1 (10.0 MHz), F2 (13.3 MHz), F3 (16.6 MHz), and F4 (20.1 MHz) are observed. In contrast to the theoretical results in Figure 8(b), where the two resonances at 9.6 MHz and 12.8 MHz are found, the experimental data clearly show the four resonances. The first two resonances are comparable with the theoretical model. However, the higher resonances of F3 and F4 cannot be considered as the result of formation of the periodical structure. The F3 and F4 maximums are explained due to the nonlinear effects of coupling of the reflected modes in the finite ferroelectric substrate with considered structure and configuration. They do not appear in the FEM analysis because the low reflection boundaries were used, and all acoustical modes reflected from the ES and IDT grating are dumped on the lateral boundaries of the structure.Figure 9
(a) The periodical structure formation response signal and spectra and (b) results of the interacted signal and spectra for the +DC (red curve) and −DC (black curve), respectively.
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(b)The influence of the interacted signal at the single frequency regime was measured using the digital oscilloscope and RF power amplifier (R&K, CA010M521-4040R). At the resonance conditions, the AC signal of 9.65 MHz with an amplitude of 0.5 V was applied to the transmitted IDT 1. The DC of 200 V was applied to the ES. The output signal with an amplitude less than 0.2 V was registered and analysed as shown in Figure9(b) for apposite +DC (the red curve) and −DC (the black curve) polarities. Both +DC and −DC states show the main maximum at 9.65 MHz as the result of the applied AC and induced SH-SAW at the resonance condition. Moreover, the some influence was noted at 62 and 110 MHz. The appeared resonances are not related to the discussed interaction conditions and have been considered as the result of the spurious nonlinear interaction.For the analysis of the SAW interaction with the electro-induced periodical structure and controlling capability observation, the experimental investigations of the acoustic wave interaction with different periodical structure configurations were performed. First, the time location of the induced structure for the reflected and transmitted signals was observed experimentally. The results are shown in Figures10(a) and 10(b). Here, the red and the black curves correspond to the measured magnitude signal, when the ES was free and shorted, respectively. The obtained influence regions correspond to the induced structure location in the time domain. The measured time response is wider than the calculated one theoretically on the base information about device geometry and SH-SAW velocity. That is due to different acoustic modes with different velocities propagating and interacting simultaneously. Then, for the reflected signal time from 5.5 μs to 8.5 μs, and for the transmitted signal from 3.5 μs to 5.5 μs were considered as the region of the induced periodical structure.Figure 10
Measured time response for the (a) reflected and (b) transmitted signals. The red and black curves correspond to the free and shorted conditions of the IDT. The dotted rectangular shows the induced structure time region.
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(b)The experimental results of the reflected and transmitted signals were measured for three different induced structures. The results are shown in Figure11. The results in Figures 11(a), 11(c), and 11(e) are the reflected signals, and in Figures 11(b), 11(d), and 11(f), the results of the transmitted signal are compared. The experimental results of the reflected and transmitted signals were analysed for the different induced structure configurations and for the opposite +DC (the red curve) and −DC (the black curve) of 250 V polarities. The total measured error at the considered time regions was achieved above 10%. The thick curve describes the relative magnitude deviation, when the DC = 0 and ±DCs measured in dB. The thin curve characterizes the phase absolutely deviations. Comparison of Figures 11(a), 11(c), and 11(e) shows the reflected signal dependence on the DC polarities and structure configurations. The measured reflectance shown in Figure 11(a) corresponds to the structure induced on the surface of the thin plate. In this case, the electrostatic interaction exists only between the top side electrodes and did not occur in the volume of the waveguide (Figure 4). The opposite of the magnitude deviation on the DC polarity was observed; however, the phase parameter experiences the same influence. The measured reflected signal for the periodical structure consisted of the four “domains” induced in the volume discussed is shown in Figure 11(c). This induced structure is achievable, when the opposite electrode potentials applied to the top and bottom ESs. The electrostatic interaction occurred in the volume of each structural unit, as is shown in Figure 5. From Figure 11(c), it is found that the reflected signal magnitude and phase depend on the DC polarity. The results of the SH-SAW interaction with the structure with the two opposite directed “domains” induced in the volume of the structural unit are shown in Figure 11(e). The periodical structure was induced when opposite electric potentials simultaneously were applied to the top and bottom sides of ESs. The electrostatic interaction occurred only between two electrodes as the opposite potentials and distributed in the volume of the induced structure (Figure 6). In comparison with Figure 11(e), the distributions of the magnitude and phase in Figure 11(c) are different. Here, the relative magnitude deviations have the same direction with a maximum value of 0.06 dB for the different polarities of DC applied. The different acoustic wave interaction features were observed for different induced structures. The transmitted signal deviations for the same induced structures were investigated with the results shown in Figures 11(b), 11(d), and 11(f). The deviations of the magnitude and phase show a similar trend to the reflected signal behaviour, while the time distribution is different. About two times higher of the total influence was achieved for the magnitude, and more than 10  times increased for the phase for the transmitted signal. For the structures with results in Figures 11(e) and 11(f), the polarization effects due to opposite induced domain directions in the structural unit were predicted for both the reflected and transmitted signals. In conclusion, all of the discussed configurations characterize the electro-induced periodical structures similar to the PCs. The difference in the SH-SAW interaction was observed experimentally. However, it is still difficult to obtain the matched interaction condition due to different acoustical modes propagating in the volume of the waveguide simultaneously. Moreover, nonlinearity occurs due to coalescence at the boundaries of the induced structures. The SAW device on the thin plate structure, where exists a strong electrostatic interaction between electrodes, is promising for a future investigation.Figure 11
Experimental results of the magnitude relative (thick curves), and phase absolute (thin curves) deviations of the (a, c, and e) reflected and (b, d, and f) transmitted signals, which was measured for the positive +DC (red curve) and negative −DC (black curve) polarities. The results are compared for the induced structure (a and b) distributed on the surface of the thin plate, (c and d) the four “domains” distributed in the volume, and (e and f) the two opposite directed “domains” induced in the volume.
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## 3.1. Theoretical Investigations of the Periodical Structure Formation

To investigate of the electro-induced displacement distribution and possibility of periodical structure formation, the single structural unit cell, which was the rectangular “ABCD” in Figure1, was extracted for the detailed consideration. The configuration of a single unit is shown in Figure 2.Figure 2
The dimensions of the unit cell FEM model inμm.The finite element method (FEM) was used for the theoretical investigation. In the model, the classical descriptions of the electric and relative particle displacements were used. The quasi-static approximation was applied to describe the electric field of the SAW and an electric potential. The FEM model consists of the ferroelectric substrate and two pairs crossed electrodes of E1, E2 and E3, E4. The thicknesses of the platet were 50 and 250 μm. The periodical structure features were defined by the dimensions of the electrode structure and value of the electric field applied. All boundaries correspond to the electrical and mechanical potentials absence and the periodic boundary conditions to the lateral boundaries. To simplify the FEM model, the thickness and weight of the electrode fingers were not taken into account. As the phase velocity of the SH-SAW of the 36YX-LT is 4212 m/s, the wavelength was 420 μm and the electrode width was 105 μm. The dimensions of the structural unit are 420 × 420 μm2. The applied electric field was 1 MV/m. The parameters of the static particle displacements in the domain unit cell were measured along the X-direction and at the middle of the structure. The FEM model was solved in the time domain with a resolution of 1 ns. The results of the periodical structures were discussed for the moment of time of 1 μs. The results of the induced static displacements for the thin plate thickness of 50 μm, when the DC of 50 V is applied only to the top side electrodes, are shown in Figure 3. Figures 3(a) and 3(b) represent the calculated components of the static displacement dX (the black curve), dY (the red curve), and dZ (the blue curve) in the X, Y, and Z axes directions, respectively. The total static displacement (the dotted curve) due to the electrostatic effect was calculated as dtot=dX2+dY2+dZ2. Inspection of Figure 3(a) indicates that the total static displacement almost consists of the Z component. As the 36YX-LT was used, the results obtained are reasonable. Figure 3(b) shows the components of the static displacement distribution along the thickness of the thin plate. The particle displacement prevails in the Z direction. From Figure 3(b), the linearity of the components of static displacement along the thickness is found. The total static displacement distributions in the middle and along the thickness are, respectively, shown in Figures 3(c) and 3(d). The displacement induced in the volume clearly shows the periodic distribution with a maximum value of 1 nm.Figure 3
Static displacement distribution at a crystal thickness of 50μm measured in μm. The dX, dY, dZ, and dtot components of the static displacements measured (a) at the middle of the crystal along X-axis direction and (b) along thickness. Total static displacement measured (c) in the middle of the crystal and (d) along the thickness.
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(d)Figure4 represents the static displacements induced in the plate with a thickness of 250 μm and DC of 250 V is applied. In Figure 4(a), the periodic induced static displacement is observed. For the thick plate, the total displacement in the middle of the substrate was not zero. That is due to the components of the displacement distributions affect each other. Comparison of Figures 4(b) and 3(b) shows that the displacements distributed along the thickness for the thick plate is nonlinear with pronounced nonlinearity near the electrode region. At the far-field region from the electrodes, the displacement shows linearity. The total static displacement in the volume is shown in Figures 4(c) and 4(d). It is clearly seen that the maximum value locates near the electrode region and decreases along the volume. In the far-field region, the total displacement shows a multiplicative character. The periodical structure has been violated (Figure 4(d)). For the discussed structure and in case of the thick plate, the periodic structure has been induced almost near the surface region with a maximum value near the electrodes.Figure 4
Static displacement distribution at a crystal thickness of 250μm measured in μm. The dX, dY, dZ, and dtot components of the static displacements measured (a) at the middle of the crystal along X-axis direction and (b) along thickness. Total static displacement measured (c) in the middle of the crystal and (d) along the thickness.
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(d)The results for the induced structure, when the opposite DC potentials were applied to the top and bottom electrodes, are shown in Figure5. The electro-induced structure represents the four separated “domains” in the volume. The calculated parameters of the static displacement components are discussed in Figures 5(a) and 5(b). By inspecting Figure 5(a), the periodical displacement distribution is found. The value of the displacement in the middle of the thin plate is relatively low. The major contribution of the static displacement along the thickness is due to the dY component (red curve in Figure 5(b)), which has the same direction with the electric field action. The total static displacement achieves maximum near the electrode region and reduces to zero in the middle of the thin plate. The total static displacement in the volume is summarized in Figures 5(c) and 5(d). Here, Figure 5(c) shows the periodic acoustic impedance induced in the volume with a maximum value above 0.25 nm. The static displacement near the surface region had achieved a value of 1.7 nm.Figure 5
Static displacement distribution at a crystal thickness of 250μm measured in μm for the case of the apposite electric potentials applied to the top and bottom ESs. The dX, dY, dZ, and dtot components of the static displacements measured (a) at the middle of the crystal along X-axis direction and (b) along thickness. Total static displacement measured (c) in the middle of the crystal and (d) along the thickness.
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(d)The most complicated induced structure has been obtained in the case of the periodical structure shown in Figure6. As the opposite electrode potentials were applied to the top and bottom ESs simultaneously, the electric field was distributed in the volume and on the surface of the structure. Here, the two “domains” with opposite directions were induced in the volume of the structure. The calculated static displacement components are shown in Figures 6(a) and 6(b). Here, the main contribution to the periodical structure formation has been provided by the dY and dZ components. The results of the total static displacement have the two peaks: the first one, with an amplitude of 1.2 nm, corresponds to the between top and bottom electrode interaction. The second one, with an amplitude of 0.8 nm, is due to the effect of coalescence of the volume-distributed components of static displacement. Moreover, the static displacement has been induced between surface electrodes due to electrostatic interaction. From Figure 6(b), it is found that the static displacements have been achieved maximum near the surface region. However, the discussed structure is not symmetric. Thus, due to the nonlinearity of the component, the total static displacement had not achieved the zero value in the middle of the structure. To summarize, the total static displacement distribution is represented in Figures 6(c) and 6(d). Here, the induced periodic displacement distribution can be found. In both induced “domains,” the dY component has an opposite direction of polarization, which allows the propagated plate SAW polarization to be controlled. In addition, the results allow the prediction of the different features of the acoustic wave interaction with the periodical electro-induced structures, including the effects of polarization.Figure 6
Static displacement distribution at a crystal thickness of 250μm measured in μm for the case of the apposite electric potentials applied to the top and bottom ESs simultaneously. The dX, dY, dZ, and dtot components of the static displacements measured (a) at the middle of the crystal along X-axis direction and (b) along thickness. Total static displacement measured (c) in the middle of the crystal and (d) along the thickness.
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## 3.2. Full 3D Model and Acoustic Wave Interaction

To investigate the features of acoustic wave interaction with the electro-induced structure, the full model of the controllable SH-SAW device was developed and studied using the FEM. The theoretical model of the controllable device is shown in Figure7.Figure 7
The configuration and structure of the model of the SAW device with the controllable electro-induced periodical structure.The FEM model includes the ferroelectric substrate, two IDTs (IDT 1 and IDT 2), and the ES arranged on the top and bottom surfaces. The number of the electrode fingers of each IDT is 20 (=NE1). The ES consists of NE2 = 10 electrode fingers on the top and NE2 = 60 on the bottom surfaces. The distance between the IDTs and ES was 10λ. The total dimensions of the FEM model are 2000 × 1000 μm2. The thickness of the crystal was 50 μm. The electrical potential of 200 V was applied to the ESs to induce the periodical structure with configuration as was discussed in Figure 6. The SH-SAW propagates in the X-direction from IDT 1 to IDT 2. The FEM model was solved in the time domain, which allows the features of the induced periodical structure to be analysed. Moreover, the full wave model allows the effects of SH-SAW scattering on the periodical structure to be investigated. All results discussed were calculated for the time of 10 μs. In the model, all boundaries correspond to the electrical and mechanical potentials absence. The lateral boundaries correspond to the low reflection condition. First, the periodical structure formation was observed without the SH-SAW action. The results of the periodical structure formation are shown in Figures 8(a) and 8(b).Figure 8
Results of the theoretical investigations of the full 3D FEM model of the SAW device. (a) ThedX, dY, and dZ components of the induced static displacement distribution along the wave propagation direction, (b) the registered induced structure formation signal (the black curve) and spectra (the red curve), (c) results of the displacement at the SH-SAW interaction with the induced structure, and (d) the input signal spectra (the red curve) and the output signal and spectra (the black curve).
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(d)The induced static displacements ofdX, dY, and dZ components occurred due to the linear electrostatic effect and under external DC electric field action as plotted in Figure 8(a). The induced structure is located in the region from 8 to 10 mm. The expressed displacement component of dZ corresponds to the particle displacement in the Z direction. In the structure region, the displacements of dX and dY were also observed. However, in contrast to the expressed one, the dZ, the dX and dY components were smaller and almost unipolar. The occurred displacement distribution properties depend on the induced structure configuration and parameters of the model. When the DC is applied, due to particle displacement at the periodical structure induced region, the short SAWs generate from the ES and propagate in the IDT 1 and IDT 2 directions. This SAWs as the periodical structure formation signal was registered by IDTs. The periodical structure formation has been characterized via analysis of the registered signal spectra. The black curve in Figure 8(b) shows the registered signal by using the IDT. The short wave packet registered from 1 to 3 μs corresponds to the periodical structure formation, and the lower amplitude signal between 4 and 7 μs is the result of reflection of the SAW. The spectrum of the registered signal is the red curve in Figure 8(b). Two peaks at 9.6 and 12.8 MHz were observed: the first one corresponds to the resonance frequency of the IDT structure. The second maximum relates to the periodical structure formation in the volume of the substrate as the result of electrostatic interaction between top and bottom periodical ESs. Therefore, it depends on the actual electric field distribution in the volume of the electron-induced structure. The electric field distribution is mainly determined by the induced structure configuration, i.e., variety of applied electric potentials. The results of the acoustic wave interaction are shown in Figures 8(c) and 8(d). This process includes the SH-SAW transmission and the periodical structure formation simultaneously. Using the FEM model, the SH-SAW interaction was calculated for the time till 10 μs with a resolution of 1 ns. The propagated SH-SAW interacts with the induced periodical structure, and the results at 10 μs are plotted in Figure 8(c). Here, the dZ component of the particle displacement corresponds to the SH-SAW interaction with the electro-induced structure. Analysed results of the displacement distribution show that the propagated SH-SAW has been plotted the shape of the preinduced static displacement in the structure region (the matched interaction condition). Then, the acoustic energy redistribution in the volume of the crystal occurs. The transmitted SH-SAW amplitude was comparable with the incident SH-SAW. To analyse the acoustic wave interaction, the registered signal and spectra (the black curves) and applied signal spectra (the red curve) are compared in Figure 8(d). The registered output signal at the amplitude above 5 V shows the wave process in the SAW device. The signal consists of two parts: the short signal from 1 to 2.5 μs corresponds to the SAW propagation from the ES region as the induced structure formation signal and the second one is the result of the SH-SAW interaction. The SH-SAW interaction processes start at the time of 3 μs. The resonance frequency of the both signals at 10 MHz was found. The antiresonance frequency was observed at 12.8 MHz, which corresponds to the acoustic band gap caused due to the SH-SAW interaction on the periodical structure. Need to note that the volume-induced periodical structure has also been characterized by the same maximums. Thus, the developed full wave 3D model allows the periodical structure inducing in the volume of the thin plate to be described. The time-dependent analysis shows the result of the displacement distribution related to the SH-SAW interaction, and the acoustic band gap structure was observed.


## 3.3. Experimental Results of the SAW Interaction

The SAW device was fabricated on the 36YX-LT substrate with a thickness of 250μm. The SAW device consists of a thin plate, two IDTs, and ES. The parameters of the IDTs and ES were optimized for the centre frequency of 10 MHz using the SH-SAW phase velocity of 4212 m/s and the wavelength λ of 420 μm. The number of the electrode fingers of each IDT was 32. The ES was formed with 20 electrode fingers on the top and 116 on the bottom sides. All electrodes were made from the aluminium film with a thickness of ca. 100 nm. The distance between IDT and ES was 32λ.The response signal due to the DC applied is shown in Figure9(a). The applied DC was 200 V. The measurements were carried out using a digital oscilloscope (Keysight Technologies, DSO-X3102A). The response signal (the black curve) characterizes the short impulse of the damped oscillations occurred due to electrostatic effect between ESs and the SAWs propagating in the volume of the thin plate. The time delay around 3 μs was measured because it corresponded to the wave propagation time from ES to IDT. The spectra of the registered signal are shown in Figure 9(a) with the red curve. At list, four resonance frequencies of F1 (10.0 MHz), F2 (13.3 MHz), F3 (16.6 MHz), and F4 (20.1 MHz) are observed. In contrast to the theoretical results in Figure 8(b), where the two resonances at 9.6 MHz and 12.8 MHz are found, the experimental data clearly show the four resonances. The first two resonances are comparable with the theoretical model. However, the higher resonances of F3 and F4 cannot be considered as the result of formation of the periodical structure. The F3 and F4 maximums are explained due to the nonlinear effects of coupling of the reflected modes in the finite ferroelectric substrate with considered structure and configuration. They do not appear in the FEM analysis because the low reflection boundaries were used, and all acoustical modes reflected from the ES and IDT grating are dumped on the lateral boundaries of the structure.Figure 9
(a) The periodical structure formation response signal and spectra and (b) results of the interacted signal and spectra for the +DC (red curve) and −DC (black curve), respectively.
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(b)The influence of the interacted signal at the single frequency regime was measured using the digital oscilloscope and RF power amplifier (R&K, CA010M521-4040R). At the resonance conditions, the AC signal of 9.65 MHz with an amplitude of 0.5 V was applied to the transmitted IDT 1. The DC of 200 V was applied to the ES. The output signal with an amplitude less than 0.2 V was registered and analysed as shown in Figure9(b) for apposite +DC (the red curve) and −DC (the black curve) polarities. Both +DC and −DC states show the main maximum at 9.65 MHz as the result of the applied AC and induced SH-SAW at the resonance condition. Moreover, the some influence was noted at 62 and 110 MHz. The appeared resonances are not related to the discussed interaction conditions and have been considered as the result of the spurious nonlinear interaction.For the analysis of the SAW interaction with the electro-induced periodical structure and controlling capability observation, the experimental investigations of the acoustic wave interaction with different periodical structure configurations were performed. First, the time location of the induced structure for the reflected and transmitted signals was observed experimentally. The results are shown in Figures10(a) and 10(b). Here, the red and the black curves correspond to the measured magnitude signal, when the ES was free and shorted, respectively. The obtained influence regions correspond to the induced structure location in the time domain. The measured time response is wider than the calculated one theoretically on the base information about device geometry and SH-SAW velocity. That is due to different acoustic modes with different velocities propagating and interacting simultaneously. Then, for the reflected signal time from 5.5 μs to 8.5 μs, and for the transmitted signal from 3.5 μs to 5.5 μs were considered as the region of the induced periodical structure.Figure 10
Measured time response for the (a) reflected and (b) transmitted signals. The red and black curves correspond to the free and shorted conditions of the IDT. The dotted rectangular shows the induced structure time region.
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(b)The experimental results of the reflected and transmitted signals were measured for three different induced structures. The results are shown in Figure11. The results in Figures 11(a), 11(c), and 11(e) are the reflected signals, and in Figures 11(b), 11(d), and 11(f), the results of the transmitted signal are compared. The experimental results of the reflected and transmitted signals were analysed for the different induced structure configurations and for the opposite +DC (the red curve) and −DC (the black curve) of 250 V polarities. The total measured error at the considered time regions was achieved above 10%. The thick curve describes the relative magnitude deviation, when the DC = 0 and ±DCs measured in dB. The thin curve characterizes the phase absolutely deviations. Comparison of Figures 11(a), 11(c), and 11(e) shows the reflected signal dependence on the DC polarities and structure configurations. The measured reflectance shown in Figure 11(a) corresponds to the structure induced on the surface of the thin plate. In this case, the electrostatic interaction exists only between the top side electrodes and did not occur in the volume of the waveguide (Figure 4). The opposite of the magnitude deviation on the DC polarity was observed; however, the phase parameter experiences the same influence. The measured reflected signal for the periodical structure consisted of the four “domains” induced in the volume discussed is shown in Figure 11(c). This induced structure is achievable, when the opposite electrode potentials applied to the top and bottom ESs. The electrostatic interaction occurred in the volume of each structural unit, as is shown in Figure 5. From Figure 11(c), it is found that the reflected signal magnitude and phase depend on the DC polarity. The results of the SH-SAW interaction with the structure with the two opposite directed “domains” induced in the volume of the structural unit are shown in Figure 11(e). The periodical structure was induced when opposite electric potentials simultaneously were applied to the top and bottom sides of ESs. The electrostatic interaction occurred only between two electrodes as the opposite potentials and distributed in the volume of the induced structure (Figure 6). In comparison with Figure 11(e), the distributions of the magnitude and phase in Figure 11(c) are different. Here, the relative magnitude deviations have the same direction with a maximum value of 0.06 dB for the different polarities of DC applied. The different acoustic wave interaction features were observed for different induced structures. The transmitted signal deviations for the same induced structures were investigated with the results shown in Figures 11(b), 11(d), and 11(f). The deviations of the magnitude and phase show a similar trend to the reflected signal behaviour, while the time distribution is different. About two times higher of the total influence was achieved for the magnitude, and more than 10  times increased for the phase for the transmitted signal. For the structures with results in Figures 11(e) and 11(f), the polarization effects due to opposite induced domain directions in the structural unit were predicted for both the reflected and transmitted signals. In conclusion, all of the discussed configurations characterize the electro-induced periodical structures similar to the PCs. The difference in the SH-SAW interaction was observed experimentally. However, it is still difficult to obtain the matched interaction condition due to different acoustical modes propagating in the volume of the waveguide simultaneously. Moreover, nonlinearity occurs due to coalescence at the boundaries of the induced structures. The SAW device on the thin plate structure, where exists a strong electrostatic interaction between electrodes, is promising for a future investigation.Figure 11
Experimental results of the magnitude relative (thick curves), and phase absolute (thin curves) deviations of the (a, c, and e) reflected and (b, d, and f) transmitted signals, which was measured for the positive +DC (red curve) and negative −DC (black curve) polarities. The results are compared for the induced structure (a and b) distributed on the surface of the thin plate, (c and d) the four “domains” distributed in the volume, and (e and f) the two opposite directed “domains” induced in the volume.
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## 4. Conclusions

In the current research, the systematic studies of the advanced controllable, electro-induced, periodical structure were performed. The FEM results of the unit cell showed the 2D periodical structures in the thin crystals with optimized directions and cuts effective inducing possibility. From the theoretical model, the linearity and localization of the volume-distributed structures depend on the thickness of the substrate and the induced structure configuration. The induced structures characterize complicated distribution in the volume and highly influenced the crystal thickness and parameters of the surface arranged electrodes. With the theoretical full wave 3D model of SAW device, the SH-SAW controlling possibility was indicated at the resonance interaction conditions, where the SH-SAW scattered at the electro-induced periodical structure. The experimental results of the SH-SAW interaction show the dependence of features of interaction for both reflected and transmitted signals. The magnitude and phase of the received signal were influenced on the induced structure configuration and polarity. However, the high effective acoustic wave interaction still limited due to difficulties in achieving the matched SAW interaction condition. Thus, the structure and material improvement is required for future experimental investigation. Taken together theoretical and experimental results, the novel controllable structure provides a new opportunity for application in the advanced electronics, such as the controllable filter, delay line, and multifunctional structures for a new generation signal processing device.



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*Source: 9020637-2019-04-08.xml*