An optimization method for the Bragg reflection structure of a solid-state assembled resonator to suppress shear wave mode leakage.

Abstract

This invention provides an optimization method for the Bragg reflection structure of a solid-state assembled resonator to suppress shear wave mode leakage. The method targets a piezoelectric oscillator stack consisting of an upper electrode, a piezoelectric film, and a lower electrode, and a Bragg reflection structure positioned below the piezoelectric oscillator stack. By establishing a Lamb wave dispersion model of the piezoelectric oscillator stack, the actual propagation characteristics of the thickness stretching working mode and the second-order thickness shear parasitic mode are obtained. Furthermore, the thickness parameters of the high and low acoustic impedance layers in the Bragg reflection structure are optimized using phase error theory. This optimized Bragg reflection structure can simultaneously improve the reflection capability of both the thickness stretching working mode and the second-order thickness shear parasitic mode, thereby reducing acoustic energy loss caused by leakage of acoustic wave energy towards the Bragg reflection structure and the substrate, and improving the resonator's quality factor (Q value) and overall device performance.

Description

Technical Field

[0001] This invention relates to the field of resonator technology, and more specifically, to an optimization method for the Bragg reflection structure of a solid-state assembled resonator to suppress shear wave mode leakage. Background Technology

[0002] Solid-mounted resonators (SMRs) are bulk acoustic wave devices that achieve high-frequency resonance based on the electro-piezoelectric coupling effect of piezoelectric thin films. They can provide a stable frequency reference for core electronic components such as filters and sensors. These devices have advantages such as high operating frequency, small size, high mechanical strength, easy integration, and strong environmental adaptability, and have been widely used in 5G communication, satellite communication, high-precision sensing, and other fields.

[0003] SMR typically comprises a piezoelectric resonator consisting of an upper electrode, a piezoelectric thin film, and a lower electrode, and an acoustic reflection structure disposed below the piezoelectric resonator. To suppress the leakage of acoustic energy towards the substrate during resonance, existing technologies typically employ a Bragg reflection structure formed by alternating stacks of high and low acoustic impedance layers. The thickness of each layer is determined according to the quarter-wavelength of the acoustic wave corresponding to the material of each reflection layer at the target operating frequency, thereby improving the reflection capability for the thick-stretching operating mode acoustic wave. This quarter-wavelength-based Bragg reflection structure design method is currently the closest existing technology.

[0004] However, in the actual operation of SMR devices, the piezoelectric oscillator often excites other non-target modes, including the second-order thickness shear parasitic mode, while simultaneously exciting the thickness stretching working mode, and these modes couple with the thickness stretching working mode. Existing Bragg reflection structures designed based on the quarter-wavelength principle are mainly optimized for the reflection isolation of the thickness stretching working mode. They have weak reflection capabilities for the acoustic waves corresponding to the second-order thickness shear parasitic mode, causing the energy of this type of shear wave mode to easily penetrate the Bragg reflection structure and leak downwards into the reflective layer or even the substrate.

[0005] The aforementioned shear wave mode leakage will significantly increase the acoustic energy loss of the device, reduce the quality factor Q of the resonator, and may cause problems such as enhanced spurious response, decreased modal purity and deterioration of frequency response, making it difficult for the device performance to meet the requirements of high Q value, high stability and high signal purity for application scenarios such as 5G communication and high sensitivity sensing.

[0006] Therefore, how to optimize the thickness parameters of the high and low acoustic impedance layers in the Bragg reflector structure to address the shear wave parasitic mode leakage problem in SMR, and suppress shear wave mode energy leakage while ensuring effective reflection of the working mode under thickness stretching, has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0007] To address the technical problems mentioned above, this invention provides an optimization method for the Bragg reflection structure of a solid-state assembled resonator to suppress shear wave mode leakage.

[0008] This invention provides an optimization method for the Bragg reflection structure of a solid-state assembled resonator to suppress shear wave mode leakage. The solid-state assembled resonator includes a piezoelectric oscillator stack and a Bragg reflection structure disposed below the piezoelectric oscillator stack. The piezoelectric oscillator stack includes a sandwich-structured upper electrode, a piezoelectric thin film, and a lower electrode. The Bragg reflection structure is composed of alternating layers of high acoustic impedance and low acoustic impedance. The method includes the following steps: S1. Obtain the technical parameters and design objectives of the solid-state assembled resonator, including structural parameters, material parameters, operating modes, and parasitic modes; based on the structural parameters, establish a Lamb wave dispersion model for the piezoelectric resonator. S2. Based on the Lamb wave dispersion model, identify the mode shape corresponding to the dispersion curve, obtain the dispersion branches corresponding to the working mode and the parasitic mode, determine the target working frequency by the frequency of the dispersion branch corresponding to the working mode at the target working point, and extract the in-plane wavenumbers corresponding to the working mode and the parasitic mode at the target working frequency. S3. Based on the target operating frequency and in-plane wavenumber, solve for the Lamb wave propagation parameters of the operating mode and parasitic mode along the thickness direction in the high acoustic impedance layer and the low acoustic impedance layer. S4. Based on the acoustic propagation parameters corresponding to the working mode, establish the initial thickness model of the Bragg reflection structure; optimize the thickness parameters of the Bragg reflection structure based on the Lamb wave propagation parameters and phase error theory to obtain the optimized high acoustic impedance layer thickness and low acoustic impedance layer thickness. S5. Determine the optimized Bragg reflective structure layer parameters based on the optimized high acoustic impedance layer thickness and low acoustic impedance layer thickness. S6. Apply the optimized Bragg reflection structure layer parameters to the solid-state assembled resonator model, and verify and iteratively correct the optimization results.

[0009] In step S1, the structural parameters include the thickness of the upper electrode, the thickness of the piezoelectric film, and the thickness of the lower electrode; the material parameters include the density, elastic constant, piezoelectric constant, and dielectric constant of the piezoelectric film, the upper electrode, and the lower electrode, as well as the density, elastic constant, and longitudinal wave / shear wave propagation parameters of the high acoustic impedance layer and the low acoustic impedance layer; the working mode is preferably the thickness tensile working mode, and the parasitic mode is preferably the second-order thickness shear parasitic mode.

[0010] In step S1, the Lamb wave dispersion model of the piezoelectric oscillator is established, specifically including: For piezoelectric thin films, the governing equations and constitutive equations of the piezoelectric medium are used to describe their electromechanical coupling vibration behavior. The governing equations and constitutive equations are as follows: (1) (2) For the upper and lower electrodes, the elastic vibration behavior is described using the governing equations and constitutive equations of the elastic medium, as follows: (3) (4) Assuming the wave propagates along the plane of the device and is distributed along the thickness direction, the displacement field and potential field wave solutions in the piezoelectric layer and electrode layer are constructed respectively: (5) and (6) Among them, superscript f This represents the wave solution related to the piezoelectric thin film, where i is the imaginary unit. ω Represents angular frequency. ξ and ζ These are the wavenumbers along the propagation direction and the thickness direction, respectively. A 1. A 2 and A 3 is an undetermined constant; During the modeling process, the boundary conditions include: the upper and lower free surfaces of the piezoelectric oscillator satisfy the stress free boundary conditions; the interface between adjacent layers satisfies the displacement continuity and stress continuity conditions; the corresponding boundaries of the upper and lower electrodes of the piezoelectric layer satisfy the electrical boundary conditions, preferably the electric potential known boundary conditions, in which one side has a zero potential and the other side has a driving potential or equivalent short circuit conditions. Substituting the wave solutions of each layer into the above boundary conditions, the dispersion equation of the piezoelectric oscillator is established.

[0011] In step S1, the dispersion equation is constructed using the displacement method, and the dispersion equation is solved using the bisection method or other numerical root-finding methods to obtain the Lamb wave dispersion curve of the piezoelectric oscillator within the preset dimensionless wavenumber range.

[0012] Step S2 specifically includes: Obtain the Lamb wave dispersion curve of the piezoelectric oscillator, extract data points of several low-order dispersion branches under the preset wavelet number condition, and draw the corresponding displacement mode diagram. Based on the dominant components of thickness direction displacement and in-plane displacement in the mode shape, displacement symmetry and node distribution characteristics, the Lamb wave branch corresponding to the thickness tensile working mode and the Lamb wave branch corresponding to the second-order thickness shear parasitic mode are identified. The target operating frequency of the device is determined by the frequency of the dispersion branch corresponding to the thickness stretching operating mode at the target operating point, and the in-plane wavenumbers corresponding to the thickness stretching operating mode and the second-order thickness shear parasitic mode at the target operating frequency are extracted.

[0013] Step S3 specifically includes: Substituting the target operating frequency and in-plane wavenumber into the governing equations of the elastic media corresponding to the high acoustic impedance layer and the low acoustic impedance layer, we obtain: (7) The wave number solution of Lamb wave along the thickness direction in each reflective layer material is obtained by solving, and the phase velocity of the corresponding mode in the thickness direction in each reflective layer is further obtained. During the solution process, for multiple solutions of wavenumber in the thickness direction, the physical solution that satisfies the actual propagation conditions is preferred, including the wavenumber solution with a larger absolute value that represents the propagation of the shear wave. The thickness-direction Lamb wave phase velocities corresponding to the thickness tensile working mode and the second-order thickness shear parasitic mode in the high and low acoustic impedance layers are calculated from the selected thickness-direction wavenumbers.

[0014] In step S4, the initial thickness parameter is determined based on the traditional quarter-wavelength reflection principle, so that the working mode satisfies the corresponding initial reflection conditions in the high acoustic impedance layer and the low acoustic impedance layer, respectively, and the initial thickness of the high acoustic impedance layer and the initial thickness of the low acoustic impedance layer are obtained.

[0015] In step S4, the thickness parameters of the Bragg reflective structure are optimized based on the Lamb wave propagation parameters and phase error theory. The phase error theory formula is as follows: (8) in, n Take the integer. The phase drop of the wave after passing through the low-impedance layer. The phase drop of the wave after passing through the high-impedance layer; The phase drop of the thickness tensile working mode and the second-order thickness shear parasitic mode propagating in high and low acoustic impedance layers were calculated respectively, and the correspondence between the reflector layer thickness parameters and the phase drop was established: (9) in, The resonant frequency is indicated by the subscript v, where long and Lamb represent the wave velocities associated with longitudinal and Lamb waves, respectively. and It refers to the phase drop of longitudinal waves and Lamb waves at the same frequency in the low-impedance layer; and It refers to the phase drop of longitudinal waves and Lamb waves at the same frequency in the high-impedance layer; In the phase error correction process, an integer-order phase condition is introduced to match the phase drop of the high acoustic impedance layer and the low acoustic impedance layer, in order to obtain a smaller layer thickness and a stronger modal reflection effect. n 1 equals 1. n 2 is taken as 2; By setting an allowable phase error range, the thickness parameters of the high acoustic impedance layer and the low acoustic impedance layer are solved simultaneously to obtain the optimized thicknesses of the high acoustic impedance layer and the low acoustic impedance layer, as follows: Phase error is allowed in equation (9) ,Right now: (10) make get: (11) Combining equations (10) and (11), we get: (12) Introduction Substituting it into equation (12), we get: (13) The optimized thicknesses of the high acoustic impedance layer and the low acoustic impedance layer are thus obtained as follows: (14) in, .

[0016] Step S5 specifically includes: the arrangement order of the high acoustic impedance layer and the low acoustic impedance layer; the number of repetition cycles of the high acoustic impedance layer and the low acoustic impedance layer; the thickness value of each reflective layer; and the total thickness of the Bragg reflective structure.

[0017] In step S6, theoretical calculations and finite element simulations are used to verify the optimization results. The verification indicators include: the displacement field distribution of the thickness tensile working mode and the second-order thickness shear parasitic mode in the reflective layer; the distribution of acoustic flux density or acoustic energy in the Bragg reflective layer and the substrate; and the degree of sound wave leakage towards the Bragg reflective layer and the substrate. If the verification results show that the optimized Bragg reflection structure has not yet achieved the preset reflection effect or device performance requirements, then return to step S4 to adjust the phase error correction parameters, layer thickness parameters, or number of periods until the preset design goal is met.

[0018] The beneficial effects of this invention are as follows: This invention obtains the actual propagation parameters of the thickness-stretched working mode and the second-order thickness-shear parasitic mode in a solid-state assembled resonator based on the Lamb wave dispersion curve. It then optimizes the thickness parameters of the high and low acoustic impedance layers in the Bragg reflector structure using phase error theory, enabling the optimized Bragg reflector structure to simultaneously improve its reflection capability for both modes. Compared with existing technologies, this invention can more accurately match the actual propagation characteristics of the parasitic shear wave mode in the device, significantly reduce the leakage of acoustic energy into the Bragg reflector structure and substrate, enhance the confinement effect of vibrational energy in the electrode-piezoelectric film-electrode sandwich oscillator, reduce device acoustic energy loss, improve the resonator's quality factor Q, and improve the device's frequency response performance. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the solid-state assembled resonator structure in this invention; Figure 2 This is a schematic diagram of the Lamb wave dispersion curve of the piezoelectric oscillator in this invention; Figure 3 This is a schematic diagram of the thickness stretching mode before optimization in this invention; Figure 4 This is a schematic diagram of the first two thickness shear modes in this invention. Figure 5 This is a schematic diagram of the optimized thickness stretching mode in this invention; Figure 6 This is a schematic diagram of the optimized second-order thickness shear mode in this invention; Figure 7 This is a schematic diagram of the vibration modes before optimization in this invention; Figure 8 This is a schematic diagram of the optimized vibration modes in this invention. Detailed Implementation

[0020] The exemplary embodiments of this disclosure are described below with reference to the accompanying drawings, including various details of the embodiments to aid understanding, and should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this disclosure. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0021] SMR is an abbreviation for Solidly Mounted Resonator; Bragg reflection structure is a multi-layer acoustic reflection structure formed by alternating layers of high acoustic impedance and low acoustic impedance; Lamb wave is a type of guided wave that propagates in a layered structure; COMSOL is a finite element multiphysics simulation software. x 1 represents the direction of wave propagation within the plane of the device. x 3 indicates the thickness direction of the device. u 1 indicates along x Displacement component in direction 1, u 3 indicates along x Displacement components in three directions.

[0022] This invention discloses an optimization method for the Bragg reflection structure of a solid-state assembled resonator to suppress shear wave mode leakage. The solid-state assembled resonator includes a piezoelectric oscillator stack and a Bragg reflection structure disposed below the piezoelectric oscillator stack. The piezoelectric oscillator stack includes a sandwich-structured upper electrode, a piezoelectric thin film, and a lower electrode. The Bragg reflection structure is composed of alternating layers of high acoustic impedance and low acoustic impedance. The method includes the following steps: S1. Obtain the technical parameters and design objectives of the solid-state assembled resonator, including structural parameters, material parameters, operating modes, and parasitic modes; based on the structural parameters, establish a Lamb wave dispersion model for the piezoelectric resonator. S2. Based on the Lamb wave dispersion model, identify the mode shape corresponding to the dispersion curve, obtain the dispersion branches corresponding to the working mode and the parasitic mode, determine the target working frequency by the frequency of the dispersion branch corresponding to the working mode at the target working point, and extract the in-plane wavenumbers corresponding to the working mode and the parasitic mode at the target working frequency. S3. Based on the target operating frequency and in-plane wavenumber, solve for the Lamb wave propagation parameters of the operating mode and parasitic mode along the thickness direction in the high acoustic impedance layer and the low acoustic impedance layer. S4. Based on the acoustic propagation parameters corresponding to the working mode, establish the initial thickness model of the Bragg reflection structure; optimize the thickness parameters of the Bragg reflection structure based on the Lamb wave propagation parameters and phase error theory to obtain the optimized high acoustic impedance layer thickness and low acoustic impedance layer thickness. S5. Determine the optimized Bragg reflective structure layer parameters based on the optimized high acoustic impedance layer thickness and low acoustic impedance layer thickness. S6. Apply the optimized Bragg reflection structure layer parameters to the solid-state assembled resonator model, and verify and iteratively correct the optimization results.

[0023] The present invention is illustrated using a solid-state assembled thin-film resonator as an example, the structure of which is as follows: Figure 1 As shown: The solid-state assembled resonator includes an electrode-piezoelectric film-electrode sandwich oscillator consisting of an upper electrode, a piezoelectric film, and a lower electrode, as well as a Bragg reflector structure disposed below the oscillator. in, h t Indicates the thickness of the upper electrode. h f Indicates the thickness of the piezoelectric film. h b Indicates the thickness of the bottom electrode. h l Indicates the thickness of the low acoustic impedance layer. h h Indicates the thickness of the high acoustic impedance layer. x 1 represents the direction of wave propagation within the plane of the device. x 3 represents the thickness direction of the device; the polarization direction of the piezoelectric thin film is along... x 3 directions; In the solid-state assembled thin-film resonator of this embodiment, the upper electrode thickness is 0.2 μm, the piezoelectric film thickness is 3.4 μm, and the lower electrode thickness is 0.2 μm. The upper and lower electrodes are both made of aluminum (Al), the piezoelectric film is made of zinc oxide (ZnO), the high acoustic impedance layer in the Bragg reflector structure is made of platinum (Pt), and the low acoustic impedance layer in the Bragg reflector structure is made of silicon dioxide (SiO2).

[0024] The design goal of this embodiment is to improve the reflection capability of the Bragg reflection structure for the second-order thickness shear parasitic mode, while ensuring good acoustic isolation of the working mode of the solid-state assembled resonator with good thickness stretching, and to reduce the leakage of related mode acoustic energy into the Bragg reflection structure and the substrate.

[0025] According to the method steps of the present invention, a Lamb wave propagation model is first established for the electrode-piezoelectric film-electrode sandwich oscillator.

[0026] For the piezoelectric thin film ZnO, the governing equations and constitutive equations of the piezoelectric medium are used to describe its electromechanical coupling behavior; for the upper and lower aluminum electrodes, the governing equations and constitutive equations of the elastic medium are used to describe its elastic vibration behavior. Combining the interface continuity conditions between the layers in the sandwich layered structure, the stress free boundary conditions of the upper and lower free surfaces, and the electrical boundary conditions of the upper and lower boundaries of the piezoelectric layer, the Lamb wave dispersion equation of the sandwich oscillating reactor is established, and numerical solutions are obtained using the displacement method and the bisection method.

[0027] The Lamb wave dispersion curve of the sandwich oscillator was calculated, as follows: Figure 2 As shown, Figure 2 The horizontal axis represents the dimensionless wavenumber. ξL The vertical axis represents the dimensionless frequency Ω. Through analysis and identification of the dispersion curves and corresponding displacement modes, it can be determined that: the dispersion branch corresponding to A is the working mode of thickness tension; the dispersion branch corresponding to B is the second-order parasitic mode of thickness shear.

[0028] The target resonant frequency of the solid-state assembled resonator can be further determined from the dispersion branch at point A; the propagation characteristic parameters of the second-order thickness shear mode under the target operating state can be obtained from the dispersion branch at point B. The above results provide the basic input for the subsequent optimization of the thickness parameters of the Bragg reflection structure.

[0029] To illustrate the technical effects of the present invention, this embodiment first uses the traditional quarter-wavelength principle to design the thickness of the high and low acoustic impedance layers in the Bragg reflection structure, and analyzes its modal constraint capability under the same material system and device structure conditions as a comparative example.

[0030] In this traditional design, the thickness of the high and low acoustic impedance layers is mainly determined based on the wavelength relationship of the target working mode. The design focuses on improving the reflection capability of the thickness stretching working mode, without fully considering the dispersion effect and phase deviation problem when the second-order thickness shear parasitic mode actually propagates in the form of Lamb wave.

[0031] Figure 3 and Figure 4 The acoustic mode distributions of the thickness stretching mode and the second-order thickness shear mode in a solid-state assembled resonator using a conventional quarter-wavelength Bragg reflection structure are presented. The horizontal axis in the figure represents the dimensionless length coordinate. x 1 / L The vertical axis represents the dimensionless thickness coordinate. x 3 / L ;in, Figure 3 For the thickness direction displacement distribution of the thickness tensile mode u 3, Figure 4 In-plane displacement distribution of the second-order thickness shear mode u 1; Depend on Figure 3 and Figure 4 It can be seen that the traditional Bragg reflection structure has a good reflection effect on the tensile mode, and the relevant vibration energy is mainly concentrated in the electrode-piezoelectric film-electrode sandwich oscillator region; however, for the second-order shear mode, the acoustic energy extends significantly into the interior of the Bragg reflection structure, indicating that the traditional design method has a weak reflection capability for this type of parasitic mode and is difficult to effectively suppress the energy leakage of the shear wave mode; that is, under the Bragg reflection structure condition before optimization, only the tensile mode has a good acoustic reflection effect, while the second-order shear mode exhibits acoustic extension into the reflection structure region.

[0032] According to the method described in this invention, the thickness parameters of the Bragg reflective structure are further optimized.

[0033] First, according to Figure 2 The obtained Lamb wave dispersion curves are used to obtain the propagation parameters of the thickness tensile working mode and the second-order thickness shear parasitic mode at the target working frequency. Then, combined with the elastic propagation models of the high acoustic impedance layer material Pt and the low acoustic impedance layer material SiO2, the wave number, phase velocity and corresponding wavelength of the Lamb wave propagation in the thickness direction of the high and low acoustic impedance layers are solved.

[0034] Based on this, the traditional Bragg reflection structure thickness design is modified using phase error theory, so that the optimized high acoustic impedance layer thickness and low acoustic impedance layer thickness no longer only meet the traditional quarter-wavelength reflection condition, but also simultaneously take into account: 1. High-efficiency reflection of the working mode of thickness stretching at the target operating frequency; 2. Enhanced reflection of the second-order thickness shear parasitic mode in the same or adjacent frequency bands; 3. The total thickness of the reflective layer and the interlayer structure meet the actual processing requirements.

[0035] The optimized Bragg reflector structure can be obtained by using the formulas in the preceding steps, which determine the thickness parameters of the high and low acoustic impedance layers. The essence of this optimization process lies in replacing the approximate propagation characteristics of traditional pure longitudinal / pure shear waves with the actual propagation characteristics of Lamb waves, and combining this with a phase error correction method, so that the Bragg reflector structure possesses strong reflection capabilities for both the thickness-stretched working mode and the second-order thickness-shear parasitic mode.

[0036] Based on the optimized Bragg reflector thickness parameters obtained by the method of this invention, the modal distribution in the solid-state assembled resonator was analyzed, and the results are as follows: Figure 5 and Figure 6 As shown. Figure 5 To obtain the displacement distribution diagram of the optimized thickness tensile mode, Figure 6 The displacement distribution diagram for the optimized second-order thickness shear mode.

[0037] contrast Figure 3 , Figure 4 and Figure 5 , Figure 6 It can be seen that: For the working mode of thickness stretching, the optimized Bragg reflection structure can still maintain good acoustic wave reflection capability, and the acoustic wave energy is mainly concentrated in the piezoelectric oscillator region. For the second-order thickness shear parasitic mode, the optimized Bragg reflection structure significantly enhances its reflection capability, and the vibrational energy entering the interior of the Bragg reflection structure is significantly reduced, with the mode energy being more concentrated in the electrode-piezoelectric film-electrode sandwich oscillator.

[0038] The above results show that the Bragg reflective structure thickness optimization method proposed in this invention not only does not weaken its reflection effect on the thickness stretching working mode, but also significantly improves its constraint ability on the second-order thickness shear parasitic mode, thereby achieving synergistic suppression of multi-mode acoustic energy leakage.

[0039] Compared with the original, the optimized Bragg reflector structure can more effectively confine the vibrational energy of the relevant modes within the electrode-piezoelectric film-electrode sandwich oscillator region, reducing its leakage into the reflector structure. In particular, for the second-order thickness shear mode, the leakage of acoustic waves into the reflector structure is significantly suppressed.

[0040] To further verify the feasibility and beneficial effects of the optimization method of this invention, this embodiment uses COMSOL finite element software to perform vibration simulation analysis on the solid-state assembled resonator before and after optimization. The simulation maintains consistency in the device material system, geometric dimensions, and boundary conditions; only the thickness parameters of the high and low acoustic impedance layers in the Bragg reflector structure are changed to ensure the comparability of the comparison results.

[0041] Figure 7 and Figure 8 The vibration modes of the solid-state assembled resonator before and after optimization are compared. Figure 7 The vibration mode distribution before optimization. Figure 8 The optimized vibration mode distribution is shown in the two figures; the left figure represents the in-plane displacement components. u The distribution of 1, the right figure shows the displacement component in the thickness direction. u The distribution of 3.

[0042] from Figure 7 It can be seen that in the traditional Bragg reflector structure, a significant portion of the vibrational energy corresponding to the second-order thickness shear mode leaks into the Bragg reflector structure, indicating that the traditional design is unable to effectively isolate this type of parasitic mode acoustically.

[0043] And from Figure 8 It can be seen that after adopting the Bragg reflection structure optimized by the present invention, the vibration energy is more concentrated in the piezoelectric oscillator region, and the energy entering the Bragg reflection structure is significantly reduced. This indicates that the optimization method can effectively improve the reflection capability of the Bragg reflection structure for parasitic shear wave modes and reduce acoustic energy leakage.

[0044] The specific embodiments described above do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A method for optimizing a solidly mounted resonator Bragg reflector structure for suppressing a shear wave mode leakage, the solidly mounted resonator comprising a piezoelectric oscillation stack including an upper electrode, a piezoelectric thin film, and a lower electrode in a sandwich structure, and a Bragg reflector structure disposed below the piezoelectric oscillation stack, the Bragg reflector structure being composed of high acoustic impedance layers and low acoustic impedance layers alternately stacked, characterized by, Includes the following steps: ​ S1. Obtain the technical parameters and design objectives of the solid-state assembled resonator, including structural parameters, material parameters, operating modes, and parasitic modes; based on the structural parameters, establish a Lamb wave dispersion model for the piezoelectric resonator. S2. Based on the Lamb wave dispersion model, identify the mode shape corresponding to the dispersion curve, obtain the dispersion branches corresponding to the working mode and the parasitic mode, determine the target working frequency by the frequency of the dispersion branch corresponding to the working mode at the target working point, and extract the in-plane wavenumbers corresponding to the working mode and the parasitic mode at the target working frequency. S3. Based on the target operating frequency and in-plane wavenumber, solve for the Lamb wave propagation parameters of the operating mode and parasitic mode along the thickness direction in the high acoustic impedance layer and the low acoustic impedance layer. S4. Based on the acoustic propagation parameters corresponding to the working mode, establish the initial thickness model of the Bragg reflection structure; optimize the thickness parameters of the Bragg reflection structure based on the Lamb wave propagation parameters and phase error theory to obtain the optimized high acoustic impedance layer thickness and low acoustic impedance layer thickness. S5. Determine the optimized Bragg reflective structure layer parameters based on the optimized high acoustic impedance layer thickness and low acoustic impedance layer thickness. S6. Apply the optimized Bragg reflection structure layer parameters to the solid-state assembled resonator model, and verify and iteratively correct the optimization results.

2. The optimization method according to claim 1, characterized in that, In step S1, the structural parameters include the thickness of the upper electrode, the thickness of the piezoelectric film, and the thickness of the lower electrode; the material parameters include the density, elastic constant, piezoelectric constant, and dielectric constant of the piezoelectric film, the upper electrode, and the lower electrode, as well as the density, elastic constant, and longitudinal wave / shear wave propagation parameters of the high acoustic impedance layer and the low acoustic impedance layer; the working mode is preferably the thickness tensile working mode, and the parasitic mode is preferably the second-order thickness shear parasitic mode.

3. The optimization method according to claim 1, characterized in that, In step S1, the Lamb wave dispersion model of the piezoelectric oscillator is established, specifically including: For piezoelectric thin films, the governing equations and constitutive equations of the piezoelectric medium are used to describe their electromechanical coupling vibration behavior. The governing equations and constitutive equations are as follows: （1）； （2）； For the upper and lower electrodes, the elastic vibration behavior is described using the governing equations and constitutive equations of the elastic medium, as follows: (3)； (4)； Assuming the wave propagates along the plane of the device and is distributed along the thickness direction, the displacement field and potential field wave solutions in the piezoelectric layer and electrode layer are constructed respectively: (5)； and (6)； Among them, superscript f This represents the wave solution related to the piezoelectric thin film, where i is the imaginary unit. ω Represents angular frequency. ξ and ζ These are the wavenumbers along the propagation direction and the thickness direction, respectively. A 1. A 2 and A 3 is an undetermined constant; During the modeling process, the boundary conditions include: the upper and lower free surfaces of the piezoelectric oscillator satisfy the stress free boundary conditions; the interface between adjacent layers satisfies the displacement continuity and stress continuity conditions; the corresponding boundaries of the upper and lower electrodes of the piezoelectric layer satisfy the electrical boundary conditions, preferably the electric potential known boundary conditions, in which one side has a zero potential and the other side has a driving potential or equivalent short circuit conditions. Substituting the wave solutions of each layer into the above boundary conditions, the dispersion equation of the piezoelectric oscillator is established.

4. The optimization method according to claim 3, characterized in that, In step S1, the dispersion equation is constructed using the displacement method, and the dispersion equation is solved using the bisection method or other numerical root-finding methods to obtain the Lamb wave dispersion curve of the piezoelectric oscillator within the preset dimensionless wavenumber range.

5. The optimization method according to claim 4, characterized in that, Step S2 specifically includes: Obtain the Lamb wave dispersion curve of the piezoelectric oscillator, extract data points of several low-order dispersion branches under the preset wavelet number condition, and draw the corresponding displacement mode diagram. Based on the dominant components of thickness direction displacement and in-plane displacement in the mode shape, displacement symmetry and node distribution characteristics, the Lamb wave branch corresponding to the thickness tensile working mode and the Lamb wave branch corresponding to the second-order thickness shear parasitic mode are identified. The target operating frequency of the device is determined by the frequency of the dispersion branch corresponding to the thickness stretching operating mode at the target operating point, and the in-plane wavenumbers corresponding to the thickness stretching operating mode and the second-order thickness shear parasitic mode at the target operating frequency are extracted.

6. The optimization method according to claim 5, characterized in that, Step S3 specifically includes: Substituting the target operating frequency and in-plane wavenumber into the governing equations of the elastic media corresponding to the high acoustic impedance layer and the low acoustic impedance layer, we obtain: (7)； The wave number solution of Lamb wave along the thickness direction in each reflective layer material is obtained by solving, and the phase velocity of the corresponding mode in the thickness direction in each reflective layer is further obtained. During the solution process, for multiple solutions of wavenumber in the thickness direction, the physical solution that satisfies the actual propagation conditions is preferred, including the wavenumber solution with a larger absolute value that represents the propagation of the shear wave. The thickness-direction Lamb wave phase velocities corresponding to the thickness tensile working mode and the second-order thickness shear parasitic mode in the high and low acoustic impedance layers are calculated from the selected thickness-direction wavenumbers.

7. The optimization method according to claim 6, characterized in that, In step S4, the initial thickness parameter is determined based on the traditional quarter-wavelength reflection principle, so that the working mode satisfies the corresponding initial reflection conditions in the high acoustic impedance layer and the low acoustic impedance layer, respectively, and the initial thickness of the high acoustic impedance layer and the initial thickness of the low acoustic impedance layer are obtained.

8. The optimization method according to claim 6, characterized in that, In step S4, the thickness parameters of the Bragg reflective structure are optimized based on the Lamb wave propagation parameters and phase error theory. The phase error theory formula is as follows: (8)； in, n Take the integer. The phase drop of the wave after passing through the low-impedance layer. The phase drop of the wave after passing through the high-impedance layer; The phase drop of the thickness tensile working mode and the second-order thickness shear parasitic mode propagating in high and low acoustic impedance layers were calculated respectively, and the correspondence between the reflector layer thickness parameters and the phase drop was established: (9)； in, The resonant frequency is indicated by the subscript v_long and Lamb, which represent the wave velocities associated with longitudinal and Lamb waves, respectively. and It refers to the phase drop of longitudinal waves and Lamb waves at the same frequency in the low-impedance layer; and It refers to the phase drop of longitudinal waves and Lamb waves at the same frequency in the high-impedance layer; In the phase error correction process, an integer-order phase condition is introduced to match the phase drop of the high acoustic impedance layer and the low acoustic impedance layer, in order to obtain a smaller layer thickness and a stronger modal reflection effect. n 1 equals 1. n 2 is taken as 2; By setting an allowable phase error range, the thickness parameters of the high acoustic impedance layer and the low acoustic impedance layer are solved simultaneously to obtain the optimized thicknesses of the high acoustic impedance layer and the low acoustic impedance layer, as follows: Phase error is allowed in equation (9) ,Right now: （10）； make get; （11）； Combining equations (10) and (11), we get: （12）； Introduction Substituting it into equation (12), we get: （13）； The optimized thicknesses of the high acoustic impedance layer and the low acoustic impedance layer are thus obtained as follows: （14）； in, .

9. The optimization method according to claim 8, characterized in that, Step S5 specifically includes: the arrangement order of the high acoustic impedance layer and the low acoustic impedance layer; the number of repetition cycles of the high acoustic impedance layer and the low acoustic impedance layer; the thickness value of each reflective layer; and the total thickness of the Bragg reflective structure.

10. The optimization method according to claim 8, characterized in that, In step S6, theoretical calculations and finite element simulations are used to verify the optimization results. The verification indicators include: the displacement field distribution of the thickness tensile working mode and the second-order thickness shear parasitic mode in the reflective layer; the distribution of acoustic flux density or acoustic energy in the Bragg reflective layer and the substrate; and the degree of sound wave leakage towards the Bragg reflective layer and the substrate. If the verification results show that the optimized Bragg reflection structure has not yet achieved the preset reflection effect or device performance requirements, then return to step S4 to adjust the phase error correction parameters, layer thickness parameters, or number of periods until the preset design goal is met.

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