Simulation method for finite element analysis of piezoelectric material parameters

Abstract

This invention discloses a simulation method for finite element analysis of piezoelectric material parameters, comprising the following steps: fabricating a thin-film bulk acoustic resonator; determining the dimensions of the resonator and the thickness of each layer; testing the Y11 curve of the resonator and extracting the series resonant frequency and effective electromechanical coupling coefficient; filling some parameters of the elastic matrix and coupling matrix into the material properties of the finite element simulation software, selecting stress-charge type constitutive relation in the piezoelectric material properties of the finite element analysis software; establishing a resonator model; simulating the admittance-frequency domain curve Y11 of the resonator model; comparing the measured Y11 curve of the resonator with the simulated Y11 curve, confirming the parameters in the elastic matrix of the piezoelectric material through parametric scanning based on the series resonant frequency; and determining the coupling matrix of the piezoelectric material through parametric scanning based on the effective electromechanical coupling coefficient of the resonator.

Description

Technical Field

[0001] This invention relates to the field of resonators and piezoelectric material characterization and analysis, specifically a simulation method for finite element analysis of piezoelectric material parameters. Background Technology

[0002] A resonator is an acoustic device widely used in radio frequency front-end systems. Due to its high center frequency, high quality factor, large bandwidth and high integration, it is widely used in the field of modern wireless communication.

[0003] Piezoelectric materials are the core of high-performance acoustic resonators, enabling efficient conversion between electrical and mechanical energy through the direct and inverse piezoelectric effects. The parameters of piezoelectric materials directly affect the performance of the resonator.

[0004] Common piezoelectric materials include quartz crystals, zinc oxide (ZnO), lead zirconate titanate (PZT), aluminum nitride (AlN), and scandium-doped aluminum nitride (Al). 1-x Sc x The performance parameters of piezoelectric materials are related to various factors such as the material type, growth conditions, and doping ratio. Therefore, characterizing the performance parameters of piezoelectric materials is crucial during the resonator fabrication process. Using scandium-doped aluminum nitride (Al₂O₃) as an example... 1-x Sc x Taking N) as an example, Figure 2 The Y11 curves of aluminum nitride with different scandium doping ratios are shown in the finite element analysis. The piezoelectric material parameters used in the finite element analysis are reference parameters and may differ from actual parameters. Figure 2 As shown, the resonant frequency f of the resonator varies with different doping ratios of AlN. s With effective electromechanical coupling coefficient k 2 eff They are all different.

[0005] Currently, commonly used methods for analyzing and characterizing the properties of piezoelectric materials include quasi-static methods and interferometry (optical methods). These testing methods have specific requirements for the structure of the test sample, and the structure of the test sample differs from the actual resonator structure, resulting in certain errors in the test results. Quasi-static testing methods have low test frequencies and cannot reflect the true performance of resonator materials under dynamic and high-frequency conditions. Interferometry measures nanoscale displacements on the sample surface, but the equipment is expensive and the cost is high.

[0006] Al on a silicon substrate with 100 crystal orientation 0.74 Sc 0.26 In characterizing the piezoelectric properties of N, researchers grew Al under different conditions. 0.74 Sc 0.26 The N thin film was characterized using a quasi-static method, and the piezoelectric strain constant d of the piezoelectric material grown under different conditions was measured.33 Between -12 pc / N and -2 pc / N. This method can only characterize the d of the material. 33 The parameters are not comprehensive for characterizing piezoelectric materials; it requires calling atomic force microscopy (AFM) and piezoelectric microscopy (PFM) modules, and the test is highly complex (Piezoelectric characterization of Sc0.26Al0.74N layers on Si (001)substrates).

[0007] In the GHz vibration measurement and analysis of FBAR (Flat Bulk Acoustic Resonator) with square and pentagonal electrodes, a pulsed laser interferometry system is used to analyze the vibration modes of the FBAR, thereby studying methods to suppress stray modes in the FBAR resonator. The laser seismometry system can analyze the minute vibrations during FBAR resonance, and then extract the piezoelectric strain constant d of the piezoelectric material. 33 However, similar to the quasi-static method, it can only extract d. 33 The parameters are complex and costly to construct a laser interferometric vibration measurement system (Gigahertz vibration measurement and analysis of FBARs with square and pentagon electrodes). Summary of the Invention

[0008] The purpose of this invention is to provide a simulation method for finite element analysis of piezoelectric material parameters.

[0009] The present invention is achieved by at least one of the following technical solutions.

[0010] A simulation method for finite element analysis of piezoelectric material parameters includes the following steps: S101, Fabrication of a thin-film bulk acoustic resonator; S102. Analyze the fabricated resonator structure, including the dimensions of the resonator and the thickness of each layer of the resonator. S103. Test the resonator to obtain the Y11 curve, and extract the series resonant frequency and effective electromechanical coupling coefficient of the resonator from the test results. S104. Based on the material type of the piezoelectric layer, consult some parameters in the reference elastic matrix and coupling matrix, and fill the reference values ​​into the material properties of the finite element simulation software. In the piezoelectric material properties of the finite element analysis software, select the stress charge type constitutive relation. S105. Based on the prepared resonator structure, establish a resonator model in finite element analysis software; S106. Under frequency domain analysis, the admittance-frequency domain curve Y11 of the resonator model is simulated. By comparing the measured Y11 curve of the resonator with the simulated Y11 curve, the matrix parameters and elastic matrix in the piezoelectric material elastic matrix are confirmed by parametric scanning based on the series resonant frequency. This matrix is ​​used to reflect the linear relationship between stress and strain of the piezoelectric material when the applied electric field remains unchanged or no electric field is applied. S107. Based on the effective electromechanical coupling coefficient of the resonator, determine the matrix parameters in the coupling matrix of the piezoelectric material and the coupling relationship between the stress, strain and electric field and electric displacement of the piezoelectric material through parametric scanning.

[0011] Furthermore, the structure of the thin-film bulk acoustic resonator includes, from top to bottom, a top electrode, a piezoelectric layer, a bottom electrode, and a seed layer; wherein the overlapping region of the top electrode and the bottom electrode is the resonant region, and the area of ​​the overlapping region is called the size of the resonator.

[0012] Further, step S102 includes measuring the resonant region where the top electrode and bottom electrode overlap to determine the resonator size; and measuring the thickness of the top electrode, piezoelectric layer, bottom electrode and seed layer to obtain the thickness of the top electrode, piezoelectric layer, bottom electrode and seed layer.

[0013] Further, in step S103, the Y11 curve of the resonator is tested using a vector network analyzer.

[0014] Furthermore, in step S104, the elastic matrix c, which has a small impact on the Y11 curve of the resonator, E With coupling matrix e E For parameters, refer to the relevant parameters in the finite element software or consult the reference values ​​and enter them into the finite element software.

[0015] Further, in step S106, the material properties of the resonator model in the finite element analysis software are selected and the mesh is generated. The parameters in the elastic matrix and coupling matrix that affect the piezoelectric material properties are set as parametric scanning variables. The resonator model is simulated in the frequency domain to obtain the Y11 curve of the resonator model.

[0016] Furthermore, by performing parameter scanning analysis on the elastic matrix and coupling matrix of the piezoelectric layer material, the influence relationship between the parameters of the elastic matrix and coupling matrix on the Y11 curve of the resonator was determined.

[0017] Furthermore, the matrix parameters that significantly affect the series resonant frequency and effective electromechanical coupling coefficient of the resonator are parametrically scanned to obtain the Y11 parameter curves of multiple resonator models. By comparing the simulated Y11 curves with the measured Y11 curves of the fabricated resonator, the material matrix parameters corresponding to the resonator are obtained.

[0018] A computer device according to the present invention includes a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, which, when executed by the processor, causes the processor to implement the method described herein.

[0019] The present invention provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor implements the method described herein.

[0020] Compared with existing technologies, the beneficial effects of the present invention are as follows: This invention provides a method for fitting piezoelectric material parameters through finite element simulation, which is compatible with the chip fabrication process in the field of resonator manufacturing. It can analyze the performance parameters of piezoelectric materials in the resonator chip fabrication process in a non-contact, low-cost, and practical manner. Based on the extracted parameters and finite element simulation, it can provide simulation references for subsequent resonator chip fabrication. Therefore, this technical solution has high practical value and suitable application scenarios. Attached Figure Description

[0021] The following drawings, which are incorporated herein by reference as part of this invention, are provided for understanding the invention. The drawings illustrate embodiments of the invention and their descriptions, serving to explain the principles of the invention.

[0022] Figure 1 This is a schematic flowchart illustrating the simulation method for finite element analysis of piezoelectric material parameters in an embodiment. Figure 2 Y11 curves of resonators composed of AlN materials with the same structure but different scandium doping ratios; Figure 3A The following are 2D and 3D model diagrams of a resonator in a finite element simulation software according to an embodiment; Figure 3B The following are 2D and 3D model diagrams of a resonator in a finite element simulation software according to an embodiment; Figure 4A c in the frequency domain E 11 Parametric sweep analysis of resonator admittance parameters; Figure 4B c in the frequency domain E 12 Parametric sweep analysis of resonator admittance parameters; Figure 4C c in the frequency domain E 13 Parametric sweep analysis of resonator admittance parameters; Figure 4D c in the frequency domain E 33 Parametric sweep analysis of resonator admittance parameters; Figure 4E c in the frequency domain E 44 Parametric sweep analysis of resonator admittance parameters; Figure 5A e in the frequency domain E 15 Parametric sweep analysis of resonator admittance parameters; Figure 5B e in the frequency domain E 31 Parametric sweep analysis of resonator admittance parameters; Figure 5C e in the frequency domain E 33 Parametric sweep analysis of resonator admittance parameters; Figure 6 This is a flowchart illustrating the process of fitting measured and simulated results in the simulation method for fitting piezoelectric material parameters using finite element analysis, as an example. Detailed Implementation

[0023] To fully understand this invention, detailed structures and simulation methods will be presented in the following description to illustrate the technical solutions proposed by this invention. Preferred embodiments of the invention are described in detail below; however, in addition to these detailed descriptions, the invention may have other embodiments.

[0024] like Figure 1 , Figure 6 As shown in this embodiment, a simulation method for finite element analysis of piezoelectric material parameters includes the following steps: S101. Prepare a thin-film bulk acoustic resonator sample. The method for preparing the resonator can refer to the well-known preparation process in the resonator manufacturing industry, and there are no special restrictions in this embodiment.

[0025] The structure of the thin-film bulk acoustic resonator is not unique. The resonator prepared in this embodiment includes a top electrode, a piezoelectric layer, a bottom electrode, and a seed layer from top to bottom. There are no special requirements for the top electrode pattern and the bottom electrode pattern. The piezoelectric layer is sandwiched between the top electrode and the bottom electrode. The overlapping area of ​​the top electrode and the bottom electrode is the resonant region of the resonator, and the area of ​​the overlapping area is the size of the resonator.

[0026] The seed layer is located below the bottom electrode and is used to induce the lattice orientation of the bottom electrode film, thereby inducing the lattice orientation of the piezoelectric layer.

[0027] Preferably, any two sides of the top and bottom electrodes of the resonator are not parallel to each other, so as to suppress stray resonance during resonator resonance and obtain a smoother Y11 curve.

[0028] The fabrication process for resonators is not unique and can be based on MEMS processes, including photolithography, etching, coating, and vapor phase etching. The growth of piezoelectric layers can include deposition methods such as physical vapor deposition (PVD), chemical vapor deposition (CVD), low-pressure chemical vapor deposition (LPCVD), and metal-organic chemical vapor deposition (MOCVD), as well as combinations of several methods. There are no special restrictions on the formation of piezoelectric layers.

[0029] In this invention, the piezoelectric layer material is AlScN material with different scandium doping ratios, the top and bottom electrodes are made of Mo, and the seed layer material is AlN. The resonator structure is a simple top electrode-piezoelectric layer-bottom electrode-seed layer structure from top to bottom, excluding passivation layers, support layers, and other structures. Depending on the different resonator fabrication processes, the top electrode may also include a passivation layer and a temperature compensation layer, and the seed layer may include other structures such as a support layer.

[0030] in Figure 2 The elastic matrix parameter c is obtained based on finite element simulation analysis and reference. E With coupling matrix parameter e E The Y11 parameter curves of resonators composed of AlN materials with the same structure but different scandium doping ratios were obtained. As shown in the figure, the resonators composed of the four materials exhibit different resonant frequencies at the resonant frequency... With effective electromechanical coupling coefficient They are all different, therefore this invention will provide analysis of piezoelectric materials c E With e E The matrix parameter method, based on the measured Y11 curve of the resonator and the known resonator structure, obtains the elastic matrix parameter c, which reflects the performance of the piezoelectric material, through finite element simulation analysis and fitting. E With coupling matrix parameter e E This provides material parameter references for material analysis and characterization, as well as for the subsequent resonator fabrication process.

[0031] S102. Analyze the fabricated resonator structure to determine the resonator size, including the resonator structure parameters such as the size of the resonator and the thickness of each layer of the resonator.

[0032] The size of the resonator is determined by the resonant region where the top and bottom electrodes overlap. Specifically, the resonator size refers to the area of ​​the overlapping portion, which is observed under an optical microscope after the resonator structure is fabricated. Confirming the size and area of ​​the overlapping region is crucial for subsequent finite element modeling.

[0033] The thickness of each layer of the resonator can be obtained during the stages of seed layer deposition, bottom electrode deposition, piezoelectric layer deposition, and top electrode deposition. Measurements are made in the resonant region where the top and bottom electrodes overlap to determine the resonator dimensions and to measure the thicknesses of the top electrode, piezoelectric layer, bottom electrode, and seed layer. Tracking tests can be performed using various methods, including non-contact or contact methods such as ellipsometers, thickness gauges, and four-probe resistance testing. Alternatively, the thickness of each layer can be confirmed by observing the sample cross-section using SEM. There are no particular limitations on the methods used to analyze the resonator dimensions and layer thicknesses.

[0034] S103. Test the resonator to obtain the Y11 curve. A vector network analyzer is typically used to test the resonator and extract the series resonant frequency from the test results. Parallel resonant frequency Calculate the effective electromechanical coupling coefficient of the resonator. .

[0035] The admittance-frequency parameter curve Y11 of the resonator was measured using a vector network analyzer. Taking the logarithm of the Y11 curve, the frequency corresponding to the highest point is the series resonant frequency. The resonant frequency corresponding to the lowest point is the parallel resonant frequency. The effective electromechanical coupling coefficient of the resonator is obtained through calculation formula. :

[0036] S104. Based on the type of piezoelectric material in the resonator sample, confirm the elastic matrix c in the finite element material. E 11 c E 12 c E 13 With c E 44 and e in the coupling matrix E 15 With e E 31 Reference values.

[0037] In the finite element material, the elastic matrix c E 13 With c E 44 Parameters and e in the coupling matrix E 15 With e E 31 The parameters have little effect on the series resonant frequency and effective electromechanical coupling coefficient of the resonator.

[0038] In this embodiment, the elastic matrix c of the piezoelectric material EWith coupling matrix e E The parameters were consulted, and the data for these parameters came from domestic and foreign literature as well as reference parameters of similar materials in the material library of finite element analysis. After obtaining the reference values, they were filled into the material properties of the finite element simulation software as material parameters for the subsequent model simulation of piezoelectric materials under the piezoacoustic physical field in finite element simulation.

[0039] In finite element simulation, when the piezoelectric material property is selected as stress-charge type, the elastic matrix c E With coupling matrix e E This is used to reflect the properties of piezoelectric materials. Alternatively, the piezoelectric material properties can also be selected as strain-charge type, in which case the matrix reflecting the piezoelectric material properties is the compliance matrix s. E With coupling matrix d E Both stress-charge type and strain-charge type can reflect the performance characteristics of piezoelectric materials. In this invention, stress-charge type is selected as the material property of piezoelectric materials, and c is used. E Matrix and e E The matrix reflects the material properties, and c is obtained by fitting the Y11 curve. E With e E For matrix parameters that have a minor impact on material properties, reference values ​​can be entered by consulting relevant literature, without the need for additional fitting. In this implementation, the piezoelectric layer of the resonator is AlScN. The elastic matrix and coupling matrix parameters of AlScN materials with different scandium doping ratios can be found by referring to typical values.

[0040] The compliance matrix s under strain-charge type material properties is theoretically used. E With coupling matrix d E Similarly, it can reflect the performance of piezoelectric materials, and can also be based on the Y11 curve to assess the performance of s. E With d E The matrix is ​​fitted.

[0041] Under stress-charge type conditions, the elastic matrix c of piezoelectric materials is... E With coupling matrix e E The original matrix is ​​shown in the following formula:

[0042]

[0043] Where c E With e E In the matrix, the superscript E of each parameter represents the elastic matrix parameter and coupling matrix parameter of the material under a constant electric field, and the subscript of each parameter represents the row and column of the matrix where the parameter is located, such as c. E 21This represents the matrix parameter in the second row and first column of the elasticity matrix.

[0044] Where c E Elasticity matrix and coupling matrix e E The parameters of the matrix have the following relationship:

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] By replacing identical matrix parameters in the matrix, the following elasticity matrix c is obtained. E With coupling matrix e E .

[0052]

[0053]

[0054] Therefore, the elastic matrix c of the piezoelectric material E The material parameter to be fitted is c E 11 c E 12 c E 13 c E 33 With c E 44 Coupling matrix e E The material parameter to be fitted is e E 15 e E 31 With e E 33 .

[0055] according to Figures 4A to 4E For the elasticity matrix c E Parametric scan analysis of relevant parameters, elasticity matrix c E c E 11 c E 12 c E13 With c E 44 The effect on the Y11 curve of the resonator is small or almost negligible; the effect is manifested in the parallel resonant frequency f. p The amplitude of the Y11 curve varies within a small range.

[0056] Where c E c in the matrix E 33 The parameters have a significant impact on the Y11 curve of the resonator. As c... E 33 Increasing the series resonant frequency f of the resonator s Increase the effective electromechanical coupling coefficient k 2 eff Decrease.

[0057] according to Figures 5A to 5C For coupling matrix e E Parametric scan analysis of relevant parameters, e in the coupling matrix eE E 15 With e E 31 The effect on the Y11 curve of the resonator is small or almost negligible. If there is an effect, it is manifested as a small range of variation in the amplitude of the Y11 curve at the parallel resonant frequency fp.

[0058] Where e E e in the matrix E 33 The parameters have a significant impact on the Y11 curve of the resonator. As e... E 33 Increasing the value of the resonator does not change the series resonant frequency, and the effective electromechanical coupling coefficient k remains unchanged. 2 eff Increase.

[0059] According to c E Matrix and e E Analysis of the impact of matrix parameters on resonator performance, focusing on matrix parameters with relatively small impact on resonator performance, including: the elastic matrix c. E c in E 11 c E 12 c E 13 With c E 44 and coupling matrix e E e E 15 With e E 31 You can fill in the values ​​by referring to the reference values ​​of typical materials; there is no need to perform fitting at this time.

[0060] For c, which has a significant impact on resonator performance E 33 Matrix parameters, because they affect the series resonant frequency of the resonator. Factors include the thickness of each layer of the resonator material and the intrinsic parameters of the material. The thickness of each layer of the resonator has been determined in step S102, so it can be obtained in the finite element simulation by parametrically scanning the elastic matrix parameters c of the piezoelectric material. E 33 The series resonant frequencies in the test curve Y11 of the resonator sample and the multiple simulation curves Y11 obtained by parametric scanning of the resonator model were compared. The elastic matrix parameter c, which reflects the actual material properties of the piezoelectric material, was confirmed. E 33 .

[0061] For e, which has a significant impact on resonator performance E 33 Matrix parameters, due to their influence on the effective electromechanical coupling coefficient k of the resonator 2 eff The factors are mainly related to the intrinsic parameters of the material, while c E 33 The matrix parameters have been passed through the series resonant frequency f s Therefore, fitting can be performed, and the parameters e of the piezoelectric material coupling matrix can be obtained through parametric scanning in the finite element simulation. E 33 The effective electromechanical coupling coefficients in the test curve Y11 of the resonator sample and the multiple simulation curves Y11 obtained by parametric scanning of the resonator model were compared. The coupling matrix parameter e of the piezoelectric material, which reflects the actual material properties of the piezoelectric material, was confirmed. E 33 .

[0062] The above describes the basic fitting principle of a finite element simulation analysis method for piezoelectric material parameters in this invention.

[0063] S105. Based on the resonator structure, establish a finite element 2D cross-sectional model or 3D model of the resonator and perform frequency domain simulation of the resonator. The parameters in the established resonator model, including the resonator dimensions and the thickness of each layer of the resonator, need to be consistent with the resonator structure obtained from the test in step S102.

[0064] Modeling of the resonator includes two-dimensional cross-sectional views and a three-dimensional full model. Figure 3A Modeling a two-dimensional cross-section of a reference resonator. Figure 3B A three-dimensional model of a reference resonator is provided, which includes a top electrode 301, a piezoelectric layer 302, a bottom electrode 303, and a seed layer 304.

[0065] The thicknesses of the top electrode 301, piezoelectric layer 302, bottom electrode 303, and seed layer 304 must be consistent with the thicknesses of each layer in the resonator sample confirmed in step S102.

[0066] After modeling, the parameter settings for finite element analysis in the frequency domain are completed, including: selecting the materials of each layer of the resonator, setting the terminals, and mesh generation.

[0067] The materials for the top electrode 301 and the bottom electrode 303 can be selected from metallic materials in the finite element analysis material library, including but not limited to materials such as molybdenum (Mo), platinum (Pt), aluminum (Al) and lead (Pb).

[0068] Preferably, when the linear elastic material properties of the top electrode 301 and the bottom electrode 303 are known, including density, Young's modulus and Poisson's ratio, the relevant metallic materials can also be newly created.

[0069] The piezoelectric layer 302 material can be selected from the original material values ​​in the case library. When the original values ​​are not fitted, the Y11 of the frequency domain simulation will differ from the measured Y11 curve.

[0070] Frequency domain simulation analysis is performed on the resonator model, and the frequency domain simulation range and frequency domain simulation step size are limited.

[0071] S106. Fit the residual parameters of the elastic matrix and coupling matrix of the piezoelectric material; simulate the resonator model using admittance-frequency domain (Y11) curves under frequency domain analysis; and convert the elastic matrix c... E With coupling matrix e E The parameters that have a significant impact on the properties of piezoelectric materials are set as parameterized scanning variables; by comparing the measured Y11 curve of the resonator with the simulated Y11 curve, based on the series resonant frequency f... s The c in the elastic matrix of the piezoelectric material was confirmed by parametric scanning. E 33 .

[0072] In the frequency domain study of finite element simulation, add matrix parameters c related to the piezoelectric material. E 33 The parameterized scan was used to perform frequency domain simulation analysis, resulting in multiple Y11 curves.

[0073] Comparing the Y11 curves from the resonator sample test with multiple Y11 curves obtained from the resonator model simulation, based on the series resonant frequency of the resonator in the test curves... Find the closest simulated Y11 curve, and then obtain the corresponding parameterized scan c. E 33 The elastic matrix parameters of the piezoelectric material are obtained.

[0074] Preferably, since the default parameters for metallic materials in finite element analysis software can differ from their actual values, the resonant frequency of the resonator is typically controlled by the thickness of the top electrode. Therefore, resonators with different top electrode thicknesses can be fabricated, and the resonant frequency under the influence of electrode thickness can be determined. The offset is fitted to obtain more accurate electrode parameters, and then the piezoelectric layer is fitted.

[0075] Preferably, when the resonator structure is not limited to the four-layer structure of top electrode, piezoelectric layer, bottom electrode and seed layer, for example including silicon oxide support layer below the seed layer, a material from the material library in the finite element simulation can also be selected as a reference, and fitting can be performed by adjusting different thicknesses.

[0076] S707, Based on the electromechanical coupling coefficient k of the resonator 2 eff The coupling matrix e of the piezoelectric material is determined by parametric scanning. E 33 .

[0077] After step S106, the effective electromechanical coupling coefficient k of the resonator is affected. 2 eff The only remaining parameter is e in the coupling matrix. E 33 Therefore, by analyzing e E 33 The parameterized scan of the parameters yields multiple effective electromechanical coupling coefficients k. 2 eff The Y11 curves of different resonators are compared with the Y11 curves of the tested resonator samples, and the effective electromechanical coupling coefficient k is determined. 2 eff The e corresponding to the similar simulated Y11 curve E 33 represents the coupling matrix parameters of the piezoelectric material.

[0078] This completes the process of finite element simulation analysis of piezoelectric material parameters.

[0079] Subsequent verification can be performed by applying the fitted parameters to other structural resonators and comparing the simulation results with the test results. If the deviation is large, the fitting can be iterated until the simulation results and test results are more consistent.

[0080] Figure 6 The flowchart illustrates the fitting parameters of the invention method, including extracting the device structure, establishing a simulation model and a reference material model, configuring frequency domain simulation conditions, and fitting elasticity matrix and coupling matrix parameters.

[0081] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A simulation method for finite element analysis of piezoelectric material parameters, characterized in that, Includes the following steps: S101, Fabrication of a thin-film bulk acoustic resonator; S102. Analyze the fabricated resonator structure, including the dimensions of the resonator and the thickness of each layer of the resonator. S103. Test the resonator to obtain the Y11 curve, and extract the series resonant frequency and effective electromechanical coupling coefficient of the resonator from the test results. S104. Based on the material type of the piezoelectric layer, consult some parameters in the reference elastic matrix and coupling matrix, and fill the reference values ​​into the material properties of the finite element simulation software. In the piezoelectric material properties of the finite element analysis software, select the stress charge type constitutive relation. S105. Based on the prepared resonator structure, establish a resonator model in finite element analysis software; S106. Under frequency domain analysis, the admittance-frequency domain curve Y11 of the resonator model is simulated. By comparing the measured Y11 curve of the resonator with the simulated Y11 curve, the matrix parameters and elastic matrix in the elastic matrix of the piezoelectric material are confirmed by parametric scanning based on the series resonant frequency. This matrix is ​​used to reflect the linear relationship between stress and strain of the piezoelectric material when the applied electric field remains unchanged or no electric field is applied. S107. Based on the effective electromechanical coupling coefficient of the resonator, determine the matrix parameters in the coupling matrix of the piezoelectric material and the coupling relationship between the stress, strain and electric field and electric displacement of the piezoelectric material through parametric scanning.

2. The simulation method for finite element analysis of piezoelectric material parameters according to claim 1, characterized in that: The structure of the thin-film bulk acoustic resonator, from top to bottom, includes a top electrode, a piezoelectric layer, a bottom electrode, and a seed layer; the overlapping area of ​​the top electrode and the bottom electrode is the resonant region, and the area of ​​the overlapping region is called the size of the resonator.

3. The simulation method for finite element analysis of piezoelectric material parameters according to claim 1, characterized in that: Step S102 includes measuring the resonant region where the top electrode and bottom electrode overlap to determine the resonator size; and measuring the thickness of the top electrode, piezoelectric layer, bottom electrode and seed layer to obtain the thickness of the top electrode, piezoelectric layer, bottom electrode and seed layer.

4. The simulation method for finite element analysis of piezoelectric material parameters according to claim 1, characterized in that: In step S103, the Y11 curve of the resonator is tested using a vector network analyzer.

5. The simulation method for finite element analysis of piezoelectric material parameters according to claim 1, characterized in that: In step S104, the elastic matrix c, which has little impact on the Y11 curve of the resonator, E With coupling matrix e E For parameters, refer to the relevant parameters in the finite element software or consult the reference values ​​and enter them into the finite element software.

6. The simulation method for finite element analysis of piezoelectric material parameters according to claim 1, characterized in that: In step S106, the material properties of the resonator model in the finite element analysis software are selected and the mesh is generated. The parameters in the elastic matrix and coupling matrix that affect the piezoelectric material properties are set as parametric scanning variables. The resonator model is simulated in the frequency domain to obtain the Y11 curve of the resonator model.

7. The simulation method for finite element analysis of piezoelectric material parameters according to claim 6, characterized in that: By performing parameter scanning analysis on the elastic matrix and coupling matrix of the piezoelectric layer material, the influence relationship between the parameters of the elastic matrix and coupling matrix on the Y11 curve of the resonator is determined.

8. The simulation method for finite element analysis of piezoelectric material parameters according to claim 6, characterized in that: By parametrically scanning the matrix parameters that significantly affect the series resonant frequency and effective electromechanical coupling coefficient of the resonator, Y11 parameter curves of multiple resonator models are obtained. By comparing the simulated Y11 curves with the measured Y11 curves of the fabricated resonator, the material matrix parameters corresponding to the resonator are obtained.

9. A computer device comprising a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, characterized in that: When the computer program is executed by the processor, it causes the processor to implement the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the processor implements the method as described in any one of claims 1 to 8.

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