A surface acoustic wave resonator simulation method and system

Abstract

The application discloses a surface acoustic wave resonator simulation method and system, comprising: obtaining a transverse slice model of a surface acoustic wave resonator to be simulated; determining a mirror part and a non-mirror part in the transverse slice model; extracting a preset layer grid from each of the mirror part and the non-mirror part to obtain a mirror unit and a non-mirror unit; for the non-mirror unit, assembling the grid of the non-mirror unit by using a finite element method to obtain a system matrix of the finite element as a first matrix; performing sorting processing on the first matrix, applying a potential constraint and a periodic condition to obtain a second matrix; for the mirror unit, performing symmetry processing on the second matrix to obtain a third matrix; and performing cascading on the second matrix and the third matrix to obtain a simulation model of the transverse slice model of the surface acoustic wave resonator. The application can be cascaded for the case that the splicing surfaces are inconsistent, the required finite element simulation unit is reduced, the simulation speed of the transverse slice model is accelerated, and the accuracy of the simulation result is improved.

Description

Technical Field

[0001] This application relates to the field of resonator simulation and analysis technology, and in particular to a simulation method and system for surface acoustic wave resonators. Background Technology

[0002] A typical surface acoustic wave resonator usually consists of a central interdigitated electrode transducer and two reflective gratings on either side, as follows: Figure 1 As shown. In actual simulations, because a full-size resonator model is large and occupies a considerable number of degrees of freedom, researchers generally use horizontal or vertical slice models, as shown below. Figure 2 As shown in the diagram, the transverse slice model has a sliced ​​structure in the sound wave propagation direction (x-direction) and periodic boundary conditions on the sides (two surfaces perpendicular to the x-direction), but a complete structure in the direction perpendicular to the sound wave propagation direction (y-direction). The longitudinal slice model has a complete structure in the sound wave propagation direction (x-direction) but a sliced ​​structure in the direction perpendicular to the sound wave propagation direction (y-direction), and periodic conditions on the sides (two surfaces perpendicular to the y-direction). These two models can be used at different stages of the design process to simulate the characteristics of the corresponding surface acoustic wave resonators.

[0003] Currently, for longitudinal slice models, researchers have proposed a hierarchical cascade (HCT) technique. This technique leverages the high periodicity of the longitudinal model to extract a single element block for finite element simulation, and then uses matrix operations to combine the simulated element blocks, significantly accelerating the simulation of longitudinal slice models. Among the simulation techniques for surface acoustic wave (SAW) resonators involving hierarchical cascade technology are the following: 1) Dividing the resonator into identical element blocks and using matrix cascade elimination allows for rapid solution of the SAW resonator's admittance response based on the longitudinal slice model. 2) Extending the HCT technique by incorporating thermophysical fields. 3) Adding a PDE (partial differential equation) module to the traditional HCT.

[0004] However, all of the above methods have their own limitations: First, relying on the longitudinal slice model, due to the discontinuity of the transverse surfaces, traditional HCT algorithms encounter problems during transverse stitching, failing to achieve accelerated simulation of the transverse model; Second, during the stitching process of cascaded surfaces, the contact surfaces must be of the same size for complete stitching, and incomplete stitching cannot occur, meaning that it cannot be found after stitching that there are still missing degrees of freedom on the surface, as follows: Figure 3 As shown. However, if the interface is different, a corresponding transition unit needs to be added, as follows. Figure 4As shown, matching the interface before splicing will undoubtedly increase the computational load during splicing and affect simulation efficiency; third, the above method involves elimination when extracting unit blocks, which will also greatly increase the workload and computational load during extraction and increase the simulation difficulty. Summary of the Invention

[0005] The purpose of this application is to provide a simulation method and system for surface acoustic wave resonators, which at least solves one of the technical problems of existing surface acoustic wave resonator simulation methods, namely, the strong limitation of cascaded methods, large amount of simulation computation, and low efficiency.

[0006] To achieve the above objectives, this application provides a simulation method for surface acoustic wave resonators, comprising: Obtain the transverse slice model of the surface acoustic wave resonator to be simulated, and determine the mirror part and non-mirror part in the transverse slice model; Extract the preset layer mesh from the mirror part and the non-mirror part respectively to obtain mirror cells and non-mirror cells; For non-mirror elements, the mesh of the non-mirror elements is assembled using the finite element method to obtain the system matrix of the finite element, which is used as the first matrix; the first matrix is ​​sorted and electric potential constraints and periodic conditions are applied to obtain the second matrix; For the mirror element, the second matrix is ​​symmetrically processed to obtain the third matrix; By cascading the second and third matrices, a simulation model of the transverse slice model of the surface acoustic wave resonator is obtained.

[0007] Furthermore, the concatenation of the second and third matrices to obtain the simulation model of the transverse slice model of the surface acoustic wave resonator includes: Determine the size of the two cascaded surfaces to be cascaded; When two cascaded surfaces are the same size, perform regular cascade operations, including matrix expansion, matrix concatenation, and matrix elimination. When the two cascaded surfaces are of different sizes, the smaller cascaded surface is given additional degree-of-freedom constraints. The degrees of freedom of the larger cascaded surface are matched with those of the smaller cascaded surface. After eliminating the redundant degrees of freedom, the conventional cascaded operation is performed.

[0008] Furthermore, after performing the conventional cascading operation, the following is also included: The final admittance and target degrees of freedom of the matrix are calculated, and the two-dimensional Fourier transform of the grid displacements is calculated to optimize the initial transverse slice model.

[0009] Further, the step of extracting preset layer meshes from the mirrored portion and the non-mirrored portion respectively to obtain mirrored cells and non-mirrored cells includes: Extract one layer of mesh from each of the mirrored and non-mirrored parts to obtain mirrored and non-mirrored units with a single mesh structure.

[0010] Furthermore, obtaining the transverse slice model of the surface acoustic wave resonator to be simulated includes: A three-dimensional model of a surface acoustic wave resonator is constructed based on physical fields; After selecting a frequency point and setting the calculation parameters, the three-dimensional model is divided according to the calculation parameters to obtain the transverse slice model of the surface acoustic wave resonator.

[0011] This application also provides a surface acoustic wave resonator simulation system, including: The model building module is used to obtain the transverse slice model of the surface acoustic wave resonator to be simulated, and to determine the mirror part and non-mirror part in the transverse slice model; The cell partitioning module is used to extract preset layer meshes from the mirror part and the non-mirror part respectively to obtain mirror cells and non-mirror cells; The non-mirror element processing module is used to assemble the mesh of non-mirror elements using the finite element method to obtain the system matrix of the finite element, which is used as the first matrix; the first matrix is ​​sorted and subjected to potential constraints and periodic conditions to obtain the second matrix. The mirror unit processing module is used to perform symmetric processing on the second matrix for the mirror unit to obtain the third matrix; The simulation module is used to cascade the second and third matrices to obtain a simulation model of the transverse slice model of the surface acoustic wave resonator.

[0012] Furthermore, the simulation module is also used for: Determine the size of the two cascaded surfaces to be cascaded; When two cascaded surfaces are the same size, perform regular cascade operations, including matrix expansion, matrix concatenation, and matrix elimination. When the two cascaded surfaces are of different sizes, the smaller cascaded surface is given additional degree-of-freedom constraints. The degrees of freedom of the larger cascaded surface are matched with those of the smaller cascaded surface. After eliminating the redundant degrees of freedom, the conventional cascaded operation is performed.

[0013] Furthermore, the surface acoustic wave resonator simulation system also includes an optimization design module for: The final admittance and target degrees of freedom of the matrix are calculated, and the two-dimensional Fourier transform of the grid displacements is calculated to optimize the initial transverse slice model.

[0014] Furthermore, the unit partitioning module is also used for: Extract one layer of mesh from each of the mirrored and non-mirrored parts to obtain mirrored and non-mirrored units with a single mesh structure.

[0015] Furthermore, the model building module is also used for: A three-dimensional model of a surface acoustic wave resonator is constructed based on physical fields; After selecting a frequency point and setting the calculation parameters, the three-dimensional model is divided according to the calculation parameters to obtain the transverse slice model of the surface acoustic wave resonator.

[0016] Compared to existing technologies, the advantages of this application are as follows: 1) In the simulation calculation of the transverse model, the improved cascade algorithm can be applied to the case where the splicing surface is inconsistent, reducing the number of finite element simulation units required; by applying the improved algorithm and matrix mirroring algorithm, only finite element simulation of 4 or 5 basic unit slices is needed, and the response of the entire surface acoustic wave device can be simulated by combining matrix operations, which greatly speeds up the simulation speed of the transverse slice model.

[0017] 2) The basic unit extraction method is adopted. When extracting, the smallest unit contains only the splicing surface degree of freedom, which does not need to be eliminated later, greatly reducing the amount of computation.

[0018] 3) It can accurately simulate the admittance response of a surface acoustic wave resonator and the subsequent data post-processing process, making the simulation effect more ideal. Attached Figure Description

[0019] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of a typical surface acoustic wave resonator provided in this application; Figure 2 This is a schematic diagram of the slice structure using a horizontal slice model or a vertical slice model provided in this application; Figure 3 This is a schematic diagram illustrating the principle of splicing interfaces of the same or different sizes provided in this application; Figure 4 This is a schematic diagram illustrating the principle of adding transition units to the matching interface provided in this application; Figure 5 This is a flowchart illustrating a surface acoustic wave resonator simulation method provided in a certain embodiment of this application; Figure 6 This is a three-dimensional perspective view of a surface acoustic wave resonator provided in a certain embodiment of this application; Figure 7This is a schematic diagram of a horizontal model slice without a piston provided in a certain embodiment of this application; Figure 8 This is a schematic diagram of a horizontal model slice with a piston provided in a certain embodiment of this application; Figure 9 This is a schematic diagram of the process of extracting a mesh of basic units according to a certain embodiment of this application; Figure 10 This is a schematic diagram of a mirror-symmetric sliced ​​mesh structure provided in one embodiment of this application; Figure 11 This is a schematic diagram of four unit block structures required to solve the slice model without piston provided in a certain embodiment of this application; Figure 12 This is a schematic diagram of five unit block structures required to solve the slice model with piston provided in a certain embodiment of this application; Figure 13 This is a schematic diagram of the splicing process when the interfaces are different according to a certain embodiment of this application; Figure 14 This is a schematic diagram of matrix block processing in the matrix elimination process provided in a certain embodiment of this application; Figure 15 This is a schematic diagram of the structure of a surface acoustic wave resonator after adding a gradient damping layer according to a certain embodiment of this application; Figure 16 This is a schematic diagram of the process of obtaining admittance information by solving the spliced ​​matrix according to a certain embodiment of this application; Figure 17 This is a flowchart illustrating a surface acoustic wave resonator simulation method provided in another embodiment of this application; Figure 18 This is a schematic diagram comparing the finite element software analysis results provided in a certain embodiment of this application with the horizontal mesh stitching results of this application; Figure 19 This is a schematic diagram of the structure of a surface acoustic wave resonator simulation system provided in a certain embodiment of this application. Detailed Implementation

[0021] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0022] It should be understood that the step numbers used in the text are for ease of description only and are not intended to limit the order in which the steps are performed.

[0023] It should be understood that the terminology used in this application specification is for the purpose of describing particular embodiments only and is not intended to limit the application. As used in this application specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0024] The terms “comprising” and “including” indicate the presence of the described feature, whole, step, operation, element and / or component, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0025] The term “and / or” refers to any combination of one or more of the associated listed items, as well as all possible combinations, and includes these combinations.

[0026] Please see Figure 5 This application provides a simulation method for a surface acoustic wave resonator in one embodiment. For example... Figure 5 As shown, the simulation method for the surface acoustic wave resonator includes steps S10 to S40. The specific steps are as follows: Step S10: Obtain the transverse slice model of the surface acoustic wave resonator to be simulated, and determine the mirror part and non-mirror part in the transverse slice model.

[0027] In one specific implementation, obtaining the transverse slice model of the surface acoustic wave resonator to be simulated includes: 1.1) Construct a three-dimensional model of the surface acoustic wave resonator based on physical fields; 1.2) Select a frequency point and set the calculation parameters. After dividing the three-dimensional model according to the calculation parameters, the transverse slice model of the surface acoustic wave resonator is obtained.

[0028] See Figure 6 , Figure 6 First, a three-dimensional model of a surface acoustic wave resonator is provided in this embodiment. It should be noted that the model to be simulated in this embodiment is mainly divided into two types: transverse models with and without a piston.

[0029] Specifically, the transverse model with piston can be divided into the following parts: empty, busbar, front airgap, front piston, aperture, back piston, back airgap, and PML.

[0030] The slicing models for PML and empty are consistent. The front airgap and back airgap, and the front piston and back piston are mirror images of each other, symmetrically positioned, and can be reused using a mirror matrix algorithm. Therefore, without a piston, only four basic models (empty, busbar, front airgap, and aperture) need to be calculated; with a piston, five models (empty, busbar, front airgap, front piston, and aperture) need to be calculated. For ease of description, the slicing method without a piston is usually called the four-slice slicing method, and the slicing method with a piston is called the five-slice slicing method. The slicing structures for the four-slice slicing method (without a piston) and the five-slice slicing method (with a piston) are illustrated below. Figure 7 , 8 As shown.

[0031] Step S20: Extract preset layer meshes from the mirror part and the non-mirror part respectively to obtain mirror units and non-mirror units.

[0032] like Figure 9 As shown, in one specific implementation, a layer of mesh is extracted from the mirror part and the non-mirror part respectively to obtain mirror cells and non-mirror cells with a layer of mesh structure.

[0033] It should be noted that the reason for extracting one layer of mesh here is to simplify the operation by eliminating the need for matrix elimination during extraction.

[0034] Step S30: For non-mirror elements, assemble the mesh of the non-mirror elements using the finite element method to obtain the system matrix of the finite element, which is used as the first matrix; sort the first matrix and apply potential constraints and periodic conditions to obtain the second matrix.

[0035] In this step, after extracting one layer of mesh, the region is analyzed using FEM (Finite Element Method). The stiffness matrix and mass matrix of the smallest mesh region can be derived, which satisfy the following basic finite element relationships:

[0036]

[0037] Where [A] represents the system matrix of the finite element method, and K is the stiffness matrix of the finite element method. Let ω be the angular frequency, M be the mass matrix, x be the degree of freedom vector, and F be the processed load vector, which is related to the applied stress and constraint conditions.

[0038] It should be noted that [A] represents the system matrix of the finite element method, which is the first matrix mentioned in step S30. This matrix represents the basis for solving the finite element method at a certain frequency, and the first step in solving the finite element method is to assemble the system matrix based on the mesh.

[0039] Specifically, the system matrix is ​​related to the shape of the domain, the field equations governing the domain, node selection, and mesh; that is, changing or applying boundary conditions does not change the system matrix. The degree-of-freedom vector x contains three displacement components (x, y, z) and one potential component (V) from solid mechanics. The matrix language of the finite element method describes it as follows:

[0040] in, Let be the degrees of freedom of the i-th node. , ... These are the components of the load vector. arrive It is a block matrix of the system matrix.

[0041] In step S30, after obtaining the first matrix, the first matrix is ​​sorted, and potential constraints and periodic conditions are applied to obtain the second matrix.

[0042] Specifically, the matrix is ​​sorted, with the front degrees of freedom placed at the beginning and the back degrees of freedom placed at the end; when applying potential constraints, the degrees of freedom imposed by the potential are combined; when applying periodic conditions on both sides, the same degrees of freedom are added together. The specific processing steps are as follows: 1) Handling periodic conditions:

[0043] in, , , , , , In order, they are: left degree of freedom vector, right degree of freedom vector, internal degree of freedom vector, load vector corresponding to left degree of freedom, load vector corresponding to right degree of freedom, and load vector corresponding to internal degree of freedom.

[0044] exist Under these conditions, combining the first two degrees of freedom yields:

[0045] 2) Handling of potential terminals: Similarly, by adding and merging lattice points with the same potential and placing them at the end of the matrix, the final matrix is:

[0046] in, arrive It is the block matrix after the system matrix transformation. , , , In order: front degree of freedom vector, rear degree of freedom vector, potential degree of freedom, grounding degree of freedom; , All of these are the charge components accumulated on the electrodes.

[0047] Therefore, through the above processing, matrix elimination is not required to obtain the B matrix of the basic unit, which is the second matrix mentioned in step S30.

[0048] Step S40: For the mirror unit, perform symmetric processing on the second matrix to obtain the third matrix.

[0049] For mirrored units, the following algorithm is used in this step. Please refer to [link / reference]. Figure 10 ,like Figure 10 The symmetric unit shown is symmetric in the x-direction. Extract the matrix of the front airgap and divide it into vertical ( l ) and horizontal ( t ) ,get:

[0050] in, , , , In order: left horizontal degree of freedom vector, left vertical degree of freedom vector, right horizontal potential degree of freedom vector, right vertical potential degree of freedom vector; , , , The components are in the following order: load vector components corresponding to the left lateral degree of freedom, load vector components corresponding to the left longitudinal degree of freedom, load vector components corresponding to the right lateral degree of freedom, and load vector components corresponding to the right longitudinal degree of freedom.

[0051] The symmetric matrix is:

[0052] in, , , , , , , , The vectors represent, in sequence, the left lateral degree of freedom vector, the left longitudinal degree of freedom vector, the right lateral potential degree of freedom vector, the right longitudinal potential degree of freedom vector, the load vector component corresponding to the left lateral degree of freedom, the load vector component corresponding to the left longitudinal degree of freedom, and the load vector component corresponding to the right lateral degree of freedom.

[0053] Therefore, the third matrix can be obtained through the above steps. For the model without piston, the cell block that needs to be solved by FEM is... Figure 11 The four types shown, for models with pistons, require the following element blocks to be solved by FEM: Figure 12 The five types shown.

[0054] Step S50: Cascade the second and third matrices to obtain the simulation model of the transverse slice model of the surface acoustic wave resonator.

[0055] Understandably, in steps S10-S40 above, the matrices of mirror and non-mirror elements (basic elements) in the model have already been solved. The main difference between the model without and with a mirror element is the type of element blocks solved by the FEM, namely four and five types respectively. Once the smallest element block is determined, this step involves concatenating these element block matrices.

[0056] In the aforementioned existing cascading methods, the contact surfaces must be of the same size during the splicing process; that is, complete splicing is required, and incomplete splicing is not allowed. However, in actual splicing, there are often cases where the contact surfaces are different. Therefore, in this step, by improving the conventional cascading algorithm, cascading can be performed regardless of whether the contact surfaces are the same or different sizes, thereby avoiding the limitations of existing methods.

[0057] In one specific embodiment, step S50 involves cascading the second and third matrices to obtain a simulation model of the transverse slice model of the surface acoustic wave resonator, including: 5.1) Determine the size of the two cascaded surfaces to be cascaded; 5.2) When two cascaded surfaces are the same size, perform regular cascading operations, including matrix expansion, matrix concatenation, and matrix elimination; 5.3) When the two cascaded surfaces are of different sizes, the smaller cascaded surface is given additional degree-of-freedom constraints. The degree-of-freedom of the larger cascaded surface is matched with that of the smaller cascaded surface. After eliminating the redundant degree-of-freedom, the conventional cascaded operation is performed.

[0058] Please see Figure 13 , Figure 13 A schematic diagram illustrating the principle of cascading methods for cascaded surfaces of different sizes is provided. In one exemplary embodiment, such as... Figure 13 As shown, step 5.3) further includes: 5.31) Identify larger and smaller cascaded surfaces; cascaded surfaces are also known as... Figure 13 The interface described in the text; 5.32) Identify the constraints of the larger cascaded surfaces (potential constraints in this example), and add the matrix elements of the corresponding positions of the smaller cascaded surfaces to the same constraints according to the node position index; 5.33) Traverse the matrix elements of the smaller cascaded surfaces, match the degrees of freedom of the larger cascaded surfaces at the corresponding node positions based on the node position index, and eliminate the redundant degrees of freedom of the larger cascaded surfaces after matching them one by one.

[0059] To aid understanding, step 5.3) will be described below using mathematical language (matrix operations): Step 1: Based on the size of the interface, divide it into larger and smaller interfaces. In this example, the larger interface is the rear side of the front block, and the front block matrix is:

[0060] in, arrive The submatrix representing the front block B matrix, , , These represent the degrees of freedom of the front surface of the front block matrix, the degrees of freedom of the rear surface of the front block matrix, and the undetermined degrees of freedom of the target of the front block matrix. , All represent the degree of freedom components of electric potential. , All of these are the charge components accumulated on the electrodes.

[0061] The smaller interface is the front side of the rear side block, and the rear side block matrix is:

[0062] in, arrive The submatrix representing the back side block B matrix, , , These represent the degrees of freedom of the front surface of the rear block matrix, the degrees of freedom of the rear surface of the rear block matrix, and the undetermined degrees of freedom of the target rear block matrix, respectively. , All represent the degree of freedom components of electric potential. , All of these are the charge components accumulated on the electrodes.

[0063] Step 2: Identify the constraints of larger interfaces. Figure 13The circled portion of the smaller interface is constrained by a 1V potential. Therefore, the constrained portions in the matrix are also located on the front side using the degree-of-freedom-coordinate index. After reordering the front sides of the rear block and selecting the degrees of freedom that need additional constraints, the matrix is:

[0064] in, … The equal components represent the block submatrices of the processed back block B matrix. The equal components are the matrix components corresponding to the supplementary constraint degrees of freedom. The degrees of freedom of the front surface of the processed rear side block matrix, The amount of charge accumulated on the electrode corresponding to the degree of freedom of the rear block to which the potential constraint is to be applied; The degrees of freedom of the lattice points that require constraints.

[0065] We categorize these according to constraints, sum the matrix rows and columns, and combine the degrees of freedom into voltage values, resulting in the following matrix:

[0066] Among them, the subscript " "This represents the m-th processing step." , This represents the cumulative charge component on the treated electrode.

[0067] Step 3: Eliminating redundant degrees of freedom for larger surfaces. First, filter the locations of redundant degrees of freedom, locate them in the matrix, and then swap rows and columns until the last row and column, resulting in:

[0068] in, The equal components represent the system matrix components corresponding to the redundant degrees of freedom. This represents the redundant degree-of-freedom vector. The redundant parts are then eliminated using an elimination algorithm, specifically as follows: For example, a matrix It can be written as: From expression ①, we can obtain Substituting into ②, we get That's how it's eliminated. ; Divide the matrix into blocks as follows, and then perform the elimination process described above to eliminate the variables. The block structure is as follows: Figure 14 As shown.

[0069] Specifically, the elimination process includes the following steps: 1) The processed front matrix is ​​obtained as follows:

[0070] 2) Expand the front and back matrices. The expanded matrices are as follows:

[0071]

[0072] The sum is:

[0073] Then, the eliminated degrees of freedom should be placed in the last row and column, as follows:

[0074] Finally, using the elimination algorithm described above, the matrix after elimination is:

[0075] In summary, this operation completes the splicing of two unit layers. By following this process step by step, a simulation of a transverse slice model of a surface acoustic wave resonator can be completed.

[0076] In a preferred embodiment, a "gradient damping layer" is added to absorb sound waves leaking from the boundary. The damping layer consists of 15-20 layers of grid cells, and its equation is as follows:

[0077] The values ​​of Q in the damping layer, from the inside to the outside, are a monotonically non-increasing sequence. A typical Q array is [200, 150, 100, 50, 20, 10, 10, 10, 10, 10, 10, 10]. The damping layer is synthesized in the same way as above and can absorb sound waves. A schematic diagram of the structure of the transverse slice model of the surface acoustic wave resonator with the addition of the "gradually varying damping layer" is shown below. Figure 15 As shown In one embodiment, after performing the conventional cascading operation, the final admittance and degrees of freedom of the matrix are calculated to optimize the initial transverse slice model.

[0078] In this embodiment, the admittance and other information can be obtained by solving the matrix. The admittance solving process is as follows: Figure 16 As shown.

[0079] Furthermore, the degrees of freedom are solved:

[0080] Seek Extract from That's it. After determining the degrees of freedom, the initial design can be further adjusted to achieve optimization iteration and loop.

[0081] In summary, the surface acoustic wave (SAW) resonator simulation method provided in this application, during the simulation calculation of the transverse model, utilizes an improved cascade algorithm that can be applied to cases where the splicing surfaces are inconsistent, reducing the required finite element simulation units. Applying the improved algorithm and matrix mirroring algorithm, only finite element simulation of 4 or 5 basic element slices is needed, combined with matrix operations, to simulate the response of the entire SAW device, significantly accelerating the simulation speed of the transverse slice model. By employing a basic element extraction method, the extracted minimum element contains only the splicing surface degrees of freedom, eliminating the need for subsequent elimination and greatly reducing the computational load. Furthermore, this method can accurately simulate the admittance response of a SAW resonator and the subsequent data post-processing process, resulting in more ideal simulation effects.

[0082] See Figure 17 In one exemplary embodiment, the complete process of the surface acoustic wave resonator simulation method is also provided. Figure 17 As shown, firstly, a complete surface acoustic wave resonator model is established by selecting the physical field, setting the calculation parameters by selecting the frequency point, and dividing the model into transverse slices. Then, finite element simulation is performed on the basic elements (non-mirror elements) to derive the system matrix, and B-matrix symmetry processing is performed on the symmetrical elements (mirror elements). Next, the cascading operation begins. First, the sizes of the two cascaded surfaces are determined. If the two cascaded surfaces are the same size, the conventional cascading process is executed, including matrix expansion, addition, and elimination. If the two cascaded surfaces are not the same size, the smaller and larger cascaded surfaces are identified. The smaller cascaded surface is given additional constraints on its degrees of freedom, and then the degrees of freedom of the larger cascaded surface are matched with those of the smaller cascaded surface, eliminating redundant degrees of freedom. Then, the conventional cascading operation is executed. After cascading is completed, the final admittance and degrees of freedom can be calculated to optimize the sliced ​​model.

[0083] For example, in a practical application, if the admittance response of a resonator needs to be solved, its electrodes are aluminum electrodes, and the substrate is a heterogeneous integrated lithium tantalate-silicon carbide structure. The wavelength is 1.4 μm, the duty cycle is 0.5, the electrode thickness is 120 nm, the lithium tantalate thickness is 400 nm, the substrate simulation thickness is 4.2 μm, the aperture length is 20 wavelengths, the air gap is 2 wavelengths, the busbar is 2.5 wavelengths, and the blank area is 2 wavelengths, with a gradually increasing damping added on top of this. The simulation results are compared with the calculation results of the method in this patent. Figure 18 As shown, by Figure 18As can be seen, the frequencies of the two are very close. The simulation equipment configuration can be: CPU i9-12900KF, graphics card RTX3050, and memory 3600MHz DDR4 16GB×2 (without overclocking). Under the premise that the two achieve almost identical simulation results, the algorithm provided in this application consumes only 1 / 5 of the time required for finite element software analysis. Therefore, this application can significantly accelerate the simulation speed of surface acoustic wave resonators.

[0084] See Figure 19 In one embodiment of this application, a surface acoustic wave resonator simulation system is also provided, comprising: Model building module 01 is used to obtain the transverse slice model of the surface acoustic wave resonator to be simulated, and to determine the mirror part and non-mirror part in the transverse slice model; The cell partitioning module 02 is used to extract preset layer meshes from the mirror part and the non-mirror part respectively to obtain mirror cells and non-mirror cells; The non-mirror element processing module 03 is used to assemble the mesh of the non-mirror element using the finite element method to obtain the system matrix of the finite element, which is used as the first matrix; and to sort the first matrix and apply potential constraints and periodic conditions to obtain the second matrix. The mirror unit processing module 04 is used to perform symmetric processing on the second matrix for the mirror unit to obtain the third matrix; Simulation module 05 is used to cascade the second and third matrices to obtain a simulation model of the transverse slice model of the surface acoustic wave resonator.

[0085] In a preferred embodiment, simulation module 05 is further used for: Determine the size of the two cascaded surfaces to be cascaded; When two cascaded surfaces are the same size, perform regular cascade operations, including matrix expansion, matrix concatenation, and matrix elimination. When the two cascaded surfaces are of different sizes, the smaller cascaded surface is given additional degree-of-freedom constraints. The degrees of freedom of the larger cascaded surface are matched with those of the smaller cascaded surface. After eliminating the redundant degrees of freedom, the conventional cascaded operation is performed.

[0086] In a preferred embodiment, the surface acoustic wave resonator simulation system further includes an optimization design module for: The final admittance and degrees of freedom of the matrix are calculated to optimize the initial transverse slice model.

[0087] In a preferred embodiment, the unit division module 02 is further configured to: Extract one layer of mesh from each of the mirrored and non-mirrored parts to obtain mirrored and non-mirrored units with a single mesh structure.

[0088] In a preferred embodiment, the model building module 01 is further configured to: A three-dimensional model of a surface acoustic wave resonator is constructed based on physical fields; After selecting a frequency point and setting the calculation parameters, the three-dimensional model is divided according to the calculation parameters to obtain the transverse slice model of the surface acoustic wave resonator.

[0089] It is understood that the above-described surface acoustic wave resonator simulation system can implement the surface acoustic wave resonator simulation method of the above-described method embodiments. The options in the above method embodiments are also applicable to this embodiment, and will not be detailed here. The remaining content of this application's embodiments can be referred to the content of the above method embodiments, and will not be repeated in this embodiment.

[0090] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative. For instance, the division of units is only a logical functional division, and in practical applications, there may be other division methods. For example, multiple units or page components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual couplings, direct couplings, or communication connections may be through some interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.

[0091] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0092] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0093] The integrated units implemented as software functional units described above can be stored in a computer-readable storage medium. These software functional units, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0094] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and not to limit them; although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A simulation method for surface acoustic wave resonators, characterized in that, include: Obtain the transverse slice model of the surface acoustic wave resonator to be simulated, and determine the mirror part and non-mirror part in the transverse slice model; Extract the preset layer mesh from the mirror part and the non-mirror part respectively to obtain mirror cells and non-mirror cells; For non-mirror elements, the mesh of the non-mirror elements is assembled using the finite element method to obtain the system matrix of the finite element, which is used as the first matrix; The first matrix is ​​sorted, and potential constraints and periodic conditions are applied to obtain the second matrix. For the mirror element, the second matrix is ​​symmetrically processed to obtain the third matrix; By cascading the second and third matrices, a simulation model of the transverse slice model of the surface acoustic wave resonator is obtained. The concatenation of the second and third matrices yields a simulation model of the transverse slice model of the surface acoustic wave resonator, including: Determine the size of the two cascaded surfaces to be cascaded; When two cascaded surfaces are the same size, perform regular cascade operations, including matrix expansion, matrix concatenation, and matrix elimination. When the two cascaded surfaces are of different sizes, the smaller cascaded surface is given additional degree-of-freedom constraints, the degree-of-freedom of the larger cascaded surface is matched with that of the smaller cascaded surface, and the redundant degree-of-freedom is eliminated before the conventional cascaded operation is performed. The step of extracting preset layer meshes from the mirrored portion and the non-mirrored portion to obtain mirrored cells and non-mirrored cells includes: Extract one layer of mesh from each of the mirrored and non-mirrored parts to obtain mirrored and non-mirrored units with a single mesh structure.

2. The surface acoustic wave resonator simulation method according to claim 1, characterized in that, Following the execution of the conventional cascading operation, the following is also included: The final admittance and target degrees of freedom of the matrix are calculated, and the two-dimensional Fourier transform of the grid displacements is calculated to optimize the initial transverse slice model.

3. The surface acoustic wave resonator simulation method according to claim 1, characterized in that, The process of obtaining the transverse slice model of the surface acoustic wave resonator to be simulated includes: A three-dimensional model of a surface acoustic wave resonator is constructed based on physical fields; After selecting a frequency point and setting the calculation parameters, the three-dimensional model is divided according to the calculation parameters to obtain the transverse slice model of the surface acoustic wave resonator.

4. A simulation system for surface acoustic wave resonators, characterized in that, include: The model building module is used to obtain the transverse slice model of the surface acoustic wave resonator to be simulated, and to determine the mirror part and non-mirror part in the transverse slice model; The cell partitioning module is used to extract preset layer meshes from the mirror part and the non-mirror part respectively to obtain mirror cells and non-mirror cells; The non-mirror element processing module is used to assemble the mesh of non-mirror elements using the finite element method to obtain the system matrix of the finite element, which is used as the first matrix. The first matrix is ​​sorted, and potential constraints and periodic conditions are applied to obtain the second matrix. The mirror unit processing module is used to perform symmetric processing on the second matrix for the mirror unit to obtain the third matrix; The simulation module is used to cascade the second and third matrices to obtain a simulation model of the transverse slice model of the surface acoustic wave resonator. The simulation module is also used for: Determine the size of the two cascaded surfaces to be cascaded; When two cascaded surfaces are the same size, perform regular cascade operations, including matrix expansion, matrix concatenation, and matrix elimination. When the two cascaded surfaces are of different sizes, the smaller cascaded surface is given additional degree-of-freedom constraints, the degree-of-freedom of the larger cascaded surface is matched with that of the smaller cascaded surface, and the redundant degree-of-freedom is eliminated before the conventional cascaded operation is performed. The unit partitioning module is also used for: Extract one layer of mesh from each of the mirrored and non-mirrored parts to obtain mirrored and non-mirrored units with a single mesh structure.

5. The surface acoustic wave resonator simulation system according to claim 4, characterized in that, It also includes an optimization design module for: The final admittance and target degrees of freedom of the matrix are calculated, and the two-dimensional Fourier transform of the grid displacements is calculated to optimize the initial transverse slice model.

6. The surface acoustic wave resonator simulation system according to claim 4, characterized in that, The model building module is also used for: A three-dimensional model of a surface acoustic wave resonator is constructed based on physical fields; After selecting a frequency point and setting the calculation parameters, the three-dimensional model is divided according to the calculation parameters to obtain the transverse slice model of the surface acoustic wave resonator.

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