Method and System for Evaluating Transmission Angle of Lithium Niobate-based Piezoelectric Ultrasonic Transducer

Abstract

The present invention relates to the technical field of electronic materials and devices, and specifically relates to a method and system for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate. The method includes: obtaining a physical parameter matrix of a target cut-type lithium niobate crystal in a standard coordinate system; performing a rotation transformation on the physical parameter matrix according to a preset rotation axis and different transmission angles; extracting a first transmission angle with the aim of maximizing the target piezoelectric matrix component according to the rotated physical parameter matrix; extracting a second transmission angle with the aim of maximizing the electromechanical coupling coefficient according to the rotated physical parameter matrix; constructing a transducer simulation model, and simulating and extracting an optimal transmission angle according to the first transmission angle and the second transmission angle. The purpose is to optimize the sensitivity and bandwidth of the piezoelectric ultrasonic transducer prepared from lithium niobate.

Description

Technical Field

[0001] The present invention relates to the technical field of electronic materials and devices, and particularly to a method and system for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate. Background Art

[0002] An ultrasonic transducer is a key component of an ultrasonic system, responsible for the conversion between electrical energy and mechanical energy. Traditional ultrasonic transducers are mainly produced using piezoelectric materials through a series of complex manufacturing processes, which result in high costs and low production efficiency. To address these issues, microelectromechanical systems (MEMS) technology has been introduced to fabricate miniaturized and integrated ultrasonic transducers, namely microelectromechanical ultrasonic transducers (MUTS), which include two types: capacitive ultrasonic transducers (CMUT) and piezoelectric ultrasonic transducers (PMUT); among them, PMUT has been widely used due to its lack of need for a bias voltage, high sensitivity, and reliability.

[0003] In recent years, lithium niobate (LiNbO3, LN) has received extensive attention as a crystal material with a strong piezoelectric effect; by using the ion implantation and stripping method to prepare LN single crystal thin films, not only the excellent properties of LN are retained, but also outstanding performance is shown in terms of thickness control, surface flatness, etc., which provides new possibilities for the development of high-performance PMUT devices; compared with traditional piezoelectric materials such as aluminum nitride (AlN) and lead zirconate titanate (PZT), LN has higher piezoelectric coefficients and dielectric constants, which means stronger electromechanical coupling ability; at the same time, although the piezoelectric coefficient of LN is lower than that of PZT, its much lower dielectric loss enables PMUT based on LN to achieve lower energy consumption while maintaining a high signal-to-noise ratio. In addition, LN materials also have excellent biocompatibility and process compatibility, especially single crystal LN in a specific cutting direction can provide a very high electromechanical coupling coefficient, which is crucial for improving the working efficiency of PMUT.

[0004] However, there are deficiencies in the existing technology regarding how to fully utilize the unique properties of LN single crystal materials to optimize the performance of PMUT, and there is a lack of analysis methods for the response characteristics of PMUT under different working conditions, resulting in deficiencies in how to effectively adjust the relationship between LN material parameters and PMUT performance indicators under different working conditions, thereby limiting the sensitivity and bandwidth of PMUT devices, especially for situations that require high-resolution imaging or precise detection tasks. Summary of the Invention

[0005] In order to optimize the sensitivity and bandwidth of piezoelectric ultrasonic transducers prepared from lithium niobate, the purpose of the present invention is to provide a method and system for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate, and the specific technical solutions adopted are as follows:

[0006] The technical solution of the first aspect of the present invention provides a method for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate, and the method includes:

[0007] Obtain the physical parameter matrix of the target cut lithium niobate crystal in the standard coordinate system;

[0008] Perform rotation transformation on the physical parameter matrix according to the preset rotation axis and different transmission angles;

[0009] Extract the first transmission angle with the goal of maximizing the target piezoelectric matrix component according to the physically parameter matrix after rotation transformation;

[0010] Extract the second transmission angle with the goal of maximizing the electromechanical coupling coefficient according to the physically parameter matrix after rotation transformation;

[0011] Construct a transducer simulation model, and simulate and extract the optimal transmission angle according to the first transmission angle and the second transmission angle.

[0012] Further, obtaining the physical parameter matrix of the target cut lithium niobate crystal in the standard coordinate system includes:

[0013] Obtain the piezoelectric constant matrix, dielectric constant matrix and elastic constant matrix of the target cut lithium niobate crystal in the standard coordinate system.

[0014] Further, performing rotation transformation on the physical parameter matrix according to the preset rotation axis and different transmission angles includes:

[0015] Use the Bond matrix method to perform rotation transformation on the piezoelectric constant matrix, dielectric constant matrix and elastic constant matrix respectively.

[0016] Further, using the Bond matrix method to perform rotation transformation on the piezoelectric constant matrix, dielectric constant matrix and elastic constant matrix respectively includes:

[0017] Define the orthogonal transformation matrix and stress tensor transformation matrix according to the preset rotation axis and different transmission angles;

[0018] Use the orthogonal transformation matrix to perform rotation transformation on the dielectric constant matrix to obtain the rotated dielectric constant matrix;

[0019] Use the stress tensor transformation matrix to perform rotation transformation on the piezoelectric constant matrix and the elastic constant matrix respectively to obtain the rotated piezoelectric constant matrix and elastic constant matrix.

[0020] Further, extracting the first transmission angle with the goal of maximizing the target piezoelectric matrix component according to the physically parameter matrix after rotation transformation includes:

[0021] Select the transmission angle corresponding to the maximum value of the target piezoelectric matrix component from the rotated piezoelectric constant matrix as the first transmission angle.

[0022] Further, extracting the second transmission angle based on the physically parameter matrix after rotation transformation with the goal of maximizing the electromechanical coupling coefficient includes:

[0023] Calculating the electromechanical coupling coefficients at different transmission angles according to the physically parameter matrix after rotation transformation at different transmission angles;

[0024] Extracting the second transmission angle according to the variation relationship between the electromechanical coupling coefficient and the transmission angle.

[0025] Further, the expression of the electromechanical coupling coefficient is:

[0026]

[0027] In the formula, represents the electromechanical coupling coefficient; represents the piezoelectric constant after rotation transformation; ε ij represents the permittivity after rotation transformation; c ij the elastic constant after rotation transformation; i, j represent the row and column indices in the matrix.

[0028] Further, constructing a transducer simulation model and simulating and extracting the optimal transmission angle according to the first transmission angle and the second transmission angle includes:

[0029] Constructing a finite element simulation model of the transducer;

[0030] Selecting a transmission angle constant from the closed interval range of the first transmission angle and the second transmission angle, extracting the piezoelectric constant, permittivity and elastic constant at different transmission angle constants and inputting them into the finite element simulation model, and outputting the amplitude response result;

[0031] Extracting the optimal transmission angle according to the amplitude response result.

[0032] The technical solution of the second aspect of the present invention provides a transmission angle evaluation system for a piezoelectric ultrasonic transducer based on lithium niobate, and the system includes:

[0033] A physical parameter acquisition module configured to acquire the physical parameter matrix in the standard coordinate system of a target cut-type lithium niobate crystal;

[0034] A rotation transformation module configured to perform rotation transformation on the physical parameter matrix according to a preset rotation axis and different transmission angles;

[0035] A first transmission angle extraction module configured to extract the first transmission angle with the goal of maximizing the target piezoelectric matrix component according to the physically parameter matrix after rotation transformation;

[0036] A second transmission angle extraction module configured to extract the second transmission angle with the goal of maximizing the electromechanical coupling coefficient according to the physically parameter matrix after rotation transformation;

[0037] The optimal transmission angle extraction module is configured to construct a transducer simulation model and simulate and extract the optimal transmission angle according to the first transmission angle and the second transmission angle.

[0038] The present invention has the following beneficial effects:

[0039] The method and system for evaluating the transmission angle of a lithium niobate-based piezoelectric ultrasonic transducer provided by the present invention perform a rotation transformation on the physical parameter matrix of the target cut-type lithium niobate crystal. According to the rotated physical parameter matrix, the first transmission angle is extracted with the goal of maximizing the target piezoelectric matrix component, and the second transmission angle is extracted with the goal of maximizing the electromechanical coupling coefficient. Furthermore, the optimal transmission angle of the lithium niobate piezoelectric ultrasonic transducer is determined through simulation. By fabricating the lithium niobate piezoelectric ultrasonic transducer within the closed interval of the first transmission angle and the second transmission angle, a lithium niobate piezoelectric ultrasonic transducer with large bandwidth and high sensitivity under the target cut type can be fabricated, thereby providing more efficient and accurate ultrasonic detection and imaging capabilities. Description of the Drawings

[0040] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0041] Figure 1 It is a flowchart of the method for evaluating the transmission angle of a lithium niobate-based piezoelectric ultrasonic transducer provided by an embodiment of the present invention;

[0042] Figure 2 It is a schematic diagram of the linear relationship between the piezoelectric matrix component, the electromechanical coupling coefficient and the transmission provided by an embodiment of the present invention;

[0043] Figure 3 It is a schematic diagram of the signal waveform of the LN PMUT provided by an embodiment of the present invention;

[0044] Figure 4 It is a schematic diagram of the bandwidth of the LN PMUT provided by an embodiment of the present invention;

[0045] Figure 5 It is a schematic diagram of the structure of the system for evaluating the transmission angle of a lithium niobate-based piezoelectric ultrasonic transducer provided by an embodiment of the present invention;

[0046] Figure 6 It is a schematic diagram of the structure of the LN PMUT provided by an embodiment of the present invention;

[0047] Icons: 101 - Metal electrode, 102 - Lithium niobate thin film, 103 - Silicon dioxide, 104 - Silicon substrate. Detailed implementation manners

[0048] In order to further elaborate on the technical means and effects adopted by the present invention to achieve the intended invention purpose, the following combines the accompanying drawings and preferred embodiments to detail the specific implementation manners, structures, features and effects of the method and system for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. In addition, the specific features, structures or characteristics in one or more embodiments can be combined in any suitable form.

[0049] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the technical field to which the present invention belongs.

[0050] The following specifically describes the specific solution of a method and system for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate provided by the present invention with reference to the accompanying drawings.

[0051] Please refer to Figure 1 , which shows the flowchart of the method for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate provided by an embodiment of the present invention. The technical solution of the first aspect of the present invention provides a method for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate, and the method includes:

[0052] Step S100: Obtain the physical parameter matrix of a lithium niobate crystal of a target cut type in the standard coordinate system; specifically, the common cut types of lithium niobate crystals include X-cut, Y-cut, and Z-cut, and each cut type has different performance advantages in different applications; in this embodiment, the physical parameter matrix of the X-cut type lithium niobate crystal is mainly used; as an anisotropic material, the physical parameter matrices of lithium niobate with different transmission angles have significant differences; therefore, in order to fabricate a piezoelectric ultrasonic transducer with high sensitivity and large bandwidth, it is necessary to maximize the use of the piezoelectric performance and the performance advantages of the electromechanical coupling coefficient of the lithium niobate crystal.

[0053] Step S100 specifically includes:

[0054] Step S110: Obtain the piezoelectric constant matrix, dielectric constant matrix, and elastic constant matrix of a lithium niobate crystal of a target cut type in the standard coordinate system;

[0055] Step S200: Perform a rotation transformation on the physical parameter matrix according to a preset rotation axis and transmission angle; specifically, use the Bond matrix method to perform rotation transformations on the piezoelectric constant matrix, dielectric constant matrix, and elastic constant matrix respectively.

[0056] Step S200 specifically includes:

[0057] Step S210: Define an orthogonal transformation matrix and a stress tensor transformation matrix according to a preset rotation axis and different transmission angles; for example, taking the coordinate transformation matrix when rotating by an angle θ around the x-axis for the physical parameter matrix of an X-cut lithium niobate crystal as an example, the orthogonal transformation matrix can be expressed as:

[0058]

[0059] In the formula, A represents the orthogonal transformation matrix; θ represents the transmission angle, that is, the included angle between the electrode arrangement direction and the x-axis direction of the material; represents the element of the orthogonal transformation matrix;

[0060] The stress tensor transformation matrix M is used to describe the transformation of stress and strain in the rotated coordinate system. For rotation in 3D space, the stress tensor transformation matrix M can be expressed as:

[0061]

[0062] Step S220: Use the orthogonal transformation matrix to perform a rotation transformation on the dielectric constant matrix to obtain the rotated dielectric constant matrix, which can be expressed as:

[0063] [ε`] = [A][ε][A] T

[0064] In the formula, [ε`] represents the rotated dielectric constant matrix; [A] T represents the transpose matrix of the orthogonal transformation matrix;

[0065] Step S230: Use the stress tensor transformation matrix to perform rotation transformations on the piezoelectric constant matrix and the elastic constant matrix respectively to obtain the rotated piezoelectric constant matrix and the elastic constant matrix, which can be expressed as:

[0066] [e`] = [M][e][M] T

[0067] [c`] = [M][c][M] T

[0068] In the formula, [e`] represents the rotated piezoelectric constant matrix; [M] T represents the transpose matrix of the stress tensor transformation matrix; [c`] represents the rotated elastic constant matrix;

[0069] In this embodiment, through the orthogonal transformation matrix and the stress tensor transformation matrix, the physical parameter matrix in the standard coordinate system can be accurately converted to a new coordinate system under different transmission angles, and the physical parameter matrices under different transmission angles reflect the performance differences of the lithium niobate crystal in different directions;

[0070] Step S300: Extract the first transmission angle with the goal of maximizing the target piezoelectric matrix component based on the physically transformed parameter matrix after rotation; specifically, according to Figure 6 the structural schematic diagram of the LN PMUT shown, the target piezoelectric matrix component is preferably e 11 , that is, the component in the first row and first column of the piezoelectric matrix; it should be noted that for different structures, different piezoelectric matrix components can be selected as the optimization goal;

[0071] Step S300 specifically includes:

[0072] Step S310: Select the transmission angle corresponding to the maximum value of the target piezoelectric matrix component from the rotated piezoelectric constant matrix as the first transmission angle; specifically, please refer to Figure 2 shown, the value of e 11 is the largest when the transmission angle is 29°, so 29° can be selected as the first transmission angle; it should be noted that the amplitude response of the LN PMUT is related to e 11 , so selecting 29° as the first transmission angle represents the optimal amplitude response;

[0073] Step S320: Extract the second transmission angle with the goal of maximizing the electromechanical coupling coefficient based on the physically transformed parameter matrix after rotation;

[0074] Step S320 specifically includes:

[0075] Step S321: Calculate the electromechanical coupling coefficients at different transmission angles based on the physically transformed parameter matrix after rotation at different transmission angles; the expression of the electromechanical coupling coefficient is:

[0076]

[0077] In the formula, represents the electromechanical coupling coefficient; represents the piezoelectric constant after rotation; ε` ij represents the dielectric constant after rotation; c` ij the elastic constant after rotation; i, j represent the row and column indices in the matrix;

[0078] Step S322: Extract the second transmission angle according to the variation relationship between the electromechanical coupling coefficient and the transmission angle; specifically, taking the electromechanical coupling coefficient as an example, which is used to describe the coupling between the electric field and mechanical strain in the X-axis direction, can be expressed as:

[0079]

[0080] Please refer to Figure 2 shown, the electromechanical coupling coefficients at different transmission angles is plotted as a curve, where the horizontal axis is the transmission angle. It can be understood that according to the extreme value of, the transmission angle of 30° can be extracted as the second transmission angle;

[0081] Step S400: Construct a transducer simulation model, and simulate and extract the optimal transmission angle according to the first transmission angle and the second transmission angle;

[0082] Step S400 specifically includes:

[0083] Step S410: Construct a finite element simulation model of the transducer; specifically, according to the actual design parameters, establish a geometric model of the X-cut LNPMUT. Please refer to Figure 6 as shown, which shows an embodiment of the basic structure of a piezoelectric ultrasonic transducer based on lithium niobate. Its longitudinal structure is, in sequence, a metal electrode 101, a lithium niobate thin film 102, silicon dioxide 103, and a silicon substrate 104. The dotted line represents a cavity. By applying an alternating voltage to the metal electrode, in the voltage direction, the piezoelectric effect causes the thin film to expand and contract regularly, generating vibrations;

[0084] Step S420: Select a transmission angle constant from the closed interval of the first transmission angle and the second transmission angle, extract the piezoelectric constant, dielectric constant, and elastic constant under different transmission angle constants and input them into the finite element simulation model, and output the amplitude response result; specifically, preferably select the mean value of the first transmission angle and the second transmission angle as the transmission angle constant; it is also possible to select a preset number of transmission angle constants starting from the first transmission angle according to the step size in the closed interval of

the first transmission angle, the second transmission angle

[0085] As a further preferred technical solution, a selection method based on Bayesian optimization is also provided. For example, randomly select 5 transmission angles from the closed interval and perform finite element simulation, and record the amplitude response respectively; use the RBF kernel function to construct a Gaussian process regression model, which can be expressed as:

[0086]

[0087] In the formula, k(θ i , θ j ) represents the similarity between the i-th transmission angle θ i and the j-th transmission angle θ j ; l represents the length scale parameter, which is used to control the smoothness of the kernel function;

[0088] Then, by training a Gaussian process regression model, the predicted mean and predicted variance are obtained. Finally, the expected improvement is used as the acquisition function for iterative optimization. In each iteration, the acquisition function values of all transmission angles within the search interval are calculated; the transmission angle that maximizes the acquisition function value is selected for finite element simulation, and the amplitude response is recorded; the training set is updated and the Gaussian process regression model is retrained; the above process is repeated until the maximum number of iterations (e.g., 20 times) is reached or the amplitude response no longer improves significantly; the transmission angle that maximizes the amplitude response among all simulated transmission angles is selected as the optimal transmission angle; where the expression of the acquisition function is:

[0089]

[0090] In the formula, μ(θ) represents the predicted mean of the transmission angle θ; σ(θ) represents the predicted variance of the transmission angle θ; f* represents the current optimal amplitude response value; Φ represents the cumulative distribution function of the standard normal distribution; σ represents the probability density function of the standard normal distribution; in this embodiment, Bayesian optimization can find the optimal transmission angle with fewer simulation times, saving a large amount of computing resources;

[0091] Preferably, the sound pressure can also be calculated based on the amplitude response result, and the sensitivity simulation data is extracted. The expression is:

[0092]

[0093] In the formula, P represents the sound pressure; d0 represents the amplitude response result, that is, the maximum displacement of the transducer during vibration; f0 represents the center frequency of the transducer; S represents the area of the transducer; z represents the preset propagation distance; ρ represents the medium density; finally, the optimal transmission angle is verified based on the sensitivity simulation data; when the sound pressure is the largest, the PMUT sensitivity is also the highest; after obtaining the optimal transmission angle, the PMUT under the optimal transmission angle can be fabricated; for example, according to this method, a piezoelectric ultrasonic transducer (PMUT) based on X-cut lithium niobate (LN) is designed. Its longitudinal structure is successively a 0.3-μm gold electrode for applying voltage excitation, deposited on the surface of lithium niobate by sputtering or evaporation, etc., a 0.7-μm X-cut lithium niobate thin film as the piezoelectric layer, 2-μm silica used as the insulating layer to prevent short circuits between electrodes, and a 350-μm-thick silicon substrate providing mechanical support; the direction of the electrode forms an angle of 29° with the crystal X-axis direction; and a cavity with a length of 80 μm and a width of 50 μm is opened on the silicon substrate to form a diaphragm; we package the prepared LN PMUT device and test the receiving sensitivity in water, including the prepared transducer, receiving sensor, and signal processing equipment; apply voltage excitation to make the transducer work, and record the signal of the receiving sensor; perform Fourier transform on the received signal to obtain the frequency domain response, so as to determine the bandwidth; please refer to Figure 3 and Figure 4As shown, it records the signal waveform of the LN PMUT and the bandwidth after Fourier transform. It can be understood that the LN PMUT device prepared according to the transmission angle determined by this method has the characteristics of high sensitivity and large bandwidth compared with the traditional method. Therefore, this method can effectively improve the sensitivity and bandwidth of the lithium niobate piezoelectric ultrasonic transducer.

[0094] In summary, the method for evaluating the transmission angle of the lithium niobate-based piezoelectric ultrasonic transducer provided by the present invention performs a rotation transformation on the physical parameter matrix of the target cut-type lithium niobate crystal. According to the rotated physical parameter matrix, the first transmission angle is extracted with the goal of maximizing the target piezoelectric matrix component, and the second transmission angle is extracted with the goal of maximizing the electromechanical coupling coefficient. Then, the optimal transmission angle of the lithium niobate piezoelectric ultrasonic transducer is determined through simulation. By fabricating the lithium niobate piezoelectric ultrasonic transducer within the closed interval of the first transmission angle and the second transmission angle, a lithium niobate piezoelectric ultrasonic transducer with large bandwidth and high sensitivity under the target cut type can be fabricated, thereby providing more efficient and accurate ultrasonic detection and imaging capabilities. This method ensures the scientificity and reliability of the design of the lithium niobate piezoelectric ultrasonic transducer through systematic theoretical calculations, simulation simulations, and experimental verifications, and finally fabricates a piezoelectric ultrasonic transducer with excellent performance, which is suitable for various high-frequency ultrasonic application fields such as medical imaging and non-destructive testing.

[0095] Please refer to Figure 5 , which shows a schematic structural diagram of a system for evaluating the transmission angle of a lithium niobate-based piezoelectric ultrasonic transducer provided by an embodiment of the present invention. The technical solution of the second aspect of the present invention provides a system for evaluating the transmission angle of a lithium niobate-based piezoelectric ultrasonic transducer, and the system includes:

[0096] A physical parameter acquisition module configured to acquire the physical parameter matrix of the target cut-type lithium niobate crystal in the standard coordinate system;

[0097] A rotation transformation module configured to perform a rotation transformation on the physical parameter matrix according to a preset rotation axis and different transmission angles;

[0098] A first transmission angle extraction module configured to extract a first transmission angle with the goal of maximizing the target piezoelectric matrix component according to the rotated physical parameter matrix;

[0099] A second transmission angle extraction module configured to extract a second transmission angle with the goal of maximizing the electromechanical coupling coefficient according to the rotated physical parameter matrix;

[0100] An optimal transmission angle extraction module configured to construct a transducer simulation model and simulate and extract the optimal transmission angle according to the first transmission angle and the second transmission angle.

[0101] It should be noted that the above sequence of embodiments of the present invention is only for description and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require the particular order or sequential order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0102] Each embodiment in this specification is described in a progressive manner. For the same or similar parts among the embodiments, reference can be made to each other. The key point of each embodiment is to illustrate the differences from other embodiments.

Claims

1. A method for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate, characterized in that: The method comprises: Obtain the physical parameter matrix of the target cut lithium niobate crystal in the standard coordinate system; Rotate and transform the physical parameter matrix according to the preset rotation axis and different transmission angles; According to the physical parameter matrix after the rotation transformation, a first transmission angle is extracted with the goal of maximizing the target piezoelectric matrix component; According to the physical parameter matrix after the rotation transformation, the second transmission angle is extracted with the goal of maximizing the electromechanical coupling coefficient; A transducer simulation model is constructed, and the optimal transmission angle is simulated and extracted according to the first transmission angle and the second transmission angle.

2. The method for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate according to claim 1, characterized in that: Obtaining the physical parameter matrix of the target cut lithium niobate crystal in the standard coordinate system includes: Obtain the piezoelectric constant matrix, dielectric constant matrix, and elastic constant matrix of the target cut lithium niobate crystal in the standard coordinate system.

3. The method for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate according to claim 2, characterized in that: The rotation transformation of the physical parameter matrix according to the preset rotation axis and different transmission angles includes: The Bond matrix method is used to rotate the piezoelectric constant matrix, dielectric constant matrix and elastic constant matrix respectively.

4. The method for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate according to claim 3, characterized in that: The Bond matrix method is used to rotate the piezoelectric constant matrix, dielectric constant matrix and elastic constant matrix respectively, including: Define the orthogonal transformation matrix and stress tensor transformation matrix according to the preset rotation axis and different transmission angles; The dielectric constant matrix is ​​rotated by using the orthogonal transformation matrix to obtain the rotated dielectric constant matrix; The piezoelectric constant matrix and the elastic constant matrix are respectively rotated and transformed using the stress tensor transformation matrix to obtain the rotated piezoelectric constant matrix and the elastic constant matrix.

5. The method for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate according to claim 4, characterized in that: According to the physical parameter matrix after the rotation transformation, extracting the first transmission angle with the goal of maximizing the target piezoelectric matrix component includes: The transmission angle corresponding to the maximum value of the target piezoelectric matrix component is selected from the rotated piezoelectric constant matrix as the first transmission angle.

6. The method for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate according to any one of claims 1 to 5, characterized in that: According to the physical parameter matrix after the rotation transformation, the second transmission angle is extracted with the goal of maximizing the electromechanical coupling coefficient, including: According to the physical parameter matrix after rotation transformation at different transmission angles, the electromechanical coupling coefficient at different transmission angles is calculated; The second transmission angle is extracted according to the variation relationship between the electromechanical coupling coefficient and the transmission angle.

7. The method for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate according to claim 6, characterized in that: The expression of electromechanical coupling coefficient is: In the formula, represents the electromechanical coupling coefficient; represents the piezoelectric constant after rotation transformation; ε ij represents the dielectric constant after rotation transformation; c ij The elastic constant after rotation transformation; i and j represent the row and column indices in the matrix.

8. The method for evaluating the transmission angle of a piezoelectric ultrasonic transducer based on lithium niobate according to claim 6, characterized in that: Constructing a transducer simulation model, simulating and extracting the optimal transmission angle according to the first transmission angle and the second transmission angle includes: Construct a finite element simulation model of the transducer; Selecting a transmission angle constant from a closed interval between the first transmission angle and the second transmission angle, extracting the piezoelectric constant, dielectric constant and elastic constant under different transmission angle constants and inputting them into a finite element simulation model, and outputting an amplitude response result; The optimal transmission angle is extracted based on the amplitude response results.

9. A piezoelectric ultrasonic transducer transmission angle evaluation system based on lithium niobate, characterized in that: The system comprises: A physical parameter acquisition module, configured to acquire a physical parameter matrix of a target cut lithium niobate crystal in a standard coordinate system; A rotation transformation module, configured to perform rotation transformation on the physical parameter matrix according to a preset rotation axis and different transmission angles; A first transmission angle extraction module is configured to extract a first transmission angle based on the physical parameter matrix after the rotation transformation with the goal of maximizing the target piezoelectric matrix component; A second transmission angle extraction module is configured to extract a second transmission angle according to the physical parameter matrix after the rotation transformation with the goal of maximizing the electromechanical coupling coefficient; The optimal transmission angle extraction module is configured to construct a transducer simulation model, simulate and extract the optimal transmission angle according to the first transmission angle and the second transmission angle.

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