Method for accurately measuring crystal axis orientation of gallium oxide single crystal

Abstract

The invention discloses a method for accurately measuring crystal axis orientation of gallium oxide single crystal, and relates to the technical field of material science, and the method comprises the following steps: collecting acoustic original data of the gallium oxide single crystal through a quantum entanglement sensor network; carrying out compression reconstruction processing on the acoustic original data, constructing a sound velocity anisotropy tensor, and generating a lattice vibration characteristic spectrum; constructing an enzymatic reaction kinetic model according to the lattice vibration characteristic spectrum, defining an enzymatic differential equation, and calculating a steady-state crystal orientation angle concentration value; mapping the steady-state crystal orientation angle concentration value to a wafer space coordinate, establishing a steady-state crystal orientation angle concentration field distribution matrix by solving a diffusion equation, and converting the steady-state crystal orientation angle concentration field distribution matrix into a crystal axis orientation deviation thermodynamic diagram; through the superconducting sensor network in the quantum entangled state, the spatial resolution and the time resolution are improved, and the dependency of an existing physical characterization method on the flatness and cleanliness of the surface of a sample is overcome.

Description

Technical Field

[0001] This invention relates to the field of materials science and technology, and in particular to a method for accurately determining the crystal axis orientation of gallium oxide single crystals. Background Technology

[0002] In the field of gallium oxide single crystal orientation determination, existing methods mainly rely on physical characterization techniques such as X-ray diffraction, electron backscattering diffraction, or Raman spectroscopy. X-ray diffraction determines crystal axis orientation by analyzing the diffraction pattern of X-rays, its core principle being based on the correspondence between the Bragg equation and the interplanar spacing. Electron backscattering diffraction utilizes the backscattering diffraction pattern generated by the interaction of the electron beam with the crystal surface, combined with pattern recognition algorithms to extract crystal axis information. Raman spectroscopy indirectly derives crystal symmetry and orientation through the frequency shift of phonon vibration modes. Existing methods have been widely applied in materials science for crystal axis orientation analysis, especially in the semiconductor industry, providing key parameter support for wafer dicing and device fabrication.

[0003] Existing methods have two shortcomings. First, there is a contradiction between the spatial and temporal resolution of existing physical characterization methods. Second, existing methods mostly rely on static physical models and do not fully consider the coupling relationship between crystal acoustic anisotropy and lattice dynamics. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides a method for accurately determining the crystal axis orientation of gallium oxide single crystals, solving the problems of low accuracy and poor consistency in crystal axis orientation determination caused by the contradiction of spatial / temporal resolution and insufficient coupling of lattice dynamics in existing physical characterization methods.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] In a first aspect, the present invention provides a method for accurately determining the crystal axis orientation of a gallium oxide single crystal, comprising,

[0008] Acoustic raw data of gallium oxide single crystals were acquired using a quantum entangled sensor network;

[0009] The raw acoustic data is compressed and reconstructed to construct the sound velocity anisotropy tensor and generate a lattice vibration characteristic spectrum.

[0010] Based on the lattice vibration characteristic spectrum, an enzyme-catalyzed reaction kinetic model was constructed, an enzyme-catalyzed differential equation was defined, and the steady-state crystal orientation angle concentration value was calculated.

[0011] The steady-state crystal orientation angle concentration values ​​are mapped to wafer space coordinates. The steady-state crystal orientation angle concentration field distribution matrix is ​​established by solving the diffusion equation. The steady-state crystal orientation angle concentration field distribution matrix is ​​then converted into a thermogram of crystal axis orientation deviation.

[0012] The cutting compensation angle is calculated based on the crystal axis orientation deviation thermogram, and the wafer dicing machine is driven to perform processing compensation according to the cutting compensation angle.

[0013] As a preferred embodiment of the method for accurately determining the crystal axis orientation of gallium oxide single crystal according to the present invention, the specific steps of acquiring the raw acoustic data of gallium oxide single crystal through a quantum entanglement sensor network are as follows:

[0014] A detection area is selected on the surface of a gallium oxide single crystal, and a superconducting quantum bit sensor node is deployed on the surface of the detection area;

[0015] All superconducting qubit sensor nodes are synchronized into a quantum entangled state to form a quantum entangled sensor network;

[0016] Rayleigh waves are generated by exciting gallium oxide single crystals with femtosecond Ti:sapphire lasers, and absolute timestamps corresponding to the instantaneous amplitude values ​​of the Rayleigh waves are captured by quantum entanglement sensor networks.

[0017] Each superconducting quantum bit sensor node is assigned a node position identifier, and each superconducting quantum bit sensor node synchronously measures the amplitude value and phase angle of the quantum state induced by Rayleigh wave;

[0018] The absolute timestamp, node location identifier, quantum state amplitude value, and quantum state phase angle are integrated into the raw acoustic data.

[0019] As a preferred embodiment of the method for accurately determining the crystal axis orientation of gallium oxide single crystals according to the present invention, the specific steps for compressing and reconstructing the raw acoustic data to construct the sound velocity anisotropy tensor are as follows:

[0020] The absolute timestamp and quantum state amplitude value are extracted from the raw acoustic data, and the quantum state amplitude value is normalized.

[0021] The normalized quantum state amplitude values ​​are arranged according to absolute timestamps to generate an amplitude sequence;

[0022] The complete frequency domain acoustic spectrum is reconstructed based on the amplitude sequence using the orthogonal matching pursuit algorithm;

[0023] The sound velocity components are calculated based on the complete frequency domain sound spectrum, and the sound velocity anisotropy tensor is constructed.

[0024] As a preferred embodiment of the method for accurately determining the crystal axis orientation of gallium oxide single crystals according to the present invention, the specific steps for generating the lattice vibration characteristic spectrum are as follows:

[0025] Identify the frequency of maximum amplitude peak in the complete frequency domain acoustic spectrum, and record the characteristic frequency value based on the frequency of maximum amplitude peak;

[0026] Calculation of sound velocity ellipticity based on sound velocity anisotropic tensor;

[0027] A two-dimensional grid spatial coordinate system is created, and the characteristic frequency value, sound velocity ellipticity, and sound velocity component are labeled at the coordinates of each grid node to generate a lattice vibration characteristic spectrum.

[0028] As a preferred embodiment of the method for accurately determining the crystal axis orientation of gallium oxide single crystal as described in this invention, wherein: the construction of an enzyme-catalyzed reaction kinetic model based on the lattice vibration characteristic spectrum and the definition of the enzyme-catalyzed differential equation refers to constructing an enzyme-catalyzed reaction kinetic model based on characteristic frequency values, sound velocity ellipticity, and sound velocity anisotropy tensor, and defining the enzyme-catalyzed differential equation based on the enzyme-catalyzed reaction kinetic model.

[0029] As a preferred embodiment of the method for accurately determining the crystal axis orientation of gallium oxide single crystals according to the present invention, the specific steps for calculating the steady-state crystal orientation angle concentration value are as follows:

[0030] The enzyme-catalyzed differential equation was solved using the fourth-order Runge-Kutta numerical integration method to obtain a numerical sequence of crystal orientation angle concentrations;

[0031] Calculate the rate of change of crystal orientation angle concentration, select effective marker points based on the rate of change of crystal orientation angle concentration, and calculate the steady-state crystal orientation angle concentration value based on the effective marker points.

[0032] As a preferred embodiment of the method for accurately determining the crystal axis orientation of gallium oxide single crystals according to the present invention, the step of establishing a steady-state crystal orientation angle concentration field distribution matrix by solving the diffusion equation and converting the steady-state crystal orientation angle concentration field distribution matrix into a crystal axis orientation deviation thermogram includes the following specific steps:

[0033] The diffusion equation is constructed based on the sound velocity anisotropic tensor. The diffusion equation is transformed into a discrete equation using a five-point difference scheme and combined into a discretized linear equation system.

[0034] The discretized linear equations were solved iteratively using the conjugate gradient method to obtain the steady-state crystal orientation angle concentration field distribution matrix;

[0035] Perform Sobel operator gradient operation on the steady-state crystal orientation angle concentration field distribution matrix to obtain the gradient components;

[0036] The gradient magnitude is calculated based on the gradient components, and the crystal orientation deviation angle is calculated based on the gradient magnitude.

[0037] A thermogram of crystal axis orientation deviation is generated by color mapping based on the crystal orientation deviation angle.

[0038] As a preferred embodiment of the method for accurately determining the crystal axis orientation of gallium oxide single crystal according to the present invention, the specific steps of calculating the cutting compensation angle based on the crystal axis orientation deviation thermogram and driving the wafer dicing machine to perform processing compensation according to the cutting compensation angle are as follows:

[0039] The crystal orientation deviation thermogram is divided into grid blocks, and the arithmetic mean and standard deviation of the crystal orientation deviation angles in each grid block are calculated.

[0040] The cutting compensation angle is calculated based on the arithmetic mean and standard deviation of the crystal orientation deviation angle;

[0041] The cutting compensation angle is converted into a wafer dicing machine rotation axis command and executed.

[0042] In a second aspect, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program, wherein: when the computer program is executed by the processor, it implements any step of a method for accurately determining the crystal axis orientation of a gallium oxide single crystal as described in the first aspect of the present invention.

[0043] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein, when the computer program is executed by a processor, it implements any step of a method for accurately determining the crystal axis orientation of a gallium oxide single crystal as described in the first aspect of the present invention.

[0044] The beneficial effects of this invention are as follows: Through a superconducting sensor network of quantum entangled states, high-precision and low-noise acquisition of acoustic signals from gallium oxide single crystal surfaces is achieved, improving spatial and temporal resolution. This overcomes the dependence of existing physical characterization methods on sample surface flatness and cleanliness, and breaks through the limitations of inefficient point-by-point scanning and insufficient detection accuracy over wide areas. By constructing an enzyme-catalyzed reaction kinetic model, the dynamic changes of crystal orientation angle concentration with time and space can be simulated, overcoming the limitations of existing static physical models, improving the adaptability of crystal axis orientation resolution, compensating for the influence of internal material defects or non-uniformity on crystal orientation angle concentration, reducing measurement errors caused by local anomalies in existing methods, realizing dynamic correlation analysis of crystal acoustic behavior, and solving the defects of existing static models that are sensitive to material defects and have poor consistency. Attached Figure Description

[0045] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1This is a flowchart of a method for accurately determining the crystal axis orientation of gallium oxide single crystals.

[0047] Figure 2 A schematic diagram of the deployment of a quantum entangled sensor network.

[0048] Figure 3 This is a schematic diagram of the characteristic spectrum of lattice vibrations.

[0049] Figure 4 This is a schematic diagram of the thermogram of crystal axis orientation deviation. Detailed Implementation

[0050] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0051] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0052] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0053] Reference Figures 1-4 As an embodiment of the present invention, a method for accurately determining the crystal axis orientation of gallium oxide single crystal is provided, comprising the following steps:

[0054] S1: Acoustic raw data of gallium oxide single crystal is acquired through a quantum entangled sensor network.

[0055] The specific steps are as follows:

[0056] A detection area is selected on the gallium oxide single crystal surface, and the surface of the detection area is cleaned. The detection area is square in shape, and the side length is matched with the measurable area on the gallium oxide single crystal surface. Superconducting quantum bit sensor nodes are deployed, and each superconducting quantum bit sensor node is in direct contact with the gallium oxide single crystal surface.

[0057] The superconducting quantum bit sensor nodes are arranged in a grid array with equal spacing between nodes. All superconducting quantum bit sensor nodes are physically connected by aluminum-based coplanar waveguide connecting cables, and the ends of the aluminum-based coplanar waveguide connecting cables are connected to the radio frequency signal interface of the central control unit.

[0058] The central control unit generates a shared quantum state initialization command, which is transmitted to all superconducting quantum bit sensor nodes through an aluminum-based coplanar waveguide connection cable. All superconducting quantum bit sensor nodes synchronously enter the quantum entangled state, forming a quantum entangled sensor network. The quantum entangled state is a Bell state superposition type, specifically manifested as an equally probable coherent state of ground state zero and ground state one.

[0059] The infrared laser pulse output from the femtosecond Ti:sapphire laser is collimated by a mirror unit; the angle of the mirror is adjusted so that the infrared laser pulse is perpendicular to the center of the gallium oxide single crystal detection area; the beam expander is used to adjust the spot diameter of the infrared laser pulse so that the spot diameter covers the side length of the detection area.

[0060] Infrared laser pulses undergo photon-phonon energy conversion on the surface of gallium oxide single crystal, generating longitudinal mechanical vibration. The mechanical vibration propagates along the

[100] ,

[010] and

[001] crystal directions in the form of stress waves. The propagating stress waves superimpose to form Rayleigh waves, and the amplitude of the Rayleigh waves is uniformly distributed within the detection area of ​​the gallium oxide single crystal. The quantum entanglement sensor network synchronously senses the Rayleigh waves.

[0061] The central control unit calculates the maximum allowable sampling rate in real time based on the intrinsic sparsity factor of gallium oxide single crystal, as expressed by:

[0062] R = μ·S δ-1 ;

[0063] Where R is the maximum allowable sampling rate, μ is the correlation coefficient of the superconducting quantum bit sensor, which is determined by the decoherence time of the superconducting quantum bit and the signal bandwidth, S is the time-domain signal sparsity, which represents the proportion of non-zero amplitude values ​​in the Rayleigh wave main frequency band, and δ is the intrinsic sparsity factor of gallium oxide single crystal.

[0064] All superconducting qubit sensor nodes in the quantum entanglement sensor network use an adaptive frequency scanning strategy to capture Rayleigh waves. Each superconducting qubit sensor node records the instantaneous amplitude value of the Rayleigh wave in the order of reception. The central control unit controls the start and stop of data acquisition of the quantum entanglement sensor network in an event-driven mode, and the acquisition duration is fixed to the length of the complete Rayleigh wave decay period.

[0065] Each superconducting qubit sensor node is assigned a node location identifier; each superconducting qubit sensor node records an absolute timestamp when capturing the instantaneous value of the Rayleigh wave amplitude; each superconducting qubit sensor node synchronously measures the amplitude value of the quantum state induced by the Rayleigh wave, and the quantum state amplitude value records the transition probability of the superconducting qubit ground state energy level; each superconducting qubit sensor node synchronously measures the phase angle of the quantum state, and the quantum state phase angle records the coherent oscillation angle of the superconducting qubit.

[0066] The node position identifier, absolute timestamp, quantum state amplitude value, and quantum state phase angle of a single superconducting quantum bit sensor node are collected as data record tuples. All data record tuples of the superconducting quantum bit sensor nodes are sorted in chronological order. The sorted data record tuples are then encoded into a structured data file to obtain the raw acoustic data.

[0067] It should also be noted that: multi-node synchronous measurement is achieved through a quantum entangled sensor network, eliminating the clock drift error of existing sensors; the compressed sampling constraint condition breaks through the Shannon sampling theorem limit, and high-frequency phonon signals are fully captured at low sampling rates; superconducting qubits work in low-temperature environments to shield electromagnetic interference, and the event-driven acquisition mode avoids lattice thermal noise, improving the signal-to-noise ratio and spatial resolution of gallium oxide single crystal acoustic signals.

[0068] S2: Compress and reconstruct the raw acoustic data to construct the sound velocity anisotropic tensor and generate a lattice vibration characteristic spectrum.

[0069] The specific steps are as follows:

[0070] The quantum state amplitude value, quantum state phase angle, and absolute timestamp recorded by each superconducting quantum bit sensor node are extracted from the raw acoustic data. The quantum state amplitude value is normalized to zero mean and then arranged in ascending order by absolute timestamp to generate a time-aligned amplitude sequence.

[0071] Initialize the discrete cosine transform orthogonal basis as a sparse basis, match the dimension of the discrete cosine transform orthogonal basis with the length of the amplitude sequence, and set the maximum number of iterations threshold for the orthogonal matching pursuit algorithm;

[0072] Using the amplitude sequence as the input signal vector, the inner product value of the amplitude sequence and each atom in the discrete cosine transform orthogonal basis is calculated in each iteration, and the atom with the largest absolute value of the inner product value is selected to be added to the supporting atom set.

[0073] Solve for the least squares approximation solution of the amplitude sequence for the supporting atom set, calculate the approximation residual corresponding to the least squares approximation solution, and use the approximation residual as a new amplitude sequence for the next iteration. After completing all iterations, obtain the sparse representation coefficient set of the amplitude sequence. Linearly superimpose the discrete cosine transform spectra of all atoms according to the sparse representation coefficients, set the frequency points on the frequency axis with the minimum interval required by Rayleigh wave wavelength analysis, and generate a continuous spectrum curve through interpolation operation to form a complete frequency domain acoustic spectrum.

[0074] Search for the frequency position corresponding to the maximum amplitude point in the complete frequency domain acoustic spectrum, and mark the frequency position corresponding to the maximum amplitude point as the Rayleigh wave dominant frequency component; based on the Rayleigh wave dominant frequency component, query the wavelength values ​​of the propagation paths of the

[100] crystal direction,

[010] crystal direction, and

[001] crystal direction, and take the product of the Rayleigh wave dominant frequency component and the wavelength value of the propagation path of the

[100] crystal direction as the sound speed component of the propagation path of the

[100] crystal direction, the product of the Rayleigh wave dominant frequency component and the wavelength value of the propagation path of the

[010] crystal direction as the sound speed component of the propagation path of the

[010] crystal direction, and the product of the Rayleigh wave dominant frequency component and the wavelength value of the propagation path of the

[001] crystal direction as the sound speed component of the propagation path of the

[001] crystal direction.

[0075] Create a third-order diagonal matrix data structure. Fill the sound velocity component of the propagation path of the

[100] crystal direction into the first row and first column of the third-order diagonal matrix. Fill the sound velocity component of the propagation path of the

[010] crystal direction into the second row and second column of the third-order diagonal matrix. Fill the sound velocity component of the propagation path of the

[001] crystal direction into the third row and third column of the third-order diagonal matrix. Keep the off-diagonal elements at zero value to obtain the sound velocity anisotropy tensor.

[0076] The full frequency spectrum is scanned again to determine the location of the maximum amplitude peak frequency point. The frequency value of the maximum amplitude peak frequency point is extracted. The intrinsic vibration frequency range of the gallium oxide single crystal

[010] crystal direction is queried. The coverage percentage of the frequency value of the maximum amplitude peak frequency point and the intrinsic vibration frequency range is calculated. The coverage threshold is set using the percentile method based on the historical coverage percentage. For example, the 95th percentile value of the historical coverage percentage is used as the coverage threshold. When the coverage percentage is not lower than the coverage threshold, the maximum amplitude peak frequency point is marked as the characteristic frequency, and the frequency value of the maximum amplitude peak frequency point is recorded as the characteristic frequency value.

[0077] The ratio of the absolute value of the difference between the sound velocity component of the

[100] crystal direction propagation path and the sound velocity component of the

[001] crystal direction propagation path to the sound velocity component of the

[010] crystal direction propagation path is taken as the sound velocity ellipticity. The theoretical range of the sound velocity ellipticity of gallium oxide single crystal is consulted. When the sound velocity ellipticity is within the theoretical range of the sound velocity ellipticity of gallium oxide single crystal, the sound velocity ellipticity is determined to be valid. When the sound velocity ellipticity is not within the theoretical range of the sound velocity ellipticity of gallium oxide single crystal, the sound velocity ellipticity is remeasured. If the sound velocity ellipticity is still not within the theoretical range of the sound velocity ellipticity of gallium oxide single crystal after three consecutive remeasurements, the detection area is marked as "lattice distortion region".

[0078] A two-dimensional grid spatial coordinate system is created, with the origin of the two-dimensional grid spatial coordinate system coinciding with the geometric center of the gallium oxide single crystal detection area. The X-axis of the two-dimensional grid spatial coordinate system is set to be parallel to the

[100] crystal direction of the gallium oxide single crystal, and the Y-axis is set to be parallel to the

[010] crystal direction of the gallium oxide single crystal. Each grid node coordinate corresponds to the position identifier of a superconducting quantum bit sensor node. The grid node spacing is equal to the physical spacing of the superconducting quantum bit sensor nodes. The characteristic frequency value, sound velocity ellipticity, and sound velocity component are marked at the grid node coordinates to generate a lattice vibration characteristic spectrum.

[0079] It should also be noted that: the orthogonal matching pursuit algorithm reconstructs the complete frequency domain acoustic spectrum by utilizing the sparse characteristics of acoustic signals, thereby reducing data storage requirements; the sound velocity component is calculated based on the Rayleigh wave dominant frequency component and the crystal direction wavelength, accurately quantifying the sound velocity anisotropy of the

[100] ,

[010] , and

[001] crystal directions; the sound velocity ellipticity verification mechanism automatically identifies the lattice distortion region, avoiding invalid data from polluting the lattice vibration feature spectrum.

[0080] S3: Construct an enzyme-catalyzed reaction kinetic model based on the lattice vibration characteristic spectrum, define the enzyme-catalyzed differential equation, and calculate the steady-state crystal orientation angle concentration value.

[0081] The specific steps are as follows:

[0082] The adjustment gain factor was determined by calibration experiments on the mapping relationship between the acoustic ellipticity of gallium oxide single crystal and enzyme concentration. The adjustment gain factor is the slope coefficient of the linear regression equation between the natural logarithm of the acoustic ellipticity and the enzyme concentration.

[0083] The characteristic frequency value is mapped to the substrate concentration; the natural logarithm of the sound velocity elliptic is taken, and the product of the natural logarithm of the sound velocity elliptic and the adjustment gain factor is used as the enzyme concentration;

[100] the numerical correlation of the sound velocity component of the crystal direction propagation path is the first reaction rate constant,

[001] the numerical correlation of the sound velocity component of the crystal direction propagation path is the second reaction rate constant, the temperature fluctuation suppression term is initialized to the unit concentration value, and the enzyme-catalyzed reaction kinetic model is obtained.

[0084] Based on the first reaction rate constant, enzyme concentration, substrate concentration, second reaction rate constant, and temperature fluctuation inhibition term, an enzyme-catalyzed ordinary differential equation is constructed, expressed as:

[0085]

[0086] Where θ is the crystal orientation angle concentration, k1 is the first reaction rate constant, E is the enzyme concentration, A is the substrate concentration, k3 is the second reaction rate constant, and T is the temperature fluctuation suppression term. denoted as the rate of change of crystal orientation angle concentration, and t is the virtual time parameter for simulating the reaction process;

[0087] The fourth-order Runge-Kutta numerical integration method was used to solve the enzyme-catalyzed differential equation: the integration time step was set to one-tenth of the reciprocal of the characteristic frequency value, and the total integration time covered three complete reaction cycles. The initial crystal orientation angle concentration was taken as zero, and substituted into the enzyme-catalyzed differential equation to obtain the initial crystal orientation angle concentration change rate. When the time was advanced to the half-integration time step, the product of the initial crystal orientation angle concentration change rate and half of the integration time step was taken as the temporary value of the crystal orientation angle concentration. The temporary value of the crystal orientation angle concentration was substituted into the enzyme-catalyzed differential equation to obtain the temporary change rate of the crystal orientation angle concentration. The temporary value of the crystal orientation angle concentration was updated to the product of the temporary change rate of the crystal orientation angle concentration and half of the integration time step, and the temporary change rate of the crystal orientation angle concentration was recalculated. When the time was advanced to the full integration time step, the product of the recalculated temporary change rate of the crystal orientation angle concentration and the integration time step was taken as the final value of the crystal orientation angle concentration. Substituted into the enzyme-catalyzed differential equation to obtain the final change rate of the crystal orientation angle concentration.

[0088] The fourth-order Runge-Kutta numerical integration method was used to solve the enzyme-catalyzed differential equation. The integration time was increased by one step in each cycle, and the total number of cycles covered the duration of three reaction cycles. The crystal orientation angle concentration value was recorded at each time point to obtain the crystal orientation angle concentration value sequence.

[0089] Traverse all time points in the sequence of crystal orientation angle concentration values ​​except for the first and last points. Take the absolute value of the difference between the crystal orientation angle concentration values ​​at the next time point and the crystal orientation angle concentration values ​​at the previous time point and the ratio of the integral time step size as the crystal orientation angle concentration change rate. Calculate the crystal orientation angle concentration change rate for each time point.

[0090] The lattice relaxation time constant of gallium oxide single crystal is set as the rate of change threshold, and all time points where the rate of change of crystal orientation angle concentration is less than the rate of change threshold are marked; the marked points within the first and last ten percentage points of the crystal orientation angle concentration value sequence are excluded to obtain the effective marked points; the arithmetic mean of the crystal orientation angle concentration values ​​of all effective marked points is calculated to obtain the steady-state crystal orientation angle concentration value;

[0091] Query the theoretical range of GaO single crystal orientation angle concentration. When the steady-state orientation angle concentration value is not in the theoretical range, readjust the enzyme concentration regulation factor, increase the concentration value of the temperature inhibition term by an order of magnitude, reconstruct the enzyme-catalyzed ordinary differential equation, and solve for the new steady-state orientation angle concentration value. If it still exceeds the theoretical range after three consecutive adjustments, add invalid data point markers to the corresponding grid nodes of the lattice vibration characteristic spectrum.

[0092] For each grid node in the lattice vibration feature map that has no unmarked invalid data points, a crystal orientation angle concentration recording unit is created. The steady-state crystal orientation angle concentration value is written into the crystal orientation angle concentration recording unit. The crystal orientation angle concentration recording units of all valid nodes are integrated to form a crystal orientation angle concentration distribution matrix with spatial coordinate index.

[0093] It should also be noted that: the enzyme-catalyzed reaction kinetic model maps the sound velocity ellipticity to enzyme concentration and the characteristic frequency to substrate concentration, establishing a cross-domain correlation between acoustic parameters and chemical reaction variables; the temperature fluctuation suppression term dynamically compensates for crystal orientation drift caused by thermal expansion; the fourth-order Runge-Kutta method combined with the lattice relaxation time threshold locks the steady-state point, improving the convergence speed and reliability of the crystal orientation angle concentration value.

[0094] S4: Map the steady-state crystal orientation angle concentration values ​​to wafer space coordinates, establish the steady-state crystal orientation angle concentration field distribution matrix by solving the diffusion equation, and convert the steady-state crystal orientation angle concentration field distribution matrix into a crystal axis orientation deviation thermogram.

[0095] The specific steps are as follows:

[0096] Read the spatial coordinate index information of the crystal orientation angle concentration distribution matrix to ensure that the row index of the crystal orientation angle concentration distribution matrix corresponds to the

[010] crystal orientation of gallium oxide single crystal, the column index corresponds to the

[100] crystal orientation of gallium oxide single crystal, the grid origin position coincides with the geometric center of the detection area, and the grid spacing is equal to the physical spacing of the superconducting quantum bit sensor nodes.

[0097] Using the elements in the first row and first column of the sound velocity anisotropy tensor as the diffusion coefficients along the X-axis and the elements in the second row and second column as the diffusion coefficients along the Y-axis, a diffusion equation is constructed, expressed as:

[0098]

[0099] Where C is the steady-state crystal orientation angle concentration, s is the diffusion time, and D is the diffusion time. x D is the diffusion coefficient in the X direction. y y is the diffusion coefficient in the Y direction, x is the spatial coordinate parallel to the

[100] crystal direction, and y is the spatial coordinate parallel to the

[010] crystal direction.

[0100] The diffusion equation is discretized using a five-point difference scheme: each grid node of the crystal orientation angle concentration distribution matrix is ​​numbered in row and column order, with the row number corresponding to the increasing direction of the Y-axis coordinate and the column number corresponding to the increasing direction of the X-axis coordinate. The center node is defined as the current position to be solved.

[0101] For each central node, calculate the approximate values ​​of the second-order partial derivatives along the X-axis and Y-axis. Substitute these approximate values ​​into the diffusion equation. Under steady-state conditions, set the partial derivative of the steady-state crystal orientation angle concentration value with respect to diffusion time to zero, thus transforming the diffusion equation into a discrete equation, expressed as:

[0102]

[0103] Among them, C i,jHere, Δx represents the steady-state crystal orientation angle concentration value of the center node (i,j), Δy represents the grid spacing along the X-axis, Δy represents the grid spacing along the Y-axis, i represents the row index, j represents the column index, and C represents the column index. i,j-1 C represents the steady-state crystal orientation angle concentration value of the left-side adjacent node of the center node (i,j). i,j+1 C represents the steady-state crystal orientation angle concentration value of the right-hand adjacent node of the center node (i,j). i-1,j C represents the steady-state crystal orientation angle concentration value of the node adjacent to the center node (i,j) above it. i+1,j The steady-state crystal orientation angle concentration value of the node adjacent to the center node (i,j) below;

[0104] The discrete equations of all the center nodes are combined into a discretized linear equation system. The steady-state crystal orientation angle concentration values ​​of all grid nodes are initialized to zero to obtain the steady-state crystal orientation angle concentration value vector. The maximum number of iterations is set and the iteration counter is reset to zero.

[0105] The constant term vector of the discretized linear equation system is used as the initial residual vector. The residual norm of the initial residual vector is calculated, and the initial residual vector is copied as the initial search direction vector. A tolerance threshold is set proportionally based on the historical residual norm. For example, 1% of the historical maximum residual norm is taken as the tolerance threshold. When the iteration counter is less than the maximum number of iterations and the residual norm is greater than the tolerance threshold, the following is executed: The step size coefficient is calculated, and the expression is:

[0106]

[0107] Where, α k Let r be the step size coefficient for the k-th iteration. k p is the current residual vector. k Let B be the current search direction vector, B be the coefficient matrix of the discretized linear equation system, and k be the number of iterations.

[0108] The vector of steady-state crystal orientation angle concentration values ​​is updated by the following expression:

[0109] X k+1 =X k +α k ×p k ;

[0110] Among them, X k+1 X is the updated steady-state crystal orientation angle concentration vector. k This represents the current steady-state crystal orientation angle concentration vector;

[0111] The expression for updating the residual vector is:

[0112] r k+1 =r k -α k ×(B×p k );

[0113] Where, r k+1 For the updated residual vector, r k This is the current residual vector;

[0114] Calculate the residual norm of the updated residual vector. Terminate the iteration when the residual norm of the updated residual vector is less than the tolerance threshold.

[0115] Update the search direction vector, the expression is:

[0116] p k+1 =r k+1 +β k ×p k ;

[0117] Where, p k+1 For the updated search direction vector, β k This is the ratio of the inner quotient of the updated residual vector to the current residual vector;

[0118] The updated steady-state crystal orientation angle concentration value vector is rearranged according to the grid node coordinates to generate a steady-state crystal orientation angle concentration field distribution matrix. The row number of the steady-state crystal orientation angle concentration field distribution matrix corresponds to the incremental sequence number of the Y coordinate, and the column number corresponds to the incremental sequence number of the X coordinate.

[0119] Prepare a gradient operator template for the X direction, with weights of -1, 0, and +1 in the first row, -2, 0, and +2 in the second row, and -1, 0, and +1 in the third row; prepare a gradient operator template for the Y direction, with weights of -1, -2, and -1 in the first row, -0, 0, and -0 in the second row, and +1, +2, and +1 in the third row.

[0120] A virtual boundary layer is added around the steady-state crystal orientation angle concentration field distribution matrix. The width of the virtual boundary layer is a ring of grid nodes. The steady-state crystal orientation angle concentration value of the virtual boundary node is copied from the steady-state crystal orientation angle concentration value of the adjacent internal grid node.

[0121] A window is created with each internal grid node as the center. The window row direction is parallel to the Y-axis, the window column direction is parallel to the X-axis, and the window center corresponds to the steady-state crystal orientation angle concentration value.

[0122] Perform a two-dimensional discrete convolution operation between the X-direction gradient operator template and the window to obtain the X-direction gradient component values; perform a two-dimensional discrete convolution operation between the Y-direction gradient operator template and the window to obtain the Y-direction gradient component values.

[0123] The arithmetic square root of the sum of the squares of the two directional gradient components of each grid node is taken as the gradient magnitude of each grid node. If the grid node is marked as a "lattice distortion region", the corresponding gradient magnitude is assigned to zero.

[0124] By measuring a standard sample with a known precise crystal orientation deviation angle, the least squares method is used to fit a linear scaling factor between the known precise crystal orientation deviation angle and the gradient magnitude of the standard sample; the gradient magnitude of each grid node is read, and the product of the gradient magnitude and the linear scaling factor is taken as the crystal orientation deviation angle; if the grid node is marked as a "lattice distortion region", the crystal orientation deviation angle is forced to zero and a distortion marker is added.

[0125] The offset direction is determined by the sign of the gradient component value in the X direction. A positive sign indicates that the crystal orientation deviation angle is offset counterclockwise along the

[100] crystal orientation, and a negative sign indicates that the crystal orientation deviation angle is offset clockwise along the

[100] crystal orientation. A positive or negative sign is added before the crystal orientation deviation angle.

[0126] A positive zero-degree crystal orientation deviation angle is mapped to pure red, a zero-degree crystal orientation deviation angle is mapped to pure green, and a negative zero-degree crystal orientation deviation angle is mapped to pure blue. For the crystal orientation deviation angle of each grid node, the ratio of the absolute value of the crystal orientation deviation angle to zero-degree is used as the color adjustment coefficient. When the crystal orientation deviation angle is positive and the color adjustment coefficient is not greater than one, the crystal orientation deviation angle is mapped to the RGB color corresponding to the red channel value of 255 and the color adjustment coefficient, the green channel value of 255 and (1 - color adjustment coefficient), and the blue channel value of zero. If the color adjustment coefficient is greater than one, the crystal orientation deviation angle is mapped to pure red. When the crystal orientation deviation angle is negative and the color adjustment coefficient is not greater than one, the crystal orientation deviation angle is mapped to the RGB color corresponding to the red channel value of zero, the green channel value of 255 and (1 - color adjustment coefficient), and the blue channel value of 255 and the color adjustment coefficient. If the color adjustment coefficient is greater than one, the crystal orientation deviation angle is mapped to pure blue.

[0127] If a grid node is marked as a "lattice distortion region", a black crosshair is added to the center of the color block; if a grid node has no effective crystal orientation deviation angle, it is mapped to pure white.

[0128] The RGB values ​​are arranged in spatial order according to the grid nodes. Each grid node outputs a pixel unit to form a crystal axis orientation deviation heat map. Direction indicators are added to the edge of the crystal axis orientation deviation heat map. The positive direction of the X-axis is marked with

[100] crystal direction and the positive direction of the Y-axis is marked with

[010] crystal direction. Red arrows indicate counterclockwise offset and blue arrows indicate clockwise offset.

[0129] It should also be noted that: the five-point difference scheme discretization ensures the accuracy of spatial derivative calculation of the diffusion equation; the conjugate gradient iteration method efficiently solves large-scale linear equation systems and generates a high-fidelity steady-state crystal orientation angle concentration field distribution matrix; the Sobel operator gradient operation extracts the spatial rate of change of the concentration field, and combined with the scaling factor, realizes the physically interpretable transformation of the crystal orientation deviation angle.

[0130] S5: Calculate the cutting compensation angle based on the crystal axis orientation deviation thermogram, and drive the wafer dicing machine to perform processing compensation according to the cutting compensation angle.

[0131] The specific steps are as follows:

[0132] The crystal orientation deviation heatmap is divided into grid blocks, and the size of each grid block matches the single-blade cutting range of the wafer dicing machine. The crystal orientation deviation angles of all pixel units in the grid block are extracted, and the crystal orientation deviation angles marked as "lattice distortion regions" are excluded.

[0133] Calculate the arithmetic mean and standard deviation of the crystal orientation deviation angles within each grid block. Based on the arithmetic mean and standard deviation of the crystal orientation deviation angles, calculate the cutting compensation angle, expressed as:

[0134]

[0135] Where w is the cutting and machining compensation angle, σ is the arithmetic mean of the crystal orientation deviation angles. f σ0 represents the standard deviation of the crystal orientation deviation angle, and σ0 represents the limit value of the intrinsic angle fluctuation caused by the lattice thermal vibration of gallium oxide single crystal at room temperature, which is determined by phonon spectral density experiments.

[0136] Convert the cutting compensation angle into a wafer dicing machine rotation axis command, and then use the wafer dicing machine to execute the wafer dicing machine rotation axis command.

[0137] It should also be noted that the standard deviation weighted compensation angle formula suppresses the risk of overcutting in high volatility regions.

[0138] This embodiment also provides a computer device applicable to a method for accurately determining the crystal axis orientation of a gallium oxide single crystal, comprising: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the method for accurately determining the crystal axis orientation of a gallium oxide single crystal as proposed in the above embodiment.

[0139] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0140] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements a method for accurately determining the crystal axis orientation of a gallium oxide single crystal as described in the above embodiments. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Red-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0141] In summary, this invention achieves high-precision and low-noise acquisition of acoustic signals from gallium oxide single-crystal surfaces through a quantum entangled superconducting sensor network, improving spatial and temporal resolution. It overcomes the dependence of existing physical characterization methods on sample surface flatness and cleanliness, and breaks through the limitations of inefficient point-by-point scanning and insufficient detection accuracy over wide areas. By constructing an enzyme-catalyzed reaction kinetic model, it can simulate the dynamic changes of crystal orientation angle concentration over time and space, overcoming the limitations of existing static physical models, improving the adaptability of crystal axis orientation resolution, compensating for the influence of internal material defects or non-uniformity on crystal orientation angle concentration, reducing measurement errors caused by local anomalies in existing methods, and realizing dynamic correlation analysis of crystal acoustic behavior. This solves the defects of existing static models, such as sensitivity to material defects and poor consistency.

[0142] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for accurately determining the crystal axis orientation of gallium oxide single crystal, characterized in that: include, Acoustic raw data of gallium oxide single crystals were acquired using a quantum entangled sensor network; The raw acoustic data is compressed and reconstructed to construct the sound velocity anisotropy tensor and generate a lattice vibration characteristic spectrum. Based on the lattice vibration characteristic spectrum, an enzyme-catalyzed reaction kinetic model was constructed, an enzyme-catalyzed differential equation was defined, and the steady-state crystal orientation angle concentration value was calculated. The steady-state crystal orientation angle concentration values ​​are mapped to wafer space coordinates. The steady-state crystal orientation angle concentration field distribution matrix is ​​established by solving the diffusion equation. The steady-state crystal orientation angle concentration field distribution matrix is ​​then converted into a thermogram of crystal axis orientation deviation. The cutting compensation angle is calculated based on the crystal axis orientation deviation thermogram, and the wafer dicing machine is driven to perform processing compensation according to the cutting compensation angle.

2. The method for accurately determining the crystal axis orientation of gallium oxide single crystal as described in claim 1, characterized in that: The specific steps for acquiring raw acoustic data from gallium oxide single crystals via a quantum entangled sensor network are as follows: A detection area is selected on the surface of a gallium oxide single crystal, and a superconducting quantum bit sensor node is deployed on the surface of the detection area; All superconducting qubit sensor nodes are synchronized into a quantum entangled state to form a quantum entangled sensor network; Rayleigh waves are generated by exciting gallium oxide single crystals with femtosecond Ti:sapphire lasers, and absolute timestamps corresponding to the instantaneous amplitude values ​​of the Rayleigh waves are captured by quantum entanglement sensor networks. Each superconducting quantum bit sensor node is assigned a node position identifier, and each superconducting quantum bit sensor node synchronously measures the amplitude value and phase angle of the quantum state induced by Rayleigh wave; The absolute timestamp, node location identifier, quantum state amplitude value, and quantum state phase angle are integrated into the raw acoustic data.

3. The method for accurately determining the crystal axis orientation of gallium oxide single crystal as described in claim 2, characterized in that: The specific steps for compressing and reconstructing the raw acoustic data to construct the sound velocity anisotropic tensor are as follows: The absolute timestamp and quantum state amplitude value are extracted from the raw acoustic data, and the quantum state amplitude value is normalized. The normalized quantum state amplitude values ​​are arranged according to absolute timestamps to generate an amplitude sequence; The complete frequency domain acoustic spectrum is reconstructed based on the amplitude sequence using the orthogonal matching pursuit algorithm; The sound velocity components are calculated based on the complete frequency domain sound spectrum, and the sound velocity anisotropy tensor is constructed.

4. The method for accurately determining the crystal axis orientation of gallium oxide single crystal as described in claim 3, characterized in that: The specific steps for generating the lattice vibration characteristic spectrum are as follows: Identify the frequency of maximum amplitude peak in the complete frequency domain acoustic spectrum, and record the characteristic frequency value based on the frequency of maximum amplitude peak; Calculation of sound velocity ellipticity based on sound velocity anisotropic tensor; A two-dimensional grid spatial coordinate system is created, and the characteristic frequency value, sound velocity ellipticity, and sound velocity component are labeled at the coordinates of each grid node to generate a lattice vibration characteristic spectrum.

5. The method for accurately determining the crystal axis orientation of gallium oxide single crystal as described in claim 1, characterized in that: The construction of an enzyme-catalyzed reaction kinetic model based on lattice vibration characteristic spectrum, and the definition of the enzyme-catalyzed differential equation, refers to the construction of an enzyme-catalyzed reaction kinetic model based on characteristic frequency values, sound velocity ellipticity, and sound velocity anisotropy tensor, and the definition of the enzyme-catalyzed differential equation based on the enzyme-catalyzed reaction kinetic model.

6. The method for accurately determining the crystal axis orientation of gallium oxide single crystal as described in claim 1, characterized in that: The specific steps for calculating the steady-state crystal orientation angle concentration value are as follows: The enzyme-catalyzed differential equation was solved using the fourth-order Runge-Kutta numerical integration method to obtain a numerical sequence of crystal orientation angle concentrations; Calculate the rate of change of crystal orientation angle concentration, select effective marker points based on the rate of change of crystal orientation angle concentration, and calculate the steady-state crystal orientation angle concentration value based on the effective marker points.

7. The method for accurately determining the crystal axis orientation of gallium oxide single crystal as described in claim 6, characterized in that: The steps for establishing a steady-state crystal orientation angle concentration field distribution matrix by solving the diffusion equation and converting the steady-state crystal orientation angle concentration field distribution matrix into a crystal axis orientation deviation thermogram are as follows: The diffusion equation is constructed based on the sound velocity anisotropic tensor. The diffusion equation is transformed into a discrete equation using a five-point difference scheme and combined into a discretized linear equation system. The discretized linear equations were solved iteratively using the conjugate gradient method to obtain the steady-state crystal orientation angular concentration field distribution matrix. Perform Sobel operator gradient operation on the steady-state crystal orientation angular concentration field distribution matrix to obtain the gradient components; The gradient magnitude is calculated based on the gradient components, and the crystal orientation deviation angle is calculated based on the gradient magnitude. A thermogram of crystal axis orientation deviation is generated by color mapping based on the crystal orientation deviation angle.

8. The method for accurately determining the crystal axis orientation of gallium oxide single crystal as described in claim 1, characterized in that: The specific steps for calculating the cutting compensation angle based on the crystal axis orientation deviation thermogram and driving the wafer dicing machine to perform processing compensation according to the cutting compensation angle are as follows: The crystal orientation deviation thermogram is divided into grid blocks, and the arithmetic mean and standard deviation of the crystal orientation deviation angles in each grid block are calculated. The cutting compensation angle is calculated based on the arithmetic mean and standard deviation of the crystal orientation deviation angle; The cutting compensation angle is converted into a wafer dicing machine rotation axis command and executed.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the method for accurately determining the crystal axis orientation of a gallium oxide single crystal as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the steps of the method for accurately determining the crystal axis orientation of a gallium oxide single crystal as described in any one of claims 1 to 8.

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