A high-speed micro-design method for semiconductor process based on artificial intelligence algorithm

Abstract

The application belongs to the field of semiconductor process, and discloses a high-speed microscopic design method for semiconductor process based on an artificial intelligence algorithm. The application firstly trains a high-dimensional potential energy surface model of a system by using an artificial intelligence algorithm of deep learning and active learning, then tests the accuracy of the model, and under the premise of ensuring high accuracy of the first principle calculation, uses the potential energy surface model to optimize the semiconductor process. The model based on deep potential can more quickly calculate phase transition of atomic lattices, diffusion of impurity atoms, ion implantation, photolithography, etching, thin film deposition and growth problems in the semiconductor process. The application realizes fitting of the high-dimensional potential energy surface based on the algorithm of artificial intelligence, can perform microscopic design on the semiconductor process, and has the characteristics of high calculation accuracy, fast calculation speed, short design period and low design cost.

Description

Technical Field

[0001] This invention utilizes a high-dimensional potential energy surface model based on artificial intelligence algorithms to design semiconductor processes at the microscopic atomic scale. This method can quickly and accurately describe the motion at the microscopic atomic scale and belongs to the fields of electronic design automation and semiconductor processes. Background Technology

[0002] Today, semiconductor devices are widely used in information and communication, computers, consumer electronics, aerospace, automotive electronics, and other fields. However, the design and manufacturing of semiconductor devices is a highly complex process. Semiconductor device design heavily relies on semiconductor processes and electronic design automation (EDA) technologies because semiconductor micro-design methods shorten development cycles and time to market, thereby significantly reducing the design cost of semiconductor devices (according to the authoritative report of the International Semiconductor Technology Roadmap, semiconductor process and device design tools can reduce global semiconductor industry R&D expenses by 40%). Therefore, semiconductor process micro-design methods are crucial.

[0003] As the feature size of semiconductor devices shrinks to the nanometer level (such as high-end logic chips with 7 nm and 5 nm), atomic-level simulations of related materials and devices based on quantum mechanics become increasingly important. Currently, the mainstream design method is molecular dynamics simulation based on first-principles calculations, such as density functional theory (DFT). While this method offers high accuracy, it is computationally slow (the computation time t is cubically scaled relative to the number of atoms n, i.e., O(n^2)). 3 This results in a very small system for first-principles calculations (generally no more than 10). 3 (atoms). For example, a semiconductor device with a side length of 20 nm contains at least 10 atoms. 6 For individual atoms, design tools based on first-principles calculations are unlikely to complete the calculations within a limited time.

[0004] Deep neural networks, based on artificial intelligence, have been widely proven to fit any complex high-dimensional function with arbitrary precision due to their superior fitting accuracy. Potential energy surface models based on deep neural networks not only possess the accuracy of first-principles calculations but also significantly improve computational speed (computation time t is linearly scaled with the number of atoms n, i.e., O(n)), enabling calculations on systems with hundreds of millions of atoms. Replacing first-principles calculations with high-dimensional potential energy surface models fitted by deep neural networks allows for faster and more efficient micro-design of semiconductor processes. Summary of the Invention

[0005] This invention is a high-speed microscopic design method for semiconductor processes based on artificial intelligence algorithms. The aim is to replace first-principles calculations with a high-dimensional potential energy surface model fitted by a deep neural network. By accelerating the solution of Newton's equations of motion, it significantly improves the computational speed of microscopic atomic-scale motion. This method can be widely applied to semiconductor processes such as phase change, thermal diffusion, lithography, etching, ion implantation, and thin film deposition growth.

[0006] Step S11: Train the high-dimensional potential energy surface model of the system using artificial intelligence algorithms. Collect sufficient first-principles calculation data as training samples using methods such as active learning and transfer learning. While ensuring the invariance of translation, rotation, and permutation of atomic features, input the atomic features into a neural network using deep learning methods. Utilize the mechanism of a multilayer perceptron to establish a mapping relationship between atomic features and atomic energy. The neural network calculation formula fitted by the multilayer perceptron is as follows:

[0007] (1)

[0008] in, Indicates the first Layer The output of each neuron It is a non-linear activation function. It is the connection of the first Layer and first Layer The weights between neurons It is the first Layer Bias of each neuron.

[0009] The energy of the system, after passing through the hidden layer, is finally output in the output layer. The calculation formula is:

[0010] (2)

[0011] Where Ei and E represent the energy of the i-th atom and the total energy, respectively. The force on an atom is calculated by taking the gradient of the system's energy with respect to the atom's position, using the following formula:

[0012] (3)

[0013] in, Indicates the first The forces acting on each atom.

[0014] Step S12: Predict the energy and force based on the potential energy surface model and compare it with the first-principles calculation data. Alternatively, compare the predicted structural properties from the high-dimensional potential energy surface model with the results calculated using first-principles calculations to quantitatively demonstrate the accuracy of the high-dimensional potential energy surface model. If high accuracy is ensured, proceed to step S13; otherwise, return to step S11 and continue collecting samples for retraining.

[0015] Step S13, when solving Newton's equations of motion using first-principles calculations based on density functional theory, requires iteratively solving the Schrödinger and Poisson equations of the current system using a self-consistent field method each time to obtain the total energy and atomic forces of the entire system. This frequent solving of quantum mechanical equations leads to high computational time overhead. In contrast, algorithms based on deep neural networks only require inputting atomic positions. Using a potential energy surface model with fixed parameters (describing the mapping relationship between atomic positions and energy), the system energy can be quickly predicted. The atomic forces can then be obtained by calculating the gradient of energy with respect to atomic positions. The computational time of first-principles calculations is O(n^2). 3 The value is reduced to O(n).

[0016] Step S21, based on steps S11, S12, and S13, trains an accurate deep neural network model. Molecular dynamics simulations can then be used to more quickly obtain dynamic trajectories, enabling the calculation of atomic lattice phase transitions in semiconductor processes. In atomic lattice phase transitions, the ordered lattice structure melts into a liquid state at high temperatures, then quenches at a certain rate to room temperature, forming a disordered amorphous structure, achieving the transformation from a crystalline to an amorphous phase. Then, the system is heated to a suitable temperature (between the crystallization temperature and melting point), and the disordered structure begins to crystallize and gradually grow until crystallization is complete, achieving the transformation from an amorphous to a crystalline phase. Finally, sustained isothermal treatment at a suitable temperature can also achieve transformations between crystalline phases, resulting in a more stable system. The entire phase transition process involves microscopic atomic scale issues, and deep neural networks can significantly improve the speed of phase transition simulation. In semiconductor processes, numerous heating, melting, and quenching processes can be addressed using artificial intelligence-based algorithms to accelerate molecular dynamics simulations.

[0017] Step S22, based on steps S11, S12, and S13, trains an accurate deep neural network model. Molecular dynamics simulations can then be used to obtain the dynamic trajectory more quickly, enabling the calculation of impurity atom diffusion in semiconductor processes. The distribution of impurity atoms entering the intrinsic semiconductor at different temperatures can be determined by the diffusion flux. The concentration of diffusing atoms at various points during the diffusion process... It does not change over time, but only with the distance of diffusion. If this is relevant, then the diffusion belongs to a steady-state diffusion mechanism, and the diffusion flux of the diffusion system can be calculated using Fick's first law. The calculation formula is:

[0018] (4)

[0019] If the concentration of diffusing atoms at various points during the diffusion process It changes not only over time, but also with the distance of diffusion. In cases such as ion implantation, this diffusion is a non-steady-state diffusion mechanism, and the diffusion flux of the diffusion system can be calculated using Fick's second law. The calculation formula is: (5)

[0020] in The diffusivity is calculated using the following formula:

[0021] (6)

[0022] In the formula It is migration energy. It is Boltzmann's constant. It's temperature. It is the pre-factor diffusivity, and its calculation formula is: (7)

[0023] in It is the jump distance (the distance that impurity atoms migrate after doping, i.e., the atomic distance between the initial state and the final state). It is the diffusion depth. It's the coordination number. It is a correlation factor (usually taken as 1). It's the attempt rate. It is the migration entropy (the difference between the initial state entropy and the saddle point state entropy). Coordination number. Within the cutoff radius, this refers to the number of atoms adjacent to the central atom, which can be obtained based on the atomic environment. Using a deep neural network model combined with the Nudged Elastic Band (NEB) method, the saddle point and minimum energy path can be calculated based on the initial and final state structures of the system, thereby obtaining the migration energy. Jump distance and migration entropy .

[0024] (8)

[0025] (9)

[0026] The phonon spectra of the initial and transition states of the doped system are calculated using a deep neural network model, and the attempt rate is calculated based on the phonon spectrum results. The calculation formula is: (10)

[0027] in, It is the frequency of the initial state phonon spectrum. It is the frequency of the transition state phonon spectrum.

[0028] Step S23, based on steps S11, S12, and S13, trains an accurate deep neural network model. Molecular dynamics simulations can then be used to obtain the dynamic trajectory more quickly, enabling the calculation of ion implantation problems in semiconductor processes. A high-energy ion beam rapidly penetrates the semiconductor material, its velocity gradually decreasing due to the barrier at the material interface, eventually remaining inside the material. The entire incident process can be simulated using molecular dynamics of microscopic particles, and a deep neural network model can accelerate the simulation. As the ion beam enters the solid material, it forms new material components. Molecular dynamics simulations can calculate changes in the material's surface composition, structure, and properties. By adjusting the incident velocity, angle, and concentration of incident ions, the material's surface properties can be optimized.

[0029] Step S24, based on steps S11, S12, and S13, trains an accurate deep neural network model. Molecular dynamics simulations can then be used to obtain the dynamic trajectory more quickly, enabling the calculation of photolithography problems in semiconductor processes. During photolithography, a layer of photoresist is applied to the wafer, which is then irradiated for a certain period. Upon exposure to light, the photoresist undergoes a chemical reaction, causing some of it to deteriorate. However, differences in the amount of photoresist and the intensity of light exposure result in different photolithography chemical rates, producing different microstructures on the thin film or substrate. Molecular dynamics simulations based on the microscopic atomic scale can calculate the photolithography process by comparing and analyzing the amounts of reactants in the chemical reaction.

[0030] Step S25, based on steps S11, S12, and S13, trains an accurate deep neural network model. Molecular dynamics simulations can then be used to obtain the dynamic trajectory more quickly, enabling the calculation of etching problems in semiconductor processes. During etching, etchants or ion bombardment are commonly used to remove the deteriorated photoresist, revealing the semiconductor device and its interconnections on the wafer surface. Another etchant is then used to further etch the wafer, forming the semiconductor device and its circuitry. The chemical reactions in photolithography etching are essentially the breaking and recombination of interatomic chemical bonds, a purely microscopic atomic-scale problem that can be simulated using deep neural network algorithms. However, different etchant dosages result in different etching rates for photoresist, thin films, and substrate materials, leading to variations in the microstructures formed on the thin film or substrate. Molecular dynamics simulations based on the microscopic atomic scale can optimize the etching process by utilizing information about the microstructure before and after the chemical reaction.

[0031] Step S26, based on steps S11, S12, and S13, trains an accurate deep neural network model. Using this deep neural network model based on artificial intelligence algorithms, thin film deposition and growth problems in semiconductor processes can be calculated more quickly. Common vapor deposition technology is a process that uses gaseous substances to generate chemical and transport reactions on a solid surface to produce solid deposits. First, volatile gaseous substances are formed, and the gas is transferred to the deposition area, where chemical reactions occur on the solid surface to produce solid matter. The general process of crystal formation is the formation of crystal nuclei (nucleation stage) followed by gradual growth (growth stage). Molecular dynamics simulations based on the microscopic atomic scale can simulate changes in the atomic lattice during thin film deposition and growth, and the nucleation and growth processes can be optimized by adjusting external simulation conditions.

[0032] Step S27, based on steps S11, S12 and S13, can train an accurate deep neural network model.

[0033] By utilizing deep neural network models based on artificial intelligence algorithms, problems related to the movement of microscopic atoms in semiconductor processes can be calculated more quickly. In the semiconductor process, other related problems involving the microscopic atomic scale can be addressed by using artificial intelligence algorithms to train a potential energy surface model. Then, deep neural network models can be used to accelerate molecular dynamics simulations, thereby enabling faster semiconductor process design. Attached Figure Description

[0034] Figure 1 is a framework diagram;

[0035] Figure 2 shows the predictions of energy and atomic forces based on a deep neural network model;

[0036] Figure 3. Angle (radial) distribution function based on deep neural network model and density functional theory;

[0037] Figure 4 shows the relationship between time and number of atoms based on a deep neural network model and density functional theory.

[0038] Figure 5 shows the diffusion of Li atoms in silicon based on a deep neural network model and density functional theory.

[0039] Figure 6 shows the relationship between free energy, vibrational entropy, and heat capacity as a function of temperature;

[0040] Figure 7 shows the phonon spectrum of the bulk material Sb based on a deep neural network model and density functional theory.

[0041] Figure 8 shows the Si doping concentration based on experiments and simulations; Detailed Implementation

[0042] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0043] This invention relates to a high-speed micro-design method for semiconductor processes based on artificial intelligence algorithms. Deep neural network models can be used to calculate and optimize semiconductor processes, such as phase transitions in atomic lattices, diffusion, photolithography, etching, ion implantation, and thin film deposition growth. The overall framework of this invention is shown in Figure 1.

[0044] Step S11: First, lattice relaxation is performed using first-principles calculations. Convergence criteria for energy and force are set to obtain the steady-state structure of the system. Random perturbations are made to the atomic positions and unit cell structure. Single-point energy calculations are performed using density functional theory, and a small number of initial samples are collected. A potential energy surface model is trained using a deep learning algorithm. To collect more data to generate a better potential energy surface model, an active learning artificial intelligence algorithm is used to perform molecular dynamics simulations on the existing model. By setting the maximum error criterion for atomic forces among multiple models, untrained structures are screened, and single-point energy calculations are performed on these structures, adding them to the initial training samples. Through repeated iterative training, the sample size gradually increases, and the model gradually converges. Finally, all sample data are collected, and a better deep potential energy model is generated using a larger number of training steps.

[0045] Step S12: Based on the fitted high-dimensional potential energy surface model, the energy and force of the system can be predicted. A set of single-point energy data (different from the training sample data) is collected, and the comparison results of energy and force can be obtained through prediction, as shown in Figure 2. For 252 test sets, the root mean square error of energy is 1.0 meV / atom, and the root mean square error of force is 47.6 meV / Å. Using a deep neural network model, the system structure at different temperatures can be obtained. The accuracy is compared by calculating the radial distribution function and the angular distribution function. For example, the structural properties of Sb at 1200 K are calculated, and the results are shown in Figure 3. Simulation results show that the model based on deep neural networks has high accuracy.

[0046] Step S13 shows that the computation time and number of atoms for the deep neural network-based model have a linear scaling relationship, i.e., O(n), while the computation time and number of atoms for the first-principles calculation have a cubic scaling relationship, i.e., O(n³). The results are shown in Figure 4. The high-dimensional potential energy surface model based on artificial intelligence algorithms not only achieves the same accuracy as the first-principles calculation but also significantly improves speed. The micro-design method for semiconductor processes based on high-dimensional potential energy surface fitting can significantly improve computational efficiency and reduce computational costs.

[0047] Step S21 utilizes a deep neural network model based on artificial intelligence algorithms to more quickly calculate the phase transition of atomic lattices in semiconductor processes. For example, a simple cubic GeTe system containing 1728 atoms has a melting point of 998 K. Through molecular dynamics simulation, the system is first isothermated at 1500 K for 200 ps, ​​causing the standard lattice to gradually disintegrate and melt into a liquid state. Then, it is quenched at a rate of 25 K / ps to 300 K, forming an amorphous structure, thus realizing the transformation from a crystalline phase to an amorphous phase. Next, the amorphous GeTe is heated to 600 K, causing nucleation to begin inside the amorphous phase. Then, the crystal gradually grows until crystallization is complete, forming a rock-salt crystalline phase, thus realizing the transformation from an amorphous phase to a crystalline phase. Finally, sustained isothermal treatment at 600 K or a higher temperature of 700 K can realize the transformation from a rock-salt crystalline phase to a hexagonal crystalline phase. The entire process of heating, melting, quenching, and crystallization is a common phenomenon in semiconductor manufacturing. Artificial intelligence-based algorithms can be used to accelerate the study of the process.

[0048] Step S22: Lattice relaxation of the initial and final state structures of the doped system is calculated using first-principles calculations, and the coordination number Z of the impurity atoms is calculated based on the stable atomic environment. The number of replicas on the reaction path is set, and the saddle point and minimum energy path are calculated using the NEB algorithm. For example, when calculating the diffusion of Li atoms in silicon, the reaction path results obtained based on first-principles calculations and deep neural network models are highly consistent, as shown in Figure 5. Thus, the migration energy Em and jump distance a are obtained, and the migration entropy Sm is the difference between the vibrational entropy of the initial and transition states, as shown in Figure 6. A deep neural network model can directly predict the atomic forces. Combined with the frozen phonon method or density functional perturbation theory, the phonon spectra of the initial and transition states are calculated. The attempt rate v0 is calculated based on the frequency values ​​in the phonon spectra, as shown in Figure 7. For two common diffusion modes, constant surface source diffusion and finite surface source diffusion... For constant surface source diffusion, the concentration C of surface impurity atoms does not change with time during diffusion. As the diffusion distance x changes, the impurity atom concentration exhibits a residual error distribution, representing a steady-state diffusion mechanism. The diffusion flux J of the diffusion system is calculated using Fick's first law. For finite surface source diffusion, the total amount of impurities within the surface thin layer is constant, and no further impurities are added during subsequent doping. The concentration of internal impurity atoms exhibits a Gaussian distribution, and the diffusion flux J of the diffusion system is calculated using Fick's second law. The thermal diffusion equation can be used to calculate the impurity distribution at different doping concentrations. First-principles calculations can yield energy band structures under different configurations, allowing comparison with the undoped band structure, i.e., comparing the occupancy of electrons near the Fermi level, thus revealing the source of the difference in electrical performance before and after doping. However, the thermal diffusion equations calculated based on first-principles calculations often involve very high impurity concentrations. Deep neural networks can be used to calculate the thermal diffusion equations for larger systems, thus obtaining diffusion equations at lower concentrations. For example, calculating the silicon doping concentration in gallium oxide at different temperatures is shown in the figure.

[0049] As shown in Figure 8.

[0050] Step S23 utilizes a deep neural network model based on artificial intelligence algorithms to more quickly calculate ion implantation issues in semiconductor processes. When an ion beam is injected at high speed into a semiconductor material, it eventually remains inside the material due to interfacial resistance. The ion distribution within the semiconductor is disordered; these amorphous ions interact with internal atoms, forming new material components. Molecular dynamics simulations can calculate changes in the material's surface composition, structure, and properties, such as calculating the thermal conductivity of the entire system to assess its heat dissipation capacity, and calculating the self-diffusion coefficients of various atoms in the constituent components. By adjusting the incident velocity, angle, and concentration of incident ions, the surface properties of the material can be optimized.

[0051] Step S24 utilizes a deep neural network model based on artificial intelligence algorithms to more quickly calculate photolithography problems in semiconductor manufacturing. During photolithography, after a period of irradiation, the photoresist coated on the wafer undergoes a chemical reaction upon exposure to light, causing some of the photoresist to deteriorate. During etching, different etchants are used to remove the deteriorated photoresist, ultimately forming the semiconductor device and its circuitry. The chemical reactions in photolithography are essentially the breaking and recombination of interatomic chemical bonds to form new bonds. This process can be simulated using deep neural network algorithms.

[0052] Step S25 utilizes a deep neural network model based on artificial intelligence algorithms to more quickly calculate etching problems in semiconductor processes. During etching, different etchants or ion bombardment methods are used to erode the deteriorated photoresist, ultimately forming semiconductor devices and their circuits. The chemical reactions during photolithography and etching can be simulated using deep neural network algorithms. Different etchant dosages result in different etching rates for photoresist, thin films, and substrate materials, leading to variations in the microstructures formed on the thin films or substrates. Molecular dynamics simulations based on the microscopic atomic scale can analyze microstructural information before and after the chemical reactions, optimizing the etching process.

[0053] Step S26 utilizes a deep neural network model based on artificial intelligence algorithms to more quickly calculate thin film deposition and growth problems in semiconductor processes. For example, in thin film deposition technology based on chemical vapor deposition, volatile gaseous substances are first transferred to the deposition area, where they react chemically with the deposited surface material to produce new substances; the general process of crystal formation involves nucleation of crystal nuclei, followed by gradual growth, eventually forming a larger crystal. Molecular dynamics simulations based on the microscopic atomic scale can simulate the movement of atomic lattices during thin film deposition and growth, such as optimizing the thin film deposition and crystal growth process by adjusting simulation conditions of temperature and pressure.

[0054] Step S27: By using a deep neural network model based on artificial intelligence algorithms, problems related to the movement of microscopic atoms in semiconductor processes can be calculated more quickly. In the semiconductor process, other related problems involving the microscopic atomic scale can be trained using artificial intelligence algorithms to create a potential energy surface model. Then, the deep neural network model can be used to accelerate the simulation of molecular dynamics. By quickly and accurately extracting intermediate parameters, such as key parameters like energy, atomic forces, atomic self-diffusion coefficient, melting point, and heat capacity, semiconductor processes can be designed more quickly.

[0055] Finally, 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 the scope of protection of the present invention. Referring to the description of these embodiments, those skilled in the art should be able to understand and make relevant modifications or substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention.

Claims

1. A high-speed micro-design method for semiconductor processes based on artificial intelligence algorithms, characterized in that, Includes the following steps: Step S11: Train the high-dimensional potential energy surface model of the system using artificial intelligence algorithms; collect first-principles calculation data as training samples using active learning and transfer learning methods; while ensuring the invariance of translation, rotation, and permutation of atomic features, input the atomic features into the neural network using deep learning methods; and establish the mapping relationship between atomic features and atomic energy using the mechanism of a multilayer perceptron. The neural network calculation formula fitted by the multilayer perceptron is as follows: Among them, the relevant parameters represent the output, non-linear activation function, weights, and biases of the corresponding layer and neuron in the neural network; The energy of the system, after passing through the hidden layer, is finally output in the output layer. The calculation formula is: in, The energy of each atom and the total energy; the energy gradient of the system with respect to the atomic positions is used to calculate the forces acting on the atoms, and the calculation formula is: in, Indicates the first The forces acting on each atom; Step S12: Predict the energy and force based on the potential energy surface model and compare it with the first-principles calculation data; also compare the structural properties predicted by the high-dimensional potential energy surface model with the results calculated by the first-principles calculation to quantitatively demonstrate the accuracy of the high-dimensional potential energy surface model; if high accuracy is ensured, proceed to step S13; otherwise, return to step S11 and continue to collect samples for retraining. Step S13: Based on the deep neural network algorithm, only the atomic position needs to be input. By describing the mapping relationship between the atomic position and energy through the potential energy surface model with fixed parameters, the system energy can be quickly predicted. The force on the atom can be obtained by calculating the gradient of energy with respect to the atomic position. Step S2, based on steps S11, S12, and S13, can train an accurate deep neural network model. Molecular dynamics simulations can be used to obtain the dynamic trajectory more quickly, enabling the calculation of impurity atom diffusion in semiconductor processes. The distribution of impurity atoms entering the intrinsic semiconductor at different temperatures can be determined by the diffusion flux. The concentration of diffusing atoms at various points during the diffusion process... C It does not change over time, but only with the distance of diffusion. If this is relevant, then the diffusion belongs to a steady-state diffusion mechanism, and the diffusion flux of the diffusion system can be calculated using Fick's first law. J The calculation formula is: If the concentration of diffusing atoms at various points during the diffusion process C It changes not only over time, but also with the distance of diffusion. In cases such as ion implantation, the diffusion is a non-steady-state diffusion mechanism, and the diffusion flux of the diffusion system can be calculated using Fick's second law. J The calculation formula is: in, D The diffusivity is calculated using the following formula: In the formula It is migration energy. It is Boltzmann's constant. T It's temperature. It is the pre-factor diffusivity, and its calculation formula is: in, It is the jump distance, the distance that impurity atoms migrate after doping, that is, the atomic distance between the initial state and the final state; d It is the diffusion depth. Z It refers to the coordination number and correlation factor. Generally, it is taken as 1. It's the attempt rate. It is the migration entropy; coordination number. Z Within the cutoff radius, the number of atoms adjacent to the central atom is calculated based on the atomic environment. Using a deep neural network model and the micro-motion elastic band method, the saddle point and minimum energy path can be calculated, thereby obtaining the migration energy. Jump distance and migration entropy The calculation formula is: The attempt rate was calculated by calculating the phonon spectra of various intermediate states in the doped system. The calculation formula is: in, It is the frequency of the initial state phonon spectrum. It is the frequency of the transition state phonon spectrum; the parameters throughout the process can be extracted using artificial intelligence algorithms, thereby describing the diffusion equation of the system and obtaining the distribution of doped atoms.

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