Simulation method for ion implantation, electronic device, and storage medium

Abstract

Embodiments of the present disclosure relate to a simulation method for ion implantation, an electronic device and a storage medium. The method comprises: determining kinetic energy of particles, the particles comprising atoms in a semiconductor material and ions implanted in the semiconductor material; determining a plurality of first-type particles with energy lower than an energy threshold based on a comparison between the kinetic energy and the energy threshold; dividing the plurality of first-type particles into at least one first-type particle group; and determining interactions between the at least one first-type particle group and particles outside the first-type particle group and interactions between the at least one first-type particle group to obtain a simulated particle-scale dynamic process. Embodiments of the present disclosure can simplify interactions, reduce the complexity of simulation calculation while maintaining physical accuracy, and improve computational efficiency.

Description

Simulation methods, electronic devices, and storage media for ion implantation Technical Field

[0001] The embodiments of this disclosure primarily relate to the field of integrated circuits, and more specifically, to simulation methods for ion implantation, electronic devices, and storage media. Background Technology

[0002] Ion implantation is a core doping process in semiconductor manufacturing. In a vacuum environment, impurity ions, such as boron (B2O3), are ionized and implanted into the semiconductor substrate. + ), phosphorus (P + ), arsenic (As + After being accelerated to a high-energy state by a high-voltage electric field, ions directly bombard and embed into the lattice of semiconductor substrates such as silicon. By controlling the dosage, energy and injection angle of the ions, the electrical properties of the semiconductor material can be precisely controlled, thereby achieving customized modification of the conductivity type and resistivity of semiconductor devices. Therefore, it is widely used in the manufacturing of integrated circuits and the optimization of chip performance.

[0003] Ion implantation involves a variety of complex physical phenomena, including collisions between ions and target atoms (nuclear blocking), interactions between ions and electron clouds (electron blocking), lattice damage, defect formation, and channeling. Traditional methods for ion implantation simulation employ all-atom computation. All-atom computation is a method that explicitly models each atom, enabling precise description of the interactions between incident ions and atoms in the target material. However, due to the need to simulate the complex interactions between a large number of atoms, all-atom computation is extremely computationally expensive. Summary of the Invention

[0004] According to exemplary embodiments of this disclosure, a simulation scheme is provided to at least partially overcome the above or other potential defects.

[0005] In a first aspect of this disclosure, a simulation method for ion implantation is provided. The method includes: determining the kinetic energy of particles, including atoms in a semiconductor material and ions implanted into the semiconductor material; determining a plurality of first-type particles with energies below an energy threshold based on a comparison of the kinetic energy and an energy threshold; classifying the plurality of first-type particles into at least one group of first-type particles; and determining interactions between the at least one group of first-type particles and particles outside the group of first-type particles, as well as interactions between the at least one group of first-type particles, to obtain a simulated particle-scale dynamics process.

[0006] In a second aspect of this disclosure, a simulation model generated using the method of the first aspect of this disclosure is provided.

[0007] In a third aspect of this disclosure, a method for performing simulations using the simulation model of the second aspect of this disclosure is provided.

[0008] In a fourth aspect of this disclosure, an electronic device is provided. The electronic device includes a processor and a memory coupled to the processor, the memory having instructions stored therein, the instructions causing the device to perform actions when executed by the processor, the actions including: determining the kinetic energy of particles, the particles including atoms in a semiconductor material and ions injected into the semiconductor material; determining a plurality of first-type particles with energies below an energy threshold based on a comparison of the kinetic energy and an energy threshold; dividing the plurality of first-type particles into at least one first-type particle group; and determining interactions between the at least one first-type particle group and particles outside the first-type particle group, as well as interactions between the at least one first-type particle group, to obtain a simulated particle-scale dynamics process.

[0009] In some embodiments, determining the kinetic energy of a particle includes determining the mean kinetic energy of each particle and the standard deviation of the particle kinetic energy.

[0010] In some embodiments, the energy threshold includes a first energy threshold, which is determined based on the mean and standard deviation.

[0011] In some embodiments, the first energy threshold is determined by: using the average kinetic energy of the particles as the initial value of the mean; using the sample standard deviation of the particle kinetic energy as the initial value of the standard deviation; and iteratively determining the first energy threshold by Gaussian fitting based on the initial values ​​of the mean and the initial values ​​of the standard deviation.

[0012] In some embodiments, determining a first energy threshold by iteratively fitting a Gaussian fit based on an initial value of the mean and an initial value of the standard deviation includes: determining the first energy threshold based on the product of the standard deviation and the fitting coefficients and the mean.

[0013] In some embodiments, the energy threshold further includes a second energy threshold, which is a constant value determined based on the properties of the semiconductor material.

[0014] In some embodiments, determining a plurality of first-class particles with energy below an energy threshold based on a comparison of kinetic energy and an energy threshold includes: using the larger of a first energy threshold and a second energy threshold as a reference energy threshold; and classifying the particles into a plurality of first-class particles and a plurality of second-class particles with kinetic energy above an energy threshold based on a comparison of kinetic energy and the reference energy threshold.

[0015] In some embodiments, the first energy threshold is determined by: redetermining the mean and standard deviation of the kinetic energy distribution of the particles at a preset time step; using the redetermined mean of the kinetic energy distribution of the particles as the updated mean of the kinetic energy distribution of the particles, and using the redetermined standard deviation of the kinetic energy distribution as the updated standard deviation of the kinetic energy distribution of the particles; and determining the first energy threshold based on the updated mean and the updated standard deviation.

[0016] In some embodiments, the first energy threshold is determined by: determining the system energy at the current moment, the system energy at the previous moment, and the historical average energy; determining the ratio of the absolute value of the difference between the system energy at the current moment and the system energy at the previous moment to the historical average energy; in response to the ratio being greater than a preset proportion, re-determining the mean of the particle's kinetic energy distribution as the updated mean of the particle's kinetic energy distribution, and re-determining the standard deviation of the kinetic energy distribution as the updated standard deviation of the particle's kinetic energy distribution; and determining the first energy threshold based on the updated mean and the updated standard deviation.

[0017] In some embodiments, classifying a plurality of first-type particles into at least one first-type particle group includes: determining a neighborhood radius based on the properties of the semiconductor material; and classifying the plurality of first-type particles into at least one first-type particle group based on the neighborhood radius and a lower limit value for the number of particles.

[0018] In some embodiments, dividing a plurality of first-class particles into at least one first-class particle group based on a neighborhood radius and a lower limit of particle number includes: marking each of the plurality of first-class particles as a first state to obtain a plurality of first-state particles; for each of the plurality of first-state particles, determining the number of neighborhood particles within the neighborhood radius of the first-state particle; and in response to the number of neighborhood particles being greater than or equal to the lower limit of particle number, dividing the first-state particles and the neighborhood particles into a first-class particle group, and marking the first-state particles and the neighborhood particles as second-state particles.

[0019] In some embodiments, the action further includes: for each of the plurality of first-state particles, in response to the number of neighboring particles being less than a lower limit of the number of particles, marking the first-state particle as a third-state particle; determining the distances from the third-state particle to all first-class particle groups respectively; for each distance from the third-state particle to all first-class particle groups, in response to the distance being less than or equal to a preset distance, adding the third-state particle to the first-class particle group corresponding to the distance and marking the third-state particle as a second-state particle; and in response to the distance being greater than the preset distance, marking the third-state particle as an independent particle.

[0020] In some embodiments, the action further includes: for each of the at least one first type of particle groups, comparing the number of particles in the first type of particle group with an upper limit value for the number of particles; and in response to the number of particles being greater than the upper limit value for the number of particles, splitting the first type of particle group such that the number of particles is greater than or equal to a lower limit value for the number of particles and less than or equal to an upper limit value for the number of particles.

[0021] In some embodiments, splitting a first type of particle group includes: determining the local density within the first type of particle group; and segmenting the first type of particle group along the density gradient direction.

[0022] In some embodiments, classifying a plurality of first-type particles into at least one first-type particle group includes: redetermining the kinetic energy of the particles at a preset time step; and classifying the plurality of first-type particles into at least one first-type particle group based on the redetermined kinetic energy of the particles.

[0023] In some embodiments, classifying a plurality of first-type particles into at least one first-type particle group includes: determining the system energy at the current moment, the system energy at the previous moment, and the historical average energy; determining the ratio of the absolute value of the difference between the system energy at the current moment and the system energy at the previous moment to the historical average energy; and reclassifying the plurality of first-type particles into at least one first-type particle group in response to the ratio being greater than a preset proportion.

[0024] In some embodiments, determining the interaction between at least one first type of particle group and particles outside the first type of particle group, as well as the interaction between groups of at least one first type of particle group, includes: for each first type of particle group in at least one first type of particle group, determining the mass of the first type of particle group, the center of mass of the first type of particle group, and the velocity of the first type of particle group; and determining the interaction between the first type of particle group and particles outside the first type of particle group, as well as the interaction between the individual first type of particle groups, based on the mass, the center of mass, and the velocity.

[0025] In some embodiments, determining the interaction between the first type of particle group and particles outside the first type of particle group includes: in response to the distance between the first type of particle group and particles outside the first type of particle group being greater than or equal to a distance threshold, determining the parameters of an equivalent model of the first type of particle group based on mass, center of mass, and velocity; and determining the interaction between the first type of particle group as a whole and particles outside the first type of particle group based on the parameters of the equivalent model.

[0026] In some embodiments, determining the interaction between each group of first-type particles includes: in response to a distance between a group of first-type particles and a group of first-type particles outside the group of first-type particles being greater than or equal to a distance threshold, determining the parameters of an equivalent model of the group of first-type particles based on mass, centroid, and velocity; and determining the interaction between each group of first-type particles based on the parameters of the equivalent model.

[0027] In some embodiments, determining the interaction between at least one first type of particle group and particles outside the first type of particle group, and the interaction between groups of at least one first type of particle group, includes: determining the interaction between each particle in the first type of particle group and particles outside the first type of particle group in response to the distance between the first type of particle group and particles outside the first type of particle group being less than a distance threshold; or determining the interaction between each particle in the first type of particle group and first type of particle groups outside the first type of particle group in response to the distance between the first type of particle group and first type of particle groups outside the first type of particle group being less than a distance threshold.

[0028] In a fifth aspect of this disclosure, a computer-readable storage medium is provided. The medium stores machine-executable instructions that, when executed by a processor, cause the processor to implement the method according to a first aspect of this disclosure.

[0029] It should be understood that the description in the Summary of the Invention is not intended to limit the key or essential features of the embodiments of this disclosure, nor is it intended to restrict the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description

[0030] The above and other features, advantages, and aspects of the embodiments of this disclosure will become more apparent from the accompanying drawings and the following detailed description. In the drawings, the same or similar reference numerals denote the same or similar elements, wherein:

[0031] Figure 1 shows a schematic diagram of some particles according to some embodiments of the present disclosure;

[0032] Figure 2 shows a schematic diagram of an example environment in which embodiments of the present disclosure can be implemented;

[0033] Figure 3 shows a flowchart of a simulation method for ion implantation according to some embodiments of the present disclosure;

[0034] Figure 4 illustrates a schematic diagram of particle division according to some embodiments of the present disclosure;

[0035] Figure 5 shows a schematic flowchart of particle clustering according to some embodiments of the present disclosure;

[0036] Figure 6 shows a block diagram of a computing device according to some embodiments of the present disclosure. Detailed Implementation

[0037] Embodiments of this disclosure will now be described in more detail with reference to the accompanying drawings. While some embodiments of this disclosure are shown in the drawings, it should be understood that this disclosure can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this disclosure. It should be understood that the accompanying drawings and embodiments of this disclosure are for illustrative purposes only and are not intended to limit the scope of protection of this disclosure.

[0038] In the description of embodiments of this disclosure, the term "comprising" and similar terms should be understood as open-ended inclusion, i.e., "including but not limited to". The term "based on" should be understood as "at least partially based on". The term "one embodiment" or "the embodiment" should be understood as "at least one embodiment". The terms "first", "second", etc., may refer to different or the same objects. Other explicit and implicit definitions may also be included below.

[0039] As mentioned earlier, in ion implantation simulations, every atom in the semiconductor substrate material can be explicitly represented through all-atom calculations, rather than approximating it with a continuous medium or average potential. The interactions between the incident ions and these atoms are described using interatomic potential functions or first-principles calculations (such as DFT). Time evolution is typically simulated using molecular dynamics (MD). Therefore, all-atom calculations can accurately simulate atomic-level collision processes, providing highly precise microscopic information.

[0040] Figure 1 illustrates a subset of particles in some embodiments of this disclosure. Dots 101-d (d is a positive integer) in Figure 1 represent particles during ion implantation, including incident ions and atoms in the semiconductor. For example, if all-atom computation is used to simulate the particles shown in Figure 1, assuming the number of particles shown in Figure 1 is N, and the maximum value of d is N, then for each particle, the interaction with the other N-1 particles needs to be considered. Therefore, the computational complexity of all-atom computation is approximately proportional to the square of the number of particles N. Alternatively, the time complexity of all-atom computation can be described as O(N^2). 2 When N is on the scale of millions of particles, all-atom calculations are extremely time-consuming, resulting in very low computational efficiency.

[0041] To improve the computational efficiency of all-atom computing, various acceleration schemes have been attempted. For example, energy truncation is used, which ignores long-range interactions by setting a cutoff radius; however, this leads to distortion of some atomic dynamics. Another approach is to use larger time steps for slow atoms, but this easily causes atomic trajectory drift. The inventors noted that current acceleration schemes all suffer from a trade-off between physical accuracy and computational efficiency; sacrificing physical accuracy for computational efficiency makes it difficult to meet the requirements of advanced manufacturing processes.

[0042] In view of this, the present disclosure provides a simulation method for ion implantation. The method includes: determining the kinetic energy of particles, including atoms in a semiconductor material and ions implanted into the semiconductor material; determining a plurality of first-type particles with energies below an energy threshold based on a comparison of kinetic energy and an energy threshold; dividing the plurality of first-type particles into at least one first-type particle group; and determining the interactions between the at least one first-type particle group and particles outside the first-type particle group, as well as the interactions between the at least one first-type particle group, to obtain a simulated particle-scale dynamic process. Embodiments of the present disclosure simplify interactions, reduce the complexity of simulation calculations while maintaining physical accuracy, thereby improving computational efficiency.

[0043] The embodiments of this disclosure will now be described in detail with reference to the accompanying drawings.

[0044] Referring first to FIG2, a schematic diagram of an example environment 200 in which various embodiments of the present disclosure can be implemented is shown. As shown in FIG2, the example environment 200 includes a computing device 210 and a client 220.

[0045] In some embodiments, the computing device 210 can interact with the client 220. For example, the computing device 210 can receive input messages from the client 220 and output feedback messages to the client 220. In some embodiments, the input messages from the client 220 may be ion implantation-related data. The computing device 210 can perform corresponding mathematical operations related to ion implantation. The computing device 210 can output the corresponding operation results to the client 220.

[0046] In some embodiments, the computing device 210 may include, but is not limited to, a personal computer, a server computer, a handheld or laptop device, a mobile device (such as a mobile phone, a personal digital assistant PDA, a media player, etc.), a consumer electronics product, a minicomputer, a mainframe computer, cloud computing resources, etc.

[0047] It should be understood that the description of the structure and functionality of example environment 200 for illustrative purposes only is not intended to limit the scope of the topics described herein. The topics described herein may be implemented in different structures and / or functionalities.

[0048] The technical solutions described above are for illustrative purposes only and are not intended to limit this disclosure. It should be understood that the example environment 200 may also have many other implementations. To more clearly explain the principles of the solutions disclosed herein, the following will describe them in more detail with reference to Figure 3.

[0049] Figure 3 shows a flowchart of a simulation method 300 for ion implantation according to some embodiments of the present disclosure.

[0050] At box 302, determine the particle's kinetic energy.

[0051] The particles used in ion implantation can include atoms from a semiconductor material (or semiconductor target) and ions implanted into the semiconductor material. Ions implanted into the semiconductor material can include, for example, high-energy particles, such as boron (B). + ), phosphorus (P + ), arsenic (As + Plasma, but the embodiments disclosed herein are not limited to this.

[0052] In some embodiments, determining the kinetic energy of a particle may include determining the mean of the particle's kinetic energy distribution and the standard deviation of the particle's kinetic energy. For example, the kinetic energy of a particle can be determined by iterating through the velocities of all particles at each time step using the following formula:

[0053]

[0054] Where i represents the i-th particle, i is a positive integer, and E ki Let m represent the kinetic energy of the i-th particle. i Let v represent the mass of the i-th particle. i This represents the velocity of the i-th particle.

[0055] The kinetic energy of all particles can be statistically analyzed to determine the mean and standard deviation of the particle kinetic energy distribution.

[0056] For example, the mean of the kinetic energy distribution of the particles in the above embodiments can be represented as μ, and the standard deviation of the kinetic energy distribution of the particles can be represented as σ. The mean μ and standard deviation σ of the particle kinetic energy distribution can be extracted by Gaussian fitting.

[0057] To perform Gaussian fitting, the kinetic energy values ​​can first be divided into several intervals, and the number of atoms in each interval can be counted. Typically, the optimal number of intervals is 50-100 to ensure a smooth distribution. For example, determining the intervals for kinetic energy values ​​may include the following steps:

[0058] (1) Determine the range: Based on the kinetic energy values ​​of all particles, determine the minimum value E. min and maximum value Emax .

[0059] (2) Divide the interval: divide [E] into intervals. min E max The interval is divided into B subintervals, and the width of each subinterval is ΔE = (E max -E min ) / B.

[0060] (3) Count the number of atoms: For each subinterval p, count the number of atoms N. p .

[0061] The formula for the Gaussian distribution function is as follows:

[0062]

[0063] Where μ is the mean of the particle kinetic energy distribution, σ is the standard deviation of the particle kinetic energy distribution, and E can represent the particle kinetic energy value. The parameters μ and σ of the Gaussian fit can be solved using the least squares method or maximum likelihood estimation (MLE).

[0064] The least squares method first requires constructing the following error function, where f(E) k N is the number of atoms in the k-th interval predicted according to the Gaussian distribution.

[0065]

[0066] Where N is the total number of atoms. μ and σ are solved using numerical optimization methods (such as the Levenberg-Marquardt algorithm) to make χ... 2 minimize.

[0067] Maximum likelihood estimation first constructs the following likelihood function, where f(E) k ) is the probability density of atoms in the k-th interval:

[0068]

[0069] Taking the logarithm of the likelihood function, we obtain the log-likelihood function lnL(μ,σ):

[0070]

[0071] And further simplified to:

[0072]

[0073] The log-likelihood function is maximized by solving for μ and σ using numerical optimization methods (such as Newton's method or gradient ascent method), that is, finding μ and σ that maximize the probability of the observed data.

[0074] For ion implantation systems on a million-scale basis, the mean and standard deviation of the particle kinetic energy distribution obtained using Gaussian fitting can reflect parameter estimates of the underlying normal distribution, facilitating comparison with process models and subsequent use in Technology Computer-Aided Design (TACD) simulations for semiconductor manufacturing processes. It should be understood that the embodiments of this disclosure are not limited thereto, and other suitable methods can also be used to determine the particle kinetic energy.

[0075] Returning to Figure 3, at box 304 in Figure 3, multiple Type I particles with energies below the energy threshold are identified based on a comparison of kinetic energy and energy threshold.

[0076] In some embodiments, an energy threshold can be specified to classify particles, and particles with kinetic energy below the energy threshold can be identified as first-class particles. The size of the energy threshold can be set as needed.

[0077] In some embodiments, the energy threshold may include a first energy threshold, which may be determined based on the mean of the particle's kinetic energy distribution and the standard deviation of the particle's kinetic energy distribution.

[0078] For example, in some embodiments, the first energy threshold may be determined by: using the average kinetic energy of the particles as the initial value of the mean of the kinetic energy distribution of the particles; using the sample standard deviation of the particle kinetic energy as the initial value of the standard deviation of the kinetic energy distribution of the particles; and iteratively determining the first energy threshold by Gaussian fitting based on the initial value of the mean and the initial value of the standard deviation.

[0079] In the aforementioned algorithm for solving Gaussian distribution parameters, the selection of initial parameters is crucial to the convergence speed and the accuracy of the results. Traditional methods manually set initial values, such as choosing random values. However, the inventors of this invention discovered that when performing Gaussian fitting, the average kinetic energy of all particles in the system can be used as the initial value for the mean of the particle kinetic energy distribution, and the sample standard deviation of the particle kinetic energy can be used as the initial value for the standard deviation of the particle kinetic energy distribution. Compared to setting random values ​​as initial values, the initial values ​​set by the inventors are closer to the true values, reducing the number of iterations in the algorithm and avoiding fitting failures caused by initial values ​​deviating too far from the true values, such as Gaussian distribution shift.

[0080] In some embodiments, determining a first energy threshold by iteratively performing Gaussian fitting based on the initial values ​​of the mean and standard deviation of the particle's kinetic energy distribution may include: determining the first energy threshold based on the product of the standard deviation and the fitting coefficients and the mean.

[0081] For example, the first energy threshold can be calculated using the following formula:

[0082]

[0083] Where E1 represents the first energy threshold, μ represents the mean, σ represents the standard deviation, and c represents the fitting coefficient.

[0084] A larger fitting coefficient results in a larger first energy threshold E1. The fitting coefficient can be set empirically; for example, the range of the fitting coefficient c can be 1 ≤ c ≤ 3. When c is 1, it is suitable for low-energy injection, such as when the energy of the injected ions is less than 1 keV. In this case, the proportion of Class I particles in all particles is small, and strict differentiation is required. When c is 3, it is suitable for high-energy injection, such as when the energy of the injected ions is greater than 10 keV. In this case, the proportion of Class I particles is large, and the first energy threshold can be relaxed to avoid misjudgment.

[0085] The first energy threshold is a value determined by the change in the kinetic energy of a particle; therefore, it can also be called the dynamic energy threshold. The first energy threshold can adapt to system energy fluctuations and more accurately determine the first type of particle.

[0086] In some embodiments, the energy threshold may further include a second energy threshold, which is a constant value determined based on the properties of the semiconductor material.

[0087] The properties of semiconductor materials can include their lattice constant, binding energy, etc. The second energy threshold can also be referred to as the fixed energy threshold.

[0088] In the above embodiments, determining a plurality of first-class particles whose energy is lower than the energy threshold based on a comparison of kinetic energy and energy threshold may include: using the larger of a first energy threshold and a second energy threshold as a reference energy threshold; and dividing the particles into a plurality of first-class particles and a plurality of second-class particles whose kinetic energy is higher than the energy threshold based on a comparison of kinetic energy and the reference energy threshold.

[0089] That is, the criteria for determining the first type of particle can be expressed as:

[0090]

[0091] Where E is the kinetic energy of each particle, E1 represents the first energy threshold, and E2 represents the second energy threshold.

[0092] The kinetic energy of Type I particles is below the energy threshold, meaning their movement is relatively slow. Multiple Type I particles can be grouped together to reduce computational load. In contrast, the kinetic energy of Type II particles is above the energy threshold, meaning their trajectories are more sensitive to collisions and require high-precision, independent simulation as individual atoms. This strategy of classifying Type I and Type II particles significantly improves computational efficiency while maintaining physical accuracy.

[0093] Using both the first and second energy thresholds simultaneously is to more reasonably determine the boundary of the first type of particles, while adapting to system energy fluctuations and preventing particles with extremely low energy from being classified as second type particles.

[0094] It should be noted that system energy includes the kinetic and potential energy of the particles, with potential energy including the interaction potential energy between particles. The system fluctuations are caused by violent collisions that occur during ion implantation, such as cascade collisions, leading to sudden energy spikes.

[0095] The second energy threshold can be set to 10eV-100eV based on the material properties. Since the second energy threshold is a fixed value, it can also be called the fixed energy threshold.

[0096] The first energy threshold (dynamic energy threshold) can adapt to system energy fluctuations, avoiding misclassification of Type I particles due to a mismatch between the second energy threshold (fixed energy threshold) and system energy changes when only the second energy threshold (fixed energy threshold) is used. The second energy threshold can serve as a lower limit to prevent particles with extremely low kinetic energy from being misclassified as Type II particles. For example, the larger the lattice constant, the weaker the interparticle forces, and the lower the energy required for particles to escape the lattice; in this case, the second energy threshold can be appropriately lowered. Conversely, when the binding energy is higher, particles require more energy to escape the lattice, requiring a higher second energy threshold to avoid misclassification as Type II particles.

[0097] In some embodiments, the first energy threshold is determined by: redetermining the mean and standard deviation of the kinetic energy distribution of the particles at a preset time step; using the redetermined mean of the kinetic energy distribution of the particles as the updated mean of the kinetic energy distribution of the particles, and using the redetermined standard deviation of the kinetic energy distribution as the updated standard deviation of the kinetic energy distribution of the particles; and determining the first energy threshold based on the updated mean and the updated standard deviation.

[0098] The determination of the first energy threshold based on the mean and standard deviation of the updated particle kinetic energy distribution is made in consideration of the slow evolution of the system.

[0099] Following ion implantation, the energy distribution or structural state of the system undergoes gradual changes over a relatively long timescale (e.g., hundreds of nanoseconds to microseconds), a process known as slow system evolution. Damage accumulation is one manifestation of this slow evolution. In semiconductor materials, atoms are gradually knocked away from their lattice positions, forming defects such as vacancies and interstitial atoms, leading to gradual changes in the local crystal structure and resulting in damage accumulation.

[0100] Because the system evolves slowly, the first energy threshold needs to be updated in real time to adapt to changes in system energy. However, updating the first energy threshold in real time consumes a lot of computational resources. Therefore, in the above embodiment, for example, the preset time step can be set to a fixed value of 100 fs. That is, every 100 fs, the mean and standard deviation of the particle kinetic energy distribution are redefined. The redefined mean of the particle kinetic energy distribution is used as the updated mean, and the redefined standard deviation is used as the updated standard deviation. Then, the first energy threshold is determined based on the updated mean and updated standard deviation. This ensures that the first energy threshold adapts to the system state and guarantees the accuracy of the simulation calculation.

[0101] A preset time step of 100 fs is a common update cycle in molecular dynamics simulations. Frequent updates, such as a preset time step of 10 fs, may consume significant computational resources, while a preset time step of 100 fs is sufficient to capture the slow evolution of the system, such as changes in energy distribution during loss accumulation. The preset time step can also be set according to the degree of energy change in the system, simulation accuracy requirements, or computational resources to balance computational efficiency and real-time performance, ensuring the accuracy of the first energy threshold.

[0102] In addition, when the system experiences a violent collision event, such as high-energy ion implantation, the system may be in a high-temperature state, and it may be necessary to reset the first energy threshold to avoid misidentifying second-type particles.

[0103] In response, this disclosure provides another method for determining the first energy threshold. For example, in some embodiments of this disclosure, the first energy threshold may be determined by: determining the system energy at the current moment, the system energy at the previous moment, and the historical average energy; determining the ratio of the absolute value of the difference between the system energy at the current moment and the system energy at the previous moment to the historical average energy; in response to the ratio being greater than a preset proportion, re-determining the mean of the particle's kinetic energy distribution as the updated mean of the particle's kinetic energy distribution, and re-determining the standard deviation of the kinetic energy distribution as the updated standard deviation of the particle's kinetic energy distribution; and determining the first energy threshold based on the updated mean and the updated standard deviation.

[0104] For example, the system energy at the current moment, the system energy at the previous moment, and the historical average energy can be calculated. The ratio of the absolute value of the difference between the system energy at the current moment and the system energy at the previous moment to the historical average energy is determined. When this ratio is greater than a preset proportion, the mean of the particle's kinetic energy distribution is redefined as the updated mean of the particle's kinetic energy distribution, and the standard deviation of the particle's kinetic energy distribution is redefined as the updated standard deviation of the particle's kinetic energy distribution. Then, a first energy threshold is determined based on the updated mean and the updated standard deviation.

[0105] The preset ratio can be set to, for example, 5%, to quickly respond to drastic changes in the system, such as cascading collisions caused by high-energy ion implantation. If the system energy suddenly increases by 5% due to a collision, a threshold update can be triggered to avoid misclassifying type I particles. If the system experiences small energy fluctuations, such as a change of less than 5%, it may be due to numerical errors or transient effects of local collisions, and can be considered an invalid trigger and filtered out.

[0106] Therefore, the first energy threshold in the above embodiments can be set according to the system state and can dynamically adapt to different system states in order to maintain the system's computational efficiency and physical accuracy.

[0107] Returning to Figure 3, at box 306 in Figure 3, multiple Type I particles are divided into at least one Type I particle group. The following is a detailed description in conjunction with Figure 4.

[0108] Figure 4 illustrates a schematic diagram 400 of particle division according to some embodiments of the present disclosure. Some embodiments of the present disclosure are further described below with reference to Figure 4.

[0109] As shown in Figure 4, the first type of particles represented by triangles are 401-e (e is a positive integer), and 401-1, 401-2, ..., 401-e can be divided into the first group of first type particles 410. The first type of particles represented by squares are 402-f (f is a positive integer), and 402-1, 402-2, ..., 402-f can be divided into the second group of first type particles 420. The first type of particles represented by rhombuses are 403-g (g is a positive integer), and 403-1, 403-2, ..., 403-g can be divided into the third group of first type particles 430. The first type of particles represented by ellipses are 404-h (h is a positive integer), and 404-1, 404-2, ..., 404-h can be divided into the fourth group of first type particles 440.

[0110] Therefore, it can be seen that there are a total of 4 groups of particles of the first type in Figure 4, and the number of particles of the first type in Figure 4 is much smaller than the number of particles of the first type. Therefore, the simulation method provided in this embodiment can reduce the number of simulation objects, thereby reducing the computational load and improving computational efficiency.

[0111] In some embodiments, classifying a plurality of first-type particles into at least one first-type particle group may include: determining a neighborhood radius based on the properties of the semiconductor material; and classifying a plurality of first-type particles into at least one first-type particle group based on the neighborhood radius and a lower limit value for the number of particles.

[0112] Properties of semiconductor materials can include their lattice constant or atomic density. For example, the neighborhood radius can be calculated using the following formula:

[0113]

[0114] Where ε represents the neighborhood radius, L lattice This represents the lattice constant of a semiconductor material; for example, the lattice constant of silicon (Si) is 5.43 Å.

[0115] Alternatively, the neighborhood radius can also be calculated using the following formula:

[0116]

[0117] ρ represents the atomic density of a semiconductor material; for example, the atomic density of silicon is 5.0 × 10⁻⁶. 22 atoms / cm 3 .

[0118] The minimum particle count represents the minimum number of Type I particles in each Type I particle group. This minimum particle count can be set empirically. For example, it can be set to 5-10 particles.

[0119] In some embodiments, dividing a plurality of first-class particles into at least one first-class particle group based on a neighborhood radius and a lower limit of particle number includes: marking each of the plurality of first-class particles as a first state to obtain a plurality of first-state particles; for each of the plurality of first-state particles, determining the number of neighborhood particles within the neighborhood radius of the first-state particle; and in response to the number of neighborhood particles being greater than or equal to the lower limit of particle number, dividing the first-state particles and the neighborhood particles into a first-class particle group, and marking the first-state particles and the neighborhood particles as second-state particles.

[0120] In some embodiments, the simulation method may further include: for each of a plurality of first-state particles, in response to the number of neighboring particles being less than a lower limit of the number of particles, marking the first-state particle as a third-state particle; determining the distances from the third-state particle to all first-class particle groups respectively; for each distance from the third-state particle to all first-class particle groups, in response to the distance being less than or equal to a preset distance, adding the third-state particle to the first-class particle group corresponding to the distance and marking the third-state particle as a second-state particle; and in response to the distance being greater than the preset distance, marking the third-state particle as an independent particle.

[0121] The above embodiments, in conjunction with Figure 4, describe the division of multiple first-type particles into at least one first-type particle group. It should be understood that the division method of the embodiments of this disclosure is not limited to this, but can be varied according to actual needs.

[0122] Figure 5 illustrates a schematic flowchart of particle clustering according to some embodiments of the present disclosure. The process of dividing a plurality of first-class particles into at least one first-class particle group based on the neighborhood radius and a lower limit value of the particle number is described in detail below with reference to Figure 5.

[0123] At box 502, each first-type particle can be marked as a first state to obtain the first-type particles of the first-type state. The first-type state can be understood as an "unvisited" state. For ease of description, the first-type particles of the first state are referred to as first-state particles.

[0124] For example, the first-state particle is called an unvisited particle. For each unvisited particle, at box 504, the number of particles N in its neighborhood is determined.

[0125] At box 506, determine whether the number of particles N in the neighborhood is greater than or equal to the lower limit of the number of particles.

[0126] When the number of neighboring particles of the unvisited particle is greater than or equal to the lower limit of the number of particles, at box 508, the first state particle and its neighboring particles are divided into a first type of particle group, and the first state particle and its neighboring particles are marked as second state particles.

[0127] The second state can be understood as an "visited" state, indicating that the particle has already been judged and classified. Similarly, for ease of description, the second type of particle in the second state is called the second-state particle.

[0128] When the number of neighboring particles of an unvisited particle is less than the lower limit of the number of particles, the first-state particle is marked as a third-state particle at box 510.

[0129] The third-state particle can be understood as "noise". In the current step, the third-state particle cannot be added to the first-class particle group.

[0130] The third-state particles can be understood in conjunction with Figure 4. For example, the quadrilateral 405-q (where q represents a positive integer) in Figure 4 can be understood as including the third-state particles. Third-state particles are those that are not currently assigned to any first-class particle group. For third-state particles, their interactions with other particles or first-class particle groups can be simulated.

[0131] The third-state particles can be further processed to reduce the number of first-class particles that are not classified into the first-class particle group, thus further reducing the computational load. For example, at box 512, it can be determined whether the distance from the third-state particle to all first-class particle groups is less than a preset distance.

[0132] For each distance from the third-state particle to all first-class particle groups, if the distance is less than a preset distance, the third-state particle is added to the first-class particle group corresponding to that distance at box 514.

[0133] For example, the preset distance can be set to half of the neighborhood radius ε / 2, or other values ​​can be set based on experience.

[0134] When the distance is greater than the preset distance, the third-class state particle is marked as an independent particle at box 516.

[0135] For example, the particle represented by the quadrilateral 405-q in Figure 4 can include independent particles. Independent particles are those that are not currently classified into any Class I particle group. For independent particles, their interactions with other particles or Class I particle groups can be simulated.

[0136] Perform the steps of method 500 shown in Figure 5 on each first-class particle until all first-class particles have been labeled as second-state particles or third-state particles.

[0137] The method described above, which involves adding third-state particles to the first-class particle group or retaining them as independent particles based on the distance between the third-state particles and the first-class particle group, can effectively prevent isolated particles from being incorrectly clustered and ensure the reasonable construction of the first-class particle group.

[0138] After completing the division of the first type of particle groups, there may be a situation where the number of particles in the first type of particle groups is too large. In order to ensure a balance between computational efficiency and physical accuracy, the simulation method of some embodiments of this disclosure may further include: for each of the first type of particle groups in at least one first type of particle group, comparing the number of particles in the first type of particle group with an upper limit value for the number of particles; and in response to the number of particles being greater than the upper limit value for the number of particles, splitting the first type of particle group so that the number of particles satisfies a lower limit value for the number of particles and a lower limit value for the number of particles and an upper limit value for the number of particles.

[0139] For example, the maximum particle count can be set to 200. When the number of particles in the first type of particle group exceeds 200, the first type of particle group is split. The requirement for splitting is that the number of particles in the first type of particle group is greater than the lower limit of the particle count and less than or equal to the upper limit of the particle count.

[0140] In some embodiments, splitting a first type of particle group includes: determining the local density within the first type of particle group; and segmenting the first type of particle group along the density gradient direction.

[0141] The local density in a group of first-type particles can be calculated using the following formula:

[0142] ρ local =N local / V local

[0143] Where ρ local N represents the local density. local V represents the number of local particles in the first type of particle group. local This represents the local particle volume within the first type of particle group.

[0144] The density gradient can be calculated using the following formula:

[0145]

[0146] The first type of particle group is segmented along the density gradient direction, and the size of the resulting first type of particle group is controlled within a reasonable range to maintain computational accuracy. For example, the number of particles in the first type of particle group is controlled between 20 and 200. To avoid damaging the physical structure, the segmentation can be performed along low-density regions.

[0147] In some embodiments, classifying a plurality of first-type particles into at least one first-type particle group includes: redetermining the kinetic energy of the particles at a preset time step; and classifying the plurality of first-type particles into at least one first-type particle group based on the redetermined kinetic energy of the particles.

[0148] The kinetic energy of particles can be recalculated at a preset time step so that the simulation can reflect the actual changes in particle kinetic energy. For example, the preset time step can be set to 100 fs. The kinetic energy of particles is recalculated every 100 fs to divide multiple Class I particles into at least one Class I particle group.

[0149] The kinetic energy of particles may change due to factors such as collisions, but updating the division of the first type of particle group in real time would consume a lot of computational resources. Therefore, re-dividing the first type of particle group at preset time steps can balance the accuracy of the simulation and computational efficiency.

[0150] In some embodiments, classifying a plurality of first-type particles into at least one first-type particle group may include: determining the system energy at the current moment, the system energy at the previous moment, and the historical average energy; determining the ratio of the absolute value of the difference between the system energy at the current moment and the system energy at the previous moment to the historical average energy; and reclassifying the plurality of first-type particles into at least one first-type particle group in response to the ratio being greater than a preset proportion.

[0151] The conditions for reclassifying the first type of particles, such as the system energy at the current moment, the system energy at the previous moment, and the historical average energy, can be referred to the aforementioned embodiment for determining the first energy threshold, and will not be repeated here. When the ratio of the absolute value of the difference between the system energy at the current moment and the system energy at the previous moment to the historical average energy is greater than a preset proportion, that is, when the system energy fluctuation reaches the preset proportion, the multiple first type of particles are reclassified into at least one group of first type particles.

[0152] Since system energy includes the sum of the kinetic energies of the particles in the system, fluctuations in system energy can reflect changes in particle kinetic energy to a certain extent. By using a preset proportion that reflects system energy fluctuations as the condition for reclassifying the first type of particle group, the classification of the first type of particle group is made closer to the actual state of the particles, thus ensuring the accuracy of the simulation.

[0153] Returning to Figure 3, at box 308 in Figure 3, the interactions between at least one group of first-type particles and particles outside the group of first-type particles, as well as the interactions between at least one group of first-type particles, are determined to obtain the simulated particle-scale dynamics process.

[0154] After classifying the first type of particles into at least one group of first type particles, the interactions between particles can mainly include two parts: the interactions between the first type of particle groups and particles other than the first type of particle groups; and the interactions between at least one group of first type particles.

[0155] For example, the above steps can be understood in conjunction with Figure 4. Figure 4 also includes particle 405-q (q is a positive integer) that was not classified into the first type of particle group. Since each of the four first type of particle groups shown in Figure 4 (the first first type of particle group 410, the second first type of particle group 420, the third first type of particle group 430, and the fourth first type of particle group 440) contains multiple first type of particles, when simulating the interaction between particles, the interaction between multiple first type of particles can be simplified to the interaction between the four first type of particle groups and the interaction between the four first type of particle groups and particle 405-q. This significantly reduces the computational load of the simulation, thereby reducing the complexity of the simulation and improving computational efficiency. At the same time, an energy threshold can be used as the boundary condition for determining the first type of particles. By setting the energy threshold, the classification of the first type of particles can be controlled to balance the physical accuracy of the simulation.

[0156] In some embodiments, determining the interaction between at least one first type of particle group and particles outside the first type of particle group, as well as the interaction between groups of at least one first type of particle group, includes: for each first type of particle group in at least one first type of particle group, determining the mass of the first type of particle group, the center of mass of the first type of particle group, and the velocity of the first type of particle group; and determining the interaction between the first type of particle group and particles outside the first type of particle group, as well as the interaction between the individual first type of particle groups, based on the mass, the center of mass, and the velocity.

[0157] The above embodiments propose a simulation method for the interaction of first-type particle groups. Specifically, for each first-type particle group, when determining the interaction between the first-type particle group and particles outside the first-type particle group, as well as the interaction between the first-type particle group and other first-type particle groups, the interaction can be determined based on the mass, center of mass, and velocity of the first-type particle group.

[0158] The following sections will provide detailed explanations of two scenarios: the interaction between the first type of particle group and particles outside the first type of particle group, and the interaction between different first type of particle groups.

[0159] First, the interaction between the first type of particle group and particles outside the first type of particle group is explained.

[0160] In some embodiments, determining the interaction between the first type of particle group and particles outside the first type of particle group includes: in response to the distance between the first type of particle group and particles outside the first type of particle group being greater than or equal to a distance threshold, determining the parameters of an equivalent model of the first type of particle group based on mass, center of mass, and velocity; and determining the interaction between the first type of particle group as a whole and particles outside the first type of particle group based on the parameters of the equivalent model.

[0161] When the distance between the first type of particle group and particles outside the first type of particle group is greater than or equal to a distance threshold, it can be understood that the interaction between the first type of particle groups is a long-range interaction. In this case, the parameters of the equivalent model of the first type of particle group can be determined based on its mass, center of mass, and velocity.

[0162] For example, the mass of the first type of particle group can be calculated using the following formula:

[0163]

[0164] Where M represents the mass of the first type of particle group, m i Let i represent the mass of the i-th particle, where i is a positive integer from 1 to N, and N represents the number of first-type particles in the first-type particle group.

[0165] The centroid of the first type of particle group can be calculated using the following formula:

[0166]

[0167] Where R group Let m represent the center of mass of the first type of particle group. i The mass of the i-th particle is represented by the vector r. i This represents the position vector of the i-th particle in the coordinate system, where i is a positive integer from 1 to N, and N represents the number of first-type particles in the first-type particle group.

[0168] The velocity of the first type of particle group can be calculated using the following formula:

[0169]

[0170] Where V group The velocity m represents the velocity of the first type of particle swarm. i Let v represent the mass of the i-th particle. i This represents the velocity of the i-th particle, where i is a positive integer ranging from 1 to N, and N represents the number of first-type particles in this first-type particle group.

[0171] Based on the mass, center of mass, and velocity of the first type of particle group, an equivalent model of the interaction force between the first type of particle group and particles outside the first type of particle group can be established using the following formula:

[0172]

[0173] Where F ij M represents the interaction force between the first type of particle group and particles outside the first type of particle group. i The mass of the first type of particle group is m. j r represents the mass of particles outside the first type of particle group. ij It indicates the distance between the two.

[0174] Therefore, by clustering the first type of particles into a first type of particle group, and by using the mass, centroid, and velocity of the first type of particle group as a whole, an equivalent model of the first type of particle group can be established to determine the interaction between the first type of particle group and particles outside the first type of particle group, which can reduce computational complexity and computational load.

[0175] In some embodiments, determining the interaction between at least one first type of particle group and particles outside the first type of particle group includes: in response to the distance between the first type of particle group and particles outside the first type of particle group being less than a distance threshold, determining the interaction between each particle in the first type of particle group and particles outside the first type of particle group.

[0176] When the distance between the first type of particle group and particles outside the first type of particle group is less than a distance threshold, the interaction between the first type of particle group and particles outside the first type of particle group is no longer considered as a whole. Instead, the interaction between each particle in the first type of particle group and particles outside the first type of particle group is determined separately. This is because the difference between long-distance and short-distance interactions between particles is taken into account.

[0177] In ion implantation, cascading collisions are the process by which high-energy ions collide with atoms in a semiconductor material (target), and the atoms in the semiconductor material gain sufficient energy to further collide with neighboring atoms. This process is the core mechanism for the generation of local lattice damage (such as vacancies and interstitial atoms). After gaining sufficient energy, the atoms in the collided semiconductor material undergo secondary and tertiary collisions with neighboring atoms, forming a cascading effect.

[0178] Close-range interactions may occur in the core region of a cascade collision, requiring precise calculations of the trajectory and forces acting on each particle in the first-type particle swarm to capture atomic-level collision events, such as atoms being knocked out of the crystal lattice in semiconductor materials. Long-range interactions extend beyond the cascade collision's effective region, eliminating the need for precise simulations of each particle's trajectory and forces. The first-type particle swarm can be treated as a whole, establishing an equivalent model and ignoring localized particle motions within the swarm.

[0179] For example, the threshold distance can be set to 0.5 nm based on the region where cascade collisions occur. By setting the threshold distance, when the distance between the first type of particle group and particles outside the first type of particle group is greater than or equal to the threshold distance, the interaction is determined based on equivalent model parameters to reduce computational load and improve computational efficiency. When the distance between the first type of particle group and particles outside the first type of particle group is less than the threshold distance, the interaction between each particle in the first type of particle group and particles outside the first type of particle group is determined to accurately reflect the cascade collision process and preserve the process of generating local defects in the collision.

[0180] The interactions between the various groups of first-type particles will be explained next.

[0181] In some embodiments, determining the interaction between each group of first-type particles includes: in response to a distance between a group of first-type particles and a group of first-type particles outside the group of first-type particles being greater than or equal to a distance threshold, determining the parameters of an equivalent model of the group of first-type particles based on mass, centroid, and velocity; and determining the interaction between each group of first-type particles based on the parameters of the equivalent model.

[0182] When the distance between a group of first-type particles and other groups of first-type particles is greater than or equal to a threshold distance, the parameters of the equivalent model of the first-type particle group can be determined based on the mass, centroid, and velocity of the first-type particle group. The interaction between this first-type particle group and other groups of first-type particles is then determined based on the parameters of the equivalent model. The same operation is performed for each group of first-type particles.

[0183] The determination of the mass, velocity, and center of mass of the first type of particle group can be done using the same method as when considering the interaction between the first type of particle group and particles outside the first type of particle group, and will not be repeated here.

[0184] Based on the mass, center of mass, and velocity of the first-type particle groups, an equivalent model of the interaction forces between the various first-type particle groups can be established using the following formula:

[0185]

[0186] Where F ij M represents the interaction force between the i-th group of first-type particles and the group outside the j-th group of first-type particles. i M represents the mass of the i-th group of particles of the first type. j Let r represent the mass of the j-th particle outside the first type of particle group. ij It indicates the distance between the two.

[0187] When the distance between the first type of particle groups is greater than or equal to the threshold distance, the interaction between the first type of particle groups is determined based on the parameters of the equivalent model of the mass, centroid and velocity of the first type of particle groups. Since the number of the first type of particle groups is much smaller than the total number of particles, the computational complexity is reduced from the square of the total number of particles to the square of the number of the first type of particle groups, and the amount of computation can be significantly reduced.

[0188] In some embodiments, the interaction between at least one group of first-type particles includes: in response to the distance between the first-type particle group and a group of first-type particles outside the first-type particle group being less than a distance threshold, determining the interaction between each particle in the first-type particle group and the group of first-type particles outside the first-type particle group.

[0189] When the distance between a first-type particle group and other first-type particle groups outside of that first-type particle group is less than a distance threshold, the interaction between each particle in that first-type particle group and other first-type particle groups is determined. The same operation is performed on other first-type particle groups.

[0190] When the distance between a group of particles of the first type and other groups of particles of the first type is less than a threshold distance, the interaction between each particle in the group and each particle in the other group is considered, thereby capturing the generation of local defects and maintaining the physical accuracy of the simulation.

[0191] Some embodiments of this disclosure provide simulation models generated by simulation methods for ion implantation. It should be noted that the above embodiments are merely illustrative of the embodiments of this disclosure and should not be considered as limitations on this disclosure.

[0192] It should be understood that the embodiments shown in the accompanying drawings are merely illustrative of some embodiments of this disclosure and are not intended to limit this disclosure. Embodiments of this disclosure may also have various other forms.

[0193] Some embodiments of this disclosure provide an electronic device including a processor; and a memory coupled to the processor, the memory having instructions stored therein, the instructions causing the device to perform actions when executed by the processor, the actions including: determining the kinetic energy of particles, the particles including atoms in a semiconductor material and ions injected into the semiconductor material; determining a plurality of first-type particles with energies below an energy threshold based on a comparison of kinetic energy and an energy threshold; dividing the plurality of first-type particles into at least one first-type particle group; and determining the interactions between at least one first-type particle group and particles outside the first-type particle group, as well as the interactions between at least one first-type particle group, to obtain a simulated particle-scale dynamics process.

[0194] Some embodiments of this disclosure also provide a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the method according to embodiments of this disclosure.

[0195] Figure 6 shows a schematic block diagram of an electronic device according to some exemplary embodiments of the present disclosure. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present disclosure described and / or claimed herein.

[0196] As shown in Figure 6, device 600 includes a CPU 601, which can perform various appropriate actions and processes based on a computer program stored in read-only memory (ROM) 602 or a computer program loaded from storage unit 608 into random access memory (RAM) 603. RAM 603 can also store various programs and data required for the operation of device 600. CPU 601, ROM 602, and RAM 603 are interconnected via bus 604. Input / output (I / O) interface 605 is also connected to bus 604.

[0197] Multiple components in device 600 are connected to I / O interface 605. These components include: input unit 606, such as a keyboard or mouse; output unit 607, such as various types of displays or speakers; storage unit 608, such as a hard disk or optical disk; and communication unit 609, such as a network interface card (NIC), modem, or wireless transceiver. Communication unit 609 allows device 600 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0198] The various processes and procedures described above, such as method 300, can be executed by CPU 601. For example, in some embodiments, method 300 can be implemented as a computer software program tangibly contained in a machine-readable medium, such as storage unit 608. In some embodiments, part or all of the computer program can be loaded and / or installed on device 600 via ROM 602 and / or communication unit 609. When the computer program is loaded into RAM 603 and executed by CPU 601, one or more steps of method 300 described above can be performed.

[0199] The embodiments of this disclosure may be methods, apparatus, systems, and / or computer program products. A computer program product may include a computer-readable storage medium on which computer-readable program instructions for performing various aspects of this disclosure are loaded. The computer-readable storage medium may be a tangible device capable of holding and storing instructions used by an instruction execution device. The computer-readable program instructions may be downloaded from the computer-readable storage medium to various computing / processing devices, or downloaded via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network, to an external computer or external storage device.

[0200] The various embodiments of this disclosure have been described above. These descriptions are exemplary and represent only optional embodiments of this disclosure, and are not exhaustive, nor are they intended to limit the scope of this disclosure. Although the claims in this application are formulated for specific combinations of features, it should be understood that the scope of this disclosure also includes any novel feature or any novel combination of features, whether express or implied or generalized herein, whether or not it relates to the same scheme in any currently claimed claim. The applicant hereby informs that new claims may be formulated as these features and / or combinations of these features during the examination of this application or in any further applications derived therefrom.

[0201] The terminology used herein is chosen to best explain the principles, practical applications, or technological improvements of the various embodiments, or to enable those skilled in the art to understand the embodiments disclosed herein. Various modifications and variations can be made to this disclosure by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A simulation method for ion implantation, comprising: Determine the kinetic energy of the particles, which include atoms in a semiconductor material and ions injected into the semiconductor material; Based on the comparison between the kinetic energy and the energy threshold, a plurality of first-type particles with energy below the energy threshold are identified; the plurality of first-type particles are divided into at least one first-type particle group; and the interactions between the at least one first-type particle group and particles outside the first-type particle group, as well as the interactions between the at least one first-type particle group, are determined to obtain a simulated particle-scale dynamics process.

2. The simulation method according to claim 1, wherein determining the kinetic energy of the particle includes: Determine the mean and standard deviation of the kinetic energy distribution of the particle.

3. The simulation method according to claim 2, wherein the energy threshold includes a first energy threshold, the first energy threshold being determined based on the mean and the standard deviation.

4. The simulation method according to claim 2, wherein the first energy threshold is determined based on: using the average kinetic energy of the particle as the initial value of the mean; using the sample standard deviation of the particle kinetic energy as the initial value of the standard deviation; and iteratively determining the first energy threshold by Gaussian fitting based on the initial value of the mean and the initial value of the standard deviation.

5. The simulation method according to claim 4, wherein determining the first energy threshold by iteratively performing Gaussian fitting based on the initial value of the mean and the initial value of the standard deviation comprises: The first energy threshold is determined based on the product of the standard deviation and the fitting coefficient and the mean.

6. The simulation method according to claim 3, wherein the energy threshold further includes a second energy threshold, the second energy threshold being a constant value determined based on the characteristics of the semiconductor material.

7. The simulation method according to claim 6, wherein determining a plurality of first-type particles with energy lower than the energy threshold based on the comparison between the kinetic energy and the energy threshold comprises: The larger of the first energy threshold and the second energy threshold is used as the reference energy threshold; And based on the comparison between the kinetic energy and the reference energy threshold, the particles are divided into a plurality of first-class particles and a plurality of second-class particles whose kinetic energy is higher than the energy threshold.

8. The simulation method according to claim 4, wherein the first energy threshold is determined by: re-determining the mean and standard deviation of the kinetic energy distribution of the particles at a preset time step; using the re-determined mean of the kinetic energy distribution of the particles as the updated mean of the kinetic energy distribution of the particles, and using the re-determined standard deviation of the kinetic energy distribution as the updated standard deviation of the kinetic energy distribution of the particles; and determining the first energy threshold based on the updated mean and the updated standard deviation.

9. The simulation method according to claim 4, wherein the first energy threshold is determined by: determining the system energy at the current moment, the system energy at the previous moment, and the historical average energy; determining the ratio of the absolute value of the difference between the system energy at the current moment and the system energy at the previous moment to the historical average energy; in response to the ratio being greater than a preset proportion, re-determining the mean of the kinetic energy distribution of the particles as an updated mean of the kinetic energy distribution of the particles, and re-determining the standard deviation of the kinetic energy distribution as an updated standard deviation of the kinetic energy distribution of the particles; and determining the first energy threshold based on the updated mean and the updated standard deviation.

10. The simulation method according to claim 1, wherein dividing the plurality of first-type particles into at least one group of first-type particles comprises: Determining the neighborhood radius based on the properties of semiconductor materials; And based on the neighborhood radius and the lower limit of the particle number, the plurality of first-class particles are divided into at least one first-class particle group.

11. The simulation method according to claim 10, wherein dividing the plurality of first-type particles into the at least one first-type particle group based on the neighborhood radius and the particle number lower limit includes: Each of the plurality of first-type particles is labeled as a first state, resulting in a plurality of first-state particles; For each of the plurality of first-state particles, determine the number of neighboring particles of the first-state particle within the neighborhood radius; and in response to the number of neighboring particles being greater than or equal to the lower limit of the particle number, classify the first-state particle and the neighboring particles into a first-class particle group, and mark the first-state particle and the neighboring particles as second-state particles.

12. The simulation method according to claim 11, further comprising: For each of the plurality of first-state particles, in response to the number of neighboring particles being less than the lower limit of the number of particles, the first-state particle is marked as a third-state particle; the distances of the third-state particle to all first-class particle groups are determined respectively; for each distance of the third-state particle to all first-class particle groups, in response to the distance being less than or equal to a preset distance, the third-state particle is added to the first-class particle group corresponding to the distance, and the third-state particle is marked as a second-state particle; And in response to the distance being greater than the preset distance, the third-state particle is marked as an independent particle.

13. The simulation method of claim 11, further comprising: for each of the at least one first type of particle group, comparing the number of particles in the first type of particle group with an upper limit value for the number of particles; and in response to the number of particles being greater than the upper limit value for the number of particles, splitting the first type of particle group such that the number of particles satisfies being greater than or equal to the lower limit value for the number of particles and less than or equal to the upper limit value for the number of particles.

14. The simulation method according to claim 13, wherein splitting the first type of particle group includes: Determine the local density within the first type of particle group; And segment the first type of particle group along the density gradient direction.

15. The simulation method according to claim 1, wherein dividing the plurality of first-type particles into at least one group of first-type particles comprises: The kinetic energy of the particles is redetermined using a preset time step; And based on the redefined kinetic energy of the particles, the plurality of first-class particles are divided into at least one group of first-class particles.

16. The simulation method according to claim 1, wherein dividing the plurality of first-type particles into at least one group of first-type particles comprises: Determine the system energy at the current moment, the system energy at the previous moment, and the historical average energy; Determine the ratio of the absolute value of the difference between the system energy at the current moment and the system energy at the previous moment to the historical average energy; In response to the ratio being greater than a preset ratio, the plurality of first-class particles are reclassified into at least one first-class particle group.

17. The simulation method of claim 1, wherein determining the interaction between the at least one first type of particle group and particles outside the first type of particle group, and the interaction between groups of the at least one first type of particle group, comprises: For each of the at least one first type of particle group, determine the mass of the first type of particle group, the center of mass of the first type of particle group, and the velocity of the first type of particle group; and determine the interaction between the first type of particle group and particles outside the first type of particle group, as well as the interaction between the individual first type of particle groups, based on the mass, the center of mass, and the velocity.

18. The simulation method of claim 17, wherein determining the interaction between the first type of particle group and particles outside the first type of particle group comprises: In response to the distance between the first type of particle group and particles outside the first type of particle group being greater than or equal to a distance threshold, the parameters of the equivalent model of the first type of particle group are determined based on the mass, the centroid, and the velocity; the interaction between the first type of particle group as a whole and particles outside the first type of particle group is determined based on the parameters of the equivalent model.

19. The simulation method of claim 17, wherein determining the interactions between the respective groups of the first type of particles comprises: In response to the distance between the first type of particle group and other first type of particle groups being greater than or equal to the distance threshold, the parameters of the equivalent model of the first type of particle group are determined based on the mass, the centroid, and the velocity; the interactions between each of the first type of particle groups are determined based on the parameters of the equivalent model.

20. The simulation method of claim 1, wherein determining the interaction between the at least one first type of particle group and particles outside the first type of particle group, and the interaction between groups of the at least one first type of particle group, comprises: In response to the distance between the first type of particle group and particles outside the first type of particle group being less than a distance threshold, the interaction between each particle in the first type of particle group and particles outside the first type of particle group is determined; or in response to the distance between the first type of particle group and a first type of particle group outside the first type of particle group being less than the distance threshold, the interaction between each particle in the first type of particle group and a first type of particle group outside the first type of particle group is determined.

21. A computer program product comprising machine-executable instructions that, when executed by a processor, cause the processor to implement the simulation method according to any one of claims 1 to 20.

22. An electronic device, comprising: processor; And a memory coupled to the processor, the memory having instructions stored therein, which, when executed by the processor, cause the device to perform actions, including: determining the kinetic energy of particles, said particles including atoms in a semiconductor material and ions injected into said semiconductor material; Based on the comparison between the kinetic energy and the energy threshold, a plurality of first-type particles with energy below the energy threshold are identified; the plurality of first-type particles are divided into at least one first-type particle group; and the interactions between the at least one first-type particle group and particles outside the first-type particle group, as well as the interactions between the at least one first-type particle group, are determined to obtain a simulated particle-scale dynamics process.

23. A computer-readable storage medium storing machine-executable instructions that, when executed by a processor, cause the processor to perform the method according to any one of claims 1-20.

Images