Optimized molecular dynamics simulation method for monocrystalline silicon cutting process

Abstract

The invention discloses an optimized molecular dynamics simulation method for a monocrystalline silicon cutting process. Comprising the following steps: initializing and setting parameters, creating a workpiece area, creating an abrasive particle area, creating an atomic box, setting atomic mass, fixing a boundary layer, selecting a potential function, carrying out energy minimization processing and relaxation processing, setting cutting parameters, and carrying out operation simulation and result visualization processing. According to the method, interaction between silicon atoms and interaction between silicon and carbon can be described more accurately by using Tersoft potential; the simulation stability is improved by setting time step length, temperature control and energy minimization; by defining different temperature control layers such as a constant temperature layer and a Newton layer, complex dynamic behaviors in the material cutting process can be better simulated; by optimizing a calculation model and an algorithm, the speed and the precision of atomic motion trail and stress distribution in the process of simulating the cutting of the monocrystalline silicon are remarkably improved, and the stability of the simulation process is ensured.

Description

Technical Field

[0001] The invention relates to the technical field of molecular dynamics simulation, in particular to an optimized molecular dynamics simulation method for a single crystal silicon cutting process. Background Art

[0002] In modern semiconductor manufacturing, single crystal silicon is widely used in the manufacture of electronic components as a basic material. The atomic motion and stress distribution in the single crystal silicon cutting process are key factors affecting the processing quality and efficiency. Traditional molecular dynamics simulation methods have problems such as large amount of calculation, slow speed, insufficient precision and poor stability in simulating the cutting process of single crystal silicon. Therefore, an optimized molecular dynamics simulation method is urgently needed for the atomic scale phenomena in single crystal silicon cutting. This method can accelerate the calculation while ensuring accuracy and improve the stability of the simulation process to cope with increasingly complex processing needs. Summary of the invention

[0003] The object of the present invention is to provide an optimized molecular dynamics simulation method for a single crystal silicon cutting process to solve the problems raised in the above background technology.

[0004] To achieve the above object, the present invention provides the following technical solution: an optimized molecular dynamics simulation method for a single crystal silicon cutting process, comprising the following steps: initializing and setting various parameters → creating a workpiece region → creating an abrasive region → creating an atomic box → setting atomic mass → fixing the boundary layer → selecting a potential function → energy minimization and relaxation → setting cutting parameters → running simulation and visualizing the results, the specific steps are:

[0005] S1. Initialize and set various parameters, including simulation space dimension, boundary conditions, system units, atom types, neighbor list parameters and update frequency, and time step;

[0006] S2, create workpiece regions, generate multiple regions by specifying coordinates, and use the union command to create composite regions. All regions such as boundary layers, isothermal layers, and Newtonian layers define different physical properties;

[0007] S3, creating an abrasive grain area, establishing multiple conical abrasive grains along the Y direction, each abrasive grain is created by the cone command, generating an upper cone-shaped area to simulate the geometric shape of the diamond abrasive grain, and merging multiple abrasive grains into an overall area by union;

[0008] S4. Create an atom box, define the space where the atoms will be placed, construct a lattice, and set the lattice constant. Use the lattice command to define the arrangement of atoms, generate atoms in different regions, and create atoms for silicon Si and carbon C atoms respectively.

[0009] S5. Set atomic mass, respectively set the mass of silicon Si and carbon C atoms, so as to consider their momentum and energy transfer in the simulation, and set the grouping to facilitate the subsequent settings, effectively divide the entire simulation area, and perform subsequent operations on this basis;

[0010] S6, boundary layer fixation, use the setforse command to fix the boundary layer and keep it fixed in space to reduce boundary effects;

[0011] S7. Potential function selection. The Tersoff potential function is used to simulate the interaction between silicon and silicon, and between carbon and silicon. Different potential function parameters are set to adapt to the connection effect of the two-phase material. The Tersoff potential function expression is:

[0012]

[0013] Among them, i and j represent two adjacent atoms, V ij represents the interaction potential between atoms i and j, f c is the cutoff function, R ij represents the distance between atom i and atom j, A ij and B ij is a parameter related to the interaction between two atoms, λ ij and μ ij is a parameter related to the interaction between two atoms, which determines the rate at which the potential function changes with distance. and is an exponential decay term, which is used to describe the phenomenon that the interaction between atoms weakens with increasing distance;

[0014] S8, perform energy minimization on all atoms, and use the NVT ensemble to relax the isothermal layer and the workpiece to obtain a stable workpiece structure;

[0015] S9, setting cutting parameters to run simulation, using velocity command to set initial temperature for constant temperature layer, setting the predetermined direction of abrasive cutting speed to linear movement along Y axis, direction to negative Y direction, and setting grinding along negative X direction at the same time;

[0016] S10. Through molecular dynamics simulation, the atomic motion trajectory is recorded in real time and the stress distribution is calculated. The running results are visualized and post-processed using ovito to obtain the results.

[0017] Furthermore, in step S1, the spatial dimension is set to 3D space; the boundary conditions can be set to contraction conditions, periodic conditions, and non-periodic conditions; the system units are metal, real, and gas; the atom type is set to atomic; the initial Verlet neighbor list is generated, and the update threshold is set: the neighbor and neigh_modify commands are used to set the generation and update frequency of the neighbor list to ensure fast calculation during the simulation process; the time step can be set to 0.001 or 0.002 picoseconds.

[0018] Furthermore, in step S2, the workpiece size is established, each area is established separately, and then merged into a workpiece, the boundary layer is fixed in position, and the boundary effect is reduced, the isothermal layer maintains thermal equilibrium, and the Newtonian layer conforms to Newtonian motion.

[0019] Furthermore, the step S4 creates a simulation box size, defines a lattice constant, and creates silicon atoms in the workpiece region and carbon atoms in the tool region.

[0020] Furthermore, in step S7, the pair_style tersoff command is used to specify the use of the Tersoff potential function, and the pair_coeff command is used to read the tersoff file containing the potential function parameters. The introduction of the Tersoff potential function makes the microscopic simulation of the material more accurate, especially in the presence of a complex chemical environment. By adjusting the parameters, it can well adapt to the characteristics of different materials, quantitatively describe the interaction between atoms, and explain the change law of the potential energy and bond strength between atoms.

[0021]

[0022] In the above formula, E represents the total energy, f c represents the cutoff function, V C (r ij ), V D (r ij ) represent the repulsive force and attractive force respectively, r ij represents the potential energy between atoms, b ij Indicates the strength of the bonds between atoms.

[0023] Furthermore, in step S8, the workpiece relaxation adopts the NVT ensemble: during the simulation process, the NVT ensemble is used to control the temperature of the isothermal layer and the Newtonian layer through the fix command to ensure that the system evolves at the required temperature.

[0024] Furthermore, in step S10, the atomic motion trajectory and stress distribution are recorded in real time by molecular dynamics simulation, the simulation is started by using the run command, the atomic motion trajectory and calculated stress distribution are recorded in real time by the dump command, and the simulation results are post-processed and output to the file

[0025] ×.xyz analyzes the acquired data and draws 3D graphs and stress distribution diagrams to visualize the simulation results.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] High precision: The Tersoff potential can more accurately describe the interaction between silicon atoms and between silicon and carbon. The Tersoff potential function uses a more detailed pair_coeff setting to clearly distinguish different atomic components and their interactions, and enhance the adaptability and accuracy of the potential function. In the simulation of single-crystal silicon grinding, the Tersoff potential function is used to describe the interaction between silicon atoms and between carbon and silicon. The Tersoff potential function can more accurately describe the atomic interactions in covalent bond materials (such as silicon and carbon). The Tersoff potential function takes into account multi-body interactions and can better capture environmental changes between atoms. The Tersoff potential function has good parameter adaptability and can be applied to different material systems by adjusting parameters, including the combination of various types of carbon and silicon. A better dynamic description through the Tersoff potential function model is conducive to understanding how materials react during the grinding process. The Tersoff potential function can effectively simulate complex structures related to the grinding process, such as crystal defects, surfaces, and phase interfaces, and provide more realistic predictions of friction and wear behavior.

[0028] Fast speed: Molecular dynamics simulations using MPI parallelization distribute computing tasks to multiple processor cores during operation, increasing computing speed and effectively improving simulation efficiency. By dividing the simulation area into different areas such as tools, workpieces, and constant temperature layers, different conditions can be applied to different parts in the same simulation, which makes it more flexible when studying complex material processing processes.

[0029] Good stability: The stability of the simulation is improved by setting the time step, temperature control and energy minimization. At the same time, cutting with multiple abrasives at the same time can better improve the stability of the cutting process. By defining different temperature control layers such as constant temperature layer and Newton layer, the complex dynamic behavior of the material cutting process can be better simulated. The reasonable combination of NVT constant temperature and NVE energy conservation ensemble enables the system to maintain stable characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1is a flow chart of an optimized molecular dynamics simulation method for a single crystal silicon cutting process provided by an embodiment of the present invention;

[0031] Figure 2 It is a three-dimensional model optimization diagram of an embodiment of the present invention;

[0032] Figure 3 This is a simulation process diagram of diamond cutting of single crystal silicon according to an embodiment of the present invention;

[0033] Figure 4 is a diagram of the motion trajectory of a single atom during the single crystal silicon cutting process according to an embodiment of the present invention;

[0034] Figure 5 It is a stress distribution cloud diagram of the single crystal silicon cutting process according to an embodiment of the present invention. DETAILED DESCRIPTION

[0035] The technical solution of the present invention is described in detail below through specific embodiments.

[0036] See also Figure 1-5 The present invention provides an optimized molecular dynamics simulation method for a single crystal silicon cutting process, comprising the following steps: initializing and setting various parameters → creating a workpiece region → creating an abrasive region → creating an atomic box → setting atomic mass → fixing the boundary layer → selecting a potential function → energy minimization and relaxation → setting cutting parameters → running simulation and visualizing the results. The specific steps are:

[0037] S1. Initialize and set various parameters, including setting the space dimension to 3D space; setting the boundary conditions to contractile conditions in the X and Z directions, setting the Y direction to boundary conditions, and using the fix command to achieve linear motion in the Y direction; setting the system unit to metal; setting the atom type to atomic; generating the initial Verlet neighbor list, using the neighbor and neigh_modify commands to set the neighbor list parameter to 0.3, and the update time to 5 time steps to ensure fast calculation during the simulation; setting the time step to 0.001 picoseconds;

[0038] S2. Create a workpiece area. Generate multiple areas by specifying coordinates and use the union command to create a composite area. The workpiece size is 240×240×120. The boundary layer is composed of two parts, which are 15×240×120 and 240×240×15 cuboids. The isothermal layer is similar to the boundary layer. The Newtonian layer is a cuboid of 205×205×85. These three parts constitute the silicon atomic workpiece.

[0039] S3. Create an abrasive region, and establish multiple conical abrasives along the Y direction. Each abrasive is created by the cone command. The radius of the upper base of the cone is 1.5nm, the radius of the lower base is 0.5nm, and the height is 2nm. Multiple abrasives are merged into an overall region through union. The use of conical abrasives can better simulate the tool geometry in the actual processing process. The model is closer to the real physical process, making the result more accurate. The conical abrasive has a sharp vertex, so that it can concentrate on a smaller area during cutting. This design can improve the material removal rate in molecular dynamics simulation, which is manifested as fewer atoms being squeezed to the surroundings and producing deeper cutting grooves. The conical abrasive in the simulation can reduce the time and force required in the material removal process. The shape of the conical abrasive can lead to The stress is more evenly distributed on the material surface. Since the shape of the top can concentrate the force, this uniform stress field can reduce material cracks or failures caused by stress concentration, thereby better predicting the material behavior in actual processing; due to its sharp geometric shape, conical abrasives are very suitable for processing complex curved surfaces and micro-machining tasks. The use of multi-abrasive models can study how abrasives of different shapes and sizes affect the processing effect of complex surfaces, which is of great significance for predicting micro-nano-level surface roughness and processing quality; in the molecular dynamics simulation of nanoscale, the conical multi-abrasive model can simulate the interaction between different abrasives in the nano-machining process by simulating the simultaneous cutting of multiple abrasives through molecular dynamics, and understand how the abrasives jointly affect the material removal rate, nano-level surface morphology, and the transfer of material stress;

[0040] S4. Create an atom box, define the space where the atoms will be placed, construct a lattice, use the lattice command to define the arrangement of atoms, generate atoms in different regions, create atoms for silicon Si and carbon C atoms respectively, create the simulation box size, define the lattice constant, and create silicon atoms in the workpiece region with a lattice constant of a = 0.543nm; create carbon atoms in the tool region with a lattice constant of a = 0.357nm;

[0041] S5. Set the atomic mass, set the mass of silicon Si and carbon C atoms respectively. The atomic mass of silicon is 28 and the atomic mass of carbon is 12, which is convenient for calculating momentum so that their momentum and energy transfer can be considered in the simulation. Set the grouping, group the three parts of the workpiece separately, and group each abrasive grain separately, which is convenient for the subsequent settings, and effectively divide the entire simulation area, and perform subsequent operations on this basis;

[0042] S6, the boundary layer is fixed. Use the setforse command to fix the boundary layer, and the speed is also set to 0 to keep it fixed in space;

[0043] S7. The Tersoff potential function is used to simulate the interaction between silicon and silicon, and between carbon and silicon. Different potential function parameters are set to adapt to the connection effect of the two-phase material, and the tersoff file containing the potential function parameters is read through the pair_coeff command. Since the hardness of diamond is much greater than that of single crystal silicon, the interaction between diamonds is ignored.

[0044] Tersoff potential function mathematical expression:

[0045]

[0046] Among them, i and j represent two adjacent atoms, V ij represents the interaction potential between atoms i and j;

[0047] f c is a cutoff function used to smoothly reduce the contribution of the potential function when the interatomic distance is larger than a certain threshold to avoid interactions at infinite distance;

[0048] R ij represents the distance between atom i and atom j;

[0049] A ij and B ij It is a parameter related to the interaction between two atoms, obtained by fitting experimental data or first-principles calculations;

[0050] λ ij and μ ij It is a parameter related to the interaction between two atoms and determines the rate at which the potential function changes with distance;

[0051] and is an exponential decay term, which is used to describe the phenomenon that the interaction between atoms weakens with increasing distance;

[0052] In the Tersoff potential function, A ij , B ij , ij and μ ij The value of is usually not fixed, but can be adjusted according to different materials and chemical bond types. In addition, the truncation function f c (R ij ) may also vary depending on the material and simulation requirements;

[0053] In the presence of a complex chemical environment, the Tersoff potential function can adapt well to the characteristics of different materials by adjusting parameters, making the microscopic simulation of the material more accurate, quantitatively describing the interaction between atoms, and explaining the changing laws of the potential energy and bond strength between atoms.

[0054]

[0055] In the above formula, E represents the total energy, f c represents the cutoff function, which is used to limit the range of the potential function and ensure that when the distance between atoms exceeds a certain threshold, the potential function can smoothly tend to zero, thereby simulating the limited interaction between atoms in the real physical world;

[0056] V C (r ij ), V D (r ij ) represent repulsive force and attractive force respectively. These two forces are the main components of the interaction between atoms. Their relative magnitudes determine the distance and stability between atoms. The repulsive force usually increases sharply as the distance between atoms decreases, while the attractive force first increases and then decreases as the distance decreases. There is an optimal distance that makes the attractive force reach its maximum value.

[0057] r ij It represents the potential energy between atoms and is an important physical quantity that describes the interaction between atoms.

[0058] b ij It represents the strength of the interatomic bond, and is used to describe the strength of the interatomic bond, that is, the firmness of the interaction between atoms;

[0059] S8, set the minimization parameters to perform energy minimization processing, set the energy and force convergence tolerance to 1e-16, and set the maximum number of iterations and the maximum number of evaluations to 5000; the workpiece relaxation adopts the NVT ensemble. During the simulation process, the NVT ensemble is used to control the temperature of the isothermal layer and the Newtonian layer through the fix command to ensure that the system evolves at the required temperature and obtains a stable workpiece structure;

[0060] S9, set the cutting speed, use the velocity command to set the initial temperature of the constant temperature layer to 300K, set the speed of the abrasive to move linearly along the Y axis, the speed is 150m / s, and the direction is along the negative Y direction; at the same time, set the grinding speed along the negative X direction to 40m / s;

[0061] In the simulation of single crystal silicon grinding, the Tersoff potential function is used to describe the interaction between silicon atoms and between carbon and silicon. The Tersoff potential function can accurately describe the interaction between atoms in covalent bond materials.

[0062] S10. Record the atomic motion trajectory and stress distribution in real time through molecular dynamics simulation. Use the run command to start the simulation. Use the dump command to record the atomic motion trajectory and calculate the stress distribution in real time to facilitate subsequent analysis. Use ovito to visualize the simulation results. Analyze the obtained data through the output file ×.xyz. Use the ovito visualization software to draw three-dimensional graphics and stress distribution diagrams to visualize the simulation results.

[0063] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can replace or change the technical solution and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A molecular dynamics simulation method for optimizing a single crystal silicon cutting process, characterized in that: The following steps are involved: Initialize and set various parameters → Create workpiece area → Create abrasive area → Create atomic box → Set atomic mass → Fixed boundary layer → Select potential function → Minimize energy and relax → Set cutting parameters → Run simulation and visualize results. The specific steps are as follows: S1. Initialize and set various parameters, including simulation space dimension, boundary conditions, system units, atom types, neighbor list parameters and update frequency, and time step; S2, create workpiece regions, generate multiple regions by specifying coordinates, and use the union command to create composite regions. All regions such as boundary layers, isothermal layers, and Newtonian layers define different physical properties; S3, creating an abrasive grain area, establishing multiple conical abrasive grains along the Y direction, each abrasive grain is created by the cone command, generating an upper cone-shaped area to simulate the geometric shape of the diamond abrasive grain, and merging multiple abrasive grains into an overall area by union; S4. Create an atom box, define the space where the atoms will be placed, construct a lattice, and set the lattice constant. Use the lattice command to define the arrangement of atoms, generate atoms in different regions, and create atoms for silicon Si and carbon C atoms respectively. S5. Set atomic mass, respectively set the mass of silicon Si and carbon C atoms, so as to consider their momentum and energy transfer in the simulation, and set the grouping to facilitate the subsequent settings, effectively divide the entire simulation area, and perform subsequent operations on this basis; S6, boundary layer fixation, use the setforse command to fix the boundary layer and keep it fixed in space to reduce boundary effects; S7. Potential function selection. The Tersoff potential function is used to simulate the interaction between silicon and silicon, and between carbon and silicon. Different potential function parameters are set to adapt to the connection effect of the two-phase material. The Tersoff potential function expression is: Among them, i and j represent two adjacent atoms, V ij represents the interaction potential between atoms i and j, f c is the cutoff function, R ij represents the distance between atom i and atom j, A ij and B ij is a parameter related to the interaction between two atoms, λ ij and μ ij is a parameter related to the interaction between two atoms, which determines the rate at which the potential function changes with distance. and is an exponential decay term, which is used to describe the phenomenon that the interaction between atoms weakens with increasing distance; S8, perform energy minimization on all atoms, and use the NVT ensemble to relax the isothermal layer and the workpiece to obtain a stable workpiece structure; S9, setting cutting parameters to run simulation, using velocity command to set initial temperature for constant temperature layer, setting the predetermined direction of abrasive cutting speed to linear movement along Y axis, direction to negative Y direction, and setting grinding along negative X direction at the same time; S10. Through molecular dynamics simulation, the atomic motion trajectory is recorded in real time and the stress distribution is calculated. The running results are visualized and post-processed using ovito to obtain the results.

2. A molecular dynamics simulation method for optimizing a single crystal silicon cutting process according to claim 1, characterized in that: In step S1, the spatial dimension is set to 3D space; the boundary conditions can be set to contraction conditions, periodic conditions, and non-periodic conditions; the system units are metal, real, and gas; the atom type is set to atomic; the initial Verlet neighbor list is generated, and the update threshold is set: the neighbor and neigh_modify commands are used to set the generation and update frequency of the neighbor list to ensure fast calculation during the simulation process; the time step can be set to 0.001 or 0.002 picoseconds.

3. The molecular dynamics simulation method for optimizing the single crystal silicon cutting process according to claim 1, characterized in that: In step S2, the workpiece size is established, each area is established separately, and then merged into a workpiece, the boundary layer is fixed in position, and the boundary effect is reduced. The isothermal layer maintains thermal equilibrium, and the Newtonian layer conforms to Newtonian motion.

4. The molecular dynamics simulation method for optimizing the single crystal silicon cutting process according to claim 1, characterized in that: The step S4 creates a simulation box size, defines a lattice constant, and creates silicon atoms in the workpiece region and carbon atoms in the tool region.

5. The molecular dynamics simulation method for optimizing the single crystal silicon cutting process according to claim 1, characterized in that: In step S7, the pair_style tersoff command is used to specify the use of the Tersoff potential function, and the pair_coeff command is used to read the tersoff file containing the potential function parameters. The introduction of the Tersoff potential function makes the microscopic simulation of the material more accurate, especially in the presence of a complex chemical environment. By adjusting the parameters, it can well adapt to the characteristics of different materials, quantitatively describe the interaction between atoms, and explain the change law of the potential energy and bond strength between atoms. In the above formula, E represents the total energy, f c represents the truncation function, V C (r ij ), V D (r ij ) represent the repulsive force and attractive force respectively, r ij represents the potential energy between atoms, b ij Indicates the strength of the bonds between atoms.

6. The molecular dynamics simulation method for optimizing the single crystal silicon cutting process according to claim 1, characterized in that: In step S8, the workpiece relaxation adopts the NVT ensemble: during the simulation process, the NVT ensemble is used to control the temperature of the isothermal layer and the Newtonian layer through the fix command to ensure that the system evolves at the required temperature.

7. The molecular dynamics simulation method for optimizing the single crystal silicon cutting process according to claim 1, characterized in that: In the step S10, the atomic motion trajectory and stress distribution are recorded in real time through molecular dynamics simulation, the simulation is started using the run command, the atomic motion trajectory and calculated stress distribution are recorded in real time through the dump command to facilitate subsequent analysis, the simulation results are post-processed, the obtained data are analyzed through the output file ×.xyz, and three-dimensional graphics and stress distribution diagrams are drawn to visualize the simulation results.

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