A coarse-grained molecular dynamics simulation and analysis method for investigating the microstructure properties of electroplating solutions

Abstract

The application provides a coarse-grained molecular dynamics simulation and analysis method for researching microstructure properties of electroplating liquid, the coarse-grained model is used instead of the full atomic model, the molecular details which have less influence on system properties are ignored, a few atomic groups are used as basic units of simulation for modeling and simulation, so that the time required for the evolution of the whole system is reduced, and the time scale of the system simulation is prolonged. The interaction between components is described by a classical physical potential. By fitting and adjusting the interaction force parameters between different components, the method of the application can well approximate and model different component electroplating liquid systems, and reproduce experimental phenomena on the microscale.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of molecular dynamics simulation, and particularly relates to a coarse-grained molecular dynamics simulation and analysis method for studying the microstructure properties of electroplating solution. BACKGROUND

[0002] Electroplating is a basic and key technology in today's industrial era, and is also the cornerstone of chip manufacturing and integrated circuits. The composition and ratio of electroplating solution are one of the key factors affecting the quality of electroplating. The electroplating solution is complex and mainly contains metal ions, acid ions, solvent molecules, complexing agents, surfactants and other components. For a long time, there has been a lack of effective molecular level research methods, and the micro mechanism of the action of different components is still unclear. Various factors are coupled with each other, and it is extremely difficult to study the influence of a specific factor. Molecular dynamics simulation focuses on exploring the influence of various factors on the properties of the system at the microscale, which can not only predict the performance of the system, but also study the micro mechanism of the interaction between molecules in the system, or conduct research under extreme conditions, which helps researchers to understand the relevant mechanism and optimize the experimental scheme and path.

[0003] In traditional all-atom simulation, each component in the electroplating solution is modeled as an atom as the basic unit, and complex interatomic interactions are included. The force field used is usually a set of interatomic interaction functions, including non-bonding interactions, bonding interactions and constraint terms. Non-bonding interactions include van der Waals interactions and Coulomb electrostatic interactions. Bonding interactions include the stretching potential energy of chemical bonds between atoms, the bending potential energy of bond angles, and the torsion potential energy of dihedral angles. For example, in the all-atom model, the formaldehyde molecule (CH2O) is constructed as a molecule composed of carbon, oxygen and hydrogen atoms. The specific steps of the all-atom modeling and simulation process are as follows:

[0004] (1) Describe the properties and positions of atoms in the molecule: for example, for the formaldehyde molecule, the atomic types and atomic properties such as mass and charge of one oxygen atom, two hydrogen atoms and one carbon atom need to be described.

[0005] (2) Describe the topological information in the system: for example, for the formaldehyde molecule, one carbon-oxygen bond and two carbon-hydrogen bonds need to be described, and three bond angles also need to be described. When the topological structure becomes complex, the complexity of the simulation increases exponentially.

[0006] (3) Assign atomic types to atoms in the molecule according to different chemical environments: in step (1), usually only the element of the atom is given, but the all-atom force field usually distinguishes atoms in different chemical environments, so the element needs to be mapped to the atomic type.

[0007] (4) Assign different force field types to the topological structure of the molecule: Assign the types of topological information such as bonds, bond angles, and dihedral angles according to the newly mapped atom types.

[0008] (5) Preliminary optimization of molecular conformation: The molecular structure is preliminarily optimized to eliminate erroneous structures that are difficult to optimize.

[0009] (6) Based on the experimental data, determine the concentration of each component, and combine the optimized molecular models of different components into a simulation input file. After determining the boundary conditions and simulation parameters, use molecular dynamics simulation software to perform the simulation, and record and statistically analyze the simulation data.

[0010] All-atom simulations have the following problems:

[0011] 1. Constructing molecular and system models using all-atom molecular dynamics simulations is challenging. All-atom simulations involve a wide variety of atom types and interactions. For each molecule in a chemical system, its atomic composition and topology must first be accurately determined; then, a model must be built according to the chemical structure or environment defined by the all-atom force field; finally, the molecular structure must be optimized, eliminating erroneous configurations that are difficult to optimize. Therefore, model preparation is difficult and not universally applicable.

[0012] 2. The spatiotemporal scales that can be investigated by all-atom molecular dynamics simulation methods are extremely limited. All-atom simulations introduce more types of particles and more intricate interactions, and the relaxation of the system is extremely time-consuming. Therefore, studies can only be conducted at very small time and spatial scales, making it impossible to achieve mesoscopic-scale simulations. Due to the small temporal and spatial scales of the simulations, all-atom molecular dynamics simulation methods are insufficient for the systematic study of the microstructure and dynamic properties of electroplating solutions.

[0013] 3. The development level of force fields in all-atom molecular dynamics simulations is limited. Due to incomplete functional forms and the lack of many physical quantities, the portability and predictive ability of traditional force fields are poor, and fitting results on one system are difficult to extrapolate to other systems. Some unconventional molecules are difficult to model, and even for conventional molecules, the research results obtained under different force field parameters show significant differences, resulting in low accuracy between simulation results and conclusions. The simulation results of electroplating solution systems calculated by all-atom molecular dynamics simulations are difficult to effectively compare with commonly used macroscopic properties. Summary of the Invention

[0014] The purpose of this invention is to provide a coarse-grained molecular dynamics simulation and analysis method for studying the microstructure properties of electroplating solutions. The method in this invention reasonably simplifies the molecular details of each component and uses classical physical potential energy to describe the interactions between components, and has the characteristics of accuracy, flexibility and high efficiency.

[0015] The application provides a coarse-grained molecular dynamics simulation and analysis method for researching microstructure properties of an electroplating solution, comprising the following steps:

[0016] A) constructing a coarse-grained model, calculating sizes of each component of the electroplating solution by using Material Studio software or Avogadro software, and coarsely graining ions or molecules in the electroplating solution based on a coarse-grained force field;

[0017] B) determining simulation conditions, setting a simulation dimension as three-dimensional, setting a simulation box side length, randomly placing coarse-grained electroplating solution components in the simulation box according to respective concentrations by language programming, obtaining an initial input file for LAMMPS software simulation, importing the initial input file into LAMMPS, setting a boundary of the simulation box as a periodic boundary condition, performing energy minimization on the system, and making each component uniformly distributed in the simulation box to obtain an initial model of the coarse-grained simulation of the electroplating solution;

[0018] C) determining a potential function, calculating interactions between each particle of the electroplating solution by a force field formed by three parts, i.e., electrostatic interaction represented by a Coulomb potential, short-range interaction represented by a Lennard-Jones potential, and polymer particle bonding interaction represented by a FENE potential or a simple harmonic potential energy, and obtaining potential function parameters between each component by a Lorentz-Berthelot mixing rule;

[0019] D) system relaxation, taking the initial model of the coarse-grained simulation of the electroplating solution obtained in step B) as an initial structure, performing molecular dynamics simulation by using LAMMPS software, calculating system potential energy, atomic force and atomic position, and statistically counting calculation results at each moment until the system reaches an equilibrium state, by using the force field in step C) and the simulation conditions set in step B);

[0020] E) molecular dynamics simulation, taking the system reaching the equilibrium state in step D) as an initial structure, performing molecular dynamics simulation by using LAMMPS software, calculating system potential energy and atomic force and atomic position, and obtaining three-dimensional coordinates of a molecular trajectory, by using the force field in step C) and the simulation conditions set in step B);

[0021] F) data processing and visual processing, calculating structural factors of the electroplating solution in a statistical equilibrium state, radial distribution functions between each component, intermediate scattering functions, mean square displacements of each component and diffusion coefficients by processing program programming, and visually presenting the microstructure of the electroplating solution by Ovito software,

[0022] wherein the radial distribution function is calculated according to formula 1:

[0023]

[0024] In formula 1, r is the distance between particle pairs, Δr is a parameter representing the resolution of the function, N is the total number of particles in the system, and V is the volume of the system.

[0025] The structure factor is calculated according to formula 2:

[0026]

[0027] In formula 2, N is the number of particles, q is the inverse space format, and r j and r k respectively represent the position vectors of particle j and particle k, and <…> represents the ensemble average.

[0028] The intermediate scattering function is calculated according to formula 3:

[0029]

[0030] In formula 3, N and M respectively represent the length and number of surfactant chains, and q represents the wave vector. Different wave vectors correspond to different scattering function decay behaviors.

[0031] The mean square displacement is calculated according to formula 4:

[0032] MSD(t) = <r i (t) - r i (0)> 2 of formula 4.

[0033] In formula 4, r i (t) is the position of particle i at time t.

[0034] According to the mean square displacement, the diffusion coefficient can be calculated according to the Einstein diffusion formula, as shown in formula 5:

[0035]

[0036] Preferably, the plating solution of step A) comprises a combination of any of metal ions, acid root ions, hydrated protons, small molecule complexing agents and surfactants, and the metal ions, acid root ions, hydrated protons and small molecule complexing agents are coarse-grained into charged, polar or non-polar spherical particles based on a coarse-grained force field, and the surfactant is coarse-grained into a chain structure connected by polar or non-polar spherical particles.

[0037] Preferably, the coarse-grained force field in step A) is a Martini force field or an OPLS-UA force field.

[0038] Preferably, in the energy minimization process of the system using the Soft potential in step B), the system temperature is controlled by using a Langevin heat bath or a Nose-Hoover heat bath, and the duration of the Soft potential is 105 time step.

[0039] Preferably, the Coulomb potential in step C) is calculated by PPM algorithm, Ewald summation algorithm or PME algorithm.

[0040] Preferably, in step D) and step E), during the molecular dynamics simulation, the atomic position at the next time is calculated according to Verlet-Velocity algorithm, Verlet algorithm or Frog-Leap algorithm by calculating the potential energy of the system and the force of the atom, so as to obtain the three-dimensional coordinates of the molecular trajectory.

[0041] Preferably, in step B), the system is subjected to energy minimization by using Soft potential or a program based on Polak-Ribiere gradient descent algorithm, and the expression of Soft potential is as shown in formula 6:

[0042]

[0043] In formula 6, A is an energy coefficient, r c is a cutoff radius, r is the distance between particles, and the system is set as a canonical ensemble.

[0044] Preferably, the processing program in step F) is Fortran language, Python language or C / C++ language.

[0045] Preferably, the system adopts an implicit solvent model.

[0046] The present application provides a coarse-grained molecular dynamics simulation and analysis method for studying the microstructure properties of electroplating solution, which uses a coarse-grained model instead of a full-atom model, ignores the molecular details which have less influence on the properties of the system, uses several atomic groups as the basic unit of simulation for modeling and simulation, thereby reducing the time required for the evolution of the whole system and prolonging the time scale of the system simulation. The interaction between components is described by a classical physical potential. By fitting and adjusting the parameters of the interaction force between different components, the method of the present application can well approximate and model different component electroplating solution systems and reproduce experimental phenomena at the microscale. BRIEF DESCRIPTION OF DRAWINGS

[0047] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only embodiments of the present application, and those skilled in the art can obtain other drawings according to the provided drawings without creative labor.

[0048] Figure 1Flow chart of the method for studying the microstructure properties of electroplating solution by coarse-grained molecular dynamics simulation and analysis according to the present application;

[0049] Figure 2 Schematic diagram of the coarse-graining process of the components of the electroplating solution in Example 1 of the present application;

[0050] Figure 3 Schematic diagram of the equilibrium structure of the electroplating solution system at different temperatures in Example 1 of the present application;

[0051] Figure 4 Radial distribution function between zinc ions and methanesulfonic ions at different temperatures in Example 1 of the present application;

[0052] Figure 5 Structure factor diagram of the surfactant in Example 1 of the present application;

[0053] Figure 6 Mean square displacement of the salt ions of the electroplating solution with time in Example 1 of the present application;

[0054] Figure 7 Schematic diagram of the equilibrium structure of the system when the length of the surfactant is 20 in Example 2 of the present application;

[0055] Figure 8 Schematic diagram of the equilibrium structure of the system when the length of the surfactant is 32 in Example 2 of the present application;

[0056] Figure 9 Schematic diagram of the equilibrium structure of the system when the side length of the simulation box is 40σ in Example 1 of the present application;

[0057] Figure 10 Schematic diagram of the equilibrium structure of the system when the side length of the simulation box is 60σ in Example 3 of the present application;

[0058] Figure 11 Schematic diagram of the equilibrium structure of the system when the side length of the simulation box is 80σ in Example 3 of the present application;

[0059] Figure 12 Simulation structure diagram after reducing the interaction between the hydrophobic ends of the surfactant by 20% in Comparative Example 1 of the present application. DETAILED DESCRIPTION

[0060] The present application provides a method for studying the microstructure properties of electroplating solution by coarse-grained molecular dynamics simulation and analysis, the flow is as shown in Figure 1 , and the specific steps are as follows:

[0061] First, determine the basic model of each type of component in the electroplating solution:

[0062] The plating solution components mainly include metal ions, acid radical ions, hydrated protons, small molecule complexing agents, and surfactants, etc. According to the size of each component calculated by the Material Studio software, the metal ions, acid radical ions, hydrated protons, and small molecule complexing agents are coarsely granulated into charged, polar or non-polar spherical particles based on the Martini force field, and the surfactants are coarsely granulated into chain structures connected by polar or non-polar spherical particles.

[0063] In the present application, in addition to the Material Studio software, the Avogadro software can be used to calculate the size of the plating solution components; in addition to the Martini force field, the OPLS-UA coarse-graining force field can also be used.

[0064] Secondly, the simulation conditions are determined:

[0065] The simulation dimension is set to three dimensions, the simulation box edge length is set, and the periodic boundary condition is introduced in the system. According to the actual conditions, the concentration of each component is calculated, and the program written by Perl language, Fortran language or Python language is used to randomly place the above-mentioned components in the box to generate a read-in information file for LAMMPS software simulation. Since the randomly generated model cannot avoid particle overlap, the Soft potential in the LAMMPS software is used to minimize the energy of the system, and the overlapping particles are slowly pushed away. The expression of the Soft potential is as shown in formula 6:

[0066]

[0067] In formula 6, A is the energy coefficient, r c is the cut-off radius, and r is the distance between particles.

[0068] The system is set to a canonical ensemble (constant particle number, constant volume, constant temperature NVT), the system temperature is controlled by using the Langevin heat bath, and the Soft potential is used to adjust the structure for 10 5 steps to ensure that there is no overlap between particles, and each component is uniformly dispersed in the system. After the above optimization, the initial model of the plating solution coarse-graining simulation can be obtained.

[0069] In the present application, in addition to the Langevin heat bath, the Nose-Hoover heat bath can be used to control the system temperature; in addition to using the LAMMPS pair_style soft command to minimize the energy, the LAMMPS minimize command based on the Polak-Ribiere gradient descent algorithm can be used to minimize the energy of the system.

[0070] Thirdly, the potential energy function used to describe the interaction between each component is determined:

[0071] Molecular dynamics simulation updates the position and velocity of a particle according to the force acting on the particle, which is determined by the potential function. Therefore, the selection of the potential function determines the trajectory of the system over time. A series of mathematical functions and parameters that describe the interaction potential of particles in the system are called force field. In the coarse-grained simulation, the present application only considers the contribution of the external field and the two-body interaction, and does not consider the multi-body interaction of three or more particles. The interaction between particles is divided into three parts, the electrostatic interaction represented by the Coulomb potential (U Coul ), the short-range interaction represented by the Lennard-Jones potential (U LJ ), and the polymer particle bonding interaction represented by the FENE potential (U FENE ).

[0072] In the present application, the Lennard-Jones potential energy calculation formula between components is as follows:

[0073]

[0074] In formula 7, r ij is the distance between atoms i and j, ∈ and σ are the energy and length parameters between atoms i and j, respectively, and r c is the cutoff radius.

[0075] In the present application, the Coulomb potential energy calculation formula between ion components is as follows:

[0076]

[0077] In formula 8, q i and q j are the valence of ions i and j, respectively, e is the basic charge 1.6×10 -19 Coulomb, ε0 is the vacuum permittivity, and ε r is the relative dielectric constant of the solution.

[0078] The Coulomb potential energy calculation is realized by using the PPPM (Particle-Particle Particle-Mesh) algorithm. In addition to the PPPM algorithm, the Coulomb potential energy calculation can also be realized by using the Ewald summation algorithm or the PME algorithm.

[0079] In the present application, the FENE (Finite Extensible Nonlinear Elastic) potential energy calculation formula for describing the bonding interaction is as follows:

[0080]

[0081] In formula 9, k is an elastic coefficient, and R0 is the maximum stretching distance of a bond.

[0082] In addition to FENE, the bond interaction can be described by a harmonic potential, and the expression is as follows:

[0083] U harmonic (r)=K(r-r0) 2

[0084] Formula 10;

[0085] In formula 10, K is an elastic coefficient, and r0 is the maximum stretching distance of a bond.

[0086] In the application, the potential function parameters between components are calculated by the Lorentz-Berthelot mixing rule. The Lorentz-Berthelot mixing rule is expressed as:

[0087]

[0088] In formula 11 and formula 12, the subscripts i and j represent different types of atoms, respectively.

[0089] In the application, the aqueous solvent in the system adopts an implicit solvent model, and the dielectric constant is set to ε r = 80.

[0090] Step 4, system relaxation:

[0091] Before calculating the structure and properties of the electroplating solution model, the model is relaxed to achieve thermodynamic equilibrium, so as to ensure that the simulation conditions in the calculation process are stable, and the system equilibrium is realized by detecting kinetic energy, potential energy, temperature and total energy.

[0092] In the second step, the LAMMPS software and the soft repulsive potential (i.e., Soft potential) are used for energy minimization operation and pre-equilibrium simulation to obtain an initial structure in which each component is uniformly dispersed. The Soft potential is cancelled, and the coarse-grained force field optimized for the electroplating solution in the third step is used instead. The LAMMPS software and the simulation conditions set in the second step are used for molecular dynamics simulation to calculate the system potential energy and atomic force. According to the Verlet-Velocity integral algorithm, the atomic position at the next time is determined, and the calculation results at each time are counted until the system reaches an equilibrium state.

[0093] In the application, in addition to using the Verlet-Velocity algorithm, the Verlet and Frog-Leap algorithms can also be used.

[0094] Step 5, core algorithm molecular dynamics simulation:

[0095] In the fourth step, the equilibrium state system is used as the initial conformation, and the LAMMPS software, the system principle in the second step and the potential energy function in the third step are used for molecular dynamics simulation to calculate the system potential energy and atomic force, and the atomic position at the next time is determined according to the Verlet-Velocity integral algorithm to obtain the three-dimensional coordinates of the molecular trajectory; at the same time, sampling is carried out along the system evolution trajectory at a set interval, and the system statistics is carried out.

[0096] In the present application, in addition to using the Verlet-Velocity algorithm, the Verlet and Frog-Leap algorithms can also be used.

[0097] Step 6, data processing and visualization processing:

[0098] Fortran language, Python language or C / C++ language is used to write programs to calculate the structure factor of the statistical equilibrium state electroplating solution, the radial distribution function between each component, the structure factor, the intermediate scattering function, the mean square displacement of each component and the diffusion coefficient, which are used to represent the dynamic information of each component, and the Ovito software is used to visually present the microstructure of the electroplating solution.

[0099] The radial distribution function is calculated according to formula 1:

[0100]

[0101] In formula 1, r is the distance between the particle pair, Δr is a parameter representing the function resolution, N is the total number of particles in the system, and V is the volume of the system.

[0102] The structure factor is calculated according to formula 2:

[0103]

[0104] In formula 2, N is the particle number, q is the inverse space vector, and r j And r k Respectively represent the position vector of particle i and particle k, and <…> represents the system average.

[0105] The intermediate scattering function is calculated according to formula 3:

[0106]

[0107] In formula 3, N and M represent the length and number of surfactant chains respectively, q represents the wave vector, and different wave vectors correspond to different scattering function decay behaviors.

[0108] The mean square displacement is the deviation of the instantaneous position of the particle from the initial position with the evolution of time. The mean square displacement is calculated according to formula 4:

[0109] MSD(t)=<ri (t)-r i (0)> 2 Formula 4;

[0110] In Formula 4, r i (t) is the position of particle i at time t;

[0111] According to the mean square displacement, the diffusion coefficient can be calculated according to the Einstein diffusion formula, as shown in Formula 5:

[0112]

[0113] Compared with the prior art, the present application has the following advantages:

[0114] (1) In the first step, we use a coarse-grained model instead of a full-atom model, ignoring unnecessary details, thereby reducing the time required for the evolution of the entire system and extending the time scale of the system simulation.

[0115] (2) In the third step, we use a coarse-grained force field instead of a full-atom force field, ignoring interactions that have less impact on the system. For example, by integrating the structural unit information of the alkylphenol polyoxyethylene ether molecule, we describe the molecule as a coarse-grained particle connected by springs, and use a classical physical potential to describe the connection and rigidity of the chain. The potential function of the coarse-grained simulation has a wider range of applications and can simulate unconventional molecular systems; and compared with full-atom simulation, it is smoother and can use a larger time step.

[0116] (3) In the fifth step, we can perform high-performance parallel computing of multiple tasks, efficiently explore the parameter space, and improve the efficiency and accuracy of the simulation.

[0117] (4) In the sixth step, we use Fortran language to write high-performance software for calculating physical parameters such as structure factor, which can analyze the output structure data in parallel.

[0118] In order to further illustrate the present application, the following embodiments will describe in detail a coarse-grained molecular dynamics simulation and analysis method for studying the microstructure properties of electroplating solution provided by the present application, but it should not be understood as limiting the scope of protection of the present application.

[0119] Example 1 Copper plate galvanizing

[0120] The present example constructs a plating solution coarse-grained model to study the solution properties of the plating solution and the surface and interface properties at different temperatures. The plating solution composition mainly includes zinc methanesulfonate as the main salt, hydrated protons, complexing agent formaldehyde, and surfactants, etc. According to the Material Studio software, the size of each component is calculated, and based on the Martini force field, the metal ions, acid radical ions, hydrated protons, and small molecule complexing agents are coarse-grained into charged, polar or non-polar spherical particles, and the surfactants are coarse-grained into chain structures connected by polar or non-polar spherical particles. Figure 2 A schematic diagram of the coarse-graining process of the plating solution components is shown.

[0121] A program written in Perl language randomly places 40 surfactant molecules, 100 zinc ions, 400 methanesulfonate ions, 200 hydrated protons, and 50 formaldehyde molecules in a three-dimensional cubic simulation box with a side length of L = 40σ, and obtains the initial input file of LAMMPS. Since the randomly generated model cannot avoid particle overlap, the Soft potential and FENE potential in the LAMMPS software are used to minimize the energy of the system, and the overlapping particles are slowly pushed away. Using the LAMMPS software, the initial input file is imported, the simulation box boundary is set to a periodic boundary condition, and the particle motion in the system satisfies the Langevin motion equation. The simulation is carried out in the canonical ensemble, and the time length is 10 5 time steps to ensure that there is no overlap between particles, and each component is uniformly dispersed in the system.

[0122] In the present embodiment, the interparticle interaction force is divided into three parts: the electrostatic interaction represented by the Coulomb potential (U Coul ), the short-range interaction represented by the Lennard-Jones potential (U LJ ), and the surfactant particle bonding interaction represented by the FENE potential (U FENE ). The potential function parameters between components are calculated by the Lorentz-Berthelot mixing rule. The Coulomb potential energy is calculated using the PPPM (Particle-Particle Particle-Mesh) algorithm. Using the LAMMPS software, the model after structure optimization is imported, and the simulation parameters are set according to the selected force field to perform molecular dynamics simulation, calculate the system potential energy and atomic force, determine the atomic position at the next time according to the Verlet-Velocity integral algorithm, and statistically calculate the results at each time until the system reaches an equilibrium state.

[0123] The present embodiment studies the microstructure of the plating solution system when T * = 0.5, 0.8, 1.0, 1.1, 1.2, 1.5, and 2.0. When the system temperature T *= 1.0 corresponds to room temperature T = 298 K, T * = 0.5 corresponds to a temperature T = 0.5 x 298 K, and so on. In this example, the NVT ensemble is used, the temperature parameter is controlled by the Langevin heat bath method, and the volume of the simulation box is kept constant. The simulation time step is set to t s = 0.005τ, where τ = (mσ 2 / ε) 1 / 2 Molecular dynamics simulation is performed using the LAMMPS software and the ensemble principle in the second step and the potential energy function in the third step to calculate the potential energy of the system and the force on the atoms. The position of the atoms at the next time is determined according to the Verlet-Velocity integration algorithm to obtain the three-dimensional coordinates of the molecular trajectory; at the same time, sampling is performed along the evolution trajectory of the system at a set interval, and ensemble statistics is performed. Figure 3 is a schematic diagram of the equilibrium structure of the electroplating solution system at different temperatures.

[0124] In this example, a program is written in Fortran language to calculate the structure factor of the electroplating solution system in equilibrium state, the radial distribution function between components, the average size of clusters, and the mean square displacement of each component, and the Ovito software is used to visually present the microstructure of the electroplating solution.

[0125] Example 2

[0126] The process is exactly the same as that of Example 1, but in this Example 2, the length of the surfactant is increased from 16 (hydrophobic end length 4, hydrophilic end length 12) in Example 1 to 20 (hydrophobic end length 5, hydrophilic end length 15) and 32 (hydrophobic end length 8, hydrophilic end length 24). The structure diagram at equilibrium is shown in Figure 7 and 8 As the length of the surfactant increases, the size and number of micelles increase.

[0127] Example 3

[0128] The process is exactly the same as that of Example 1, but in this Example 3, the size of the simulation box is increased, with edge length L = 60σ and L = 80σ, respectively, while the concentration of the additive is kept constant.

[0129] The results are shown in Figures 9 to 11 As the size of the simulation box increases, the number of micelles in the electroplating solution system increases, and the size remains basically unchanged. This shows that the simulation can effectively reflect the properties of the electrolyte and is not affected by the size effect.

[0130] Comparative Example 1

[0131] The process is exactly the same as that of Example 1, but in Comparative Example 1, the energy parameter of the short-range interaction of the hydrophobic end of the surfactant is reduced by 20%, and the results are shown in Figure 12As shown by Figure 12 It is known that the energy parameter of the hydrophobic end of the surfactant decreases by 20% for short-range interactions, which cannot form surfactant micelles in a low-temperature plating solution.

[0132] In the above embodiment, the present application uses coarse-grained molecular dynamics simulation to explore the microstructure of the MSA type plating solution, in which the main salt of the plating solution is SnZn(MSA)2, the stabilizer is MSA, the surfactant is amphiphilic alkyl phenol polyoxyethylene (APEO), the brightener is formaldehyde (FA), and water is used as the solvent.

[0133] The simulation results show that at low temperatures, APEO and FA can form typical micelle structures in the MSA type plating solution. In each micelle, the hydrophobic end of APEO and FA form the micelle core, and the hydrophilic end of APEO forms the shell layer, and the aggregation structure is the same as the micelles formed by the block copolymer reported in the applicant's previous research (Ding, M.; Hou, L.; Duan, X.; Shi, T.; Li, W.; Shi, A.-C., Translocation of Micelles through a Nanochannel. Macromolecules 2022, 55(15), 6487-6492.). With the increase of temperature, the molecular kinetic energy and the molecular interaction compete with each other, which is manifested as the increase and then decrease of the size of the surfactant micelles, which is the same as the phenomenon reported in the experiment (Kato, T.; Anzai, S.-i.; Takano, S.; Seimiya, T., Intermicellar interactions and micelle size distribution in aqueous solutions of polyoxyethylene surfactants. Journal of the Chemical Society, Faraday Transactions 1: Physical Chemistry in Condensed Phases 1989, 85(8), 2499-2506.). The simulation results also show that the main salt ion Sn 2 Zn 2+ and MSA -Ionic clusters can be formed due to electrostatic interaction at low temperatures. This phenomenon is consistent with other theoretical studies and experiments (Chao, L.; Xia, Y.; Duan, X.; Wang, Y.; Ran, C.; Niu, T.; Gu, L.; Li, D.; Hu, J.; Gao, X.; Zhang, J.; Chen, Y., Direct and stable alpha-phase formation via ionic liquid solvation for formamidinium-based perovskite solar cells. Joule 2022, 6(9), 2203-2217;

[0134] Lai, Z.; Wang, C.; Huang, Y.; Chen, Y.; Wang, S.; Hong, Y.; Zhou, G.; He, W.; Su, X.; Sun, Y.; Tao, Y.; Lu, X., Temperature-dependent inhibition of PEG in acid copper plating: Theoretical analysis and experiment evidence. Materials Today Communications 2020, 24, 100973.

[0135] In summary, the trends of the various key components obtained by the method in the present application with temperature are consistent with the related experimental phenomena reported in the literature. The model and method in the present application are effective.

[0136] The above only describes the preferred embodiments of the present application. It should be noted that for those skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, and these improvements and refinements should also be considered within the scope of protection of the present application.

Claims

1. A method for studying the microstructure properties of electroplating solution by coarse-grained molecular dynamics simulation and analysis, comprising the following steps: A) constructing a coarse-grained model, calculating the size of each component of the electroplating solution using Material Studio software or Avogadro software, and coarse-graining the ions or molecules in the electroplating solution based on a coarse-grained force field; B) determining the simulation conditions, setting the simulation dimension to three dimensions, setting the edge length of the simulation box, and randomly placing the coarse-grained components of the electroplating solution in the simulation box according to their respective concentrations through language programming to obtain an initial input file for LAMMPS software simulation; importing the initial input file into LAMMPS, setting the boundary condition of the simulation box to periodic boundary condition, and performing energy minimization on the system to make the components uniformly distributed in the simulation box to obtain an initial model for the coarse-grained simulation of the electroplating solution; C) determining the potential function, calculating the interaction between each particle in the electroplating solution by a force field formed by three parts, i.e., electrostatic interaction represented by Coulomb potential, short-range interaction represented by Lennard-Jones potential, and polymer particle bonding interaction represented by FENE potential or harmonic potential energy, and obtaining the potential function parameters between each component by Lorentz-Berthelot mixing rule; D) system relaxation, using the initial model for the coarse-grained simulation of the electroplating solution obtained in step B) as the initial structure, using the force field in step C) and the simulation conditions set in step B), and using LAMMPS software to perform molecular dynamics simulation to calculate the system potential energy, atomic force and atomic position, and to statistically calculate the results at each time until the system reaches an equilibrium state; E) molecular dynamics simulation, using the system in the equilibrium state in step D) as the initial structure, using the force field in step C) and the simulation conditions set in step B), and using LAMMPS software to perform molecular dynamics simulation to calculate the system potential energy, atomic force and atomic position, and to obtain the three-dimensional coordinates of the molecular trajectory; at the same time, sampling along the evolution trajectory of the system at a set interval and performing ensemble statistics; F) data processing and visualization processing, calculating the structure factor of the electroplating solution in the statistical equilibrium state, the radial distribution function between each component, the intermediate scattering function, the mean square displacement of each component and the diffusion coefficient through processing program programming, and visually presenting the microstructure of the electroplating solution by Ovito software, wherein the radial distribution function is calculated according to formula 1: Formula 1; In formula 1, r is the distance between the particle pair, △r is a parameter representing the resolution of the function, N is the total number of particles in the system, and V is the volume of the system; the structure factor is calculated according to formula 2: Formula 2; In Equation 2, N is the number of particles, q is the inverse spatial lattice vector, r j and r k represent the position vectors of particle j and particle k, respectively. the intermediate scattering function is calculated according to formula 3: Formula 3; In formula 3, N and M represent the chain length and the number of chains of the surfactant, respectively, and q represents the wave vector, different wave vectors correspond to different scattering function decay behaviors; the mean square displacement is calculated according to formula 4: Equation 4; In formula 4, r i (t) is the position of particle i at time t; According to the mean square displacement, the diffusion coefficient can be calculated according to the Einstein diffusion formula, as shown in formula 5: Formula 5.

2. The coarse-grained molecular dynamics simulation and analysis method for investigating the microscopic structural properties of an electroplating bath according to claim 1, characterized in that, The plating solution of step A) comprises a combination of any of metal ions, acid radical ions, hydrated protons, small molecule complexing agents and surfactants, and the metal ions, acid radical ions, hydrated protons and small molecule complexing agents are coarse-grained into charged, polar or nonpolar spherical particles based on a coarse-graining force field, and the surfactants are coarse-grained into a chain structure connected by polar or nonpolar spherical particles.

3. The coarse-grained molecular dynamics simulation and analysis method for investigating the microscopic structural properties of electroplating solutions according to claim 1, characterized in that, The coarse-graining force field in step A) is a Martini force field or an OPLS-UA force field.

4. The coarse-grained molecular dynamics simulation and analysis method for investigating the microscopic structural properties of electroplating solutions according to claim 1, characterized in that, In the energy minimization process of the system in step B) using the Soft potential, the temperature of the system is controlled by using a Langevin heat bath or a Nose-Hoover heat bath, and the Soft potential is performed for 10 5 time steps.

5. The coarse-grained molecular dynamics simulation and analysis method for investigating the microscopic structural properties of electroplating solutions according to claim 1, characterized in that, The Coulomb potential in step C) is calculated by using a PPPM algorithm, an Ewald summation algorithm or a PME algorithm.

6. The coarse-grained molecular dynamics simulation and analysis method for investigating the microscopic structural properties of electroplating solutions according to claim 1, characterized in that, In steps D) and E), during the molecular dynamics simulation, the atomic positions at the next time are calculated according to a Verlet-Velocity algorithm, a Verlet algorithm or a Frog-Leap algorithm by calculating the system potential energy and the atomic force, so as to obtain the three-dimensional coordinates of the atomic trajectory.

7. The coarse-grained molecular dynamics simulation and analysis method for investigating the microscopic structural properties of electroplating solutions according to claim 1, characterized in that, In step B), the system is subjected to energy minimization by using a Soft potential or a program based on a Polak-Ribiere gradient descent algorithm, and the expression of the Soft potential is as shown in formula 6: Formula 6; In Equation 6, A is the energy coefficient, r c is the cutoff radius, and r is the distance between particles, and the system is set as a canonical ensemble.

8. The coarse-grained molecular dynamics simulation and analysis method for investigating the microscopic structural properties of electroplating solutions according to claim 1, characterized in that, The processing program in step F) is a Fortran language, a Python language or a C / C++ language.

9. The coarse-grained molecular dynamics simulation and analysis method for investigating the microscopic structural properties of electroplating solutions according to claim 1, characterized in that, The system adopts an implicit solvent model to simulate the solvent effect in the system.

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