Magnetron sputtering damage prediction and process window determination method based on two-body collision approximation-finite element coupling algorithm

Abstract

The invention discloses a magnetron sputtering damage prediction and process window determination method based on a two-body collision approximation-finite element coupling algorithm. The method comprises the following steps: taking incident particle energy, flux, incident angle, sputtering temperature and sputtering time as input, approximately calculating energy deposition distribution, sputtering yield and displacement damage by adopting two-body collision, mapping an intermediate quantity into a finite element multi-physical field heat conduction-stress coupling model, and calculating indexes such as substrate temperature rise, interlayer stress and structural deformation; and judging the low-damage process window according to preset thresholds (stress, temperature rise and surface defect damage). The method is suitable for design and evaluation of the low-damage magnetron sputtering process.

Description

Technical Field

[0001] This invention belongs to the field of simulation technology for thin film deposition and material processing, and relates to damage assessment and parameter optimization of magnetron sputtering process. Specifically, it relates to a process damage prediction method and a process window determination method that couples Monte Carlo calculations approximating two-body collisions with finite element thermo-structural mechanics multiphysics calculations. Background Technology

[0002] Magnetron sputtering is widely used in the fabrication of transparent conductive films, metal electrodes, and functional thin films. In actual processes, the kinetic energy bombardment of incident particles can cause surface sputtering thinning and displacement damage; during deposition and cooling, the mismatch in interlayer thermal expansion coefficients can also generate residual stress and deformation, leading to failures such as cracking and debonding. In recent years, with the rise of low-temperature sensitive systems such as perovskite solar cells, organic / perovskite heterojunction devices, and flexible electronics, the demand for low-damage magnetron sputtering has increased significantly: these devices have limited tolerance to ion bombardment and thermal load, and the magnetron sputtering process is prone to causing device performance degradation and yield reduction. While reducing sputtering power to decrease damage can alleviate the problem to some extent, it will significantly reduce film deposition efficiency, decrease throughput per unit machine hour, and increase device costs. Existing technologies mostly rely on empirical trial and error to search for acceptable process parameters, which makes it difficult to guarantee optimality and portability, and the trial and error costs are high, with poor reproducibility across different production lines. There is an urgent need for an efficient calculation method to quickly determine the low-damage process window.

[0003] From a modeling perspective, particle-solid interaction models can provide energy deposition distribution and sputtering yield at the molecular level, but they struggle to reflect the temperature rise, deformation, and stress response of device structures at the macroscopic level. Furthermore, macroscopic multiphysics simulations lack quantitative inputs from particle-scale equivalent heat sources, momentum loads, and defect generation. Currently, there is a lack of a system simulation method that unifies "sputtering / displacement damage" (microscopic) and "temperature rise / stress" (macroscopic). Therefore, a scientific computational method is urgently needed to simulate the damage to substrates caused by magnetron sputtering. Summary of the Invention

[0004] The purpose of this invention is to address the problems in existing magnetron sputtering processes, such as the lack of unified micro-macro coupled modeling and the difficulty in quantitatively determining the low-damage process window. This invention provides a magnetron sputtering damage prediction and process window determination method based on a two-body collision approximation-finite element coupled algorithm. This method can quickly and objectively determine whether "sputtering / displacement damage" and "temperature rise / stress" meet the requirements during the parameter design stage or the existing process evaluation stage, and output feasible process windows and recommended parameters.

[0005] The application aims to realize the technical scheme of a magnetron sputtering damage prediction and process window determination method based on a two-body collision approximation-finite element coupling algorithm. Step one: Construct a substrate layer structure and a material parameter library, and specify material parameters and their temperature dependence for each layer. The substrate layer structure and material parameters include substrate layer thickness, density, thermal conductivity, Young's modulus, and Poisson's ratio. Step two: Set the initial values of the magnetron sputtering equipment and process parameters, including incident particle energy, flux, incident angle range, sputtering temperature, and sputtering time. Step three: Based on the inputs from steps one and two, use the two-body collision approximation-Monte Carlo algorithm to solve the interaction between particles and solids, and statistically obtain the substrate energy deposition distribution, surface sputtering yield and average sputtering kinetic energy, surface defect density, and defect density distribution with depth. Step four: Construct a finite element model, map the energy deposition distribution, sputtering yield, and average sputtering kinetic energy from step three to the finite element model, perform thermal-structural mechanics multi-physics field coupling calculation, and obtain the substrate temperature rise during sputtering, thermal mismatch stress damage during cooling, and film layer deformation damage parameters. Step five: Aggregate and export film layer thinning rate, substrate surface defect damage, and maximum stress data for evaluating substrate sputtering damage under corresponding process parameters. Step six: Compare the evaluation results from step five with the preset threshold to determine whether the desired result is met. If yes, export the corresponding process window. If not, update the magnetron sputtering equipment parameters and return to step three for iteration until the desired result is met or the maximum number of iterations is reached.

[0006] Further, step three is implemented through the following sub-steps: (3.1) Monte Carlo sampling of incident particles according to given energy distribution and incident angle distribution, with a sampling particle number not less than ten thousand; (3.2) Monte Carlo propagation of each particle using two-body scattering dynamics with a shielding Coulomb potential, gradually calculating energy and momentum transfer and recording collision events until the particle energy is below the cutoff threshold; (3.3) Statistically obtain the bulk energy deposition distribution and normal momentum flux distribution; (3.4) Statistically obtain the sputtering yield and average sputtering kinetic energy by counting the number of surface particles with energy greater than the binding energy; (3.5) Calculate the surface defect density by averaging the number of surface atomic displacements per incident ion, and obtain the defect density distribution with depth based on the Monte Carlo propagation trajectory from step (3.2), and calculate the substrate thinning rate based on the sputtering speed of the magnetron sputtering equipment.

[0007] Further, the step four is realized by the following sub-steps: (4.1) Calculate the heat energy according to the particle energy on the surface of the substrate, the heat source surface is calculated as follows: Wherein, x is the average energy of each particle, is the particle flux, Q is the heat of the magnetron sputtering cavity; (4.2) Divide the grid for the substrate model, and perform thermal-structure mechanics coupling finite element calculation, first, according to the particle energy and flux of the magnetron sputtering device, solve the heat source surface power; then solve the heat conduction equation to obtain the temperature field under the condition of top surface convection, calculate the thermal expansion strain of the film layer and the substrate, solve the interlayer stress, and simulate the deformation of the substrate; (4.3) Extract the highest transient temperature, the maximum tensile stress and the maximum compressive stress value in the structure as the evaluation standard of damage degree.

[0008] Further, the step five outputs include two branches of evaluation mode and iterative optimization mode; the evaluation mode performs calculation on a single parameter combination and directly outputs the damage degree data; the iterative optimization mode adjusts the magnetron sputtering device and process parameters, including incident particle energy, flux, incident angle range, sputtering temperature, sputtering time, the parameter adjustment algorithm adopts gradient descent method, or the preset parameter space adopts grid search.

[0009] Further, the threshold judgment is given in the form of inequality, and at least one of the following is included: maximum tensile stress ≤ tensile stress standard; maximum compressive stress ≤ compressive stress standard; highest transient temperature ≤ temperature standard; surface defect density ≤ defect density standard; substrate thinning rate ≤ thinning rate standard; film layer deformation ≤ deformation standard.

[0010] Further, the step four calculation process adopts grid self-adaptation and convergence criterion control, and the relative tolerance is <0.001.

[0011] Further, the step three calculation process can calculate different particle types respectively, and for the multi-particle mixed flow scene, the damage brought by different particle beams can be quantitatively characterized.

[0012] Further, the step three calculation process can quantitatively analyze the energy flow direction, including electron ionization heat energy, lattice vibration heat energy, and sputtering atom kinetic energy. The heat energy is used in step four to simulate the substrate temperature rise and thermal mismatch stress by finite element. Further, the type of the particle is at least one of charged ions or neutral target atoms, the surface defects are calculated according to the Monte Carlo method, and the surface binding energy is combined to determine the sputtering event.

[0013] Further, the process window includes a feasible interval of incident energy, flux, sputtering temperature, and sputtering time.

[0014] The present application has the advantages of: A unified modeling and load mapping framework from particle scale to structure scale is established, which can quantify sputtering / displacement damage and temperature rise / stress simultaneously, so as to determine a low-damage process window with objective indicators; The grouping statistics and weighted aggregation of multiple particle species and multiple energy components are supported, which can decompose the damage contribution of different particle beams and be used for parameter-oriented optimization; Both the existing process can be quickly evaluated, and the recommended value and tolerance band can be obtained by iterative optimization in the parameter space, thereby reducing the number of experimental trial and error and cost; A general algorithm is used for description, which does not depend on specific commercial software implementation, and is convenient for transplantation and reproduction between different equipment and production lines. BRIEF DESCRIPTION OF DRAWINGS

[0015] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0016] Figure 1 A magnetron sputtering damage prediction and process window determination method based on two-body collision approximation-finite element coupling algorithm provided by the embodiment of the present application is shown in the flowchart. Figure 2 For 200eV O - Monte Carlo simulation results of collision trajectories of ions in C60 / MAPbI structure for 10000 times of incidence; Figure 3 For 200eV O - Monte Carlo simulation results of collision depth of ions in C60 / MAPbI structure for 10000 times of incidence; Figure 4 For 200eV O - Statistical results of normal kinetic energy of C atoms when ions are incident on C60 / MAPbI structure; Figure 5 For 200eV O - Defect position distribution on the surface of C60 when ions are incident on C60 / MAPbI structure; Figure 6 For room temperature environment, when the surface power density of the heat source is 10000W / m 2 , the temperature rise and temperature field distribution of C60 / MAPbI; Figure 7 The power density of the working heat source surface is 10000 W / m 2 The stress distribution of C60 / MAPbI after cooling to room temperature. DETAILED DESCRIPTION

[0017] The application will be described in detail below with reference to the accompanying drawings.

[0018] The application is based on a magnetron sputtering damage prediction and process window determination method based on a two-body collision approximation-finite element coupling algorithm, as shown in Figure 1 , comprising the following steps: Step one: Constructing a substrate layer structure and a material parameter library, assigning material parameters to each layer, including substrate layer thickness, density, thermal conductivity, Young's modulus, Poisson's ratio and other parameters.

[0019] Step two: Setting the initial values of the magnetron sputtering equipment and process parameters, including incident particle flow energy, flux, incident angle range, sputtering temperature, sputtering time and other parameters.

[0020] Step three: According to the input of step one and step two, the two-body collision approximation-Monte Carlo algorithm is used to solve the interaction between particles and solids, and the indexes such as substrate energy deposition distribution, surface sputtering yield, surface defect density and defect density distribution with depth are obtained.

[0021] Step three is divided into the following sub-steps: (3.1) Monte Carlo sampling of incident particles according to the given energy distribution and incident angle distribution, the number of sampled particles is not less than ten thousand; (3.2) Two-body scattering dynamics with shielding Coulomb potential is used to advance each particle by Monte Carlo, gradually calculate the energy and momentum transfer and record the collision events until the particle energy is lower than the cutoff threshold; the calculation value of 10,000 particles is shown in Figure 2 , the top area is the particle collision path. The case is to sputter ITO on C60 / MAPbI, and the damage source is 200 eV O - ( same below) (3.3) The body energy deposition distribution is obtained by statistics, and the result is shown in Figure 3 ; (3.4) The sputtering events are counted by counting the surface particle energy greater than the binding energy, and the sputtering yield and average sputtering kinetic energy are counted, and the calculation result of the normal kinetic energy of C atoms is shown in Figure 4 , because the surface binding energy of C atoms is 3.8 eV, the particles with normal kinetic energy higher than 3.8 eV will be sputtered, and the probability is 0.16; (3.5) Surface defect density is calculated by the average number of surface atom displacement per ion incidence, combined with the Monte Carlo collision trajectory in step (3.2), to obtain the distribution of defect density with depth (such as the distribution of defects at a depth of 0-5 nm from the surface), as shown in Figure 5 The thinning rate of the substrate is calculated by combining the sputtering speed of the magnetron sputtering device, and the thinning rate v is calculated according to formula (1), where x is the average number of sputtered particles per particle incidence, which is obtained by a two-body collision approximation-Monte Carlo algorithm; is the particle flux, which is a parameter of the magnetron sputtering device; n is the atomic number density, which is a parameter of the substrate.

[0022] (1) The surface defect damage of the substrate is determined by formula (2), t is the magnetron sputtering time, is the particle flux, which is a parameter of the magnetron sputtering device. Vacacies is the average number of vacancies per particle incidence, which is determined in step (3.4). Depth is the average depth of particle collision simulated by the Monte Carlo method, which is obtained in step (3.2); n is the atomic number density, which is a parameter of the substrate.

[0023] (2) In step three, it also includes: quantitative analysis of energy flow, including thermal energy and kinetic energy of sputtered atoms. Among them, the thermal energy is used in step four to calculate the substrate temperature rise, thermal mismatch stress Step four: build a finite element model, map the energy deposition distribution, sputtering yield and average sputtering kinetic energy of step three to the finite element model, and perform thermal-structural mechanics multi-physical field coupling calculation to obtain the substrate temperature rise in the sputtering process (the result is shown in Figure 6 ), the thermal mismatch stress damage in the cooling process, and the deformation of the plated film layer and other damage parameters (the result is shown in Figure 7 ).

[0024] Step four is divided into the following steps: (4.1) Calculate the thermal energy according to the particle energy reaching the substrate surface in step three, and the heat source surface The specific calculation method is shown in formula (3), which is the core of the method, mapping the particle scale calculation results to the macro scale.

[0025] (3) is the particle flux, Q is the heat of the magnetron sputtering cavity, both of which are parameters of the magnetron sputtering device. x is the average energy per particle, and the detailed calculation method is shown in formula (4): (4) E0 is the sputtering particle flux energy of the magnetron sputtering device, which is a device parameter, is the sputtering probability of each particle incidence, Ev is the average sputtering kinetic energy of the surface particles obtained from step (3.4); SBE is the surface binding energy of the atoms, which is a material parameter of the device.

[0026] (4.2) Divide the substrate model into grids and perform thermal-structural mechanical coupling finite element calculation. First, solve the heat source surface power according to the particle energy and flux of the magnetron sputtering device. Then, solve the heat conduction equation to obtain the temperature field under the condition of top surface convection. Calculate the thermal expansion strain of the film layer and the substrate using the temperature field, solve the interlayer and intralayer stress (including tensile stress and compressive stress), and simulate the deformation of the coated film layer.

[0027] (4.3) Extract the highest transient temperature, the maximum tensile stress and the maximum compressive stress in the structure as the evaluation criteria for damage degree.

[0028] Step five: Aggregate and export defect indicators such as film layer thinning rate, substrate surface defect damage, maximum stress (maximum tensile stress and maximum compressive stress), etc. to record the sputtering damage of the substrate under the corresponding process parameters.

[0029] Step six: Compare the recorded results of step five with the corresponding preset threshold values. If all threshold indicators under the corresponding working conditions are met, it is judged to meet the expectations. If it is met, the corresponding process window is exported. If it is not met, the magnetron sputtering device and process parameters are updated, and step three is returned for iteration until the threshold value is exceeded or the iteration number limit is reached.

[0030] The threshold value judgment is given in the form of an inequality and includes at least one of the following: maximum tensile stress ≤ tensile stress standard; maximum compressive stress ≤ compressive stress standard; highest transient temperature ≤ temperature standard; surface defect density ≤ defect density standard; substrate thinning rate ≤ thinning rate standard; film layer deformation ≤ deformation standard. Taking the sputtering of ITO on the top surface of a perovskite battery as an example, the threshold judgment conditions are: maximum tensile stress ≤ 100 Mpa; maximum compressive stress ≤ 100 Mpa; highest transient temperature ≤ 150 °C; surface defect density ≤ 10 22 per square meter; substrate thinning rate ≤ 0.1 nm / s. The specific damage standard is determined by the sputtering material and process flow, and can be set by those skilled in the art according to the actual situation.

[0031] The above examples are only used to illustrate the design idea and characteristics of the present application, and the purpose is to enable those skilled in the art to understand the content of the present application and implement it, and the protection scope of the present application is not limited to the above examples. Therefore, any equivalent changes or modifications made in accordance with the principles and design ideas disclosed by the present application are within the scope of protection of the present application.

Claims

1. A method for magnetron sputtering damage prediction and process window determination based on two-body collision approximation-finite element coupling algorithm, characterized in that, The method comprises the following steps: Step 1: Construct the substrate layer structure and material parameter library, and specify the material parameters and their temperature dependence for each layer. The substrate layer structure and material parameters include substrate layer thickness, density, thermal conductivity, Young's modulus, and Poisson's ratio. Step 2: Set the initial values of the magnetron sputtering equipment and process parameters, including incident particle energy, flux, incident angle range, sputtering temperature, and sputtering time. Step 3: Based on the inputs from steps 1 and 2, use the two-body collision approximation-Monte Carlo algorithm to solve the particle-solid interaction, and statistically obtain the substrate energy deposition distribution, surface sputtering yield, average sputtering kinetic energy, surface defect density, and defect density distribution with depth. Step 4: Construct a finite element model, map the energy deposition distribution, sputtering yield, and average sputtering kinetic energy from step 3 to the finite element model, perform thermal-structural mechanics multi-physics field coupling calculation, and obtain the substrate temperature rise during sputtering, thermal mismatch stress damage in the cooling process, and film layer deformation damage parameters. Step 5: Aggregate and export the film layer thinning rate, substrate surface defect damage, and maximum stress data for evaluating the substrate sputtering damage under the corresponding process parameters. Step 6: Compare the evaluation results from step 5 with the preset threshold to determine whether the desired results are met. If the desired results are met, export the corresponding process window. If the desired results are not met, update the magnetron sputtering equipment and process parameters, and return to step 3 for iteration until the desired results are met or the iteration limit is reached.

2. The method of claim 1, wherein, The step 3 is realized through the following sub-steps: (3.1) Monte Carlo sampling of incident particles according to the given energy distribution and incident angle distribution, with a sampling particle number not less than ten thousand; (3.2) Monte Carlo propagation of each particle using two-body scattering dynamics with a shielding Coulomb potential, gradually calculating energy and momentum transfer and recording collision events until the particle energy is below the cutoff threshold; (3.3) Statistically obtain the bulk energy deposition distribution and normal momentum flux distribution; (3.4) Statistically obtain the sputtering events with surface particle energy greater than the binding energy, and calculate the sputtering yield and average sputtering kinetic energy; (3.5) Calculate the surface defect density by averaging the number of surface atomic displacements per incident ion, and obtain the defect density distribution with depth based on the Monte Carlo propagation trajectory from step (3.2). Combine the sputtering speed of the magnetron sputtering equipment to calculate the substrate thinning rate.

3. The method of claim 1, wherein, The step 4 is realized through the following sub-steps: (4.1) Calculate the thermal energy based on the substrate surface particle energy from step 3, and the heat source surface is calculated as follows: where x is the average energy per particle, is the particle flux, and Q is the heat of the magnetron sputtering chamber; (4.2) Divide the substrate model into grids and perform thermal-structural mechanics coupling finite element calculation. First, solve the heat source surface power based on the particle energy and flux of the magnetron sputtering equipment. Then, solve the heat conduction equation under the condition of top surface convection to obtain the temperature field. Use the temperature field to calculate the thermal expansion strain of the film layer and the substrate, solve the interlayer stress, and simulate the deformation of the substrate; (4.3) Extract the highest transient temperature, maximum tensile stress, and maximum compressive stress values in the structure as the evaluation criteria for damage degree.

4. The method of claim 1, wherein, The step five output includes two branches of evaluation mode and iterative optimization mode; the evaluation mode performs calculation on a single parameter combination and directly outputs the damage degree data; the iterative optimization mode adjusts the magnetron sputtering device and process parameters, including incident particle energy, flux, incident angle range, sputtering temperature, and sputtering time, and the parameter adjustment algorithm adopts the gradient descent method or the preset parameter space adopts the grid search.

5. The method of claim 1, wherein, The threshold determination is given in the form of an inequality and includes at least one of the following: maximum tensile stress ≤ tensile stress standard; maximum compressive stress ≤ compressive stress standard; highest transient temperature ≤ temperature standard; surface defect density ≤ defect density standard; substrate thinning rate ≤ thinning rate standard; plated film deformation ≤ deformation standard.

6. The method of claim 1, wherein, The step four calculation process adopts grid self-adaptation and convergence criterion control, and the relative tolerance is < 0.

001.

7. The method of claim 1, wherein, The step three calculation process can calculate different particle types respectively, and for a multi-particle mixed flow scenario, the damage caused by different particle beams can be quantitatively characterized.

8. The method of claim 1, wherein, The step three calculation process can quantitatively analyze the energy flow direction, including electron ionization thermal energy, lattice vibration thermal energy, and sputtered atom kinetic energy; the thermal energy is used in step four for finite element simulation calculation of substrate temperature rise and thermal mismatch stress.

9. The method of claim 1, wherein the species of the particles are at least one of charged ions or neutral target atoms, surface defects are calculated according to the Monte Carlo method, and surface binding energy is used to determine sputtering events.

10. The method of claim 1, wherein the process window includes a feasible interval of incident energy, flux, sputtering temperature, and sputtering time.

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