Method for optimizing technological parameters of electrocoppering rewiring process based on numerical simulation

Abstract

The invention belongs to the technical field of microelectronic packaging, and discloses a method for optimizing technological parameters in the electrocoppering and rewiring process based on numerical simulation. A three-dimensional geometric model of a copper rewiring layer electroplating process is established. A relation model of the stirring frequency and the electrolyte flow velocity is constructed, and related physical property parameters and boundary conditions are set in combination with diffusion, electromigration and convection processes. Building an impressed current density model considering covering surfaces and free surfaces of an accelerator, an inhibitor and a leveling agent, and counting concentration ratio and dynamic change of the additive; electroplating parameters are used as global variables, distribution data such as cathode surface overpotential, current density, ion and additive concentration and the like are obtained, and the influence rule is analyzed to preliminarily optimize the parameter range. And finally, the optimal electroplating parameters are determined by combining microstructure characterization and resistance testing of the verification test. According to the method, the test cost and period are effectively reduced through numerical simulation, and a reliable theoretical basis is provided for optimization of a copper rewiring layer electroplating process.

Description

Technical Field

[0001] This application belongs to the field of microelectronic packaging technology, specifically relating to a method for optimizing process parameters in the electroplated copper redistribution process based on numerical simulation. Background Technology

[0002] The redistribution layer (RDL), a key structure in microelectronic packaging, plays a crucial role in optimizing chip electrical connections and improving signal transmission efficiency. Copper electroplating is one of the main processes for forming the RDL. Parameters used in this process, such as applied current density, stirring frequency, and additive concentration ratio, directly affect the overpotential, electrolyte current density, copper ion concentration, and additive concentration distribution during copper deposition, thus determining the microstructure and conductivity of the copper plating. Traditional methods for optimizing process parameters rely heavily on numerous electroplating experiments, using trial and error to select suitable parameter ranges. However, this experimental method has significant limitations: high experimental costs, long cycles, and difficulty in comprehensively capturing the influence of complex physical field interactions on plating quality.

[0003] To overcome the shortcomings of experimental methods, numerical simulation technology has been introduced into the analysis of electroplating processes. For example, the literature "Numerical simulation of copper filling within mesoporous silicon by electrodeposition, K. Fukami, ML Chourou, T. Sakka, YH Ogata, Phys.Status Solidi A, 2011, 208(6): 1407-1411" describes the simulation of copper electrodeposition in mesoporous silicon by establishing a two-dimensional coupled mapping lattice model. This model discretizes the differential equation into a difference form and considers the copper electrodeposition current density and hydrogen evolution reaction current density in the interfacial electrochemical reaction. However, when constructing the applied current density, this model does not include the influence of the concentration ratio of additives (including accelerators, inhibitors, and leveling agents), and the copper ion mass transfer process only involves diffusion and electromigration, neglecting the effect of electrolyte convection. In reality, the concentration and ratio of additives, their dynamic changes during electroplating, and the convection transport mechanism all significantly affect the cathode surface coverage and current density distribution, thereby determining the microstructure formation of copper grains and the final conductivity. Therefore, ignoring these factors will lead to significant deviations between simulation results and actual conditions, failing to provide a reliable basis for optimizing process parameters. Summary of the Invention

[0004] To address the shortcomings of existing simulation methods that deviate from actual conditions, this application provides a numerical simulation-based method for optimizing process parameters of electroplated copper rewiring. This method establishes a quantitative relationship model between stirring frequency and electrolyte flow rate, constructs an applied current density model that considers the dynamic changes in additive concentration and surface coverage state, and combines multi-physics coupled numerical simulation to accurately characterize mass transfer and electrochemical behavior during electroplating, thereby achieving efficient and accurate optimization of process parameters.

[0005] To achieve the above-mentioned technical effects, this application adopts the following technical solution: In one aspect of this application, a method for optimizing process parameters in electroplated copper rewiring based on numerical simulation is provided, comprising the following steps: S1. Establish a three-dimensional geometric model of the copper redistribution layer electroplating process and perform mesh generation. The three-dimensional geometric model includes the cathode, anode, and electrolyte domain. S2. Establish a physical model for the copper redistribution layer electroplating process. The physical model describes the mass transfer process of substances in the electrolyte. The mass transfer process includes diffusion caused by concentration gradient, electromigration caused by potential gradient, and convection caused by fluid flow. The physical model establishes a mathematical relationship between electrolyte flow rate and stirring frequency, and applies this relationship to the setting of the convection velocity field. S3. Establish an applied current density model, which considers four states of the cathode surface: a surface covered by an accelerator, a surface covered by an inhibitor, a surface covered by a leveling agent, and a free surface not covered by additives, and describes the applied current density in each of the four states based on the Butler-Volmer equation. S4. Based on the established three-dimensional geometric model, physical model, and applied current density model, a three-dimensional finite element numerical simulation system for the copper redistribution layer electroplating process is constructed. Numerical simulation is performed by changing the values ​​of electroplating process parameters, including applied current density, stirring frequency, and additive concentration ratio. The effects of the electroplating process parameters on the overpotential, electrolyte current density, copper ion concentration, and additive concentration distribution on the cathode surface are analyzed, and the range of electroplating parameters is preliminarily determined. S5. Conduct verification experiments within the initially determined parameter range, prepare copper redistribution layer samples, quantitatively characterize the microstructure of the samples and measure their resistance values, compare and analyze the macroscopic physical field distribution obtained from numerical simulation, the microstructure morphology and resistance values ​​obtained from verification experiments, and determine the optimal combination of electroplating process parameters.

[0006] In one implementation, the mesh division in step S1 includes: The near-base end surface and the far-base end surface of the cathode are divided using a free triangular mesh; The copper plating area of ​​the cathode and the electrolyte region are divided into triangular prism grids and layered by a sweep algorithm. The number of layers in the copper plating area and the electrolyte region is the same. The mesh topology of the cathode distal substrate surface is mapped to the anode surface using mesh mapping technology.

[0007] In one implementation, in step S2, the mathematical relationship between the stirring frequency and the electrolyte flow rate is as follows:

[0008] in, This represents the flow rate at any point in the electrolyte. Table stirring frequency, Table of agitation grid length, Table of grid width for agitation The vertical distance from any point in the electrolytic cell to the bottom of the hole. The vertical distance from the anode to the bottom of the cathode.

[0009] In one implementation, the total mass flux of the mass transfer process in step S2 is:

[0010] in, For total mass flux, The diffusion coefficient of ions or additives. This refers to the concentration of ions or additives. The valence number is the ion number. This represents the potential in the electrolyte solution. It is Faraday's constant. The velocity field governed by the incompressible Navier-Stokes equations. R The gas constant is T The temperature is in Kelvin.

[0011] In one implementation, in step S3, the rate of change of the additive coverage on the cathode surface in the applied current density model is:

[0012] in, Indicates the surface coverage of the additive. Indicates the adsorption coefficient of the additive. Indicates the desorption coefficient of the additive. Indicates the electrodeposition rate, Indicates the surface coverage of the accelerator. Indicates the surface coverage of the inhibitor. This indicates the surface coverage of the leveling agent.

[0013] In one implementation, the adsorption reaction rate of the additive is obtained based on the rate of change of the coverage. R i and adsorption / desorption reaction rate Rad i :

[0014]

[0015] in, This represents the surface saturation concentration of the additive.

[0016] In one implementation, in step S3, the applied current density of the surfaces covered by the accelerator, the inhibitor, and the leveling agent is:

[0017] in, i i The applied current density on the surface covered by the additive is expressed in A•m. -2 , This represents the copper ion concentration, in mol•m -3 , This is the standard concentration of copper ions, in mol•m -3 , The applied current density on the surface covered by the additive is expressed in A•m. -2 , α i For the transmission coefficient ( For the accelerator transport coefficient, The inhibitor transfer coefficient, (Leveling agent transfer coefficient) F It is Faraday's constant. η Overpotential, measured in volts (V). R The gas constant is T 0 represents the initial temperature, in Kelvin (K). The applied current density of the free surface not covered by the additive is:

[0018] in, The initial applied current density (A•m) not covered by the additive -2 ), The initial applied current density before the additive is applied, in A•m. -2 , is the cathode transfer coefficient.

[0019] In one embodiment, in step S4, the initially obtained electroplating parameters range as follows: applied current density 0.8~1.0ASD, stirring frequency 5~15 Hz, and accelerator, inhibitor and leveling agent concentration ratio 3:1:0.2.

[0020] In one embodiment, in step S5, the quantitative characterization of the microstructure includes grain thickness, grain orientation, twin type, and twin density; the determination of the optimal electroplating process parameters comprehensively considers the uniformity of the microstructure, preferred orientation, high twin density, and low resistivity.

[0021] In one embodiment, in step S5, the optimal electroplating process parameters are: current density 0.8 ASD, stirring frequency 10 Hz, and the concentration ratio of accelerator, inhibitor and leveling agent 3:1:0.2.

[0022] The beneficial effects of this application are as follows: This invention establishes a quantitative model relating stirring frequency to electrolyte flow rate, achieving accurate simulation of the electroplating process under convection. It constructs an applied current density model considering the surface coverage of accelerators, inhibitors, and leveling agents, accurately describing the impact of dynamic additive concentration changes on the electroplating process. A discretization method combining free triangular and triangular prism meshes ensures a balance between computational accuracy and efficiency under complex geometric boundary conditions. The method in this application can systematically analyze the influence of current density, stirring frequency, and additive ratio on overpotential, current density distribution, and ion transport, achieving multi-scale correlation from macroscopic physical fields to microscopic structures. This significantly reduces the process optimization cycle and experimental costs, providing an effective means for preparing highly uniform, low-resistivity copper redistribution layers. Attached Figure Description

[0023] Figure 1 Three-dimensional finite element numerical simulation modeling of the copper RDL electroplating process in the embodiments of this application is provided; (a) is the geometric model; (b) is the mesh generation. Figure 2 This is a schematic diagram of a copper RDL electroplating apparatus according to an embodiment of this application; Figure 3 The numerical simulation results of the copper RDL electroplating process in this application are shown below; (a) is the cathode surface; (b) is the corner section. Figure 4 The following are examples of the effects of applied current density on the overpotential of the cathode surface when the stirring frequency is 10 Hz and the additive concentration ratio is 3:1:0.2: (a) 0.5 ASD; (b) 0.6 ASD; (c) 0.8 ASD; (d) 1.0 ASD; (e) 2.5 ASD; (f) 3.5 ASD. Figure 5This paper illustrates the effect of stirring frequency on the overpotential (a), electrolyte current density (b), and copper ion concentration (c) of the copper RDL characteristic point in the embodiments of this application. Figure 6 In this embodiment of the application, when the applied current density is 0.8 ASD and the stirring frequency is 10 Hz, the effect of the additive concentration ratio on the overpotential at the initial time (a, d, g), intermediate time (b, e, h), and final time (c, f, i) of copper RDL electroplating is as follows: (a~c) is 2:1:0.2; (d~f) is 3:1:0.2; (g~i) is 4:1:0.2. Figure 7 The effects of additive concentration ratio on the overpotential (a), electrolyte current density (b), copper ion concentration (c), accelerator concentration (d), inhibitor concentration (e), and leveling agent concentration (f) of the copper RDL corner section deposition direction are shown in the embodiments of this application. Figure 8 This application illustrates the effects of applied current density on the horizontal overpotential (a), electrolyte current density (b), copper ion concentration (c), accelerator concentration (d), inhibitor concentration (e), and leveling agent concentration (f) of the copper RDL corner cross-section. Figure 9 The following are examples of the effects of applied current density on the inverse pole figure (IPF) of the copper RDL corner section when the stirring frequency is 10 Hz and the linewidth is 10 μm: (a) 0.5 ASD; (b) 0.6 ASD; (c) 0.8 ASD; (d) 1.0 ASD; (e) 2.5 ASD; (f) 3.5 ASD. Figure 10 The following are examples of the effects of applied current density on the thickness of copper RDL grains when the stirring frequency is 10 Hz and the linewidth is 10 μm: (a) 0.5 ASD; (b) 0.6 ASD; (c) 0.8 ASD; (d) 1.0 ASD; (e) 2.5 ASD; (f) 3.5 ASD. Figure 11 This application illustrates the effect of applied current density on the grain orientation of copper RDL in an embodiment of this application. Figure 12 This application illustrates the effect of applied current density on the twin density of copper RDL in an embodiment of this application. Figure 13 The effect of electroplating process parameters on the resistance value of copper RDL in the embodiments of this application is shown in the following: (a) is the applied current density; (b) is the stirring frequency. Detailed Implementation

[0024] The technical solution of this application will be clearly and completely described below with reference to specific embodiments. However, those skilled in the art will understand that the embodiments described below are only some embodiments of this application, not all embodiments, and are only used to illustrate this application, and should not be regarded as limiting the scope of this application. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0025] Based on the structural morphology and dimensions of copper RDLs in actual production, this application establishes a three-dimensional geometric model; constructs a model of the relationship between stirring frequency and electrolyte flow rate during copper electroplating of copper RDLs; and, combining the three modules of diffusion, electromigration, and convection in the electroplating process, sets physical property parameters such as diffusion coefficient, transfer coefficient, adsorption and desorption coefficients of electroplating solution ions and additive molecules, as well as boundary conditions of the electroplating physical field; considering the additive concentration ratio and the concentration ratio changes caused by the loss of accelerators and inhibitors during electroplating, establishes an applied current density model considering the surface covered by accelerators, surfaces covered by inhibitors, surfaces covered by leveling agents, and surfaces not covered by additives; and, using electroplating parameters as globally defined parameters, combines COMSOL Multiphysics numerical simulation software to study the distribution data of overpotential, electrolyte current density, copper ion concentration, and additive concentration on the cathode surface of copper RDLs, obtains the influence law of electroplating parameters on the copper RDL electroplating process, and preliminarily optimizes the range of electroplating parameters; and, combined with the microstructure and resistance value of copper RDLs under verification test conditions, further determines the optimal electroplating parameters.

[0026] In one specific implementation, a method for optimizing process parameters in a copper plating redistribution process based on numerical simulation includes the following steps: S1. Establish a three-dimensional geometric model of the copper redistribution layer electroplating process and perform mesh generation. The three-dimensional geometric model includes the cathode, anode, and electrolyte domain.

[0027] In some embodiments, the three-dimensional geometric model is constructed in COMSOL Multiphysics numerical simulation software.

[0028] First, configure the physics module in the software, selecting support for the three-dimensional current distribution of the electrolyte, and employing transient analysis with initialization in the study type to accurately simulate the dynamic behavior during the electroplating process. In the global definition node parameter settings section of the model developer window, set global parameters related to the electroplating process, including applied current density, stirring frequency, and additive concentration ratio. Simultaneously, define local variable parameters in the local variable settings section of the main screen toolbar to refine the local physics characteristics in the model.

[0029] Next, draw the working plane and establish the initial geometric model of the cathode and anode based on the geometric features of the actual copper RDL. In the geometry toolbar, use Boolean operations and the split function to remove the internal boundary between the cathode and anode, ensuring that the model boundary is continuous and conforms to the structure of the actual electroplating device, thus completing the establishment of the three-dimensional geometric model of the electroplated copper RDL.

[0030] Subsequently, in the Material Charge Settings section of the Model Developer window, define the charge numbers of copper and sulfate ions in the electrolyte to accurately describe the behavior of ions in the electric field. Create a boundary and define the cathode surface in the Physics toolbar. In the Electrode Surface Settings window, specify the density and molar mass of the dissolved deposited material. In the Adsorption-Desorption Material section, set the in-situ occupancy of additive molecules (accelerators, inhibitors, and leveling agents) to reflect their adsorption behavior. In the Electrode Phase Potential Conditions section, define the cathode potential boundary conditions. In the Electrode Reaction Settings window, set the number of participating electrons in the Stoichiometric Coefficients section. In the Equilibrium Potential section, select the Nernst equation and set the corresponding equilibrium potential value. In the Local Current Density Expression section of the Electrode Kinetics Settings window, check the Butler-Volmer kinetic expression to describe the electrochemical reaction kinetics. In the Exchange Current Density Type section, check the law of mass action and set the exchange current density and cathode transfer coefficient. Furthermore, in the Physics toolbar of the Model Developer window, define the non-Radidatic reaction rate, specifically setting the adsorption rate and adsorption-desorption rate parameters of additive molecules. Meanwhile, in the physics toolbar, a boundary definition anode surface is created, and in the concentration setting window, the initial concentrations of copper ions, sulfate ions, and additive molecules are defined to fully describe the electrolyte composition.

[0031] Finally, in the mesh settings module of the model developer window, the copper RDL geometric model is meshed. A combination of free triangular meshes and triangular prism meshes is used to achieve efficient discretization of the electroplating physics field. Free triangular meshes are used on the near-substrate and far-substrate surfaces. The copper plating region is divided into triangular prism meshes and layered using a sweep algorithm. To ensure consistency between the electrolyte region and the copper plating region calculations, the electrolyte is also divided into triangular prism meshes, with the same number of layers as the copper plating region. Since the mesh at the far-substrate end differs from the rest of the copper RDL coverage area, to avoid mesh mismatch between the anode and cathode and to ensure the continuity of interface flux calculations, a mesh mapping technique is used to map the mesh topology of the far-substrate surface of the cathode to the anode surface.

[0032] S2. Establish a physical model for the copper redistribution layer electroplating process. The physical model describes the mass transfer process of substances in the electrolyte. The mass transfer process includes diffusion caused by concentration gradient, electromigration caused by potential gradient, and convection caused by fluid flow. The physical model establishes a mathematical relationship between electrolyte flow rate and stirring frequency, and applies this relationship to the setting of the convection velocity field.

[0033] The mass transport process in electrolytes encompasses three fundamental mechanisms: diffusion driven by the electrolyte concentration gradient, electromigration of charged ions induced by the potential gradient, and convection generated by relative fluid displacement within the electrolyte. Based on these mechanisms, the total mass flux of ion and additive mass transfer in the electrolyte can be expressed as:

[0034] in, Total mass flux (mol•m -1 •s -1 ), The diffusion coefficient (m) of ions or additives 2 •s -1 ), The concentration of ions or additives (mol•m -3 ), The valence number is the ion number. The potential (V) in the electrolyte solution. Faraday constant (96485 A•s•mol) -1 ), The velocity field (m) governed by the incompressible Navier-Stokes equations 2 •s -1 ), R The gas constant is (8.314 J•K). -1 •mol -1 ), T Kelvin temperature (K).

[0035] The plating bath system consists of charged copper ions and electrically neutral additive molecules. The mass transfer process of copper ions involves diffusion, electromigration, and convection, while the mass transfer of additive molecules involves only diffusion and convection. The diffusion process, controlled by the concentration gradient, follows Fick's second law. The relationship between the concentrations of copper ions (Cu), accelerator (A), inhibitor (P), and leveling agent (L) and time is as follows:

[0036]

[0037] The electromigration process of charged copper ions moving from a high potential to a low potential under the influence of an electric field, and the relationship between their concentration and time, is as follows:

[0038] in, Electromobility (m) 2 •V -1 •s -1 ), It is the Laplace operator.

[0039] For the convection process, a mathematical model relating the electrolyte flow rate to the stirring frequency was established based on the boundary conditions of the convection velocity field.

[0040] in, The flow velocity at any point in the electrolyte (m·s) -1 ), The stirring frequency (Hz) is the value of the stirring frequency. The length (m) of the agitated grid. To agitate the width of the grid (m), denoted as ρ, which is the vertical distance (μm) from any point in the electrolytic cell to the bottom of the hole. The vertical distance (μm) from the anode to the bottom of the cathode is used. The mathematical relationship between electrolyte flow rate and stirring frequency is applied to the setting of the convection velocity field.

[0041] S3. Establish an applied current density model, which considers four states of the cathode surface: a surface covered by an accelerator, a surface covered by an inhibitor, a surface covered by a leveling agent, and a free surface not covered by additives, and describes the applied current density in each of the four states based on the Butler-Volmer equation.

[0042] During electroplating, copper ions and additives are transported from the anode to the cathode via mass transfer, where a series of reactions occur on the cathode surface, including the adsorption and desorption of additive molecules (Faraday reaction) and the electrodeposition of copper ions and additives (Faraday reaction). To describe the adsorption behavior of additives on the cathode surface, a rate-of-change model of additive coverage is established using the Langmuir adsorption equation. The rate-of-change expressions for the surface coverage of the accelerator (A), inhibitor (P), and leveling agent (L) are as follows:

[0043] in, For the surface coverage of the additive, i It can be an accelerator (A), an inhibitor (P), or a leveling agent (L). The adsorption coefficient of the additive (m) 3•mol -1 •s -1 ), The desorption coefficient of the additive (m) -1 ), Electrodeposition rate (m•s) -1 ).

[0044] Based on the expression for the rate of change of additive coverage, the expressions for the additive adsorption reaction rate and the adsorption-desorption reaction rate are further derived. The additive adsorption reaction rate represents the amount of additive molecules adsorbed on the cathode surface per unit time, and its expression is:

[0045] in, The adsorption reaction rate of the additive (mol•m) -2 •s -1 ), The adsorption-desorption reaction rate of the additive (mol•m) -2 •s -1 ), The surface saturation concentration of the additive (mol•m -2 The adsorption-desorption reaction rate of the additive represents the net adsorption rate. Taking into account both the adsorption and desorption processes, the expression is: .

[0046] The above reaction rate parameters are used to quantify the kinetic behavior of the additive on the cathode surface, providing a basis for the applied current density model.

[0047] At the cathode surface, metal ions are reduced to metallic copper via electrodeposition. This application considers four states of the cathode surface: an accelerator-covered surface, an inhibitor-covered surface, a leveling agent-covered surface, and a free surface without additive coverage. The electrodeposition process occurs only at the cathode, therefore the influence of the anode on the applied current density is not considered. For each of these four surface states, an applied current density model is established, and the Butler-Volmer equation is used to describe the electrochemical reaction kinetics. The specific expression is: For the accelerator-covered surface (A), the inhibitor-covered surface (P), and the leveling agent-covered surface (L), the applied current density i i is represented as:

[0048] in, i i The applied current density on the surface covered by the additive is expressed in A•m. -2 , This represents the copper ion concentration, in mol•m -3 , This is the standard concentration of copper ions, in mol•m -3 , The applied current density on the surface covered by the additive is expressed in A•m. -2 , α i For the transmission coefficient ( For the accelerator transport coefficient, The inhibitor transfer coefficient, (Leveling agent transfer coefficient) F It is Faraday's constant. η Overpotential, measured in volts (V). R The gas constant is T 0 represents the initial temperature, in Kelvin (K). For a free surface not covered by additives, the applied current density i free Represented as:

[0049] in, The initial applied current density (A•m) not covered by the additive -2 ), The initial applied current density before the additive is applied, in A•m. -2 , is the cathode transfer coefficient.

[0050] The chemical nature of electrodeposited copper is based on a redox reaction system within an electrolytic cell. In the anodic region, metallic copper, acting as a soluble anode, undergoes oxidation, continuously replenishing the electrolyte with copper ions. In the cathodic region, copper ions undergo directional electrochemical reduction, forming a copper plating layer on the substrate surface through a metal electrocrystallization process. This process follows Faraday's law, and the deposition rate of copper ions... v d The expression is:

[0051] in, The molar mass of copper (kg•mol) -1 ), The density of copper (kg•m) -3 ), The total applied current density is the number of electrons transferred. .

[0052] S4. Based on the established three-dimensional geometric model, physical model, and applied current density model, a three-dimensional finite element numerical simulation system for the copper redistribution layer electroplating process is constructed. Numerical simulation is performed by changing the values ​​of electroplating process parameters, including applied current density, stirring frequency, and additive concentration ratio. The effects of the electroplating process parameters on the overpotential, electrolyte current density, copper ion concentration, and additive concentration distribution on the cathode surface are analyzed, and the range of electroplating parameters is preliminarily determined.

[0053] In some embodiments, COMSOL Multiphysics is used as the numerical simulation software. Within this software environment, the electroplating parameters are first set as globally defined parameters, including the applied current density, stirring frequency, and the concentration ratio of accelerator, inhibitor, and leveling agent. By constructing a three-dimensional finite element numerical simulation system, the overpotential distribution, electrolyte current density distribution, copper ion concentration distribution, and the concentration distribution of accelerator, inhibitor, and leveling agent on the cathode surface under different electroplating parameter conditions are analyzed.

[0054] In some embodiments, the physical field distribution characteristics of the cathode surface and corner cross-section under different electroplating parameters are analyzed by numerical simulation. The electroplating parameter range that enables the electroplating process to reach a better state is initially selected: the applied current density is 0.8~1.0 ASD, the stirring frequency is 5~15 Hz, and the additive concentration ratio (accelerator:inhibitor:leveling agent) is 3:1:0.2.

[0055] S5. Conduct verification experiments within the initially determined parameter range, prepare copper redistribution layer samples, quantitatively characterize the microstructure of the samples and measure their resistance values, compare and analyze the macroscopic physical field distribution obtained from numerical simulation, the microstructure morphology and resistance values ​​obtained from verification experiments, and determine the optimal combination of electroplating process parameters.

[0056] In the verification experiment, copper RDL samples were prepared under the set experimental conditions based on the electroplating parameter range initially determined in step S4. After preparation, the electroplated copper RDL samples underwent systematic quantitative characterization of their microstructure. First, the grain morphology of the coating was observed and analyzed using a metallographic microscope or scanning electron microscope (SEM), and its grain thickness and distribution uniformity were statistically analyzed. Second, the orientation distribution of the grains was analyzed using electron backscatter diffraction (EBSD) technology to determine whether a specific preferred orientation exists. Simultaneously, twin boundaries in the coating were identified using EBSD technology, the twin type was qualitatively analyzed, and the twin boundary length per unit area or unit volume, i.e., twin density, was calculated to achieve quantitative characterization.

[0057] Based on the microstructure characterization, the resistance value of the copper RDL sample is accurately measured using a two-probe or four-probe tester to evaluate its conductivity.

[0058] After completing the above tests, the macroscopic electroplating physical field data (including overpotential distribution, electrolyte current density distribution, copper ion concentration distribution and additive concentration distribution) obtained by numerical simulation in step S4 are compared and correlated with the microstructure morphology (including grain thickness, grain orientation and twin density) and resistance value obtained by verification test.

[0059] This correlation analysis reveals the intrinsic relationship and influence between the macroscopic electroplating physical field, microstructure, and final conductivity. For example, when the grain thickness distribution is more uniform, has a distinct (111) preferred orientation, and has a high twin density, the copper RDL has the lowest resistance value; twin density is the main microstructural factor affecting the resistance value, followed by grain orientation. Based on this comprehensive analysis, from the initially selected parameter range, the optimal electroplating process parameters that can simultaneously obtain excellent microstructure (uniform grain thickness, (111) preferred orientation, and high twin density) and the lowest resistance value are further determined.

[0060] In some embodiments, the optimal parameters were determined to be: an applied current density of 0.8 ASD, a stirring frequency of 10 Hz, and an accelerator, inhibitor, and leveling agent concentration ratio of 3:1:0.2.

[0061] Example This embodiment provides a method for optimizing process parameters in the electroplated copper rewiring process based on numerical simulation, including the following steps: 1) Develop key technologies for 3D modeling of copper RDL electroplating process, and use COMSOL Multiphysics numerical simulation software to establish a 3D geometric model based on the geometry and dimensions of the copper RDL (see appendix). Figure 1 a).

[0062] Furthermore, mesh generation is performed on the 3D model (see appendix). Figure 1 b), its near-basal end ( Figure 2 (III) and distal basal end ( Figure 2 The surface of (II) is made of free triangular mesh, dividing the copper plating area ( Figure 2 The area between sections III and II is divided into a triangular prism mesh, which is then layered using a sweep algorithm (10 elements per layer). This is to ensure the electrolyte ( Figure 2 To ensure consistency with the calculations for the copper plating area (between I and II), the electrolyte was also divided into a triangular prism grid, with the same number of layers as the copper plating area (10 layers). Because the grid in area II differs significantly from the area covered by the copper RDL, to avoid issues with the anode (… Figure 2 (I) and cathode ( Figure 2To address the mesh mismatch issue in surface II and ensure the continuity of interface flux calculation, a mesh mapping technique is used to map the special mesh topology of surface II onto surface I. This embodiment combines the advantages of free triangular meshes and triangular prism meshes to achieve efficient discretization of complex electroplating physical fields.

[0063] 2) A physical model of the copper RDL electroplating process was established. Based on the three modules of diffusion, electromigration, and convection in the electroplating process, physical property parameters such as diffusion coefficient, transfer coefficient, and adsorption-desorption coefficient of the electroplating solution components were defined (Table 1). Furthermore, using electroplating process parameters (applied current density, stirring frequency, and additive concentration ratio) as globally defined parameters, the influence of electroplating parameters on electroplating performance was obtained through numerical simulation. The numerical simulation scheme of the copper RDL electroplating process is shown in Table 2.

[0064] Table 1. Values ​​of adsorption and desorption coefficients of additives under different applied current densities.

[0065] Table 2 Three-dimensional finite element numerical simulation scheme for copper RDL electroplating process

[0066] 3) Based on the numerical simulation results of the copper RDL electroplating process, the cathode surface and corner sections were selected for analysis. Eleven monitoring points were selected on the cathode surface, considering the spatial differences in metal end structure, circuit layout, and geometric features: Point 1 (edge ​​area) and Point 2 (center area) were selected at the metal end to analyze the differences in electroplating performance between the center and edge regions; Points 3 (beginning end), 4 (middle section), and 5 (end end) were equidistantly set along the direction of a single copper line, and Points 4, 6, 7, and 11 were selected at the same positions on the four copper lines to reveal the influence of the spatial distribution differences of the copper lines on the electroplating physical field; Points 8 (outer side of the corner), 9 (middle of the corner), and 10 (inner side of the corner) were set in the 90° corner region to analyze the differences in the distribution of electroplating physical field performance caused by geometric constraints. (Refer to Appendix) Figure 3 a.

[0067] Furthermore, at a horizontal distance of 15 μm along the corner section of the copper RDL, distribution data of overpotential, electrolyte current density, copper ion concentration, and additive concentration were acquired at specific points on the electrolyte / copper plating interface at each time point. The electrolyte / copper plating boundary at the corner section was traced at each electroplating time point. Subsequently, points were taken at a horizontal distance of 15 μm along this interface, and the distance in the deposition direction at that point was obtained at each electroplating time point, ultimately yielding the deposition line. To obtain the differences in the distribution of the electroplating physical field in the lateral dimension, a horizontal line (ranging from 0 to 16 μm) was selected during the middle electroplating period (deposition direction distance of 3.5 μm). See the appendix for details. Figure 3 b.

[0068] Furthermore, based on the distribution data of the corner section, the evolution of overpotential, electrolyte current density, copper ion concentration, and additive concentration along the deposition direction and horizontal direction under different electroplating parameters was obtained. The analytical examples are shown below. Figures 4-8 As shown, when the applied current density is 0.5 ASD and the additive concentration ratio is 2:1:0.2 or 3:1.5:0.2, the micropores in the copper plating layer are not completely filled. Based on the micropore filling state and the distribution patterns of electrolyte overpotential, electrolyte current density, copper ion concentration, and additive concentration, the optimal additive concentration ratio is 3:1:0.2, and the preliminary preferred electroplating parameter range is: applied current density 0.8~1.0 ASD, stirring frequency 5~15 Hz.

[0069] Electroplating experiments and quantitative characterization of the microstructure of copper RDL were conducted under verification experimental conditions. The grain thickness, grain orientation, twin type, and twin density of the electroplated copper RDL samples were characterized and analyzed. Examples of the analytical results are shown below. Figures 9-12 As shown, a two-probe tester was used to measure the resistance value of the copper RDL sample, as follows. Figure 13 As shown.

[0070] Furthermore, the influence of electroplating parameters on the microstructure evolution and resistance of copper RDL was obtained. The changes in the macroscopic electroplating physical field, microstructure morphology, and resistance value after electroplating in step four were compared and analyzed. The grain thickness was more uniformly distributed when the current density was 0.8 ASD and the stirring frequency was 10 Hz. Twin density was the main factor affecting the resistance value, followed by grain orientation. The higher the twin density, the lower the resistance value of copper RDL. When the twin densities were not significantly different, the sensitivity of the resistance value to grain orientation exceeded the influence of twin density. The copper plating layer dominated by (111) showed the lowest resistance value, followed by (110). Based on the microstructure and resistance value analysis, the optimal copper RDL electroplating process parameters were further determined to be: current density of 0.8 ASD and stirring frequency of 10 Hz. Under these parameters, the microstructure characteristics of the copper RDL corner section were: uniform grain thickness distribution, obvious (111) preferred grain orientation, high twin density, and the lowest resistance value.

[0071] Although the embodiments of this application have been described above in conjunction with the accompanying drawings, this application is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, not restrictive. Those skilled in the art can make many other forms based on the guidance of this specification and without departing from the scope of protection of the claims of this application, and these are all within the scope of protection of this application.

Claims

1. A method for optimizing process parameters in electroplated copper rewiring based on numerical simulation, characterized in that, Includes the following steps: S1. Establish a three-dimensional geometric model of the copper redistribution layer electroplating process and perform mesh generation. The three-dimensional geometric model includes the cathode, anode, and electrolyte domain. S2. Establish a physical model for the copper redistribution layer electroplating process. The physical model describes the mass transfer process of substances in the electrolyte. The mass transfer process includes diffusion caused by concentration gradient, electromigration caused by potential gradient, and convection caused by fluid flow. The physical model establishes a mathematical relationship between electrolyte flow rate and stirring frequency, and applies this relationship to the setting of the convection velocity field. S3. Establish an applied current density model, which considers four states of the cathode surface: a surface covered by an accelerator, a surface covered by an inhibitor, a surface covered by a leveling agent, and a free surface not covered by additives, and describes the applied current density in each of the four states based on the Butler-Volmer equation. S4. Based on the established three-dimensional geometric model, physical model, and applied current density model, a three-dimensional finite element numerical simulation system for the copper redistribution layer electroplating process is constructed. Numerical simulation is performed by changing the values ​​of electroplating process parameters, including applied current density, stirring frequency, and additive concentration ratio. The effects of the electroplating process parameters on the overpotential, electrolyte current density, copper ion concentration, and additive concentration distribution on the cathode surface are analyzed, and the range of electroplating parameters is preliminarily determined. S5. Conduct verification experiments within the initially determined parameter range, prepare copper redistribution layer samples, quantitatively characterize the microstructure of the samples and measure their resistance values, compare and analyze the macroscopic physical field distribution obtained from numerical simulation, the microstructure morphology and resistance values ​​obtained from verification experiments, and determine the optimal combination of electroplating process parameters.

2. The method for optimizing process parameters in the electroplated copper rewiring process according to claim 1, characterized in that, The mesh generation in step S1 includes: The near-base end surface and the far-base end surface of the cathode are divided using a free triangular mesh; The copper plating area of ​​the cathode and the electrolyte region are divided into triangular prism grids and layered by a sweep algorithm. The number of layers in the copper plating area and the electrolyte region is the same. The mesh topology of the cathode distal substrate surface is mapped to the anode surface using mesh mapping technology.

3. The method for optimizing process parameters in the electroplated copper rewiring process according to claim 1, characterized in that, In step S2, the mathematical relationship between the stirring frequency and the electrolyte flow rate is as follows: in, This represents the flow rate at any point in the electrolyte. Table stirring frequency, Table of agitated grid length, Table of grid width for agitation The vertical distance from any point in the electrolytic cell to the bottom of the hole. The vertical distance from the anode to the bottom of the cathode.

4. The method for optimizing process parameters in the electroplated copper rewiring process according to claim 1, characterized in that, The total mass flux of the mass transfer process described in step S2 is: in, For total mass flux, The diffusion coefficient of ions or additives. This refers to the concentration of ions or additives. The valence number is the ion number. This represents the potential in the electrolyte solution. It is Faraday's constant. The velocity field governed by the incompressible Navier-Stokes equations. R The gas constant is T The temperature is in Kelvin.

5. The method for optimizing process parameters in the electroplated copper rewiring process according to claim 1, characterized in that, In the applied current density model, the rate of change of the additive coverage on the cathode surface is: in, Indicates the surface coverage of the additive. Indicates the adsorption coefficient of the additive. Indicates the desorption coefficient of the additive. Indicates the electrodeposition rate, Indicates the surface coverage of the accelerator. Indicates the surface coverage of the inhibitor. This indicates the surface coverage of the leveling agent.

6. The method for optimizing process parameters in the electroplated copper rewiring process according to claim 5, characterized in that, The adsorption reaction rate of the additive is obtained based on the rate of change of the coverage. R i and adsorption / desorption reaction rate Rad i : in, This represents the surface saturation concentration of the additive.

7. The method for optimizing process parameters in the electroplated copper rewiring process according to claim 1, characterized in that, In step S3, the applied current density on the surfaces covered by the accelerator, the inhibitor, and the leveling agent is: in, i i Apply current density to the surface covered by the additive; This refers to the concentration of copper ions. This represents the standard concentration of copper ions. Apply current density to the surface covered by the additive; α i For the transmission coefficient, F It is Faraday's constant. η Overpotential, measured in volts (V). R The gas constant is T 0 represents the initial temperature, in Kelvin (K). The applied current density of the free surface not covered by the additive is: in, The initial applied current density before the additive is applied; The initial applied current density before the additive is applied; is the cathode transfer coefficient.

8. The method for optimizing process parameters in the electroplated copper rewiring process according to claim 1, characterized in that, In step S4, the preliminary electroplating parameter range is: applied current density 0.8~1.0 ASD, stirring frequency 5~15 Hz, and the concentration ratio of accelerator, inhibitor and leveling agent 3:1:0.

2.

9. The method for optimizing process parameters in the electroplated copper rewiring process according to claim 1, characterized in that, In step S5, the quantitative characterization of the microstructure includes grain thickness, grain orientation, twin type, and twin density; the determination of the optimal electroplating process parameters comprehensively considers the uniformity of the microstructure, preferred orientation, high twin density, and low resistivity.

10. The method for optimizing process parameters in the electroplated copper rewiring process according to claim 9, characterized in that, The optimal electroplating process parameters are: current density 0.8 ASD, stirring frequency 10 Hz, and accelerator, inhibitor and leveling agent concentration ratio 3:1:0.2.

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