Phase field method for simulating microstructure evolution of copper grains in silicon through hole

Abstract

The invention provides a phase field method for simulating copper grain microstructure evolution in a silicon through hole, and belongs to the technical field of electronic packaging. The problem that through-silicon-via copper grain microstructure evolution cannot be continuously tracked in the prior art is solved. The method comprises the following steps: constructing a phase field model of a TSV copper column polycrystalline system, and uniquely identifying crystal grains through non-conservation sequence parameters; establishing a free energy density function containing a local potential well and a gradient energy item; the free energy density function is substituted into the Allen-Cahn type kinetic equation; solving the Allen-Cahn type kinetic equation and visualizing order parameter evolution to obtain the space-time distribution of the TSV copper column crystal grain morphology and size; and performing thermal aging treatment on the TSV sample, performing electron back scattering diffraction representation on the cross section of the TSV sample subjected to thermal aging treatment, extracting grain size and orientation distribution data, and comparing the grain size and orientation distribution data with a phase field simulation result to calibrate phase field model parameters. The method is mainly used in the field of chip packaging.

Description

Technical Field

[0001] This invention belongs to the field of electronic packaging technology, and in particular relates to a phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias. Background Technology

[0002] As electronic packaging technology enters the post-Moore's Law era, 3D packaging technology has become a key path to improve chip performance. Among them, through-silicon via (TSV) technology, as an advanced 3D interconnect solution, achieves high-density integration between chips through conductive channels that vertically penetrate the silicon substrate. This structure significantly improves the performance density and functional integration of packaged devices due to its shortest electrical path and excellent mechanical strength. However, during long-term service, TSV structures face severe reliability challenges: the difference in thermal expansion coefficients between the copper filler material and the silicon substrate leads to significant thermal stress under thermal cycling or thermal aging conditions. This stress concentration effect causes copper material to be extruded from the top of the TSV, resulting in structural failure and directly threatening the long-term stability of the packaged device.

[0003] Understanding the microstructure evolution mechanism is crucial for comprehending TSV failure. Microscopic features such as copper grain size distribution, grain boundary configuration, and crystal orientation directly influence the stress release path and concentration level. For example, large-angle grain boundaries may become crack initiation points, while fine-grained structures help disperse stress. Current research primarily relies on destructive testing methods: cross-sectional cutting of TSV samples prepared using specific processes, combined with characterization techniques such as scanning electron microscopy (SEM) or electron backscatter diffraction (EBSD) to obtain static microstructure information. This method has fundamental limitations: firstly, destructive cutting cannot track the continuous evolution of the same region during thermal aging; secondly, experiments are costly and time-consuming, making it difficult to systematically explore the dynamic laws under multi-parameter coupling conditions such as different temperatures and aging times.

[0004] While numerical simulation techniques can compensate for the shortcomings of experimental research, existing models have significant limitations. Molecular dynamics simulations are limited by spatiotemporal scales, making it difficult to cover the micrometer-scale regions and hour-scale aging processes required for actual manufacturing processes; continuum mechanics models, on the other hand, cannot capture the anisotropic characteristics at the grain scale. Phase-field methods, as mesoscale simulation tools, can theoretically track grain boundary migration by coupling thermo-mechanical fields with order parameters, but existing models lack adaptability to the actual geometry of TSVs, mostly employ simplified boundary conditions, fail to consider the constraint effects in actual packaging, and lack practical verification of model parameter calibration, leading to deviations between predicted results and actual evolution patterns. Summary of the Invention

[0005] In view of this, the present invention aims to propose a phase-field method to simulate the evolution of the microstructure of copper grains in through-silicon vias (TSVs), in order to solve the problem that existing technologies cannot continuously track the evolution of the microstructure of copper grains in TSVs.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias, the method comprising: Step S1: Construct a phase-field model of the TSV copper pillar polycrystalline system and uniquely identify the grains using non-conservative order parameters; Step S2: Establish the free energy density function that includes the local potential well and gradient energy terms; Step S3: Substitute the free energy density function into the Allen-Cahn type kinetic equation to describe the evolution of the order parameter; Step S4: Solve the Allen-Cahn type kinetic equations and visualize the evolution of order parameters to obtain the spatiotemporal distribution of TSV copper pillar grain morphology and size; Step S5: Perform thermal aging treatment on the TSV sample and characterize the cross section of the thermally aged TSV sample by electron backscatter diffraction to extract grain size and orientation distribution data, and compare them with the phase field simulation results to calibrate the phase field model parameters.

[0007] Furthermore, a preferred embodiment is proposed, wherein step S2 includes:

[0008] in, η q This represents the order parameter of the q-th grain. This refers to the local free energy density or potential well energy. This is the gradient energy density term.

[0009] Furthermore, a preferred embodiment is proposed, wherein the local free energy density or potential well energy is expressed as:

[0010] in, Q The total number of grains. α 1 is a coefficient that determines the location and depth of the free potential well. α 2 represents the intensity coefficient of the penalty term for suppressing polycrystalline overlap. α 3 represents the coupling term coefficient of the grain interaction strength. Let be the order parameter of the s-th grain.

[0011] Furthermore, a preferred embodiment is proposed, wherein the gradient energy density term is expressed as:

[0012] in, Q The total number of grains. Let be the gradient of the q-th grain order parameter in space. The value is the interfacial energy coefficient.

[0013] Furthermore, a preferred embodiment is proposed, wherein the Allen-Cahn type dynamic equation in step S3 is:

[0014] in, No. i The spatial position of each grain r and time t The order parameter, L The migration energy coefficient, It is a variational operator used to represent the variation with respect to a functional.

[0015] Furthermore, a preferred embodiment is proposed, wherein the migration energy coefficient is expressed as:

[0016] in, It is an Arrhenius prefactor. S Let R be the activation energy of the system, R be the gas constant, and T be the temperature.

[0017] Furthermore, a preferred method is proposed, wherein the parameter quantity ,when η i When =1, it means that the position belongs to the first position. i Inside each grain; when η i When =0, it indicates that the position does not belong to the grain, and the order parameter of the grain boundary region is used to describe the overlapping region.

[0018] Furthermore, a preferred approach is proposed, which further includes solving the Allen-Cahn type dynamic equations using a semi-implicit Fourier spectrum method.

[0019] Based on the same inventive concept, the present invention also proposes a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes a phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias according to any one of the above claims.

[0020] Based on the same inventive concept, the present invention also proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the steps of a phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias as described above.

[0021] Compared with the prior art, the beneficial effects of the present invention are: This invention addresses the problem of existing technologies' inability to continuously track the microstructural evolution of copper grains in through-silicon vias (TSVs) by integrating phase-field simulation and experimental verification. It constructs a phase-field model based on non-conservative order parameters, driving the evolution of Allen-Cahn-type kinetic equations through the total free energy function. This model fully considers the geometric boundary constraints of real TSV copper pillars and couples temperature field physical parameters to achieve mesoscale simulation of grain growth, coalescence, and coarsening behavior. It overcomes the shortcomings of existing models, such as simplified boundary conditions and lack of experimental verification, forming a self-consistent "simulation-verification" closed-loop mechanism.

[0022] This invention substantially improves the reliability of microelectronic packaging by accurately predicting and optimizing the microstructure evolution of TSVs, thus solving the problem of copper extrusion failure caused by differences in thermal expansion coefficients. First, the phase-field model built based on real geometric boundaries can dynamically visualize the grain evolution process, avoiding the limitations of single-shot destructive tests. This allows researchers to continuously track the spatiotemporal distribution of grains under thermal aging conditions, significantly improving their understanding of interconnect failure mechanisms and risk prediction capabilities. Second, by adjusting thermal aging parameters, the model can predict the evolution of grain morphology and size under different experimental conditions. This predictive capability replaces some high-cost, long-cycle experimental operations. For example, when optimizing electrodeposition or annealing processes, it can directly simulate the impact of different temperature conditions on grain structure, significantly saving R&D resources and costs.

[0023] This invention is applied to the field of chip packaging. Attached Figure Description

[0024] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of a phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias, as described in this invention. Figure 2 This is a schematic diagram showing the grain size and morphology at different aging times (200℃) according to the present invention. Figure 3 These are experimental images of EBSD at 200℃ for three different times as described in this invention; Figure 4 This is a comparison diagram of the grain size distribution of the phase field simulation and EBSD experiment described in this invention; Figure 5 This is a schematic diagram of the three-dimensional grain morphology and size at different aging times of 200℃ as described in this invention. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other, and the described embodiments are only some embodiments of the present invention, not all embodiments.

[0026] Implementation Method 1: A phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias, as described in this implementation method, includes: Step S1: Construct a phase-field model of the TSV copper pillar polycrystalline system, and uniquely identify the grains using non-conserved order parameters, including: A set of non-conservative order parameters are introduced to identify each grain in the polycrystalline system. Each order parameter uniquely corresponds to a grain, representing the existence state of the grain in space and time. Non-conservative order parameters refer to parameters whose values ​​do not satisfy conservation laws during evolution, meaning they can freely increase or decrease. They are suitable for simulating dynamic processes such as grain growth, contraction, and disappearance. Specifically, N order parameters η1(r,t), η2(r,t), ..., ηN(r,t) are set, where ηi(r,t)∈[0,1], representing the presence degree of the i-th grain at position r and time t. When ηi = 1, it indicates that the position belongs to the interior of the i-th grain; when ηi = 0, it indicates that the position does not belong to the grain. The grain boundary region is described by the partial overlap of multiple order parameters, thus constructing a complete polycrystalline structure. Initially, each order parameter is assigned a localized distribution to represent the position of the crystal nucleus. As the evolution equation progresses, the order parameters expand in space, thereby realizing the simulation of dynamic grain growth. Step S2: Establish the free energy density function that includes the local potential well and gradient energy terms; Step S3: Substitute the free energy density function into the Allen-Cahn type kinetic equation to describe the evolution of the order parameter; Step S4: Solve the Allen-Cahn type kinetic equations and visualize the evolution of order parameters to obtain the spatiotemporal distribution of TSV copper pillar grain morphology and size; Step S5: Perform thermal aging treatment on the TSV sample and characterize the cross section of the thermally aged TSV sample by electron backscatter diffraction to extract grain size and orientation distribution data, and compare them with the phase field simulation results to calibrate the phase field model parameters.

[0027] In this embodiment, the prepared TSV sample is subjected to aging treatment under specific thermal aging conditions to simulate the thermal stress experienced by the interconnect structure in actual service environment. After aging for different time periods, the sample cross-section is characterized by electron backscatter diffraction (EBSD) to obtain its microstructure information. EBSD experiments can not only extract the grain size distribution and orientation distribution, but also reveal statistical information such as grain boundary type, orientation difference distribution, and twinning characteristics, providing multi-dimensional data support for simulation comparison.

[0028] Implementation Method 2: This implementation method further defines the phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias described in Implementation Method 1. Step S2 includes:

[0029] in, η q This represents the order parameter of the q-th grain. This refers to the local free energy density or potential well energy. This is the gradient energy density term.

[0030] Implementation Method 3: This implementation method further defines the phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias described in Implementation Method 2. The local free energy density or potential well energy is expressed as:

[0031] in, Q The total number of grains. α 1 is a coefficient that determines the location and depth of the free potential well. α 2 represents the intensity coefficient of the penalty term for suppressing polycrystalline overlap. α 3 represents the coupling term coefficient of the grain interaction strength. Let be the order parameter of the s-th grain.

[0032] Implementation Method Four: This implementation method further defines the phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias described in Implementation Method Two. The gradient energy density term is expressed as:

[0033] in, Q The total number of grains. Let be the gradient of the q-th grain order parameter in space. The value is the interfacial energy coefficient.

[0034] Implementation Method 5: This implementation method further defines the phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias described in Implementation Method 2. The Allen-Cahn type kinetic equation in step S3 is:

[0035] in, No. i The spatial position of each grain r and time t The order parameter, L The migration energy coefficient, It is a variational operator used to represent the variation with respect to a functional.

[0036] Implementation Method Six: This implementation method further defines the phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias described in Implementation Method Five. The migration energy coefficient is expressed as:

[0037] in, It is an Arrhenius prefactor. S Let R be the activation energy of the system, R be the gas constant, and T be the temperature.

[0038] Implementation Method Seven: This implementation method further defines the phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias described in Implementation Method Five. The parameter quantities... η i (r,t)∈[0,1], when η i When =1, it means that the position belongs to the first position. i Inside each grain; when η i When =0, it indicates that the position does not belong to the grain, and the order parameter of the grain boundary region is used to describe the overlapping region.

[0039] Implementation Method 8: This implementation method further defines the phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias as described in Implementation Method 1. The method further includes: solving the Allen-Cahn type kinetic equation using a semi-implicit Fourier spectroscopy method.

[0040] In the numerical solution process, the semi-implicit Fourier spectroscopy method is used. According to the technical solution provided in Implementation Method 1, the phase field simulation model and dynamic equation of the copper grain multiphase system in the through-silicon via can be constructed to simulate the microstructure evolution process of copper grains in the through-silicon via under different predetermined process conditions, as well as their size, orientation and other information.

[0041] Implementation Method Nine: A computer device according to this implementation method includes a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes a phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias according to any one of the above-mentioned methods.

[0042] Implementation Method 10: A computer-readable storage medium according to this embodiment stores a computer program, which, when executed by a processor, performs the steps of a phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias as described in any of the above embodiments.

[0043] Implementation Method 11, see below Figures 1 to 5 This embodiment describes a specific example of the phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias as described in Embodiment 1. It also serves to explain Embodiments 2 through 8. Specifically: This embodiment provides a flowchart of a phase-field method for simulating the microstructure evolution of copper grains in through-silicon vias, such as... Figure 1 As shown, the method includes: Step S101: Construct a phase-field simulation model suitable for the TSV copper pillar polycrystalline system, and model and describe the total free energy of the system. The total free energy includes a local potential well term used to characterize the polycrystalline competition and stable phase, as well as a gradient energy term related to the grain boundary energy. Step S102: Based on the constructed total free energy function, substitute it into the Allen-Cahn type dynamic equation to describe the evolution of the order parameter; Step S103: Based on the kinetic evolution equation, the evolution process of the order parameter is solved and visualized to reflect the evolution process of TSV grain morphology and size. Step S104: The TSV sample is aged under thermal aging conditions, and the cross section is characterized by EBSD to obtain grain size and orientation distribution data, which are then compared with the phase field results and the parameters are calibrated.

[0044] The phase-field method is a numerical computational approach for simulating the evolution of the microstructure of materials at the mesoscale. Its core idea is to introduce a set of order parameters to characterize regions of different phases or orientations within the material and establish partial differential equations describing the spatiotemporal evolution of these order parameters, thereby characterizing complex microstructural evolution behaviors such as grain morphology, interface migration, and phase transitions. Compared to atomic-scale molecular dynamics simulations, the phase-field method can reflect the microstructural evolution characteristics of materials at larger spatial and temporal scales. Furthermore, unlike macroscopic continuum models, it retains grain-level detail, thus possessing unique advantages in materials science research. In through-hole silicon structures, due to their limited cross-sectional size, they typically contain only a few dozen grains. This means that the morphology, orientation, and size distribution of individual grains can significantly influence the electrical, mechanical, and thermal properties of the overall structure. Traditional macroscopic models struggle to accurately describe grain evolution at this scale, while the phase-field method can realistically reveal the growth, coalescence, and orientation evolution of grains within through-hole silicon while ensuring computational feasibility. This provides theoretical support for a deeper understanding of its performance evolution mechanisms and optimization of process parameters.

[0045] In this embodiment, a set of non-conservative order parameters is introduced to describe the evolution of different grains within the TSV. In this way, each grain can be identified by an independent order parameter: when the order parameter... η i When =1, it indicates that the position belongs to the interior of the i-th grain; when η i When the value is 0, it indicates that the location does not belong to the grain region. This definition allows for the clear differentiation of different grains during evolution, enabling precise characterization of their morphology and boundary changes.

[0046] In phase-field theory, the evolution of non-conservative order parameters is typically solved using Allen-Cahn type kinetic equations. These equations, based on the variational principle of the total free energy functional, characterize the dynamic changes of order parameters in time and space by describing the decrease in the system's free energy, thus reflecting the grain growth and interface migration mechanisms. In this specific modeling example, the system parameters, initial conditions, and boundary conditions are reasonably set to ensure the physical rationality and numerical stability of the model. Subsequently, by discretizing the equations and performing numerical solutions, the spatiotemporal distribution characteristics of the grains during the evolution process can be obtained. Visualizing the calculation results not only provides a direct view of the grain morphology evolution process, but also...

[0047] EBSD is an important experimental characterization method for obtaining microstructural information of material samples. This technique can clearly reflect the morphology and size characteristics of grains and has a strong correspondence with the information obtained from phase-field simulations, making it particularly suitable for comparing and validating simulation results. In this study, TSV samples were subjected to thermal aging treatment, and their cross-sections were characterized using EBSD to obtain data on grain size and orientation distribution. Subsequently, these experimental results were compared and analyzed with phase-field simulation results to calibrate model parameters and verify the reliability of simulation results.

[0048] By solving the phase-field model and equations constructed in this embodiment, information such as the grain morphology and size evolution of TSV under different thermal aging conditions can be obtained. This makes up for the fact that experimental methods can only destroy the sample to obtain cross-sectional information at a single moment. The process of grain evolution of TSV during thermal aging can be observed, and empirical explanations can be provided for the phenomena in the thermal aging process. Information such as the grain morphology and size of TSV samples under different experimental conditions can be predicted, thereby reducing experimental costs.

[0049] By solving the phase-field model and its kinetic equations constructed in this study, key information such as the grain morphology and size evolution of TSV under different thermal aging conditions can be obtained. This method overcomes the limitations of experimental methods—experiments usually require destructive treatment of samples, only obtaining cross-sectional information at a specific moment, and cannot continuously track the dynamic changes of grains. With the help of phase-field simulation, not only can the grain evolution of TSV during thermal aging be intuitively reproduced, but theoretical explanations can also be provided for the phenomena observed in the experiment. At the same time, this method can also predict the grain morphology and size distribution of TSV samples under different heat treatment conditions, thereby effectively reducing experimental workload and cost, and providing strong support for process optimization and performance control.

[0050] In this embodiment, the system free energy function describing the TSV grain evolution is described. The description is as follows:

[0051] in, η q (r,t) represents the order parameter of the q-th grain at position r and time t. This refers to the local free energy density or potential well energy. This is the gradient energy density term.

[0052] Specifically, the local free energy density or potential well term The local function term used to describe the inter-grain competition and stable structure is expressed as:

[0053] in, Q The total number of grains. α 1 is a coefficient that determines the location and depth of the free potential well; the permissible range for this parameter is 0.5-2. α 2 represents the intensity coefficient of the penalty term for suppressing polycrystalline overlap; the permissible range for this parameter is 1-5. α 3 represents the coupling term coefficient for grain interaction strength, with a permissible parameter range of 1-10.

[0054] The gradient energy density term assigns a positive energy contribution to grain boundaries, giving them an energy penalty effect that encourages grain aggregation and coarsening, thus reducing the total interface length. The expression is:

[0055] in, Q The total number of grains. Let be the gradient of the q-th grain order parameter in space. The interfacial energy coefficient is allowed to be within the range of 0.1-1.

[0056] As a polycrystalline material, TSV grains undergo complex behaviors such as growth, coalescence, migration, and disappearance under thermal aging or thermal cycling. To accurately describe these processes, this embodiment employs an Allen-Cahn type equation system as a kinetic evolution model for grain evolution. This method can naturally handle grain boundary evolution without explicitly tracking interface positions, and is suitable for simulating the microstructure changes of copper TSV structures during thermal aging. The equations are shown below:

[0057] in, No. i The spatial position of each grain r and time t The order parameter is defined in step one. Let S be the free energy density function, defined by S102, where... L The migration energy coefficient is calculated using the following formula: ,in It is the pre-Arrhenius factor, determined experimentally. S To activate the system, S The value ranges from 0.8 to 1.0 eV, R is the gas constant with a value of 8.314, and T is the temperature.

[0058] In this embodiment, there are a total of Q grains, resulting in Q Allen-Cahn type equations, which are solved using a semi-implicit Fourier method. The specific calculation process is well understood by those in the art, and therefore will not be described in detail.

[0059] The following comparison of a specific simulation example and experimental results illustrates that this implementation method can accurately simulate the grain growth law of TSV during thermal aging. First, a set of non-conservative order parameters is introduced into the simulation to distinguish different grains within the TSV. Then, the total free energy function of the system is constructed and substituted into the Allen-Cahn type kinetic equation for solution, thereby characterizing and reflecting the evolution behavior of the grains during thermal aging. Through numerical calculation and visualization, the morphological and size changes of the TSV grains over time can be obtained, such as... Figure 2 The diagram shows the evolution of grains on the cross section. Figure 5 This demonstrates the grain evolution characteristics at a three-dimensional scale, showing the growth and coalescence trends of grains during the aging process at a three-dimensional scale.

[0060] In the experimental section, the prepared TSV samples were placed in a vacuum tube furnace for thermal aging. After a certain aging time, the sample cross-section was characterized by EBSD to extract microstructural information such as grain morphology, size, and orientation distribution. EBSD experiments can not only clearly reflect the geometric characteristics of the grains but also reveal their orientation differences, providing reliable experimental data support for subsequent comparative analysis.

[0061] Finally, the simulation results were compared with the experimental results. Figure 2 and Figure 3 The morphological comparison revealed a high degree of consistency between the simulated grain morphology and size and the experimental observations, with similar grain growth trends. Furthermore, Figure 4 Comparing the grain size distributions obtained from experiments and simulations, the results show that the data distributions of the two are basically the same, and both exhibit similar statistical patterns.

[0062] Based on the simulation results, reasonable deposition, annealing, or electromigration conditions can be optimized to obtain the desired copper grain structure, realizing the theoretical guidance and prediction of the simulation for experiments. This can be applied to practical process development and experimental research. Simultaneously, the phase-field simulation model proposed in this embodiment can provide an effective tool for the development and improvement of the theory of copper grain structure control in through-silicon vias (TSVs), and provide a reasonable explanation for the physical phenomena observed during the experiment. In practical industrial applications, a complete theoretical model and simulation method can predict the microscopic evolution characteristics of copper grains in TSVs, providing a basis for improving process technology. This can improve conductivity and reliability while reducing R&D cycle and manufacturing costs, meeting the requirements of integrated circuit packaging for TSV interconnect performance and processing costs.

[0063] The method proposed in this embodiment constructs a phase-field model based on the geometry and boundary conditions of real TSV copper pillars. During the simulation, the geometry and boundary constraints of the actual TSV copper pillars are fully considered, thus establishing a phase-field model that more closely resembles the real structure. Compared with experimental methods, this method avoids the destructive limitations of traditional characterization methods, as experiments often only obtain a static cross-section and cannot continuously reflect the entire process of grain evolution over time. Using the phase-field model, not only can the evolutionary behaviors of grain boundaries such as migration, coalescence, and coarsening under thermal aging conditions be accurately characterized, but the understanding of interconnect failure mechanisms and the ability to predict potential failure risks are also significantly improved.

[0064] The method proposed in this embodiment predicts the evolution of TSV grains under different experimental conditions. By introducing different heat treatment conditions (such as temperature and aging time) into the model, phase-field simulation can accurately predict the morphology and size evolution of TSV grains under different experimental conditions. This method can replace some expensive and time-consuming experimental methods, which not only saves experimental resources and costs significantly, but also provides guidance for the optimization design of experimental schemes, improving research efficiency and relevance.

[0065] The phase-field simulation method proposed in this embodiment can directly output a series of key histological statistical indicators, including parameters such as average grain size, size distribution, and grain boundary density. These quantitative indicators are of great significance for TSV reliability assessment: on the one hand, they can provide data support for analyzing the stability of interconnect structures under thermal aging conditions; on the other hand, they can also provide a basis for optimizing process windows and reliability design, thereby achieving an effective correlation from the microstructure level to the macroscopic performance level.

[0066] Those skilled in the art will understand that embodiments of this disclosure can be provided as methods, systems, or computer program products. Therefore, this disclosure can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this disclosure can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0067] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0068] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this disclosure and not to limit its protection scope. Although this disclosure has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading this disclosure, they can still make various changes, modifications or equivalent substitutions to the specific implementation of the invention, but these changes, modifications or equivalent substitutions are all within the protection scope of the published pending claims.

Claims

1. A phase field method to simulate the evolution of copper grain microstructure in through silicon via, characterized in that, The method comprises: Step S1: constructing a phase field model of a TSV copper column polycrystalline system, and uniquely identifying a crystal grain through a non-conservative order parameter; Step S2: establishing a free energy density function comprising a local potential well and a gradient energy term; Step S3: substituting the free energy density function into an Allen-Cahn type kinetic equation to describe the evolution process of the order parameter; Step S4: solving the Allen-Cahn type kinetic equation and visualizing the evolution of the order parameter to obtain the spatiotemporal distribution of the TSV copper column crystal grain morphology and size; Step S5: performing thermal aging treatment on the TSV sample, and performing electron backscatter diffraction characterization on the cross section of the thermal aging treated TSV sample to extract grain size and orientation distribution data, and comparing the data with the phase field simulation results to calibrate the phase field model parameters.

2. The phase field method of simulating copper grain microstructure evolution in through silicon via according to claim 1, wherein, The step S2 comprises: wherein, η q φqdenotes a order parameter of the qth grain, is a local free energy density or potential well energy, is a gradient energy density term.

3. The phase field method of simulating copper grain microstructure evolution in through silicon via according to claim 2, characterized in that, The local free energy density or potential well energy can be expressed as: wherein, Q N is the total number of grains, α 1 is a coefficient that determines the position and depth of the free energy well, α 2 is a penalty term strength coefficient that suppresses the overlap of multiple grains, α 3 is a coupling term coefficient of the grain interaction strength, is the order parameter of the s-th grain.

4. The phase field method of simulating copper grain microstructure evolution in through silicon via according to claim 2, wherein, The gradient energy density term is expressed as: wherein Q is the total number of grains, is the gradient of the q-th grain order parameter in space, is the interfacial energy coefficient.

5. The phase field method of simulating copper grain microstructure evolution in through silicon via according to claim 2, wherein, The Allen-Cahn type kinetic equation in the step S3 is: in, No. i The spatial position of each grain r and time t The order parameter, L The migration energy coefficient, It is a variational operator.

6. The phase field method of simulating copper grain microstructure evolution in through silicon via according to claim 5, wherein, The migration energy coefficient is expressed as: wherein, is the Arrhenius pre-exponential factor, S is the system activation energy, R is the gas constant, and T is the temperature.

7. The phase field method of simulating copper grain microstructure evolution in through silicon via according to claim 1, wherein, The parameter quantity η i (r,t)∈[0,1], when η i When =1, it means that the position belongs to the first position. i Inside each grain; When η i = 0, it means that the position does not belong to the grain, and the grain boundary region sequence parameter part overlaps the region description.

8. The phase field method of simulating copper grain microstructure evolution in through silicon via according to claim 1, wherein, The method further comprises: solving the Allen-Cahn type kinetic equation by using a semi-implicit Fourier spectrum method.

9. A computer device, comprising: A memory and a processor are included, and the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the phase field method for simulating the microstructure evolution of copper crystal grains in a through silicon via according to any one of claims 1-8.

10. A computer readable storage medium characterized by, The computer readable storage medium stores a computer program, and the computer program is run by the processor to execute the steps of the phase field method for simulating the microstructure evolution of copper crystal grains in a through silicon via according to any one of claims 1-8.

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