A method and apparatus for modeling heterogeneous material interfaces in an encapsulation.

Abstract

This application provides a modeling method and apparatus for heterogeneous material interfaces in encapsulations, relating to the field of encapsulation interface fracture technology. The method includes: preparing an interface sample of heterogeneous materials within the encapsulation; conducting a shear test on the interface sample to obtain a fracture curve and calculate the interface fracture energy; analyzing the load-displacement relationship of the fracture curve to construct a suitable expandable cohesive model; establishing a finite element geometric model of the interface sample, inputting the damage coefficient and separation displacement relationship data of the expandable cohesive model; iteratively adjusting the model parameters using a finite element inversion method until the simulation curve fits the experimental fracture curve, obtaining the target expandable cohesive model parameters. This application can flexibly set expandable cohesive models for different media and metal interfaces, obtain accurate parameters through inversion, and thus effectively evaluate the fracture resistance of heterogeneous material interfaces in encapsulations.

Description

Technical Field

[0001] This application relates to the field of encapsulation interface fracture technology, and in particular to a modeling method and apparatus for heterogeneous material interfaces in an encapsulation. Background Technology

[0002] In the context of advanced packaging and high-density integration, the mechanical reliability of the interface between the dielectric and heterogeneous materials such as metals within the package has become a key factor restricting the package yield and service life. Accurate characterization of interface fracture behavior is crucial for package structure design.

[0003] Currently, traditional exponential and bilinear cohesive force models are mainly used for interfacial fracture simulation. However, these models all employ fixed damage evolution patterns and cannot adapt to the multi-stage complex fracture characteristics of heterogeneous material interfaces in encapsulated bodies, exhibiting the following significant drawbacks: (1) Insufficient simulation accuracy: It is difficult to reproduce the actual multi-stage damage and softening process of the interface, and the simulation results deviate significantly from the experimental curves; (2) Poor universality: There is a lack of standardized modeling and parameter calibration methods, and different interface systems need to repeat trial and error, resulting in low evaluation efficiency; (3) Reliability distortion: Key mechanical parameters cannot be accurately matched through experiments and inversion, making it difficult to support the optimization of packaging structure design.

[0004] Therefore, there is an urgent need to propose a modeling method that can flexibly adapt to the characteristics of multi-stage fractures. Summary of the Invention

[0005] In view of the above problems, this application is made to provide a method and apparatus for modeling heterogeneous material interfaces in an encapsulation that overcomes or at least partially solves the above problems. The technical solution is as follows: In a first aspect, a method for modeling interfaces of heterogeneous materials in an encapsulation is provided, the method comprising: Prepare at least one interface sample of the heterogeneous material within the encapsulation. Shear tests were conducted on the interface samples to obtain the fracture curves of the interface samples and to calculate the interface fracture energy. The relationship between load force and displacement in the fracture curve is analyzed to determine the number of linear stages in the expandable cohesive model and to construct the expandable cohesive model. A finite element geometric model of the interface sample is established, and the damage coefficient and separation displacement relationship data of the extensible cohesive model are input into the finite element geometric model. The parameters of the expandable cohesive model are adjusted by finite element inversion until the simulation curve and the fracture curve reach a fitting state, thus obtaining the target expandable cohesive model parameters of the interface sample.

[0006] In one possible implementation, prior to performing the shear test on the interface sample, the method further includes: Apply aging tests or temperature cycling tests to the interface samples.

[0007] In one possible implementation, the calculation of the interface fracture energy includes: The interface fracture energy is calculated according to the first objective formula, which satisfies the following: (1) In equation (1), Gc Indicates the interfacial fracture energy. P Indicates the magnitude of the load force. A Indicates the contact area between the dielectric material and the metallic material. dδ This represents the length of a small element along the separation displacement path.

[0008] In one possible implementation, determining the number of linear stages in the scalable cohesive model and constructing the scalable cohesive model includes: When the fracture curve shows that the relationship between load force and displacement includes three stages, the expandable cohesive model is set to a trilinear model. The trilinear model includes the linear elastic stage, the damage initiation stage, and the first damage propagation stage; The linear elastic stage adopts the first stage stiffness. K The first-stage interface strength σ0 is used to characterize the stress, while the second-stage stiffness is used during the damage initiation stage. K d The displacement ratio R of the second stage is used to characterize the first damage propagation stage, while the final displacement is used to characterize the second stage. δ f Characterize it.

[0009] In one possible implementation, the construction of the scalable cohesion model further includes: When the fracture curve shows that the relationship between load force and displacement includes four stages, the expandable cohesive force model is set to a four-linear model. The quadlinear model adds a second damage propagation stage to the trilinear model. The linear elastic stage adopts the first stage stiffness. K The first-stage interface strength σ0 is used to characterize the stress, while the second-stage stiffness is used during the damage initiation stage. K d1 The displacement ratio R of the second stage is used to characterize the first damage propagation stage, and the stiffness of the second stage is adopted. K d2 The second stage displacement ratio R' is used to characterize the second damage propagation stage, and the final displacement is used to characterize the second damage propagation stage. δ f Characterize it.

[0010] In one possible implementation, the relationship between the cohesive traction force and the separation displacement in the extended cohesive force model satisfies: (2) In equation (2), σ This represents the cohesive traction force at the current separation displacement. δ This represents the separation displacement of the interface. δ 0 represents the critical displacement at the end of the linear elastic stage and the beginning of the damage initiation stage. δ d This indicates the displacement at the end of the damage initiation stage and the beginning of the damage propagation stage. δ f This represents the final displacement when the interface completely fails and the cohesive traction force drops to 0.

[0011] In one possible implementation, the damage coefficient versus separation displacement relationship data of the scalable cohesion model satisfies: (3) In equation (3), D It represents the damage coefficient of the interface, characterizing the degree of degradation of the interface stiffness.

[0012] In one possible implementation, inputting the damage coefficient versus separation displacement relationship data from the scalable cohesion model into the finite element geometric model includes: In the finite element simulation tool, select the option based on displacement-based damage and softening behavior; Import the pre-calculated corresponding data table containing the values ​​of separation displacement and damage coefficient into the finite element simulation tool to define the damage evolution of the cohesive element.

[0013] In one possible implementation, adjusting the parameters of the expandable cohesive model using the finite element inversion method until the simulation curve and the fracture curve reach a fitting state, to obtain the target expandable cohesive model parameters for the interface sample, includes: Input the initial parameters of the expandable cohesive force model to perform simulation calculations and obtain the curve of the simulated load force changing with displacement; Compare the differences between the simulated load force versus displacement curve and the fracture curve; Adjust at least one parameter based on the difference, repeat the simulation calculation and comparison adjustment until the overlap between the simulated load force change curve and the fracture curve reaches a preset threshold. The scalable cohesive model parameter that reaches the preset threshold is taken as the target scalable cohesive model parameter.

[0014] Secondly, a modeling apparatus for heterogeneous material interfaces in an encapsulation is provided, the apparatus comprising: The sample preparation module is used to prepare interface samples of heterogeneous materials within the package, and the number of interface samples is at least one. The test calculation module is used to perform shear tests on interface samples, obtain the fracture curve of the interface samples, and calculate the interface fracture energy. The model building module is used to analyze the relationship between load force and displacement in the fracture curve, determine the number of linear stages in the expandable cohesive model, and build the expandable cohesive model. The simulation input module is used to establish the finite element geometric model of the interface sample and input the damage coefficient and separation displacement relationship data of the expandable cohesive model into the finite element geometric model. The parameter inversion module is used to adjust the parameters of the expandable cohesive model using the finite element inversion method until the simulation curve and the fracture curve reach a fitting state, thereby obtaining the target expandable cohesive model parameters of the interface sample.

[0015] Using the above technical solutions, the present application provides a modeling method and apparatus for heterogeneous material interfaces in a package. The method includes: preparing an interface sample of heterogeneous materials within the package; performing a shear test on the interface sample to obtain a fracture curve and calculate the interface fracture energy; analyzing the relationship between load force and displacement on the fracture curve to construct a suitable expandable cohesive model; establishing a finite element geometric model of the interface sample and inputting the damage coefficient and separation displacement relationship data of the expandable cohesive model; iteratively adjusting the model parameters through a finite element inversion method until the simulation curve fits the experimental fracture curve to obtain the target expandable cohesive model parameters. The present application can flexibly set the expandable cohesive model for different media and metal interfaces, obtain accurate parameters through inversion, and thus effectively evaluate the fracture resistance of heterogeneous material interfaces in a package. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the description of the embodiments of this application will be briefly introduced below.

[0017] Figure 1 A flowchart illustrating a modeling method for heterogeneous material interfaces in an encapsulation provided in an embodiment of this application is shown. Figure 2 A flowchart illustrating a modeling method for heterogeneous material interfaces in an encapsulation body, provided in a specific embodiment of this application, is shown. Figure 3 The diagram shows a shear test curve of a PI-Cu interface sample from a specific embodiment of the modeling method for heterogeneous material interfaces in a package provided in this application. Figure 4 The diagram shows an extended CZM model applicable to the PI-Cu interface, based on a specific embodiment of the modeling method for heterogeneous material interfaces in a package provided in this application. Figure 5a The trilinear CZM diagram of the modeling method for heterogeneous material interfaces in a package provided in a specific embodiment of this application is shown. Figure 5b A quadlinear CZM diagram of a modeling method for heterogeneous material interfaces in a package provided in a specific embodiment of this application is shown. Figure 6 The diagram shows a finite element three-dimensional geometric model of a PI-Cu interface sample, illustrating the modeling method for heterogeneous material interfaces in a package provided in a specific embodiment of this application. Figure 7 The diagram shows the fitting effect of the PI-Cu interface sample simulation curve of the modeling method for heterogeneous material interfaces in a package provided in a specific embodiment of this application. Figure 8 A structural diagram of a modeling apparatus for heterogeneous material interfaces in an encapsulation provided in an embodiment of this application is shown. Detailed Implementation

[0018] Exemplary embodiments of the present application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this application will be thorough and complete, and will fully convey the scope of the present application to those skilled in the art.

[0019] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such use can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the term "comprising" and its variations should be interpreted as open-ended terms meaning "including but not limited to."

[0020] Through analysis, the inventors discovered that fracture simulation and reliability assessment of the interface between the dielectric and metallic heteromaterial within advanced packaging faces multiple structural contradictions within the existing technological framework: The packaging interface exhibits realistic fracture characteristics of multi-stage damage softening under thermal and mechanical loads, while traditional exponential, bilinear, and trapezoidal cohesion models all employ fixed, single damage evolution forms, failing to match the actual interface failure process. This results in significant deviations between simulation curves and experimental test curves, distorting the fracture behavior characterization. Furthermore, key parameters such as interface fracture energy, stiffness, and strength lack standardized inversion calibration methods, requiring repeated modeling and trial-and-error for different interface systems, leading to low assessment efficiency. Therefore, there is an urgent need for a modeling method that can flexibly extend the linear stage, accurately invert parameters based on experimental data, and adapt to various interfaces, in order to achieve efficient, accurate, and universal assessment of the reliability of advanced packaging interfaces.

[0021] To address the aforementioned technical problems, embodiments of this application provide a method for modeling interfaces of heterogeneous materials in an encapsulation, such as... Figure 1 As shown, the modeling method for heterogeneous material interfaces in an encapsulation may include the following steps S101 to S105: Step S101: Prepare an interface sample of the heterogeneous material within the encapsulation, wherein the number of interface samples is at least one.

[0022] In one possible implementation, the interface between the aforementioned heterogeneous materials serves as the contact interface between the dielectric material and the metal material in an advanced packaging structure. The dielectric material includes, but is not limited to, polyimide (PI), ABF (Ajinomoto Build-up Film), or underfill. The metal material includes, but is not limited to, copper (Cu) or copper pads.

[0023] In one possible implementation, the aforementioned interface sample can be understood as a test specimen used to characterize the actual interface mechanical properties inside the package.

[0024] In another possible implementation, the interface sample is prepared using the packaging plant's standard process to ensure that the sample structure is consistent with the actual packaged product.

[0025] In another possible implementation, the number of interface samples is set to multiple to obtain multiple sets of experimental data to improve the accuracy of the final parameters.

[0026] Step S102: Perform a shear test on the interface sample, obtain the fracture curve of the interface sample, and calculate the interface fracture energy.

[0027] In one possible implementation, a shear test is performed on the interface sample. A universal testing machine is used to apply a shear load at a constant loading rate (e.g., 0.1 mm / min), and the load-displacement data is recorded in real time to generate a fracture curve. The horizontal axis of the curve represents displacement, and the vertical axis represents load.

[0028] Step S103: Analyze the relationship between load force and displacement in the fracture curve, determine the number of linear stages in the expandable cohesive model, and construct the expandable cohesive model.

[0029] In one possible implementation, the aforementioned extended cohesive zone model (CZM) can be understood as a mechanical model used to describe the evolution of interface damage.

[0030] In another possible implementation, the number of linear stages can be understood as the number of segments in the cohesive traction force-separation displacement curve in the scalable cohesive force model.

[0031] In another possible implementation, the extensible cohesion model can be extended to an N-linear model according to the actual characteristics of the interface, where N is a positive integer greater than or equal to three.

[0032] Step S104: Establish the finite element geometric model of the interface sample and input the damage coefficient and separation displacement relationship data of the expandable cohesive model into the finite element geometric model.

[0033] In one possible implementation, the aforementioned finite element geometric model can be understood as a three-dimensional simulation model established according to the actual dimensions of the interface sample.

[0034] In another possible implementation, cohesive elements are set at the interface of the finite element geometric model to support the expandable cohesive model.

[0035] Step S105: Adjust the parameters of the expandable cohesive model using the finite element inversion method until the simulation curve and the fracture curve reach a fitting state, and obtain the target expandable cohesive model parameters of the interface sample.

[0036] This embodiment prepares an interface sample of heterogeneous materials within a package; performs shear tests on the interface sample to obtain fracture curves and calculate the interface fracture energy; analyzes the relationship between load force and displacement in the fracture curve to construct a suitable expandable cohesive model; establishes a finite element geometric model of the interface sample, inputting the damage coefficient and separation displacement relationship data of the expandable cohesive model; iteratively adjusts the model parameters using the finite element inversion method until the simulation curve fits the experimental fracture curve, obtaining the target expandable cohesive model parameters. This achieves flexible setting of the expandable cohesive model for different media and metal interfaces, and obtains accurate parameters through inversion, thereby effectively evaluating the fracture resistance of heterogeneous material interfaces in a package.

[0037] This application embodiment provides a possible implementation method, which includes the following steps before performing a shear test on the interface sample in step S102 above: Apply aging tests or temperature cycling tests to the interface samples.

[0038] In one possible implementation, shear tests are performed sequentially on the interface samples after aging tests or temperature cycling tests to obtain fracture curves under different working conditions.

[0039] This embodiment simulates the actual service environment of the package, making the obtained fracture curve and interface fracture more closely resemble the real working conditions, thus improving the accuracy of subsequent modeling and parameter inversion.

[0040] This application embodiment provides a possible implementation method. The calculation of the interface fracture energy in step S102 above specifically includes the following steps: The interface fracture energy is calculated according to the first objective formula, which satisfies the following: (1) In equation (1), Gc Indicates the interfacial fracture energy. P Indicates the magnitude of the load force. A Indicates the contact area between the dielectric material and the metallic material. dδ This represents the length of a small element along the separation displacement path.

[0041] This embodiment achieves the quantitative calculation of interfacial fracture energy through the first objective formula. By substituting experimentally measured parameters such as load force, displacement, and contact area into the formula, the interfacial fracture energy characterizing the fracture resistance of the interfacial sample is obtained, providing basic data for the subsequent construction of an expandable cohesive model and parameter inversion.

[0042] This application embodiment provides a possible implementation method. The step S103 above, which determines the number of linear stages in the scalable cohesive model and constructs the scalable cohesive model, specifically includes the following steps: When the fracture curve shows that the relationship between load force and displacement includes three stages, the expandable cohesive model is set to a trilinear model. The trilinear model includes the linear elastic stage, the damage initiation stage, and the first damage propagation stage; The linear elastic stage adopts the first stage stiffness. K The first-stage interface strength σ0 is used to characterize the stress, while the second-stage stiffness is used during the damage initiation stage. K d The displacement ratio R of the second stage is used to characterize the first damage propagation stage, while the final displacement is used to characterize the second stage. δ fCharacterize it.

[0043] This embodiment segments the load force variation characteristics of the fracture curve with displacement to adapt the interface mechanical behavior that satisfies the law of gradual decrease in force increment to a trilinear expandable cohesive force model, which can match the actual fracture characteristics of the heterogeneous material interface of the encapsulation.

[0044] This application embodiment provides a possible implementation method. The construction of the scalable cohesion model in step S103 above may further include the following steps: When the fracture curve shows that the relationship between load force and displacement includes four stages, the expandable cohesive force model is set to a four-linear model. The quadlinear model adds a second damage propagation stage to the trilinear model. The linear elastic stage adopts the first stage stiffness. K The first-stage interface strength σ0 is used to characterize the stress, while the second-stage stiffness is used during the damage initiation stage. K d1 The displacement ratio R of the second stage is used to characterize the first damage propagation stage, and the stiffness of the second stage is adopted. K d2 The second stage displacement ratio R' is used to characterize the second damage propagation stage, and the final displacement is used to characterize the second damage propagation stage. δ f Characterize it.

[0045] This embodiment can extend the scalable cohesive model to a quadlinear model, thereby improving the adaptability and simulation accuracy of the scalable cohesive model to the fracture behavior of different heterogeneous material interfaces.

[0046] This application provides a possible implementation method in which the relationship between the cohesive traction force and the separation displacement of the above-mentioned trilinear model class's extendable cohesive force model satisfies: (2) In equation (2), σ This represents the cohesive traction force at the current separation displacement. δ This represents the separation displacement of the interface. δ 0 represents the critical displacement at the end of the linear elastic stage and the beginning of the damage initiation stage. δ d This indicates the displacement at the end of the damage initiation stage and the beginning of the damage propagation stage. δ f This represents the final displacement when the interface completely fails and the cohesive traction force drops to 0.

[0047] This embodiment clarifies the relationship between cohesive traction force and separation displacement in an expandable cohesive force model, enabling precise characterization of the mechanical behavior of the heterogeneous material interface of the package from linear elastic deformation, damage occurrence, damage propagation to complete failure.

[0048] This application provides a possible implementation method in which the damage coefficient and separation displacement relationship data of the above-mentioned trilinear model class of extended cohesion model satisfy: (3) In equation (3), D It represents the damage coefficient of the interface, characterizing the degree of degradation of the interface stiffness.

[0049] This embodiment establishes a correspondence between the damage coefficient and the separation displacement, which can quantify the degree of stiffness degradation of the heterogeneous material interface of the package during the stress process, and provide an accurate basis for damage evolution for finite element simulation.

[0050] This application embodiment provides a possible implementation method. In step S104 above, the damage coefficient and separation displacement relationship data of the expandable cohesion model are input into the finite element geometric model, specifically including the following steps: In the finite element simulation tool, select the option based on displacement-based damage and softening behavior; Import the pre-calculated corresponding data table containing the values ​​of separation displacement and damage coefficient into the finite element simulation tool to define the damage evolution of the cohesive element.

[0051] This embodiment, by selecting the displacement-based damage softening law in the finite element simulation tool and importing the pre-calculated data table corresponding to the separation displacement and damage coefficient, can accurately assign the damage evolution rules of the scalable cohesive force model to the cohesive force element, thereby realizing the standardized and refined simulation definition of the interface damage behavior of heterogeneous materials in the encapsulation.

[0052] This application embodiment provides a possible implementation method. In step S105 above, the parameters of the expandable cohesive model are adjusted by the finite element inversion method until the simulation curve and the fracture curve reach a fitting state, thereby obtaining the target expandable cohesive model parameters of the interface sample. Specifically, the following steps are included: Input the initial parameters of the expandable cohesive force model to perform simulation calculations and obtain the curve of the simulated load force changing with displacement; Compare the differences between the simulated load force versus displacement curve and the fracture curve; Adjust at least one parameter based on the difference, repeat the simulation calculation and comparison adjustment until the overlap between the simulated load force change curve and the fracture curve reaches a preset threshold. The scalable cohesive model parameter that reaches the preset threshold is taken as the target scalable cohesive model parameter.

[0053] In this embodiment, the abstract interface fracture behavior is transformed into a quantifiable simulation comparison process through the finite element inversion method. This allows for the acquisition of target expandable cohesion model parameters in an iterative approximation manner, which can accurately reproduce the multi-stage damage evolution law in the actual fracture process and provide high-precision input parameters for the reliability assessment of the package.

[0054] The above introduces Figure 1 The embodiments shown have various implementation methods for each step. The following will further explain the modeling method for heterogeneous material interfaces in the encapsulation body according to specific embodiments.

[0055] like Figure 2 As shown, the implementation process of this specific embodiment is as follows: preparing test samples of key interfaces of the package, obtaining fracture curves and fracture energy through interface mechanical testing, constructing an extensible CZM model based on experimental results, modeling and simulating using a finite element platform, and inverting and calibrating CZM parameters to fit the simulated test curve.

[0056] I. Preparation of interface samples of heterogeneous materials within the encapsulation PI (polyimide)-Cu (copper) interface samples were prepared according to the standard sample preparation methods and processes of the packaging plant. At least one interface sample was prepared. In this embodiment, eight parallel interface samples, namely Sample1, Sample2, Sample3 to Sample8, were prepared for subsequent testing and parameter calibration.

[0057] II. Obtaining fracture curves and interfacial fracture energy Take the above 8 groups of PI-Cu interface samples, and according to requirements, add environmental pretreatment such as aging test and temperature cycling test. Then, perform shear test on the PI-Cu interface samples to obtain the load-displacement curve, such as... Figure 3 As shown, the horizontal axis of the curve represents the separation displacement. δ The unit is μm (micrometer), and the vertical axis represents the load force. F The unit is N (Newtonian) The displacement range is 0 μm to 18 μm. The interfacial fracture energy of each sample group is calculated according to the first objective calculation formula.

[0058] III. Constructing an Extensible Cohesion Model Analyzing the force-displacement experimental curves obtained from the shear test, the curves in this embodiment can be roughly divided into three stages: the first stage (0~5μm) shows a large force increment; the second stage (5~14μm) shows a smaller force increment; and the third stage (after 14μm) shows a rapid decrease in force. This satisfies the characteristic that the force increment in the first stage is greater than that in the second stage, and the force increment in the second stage is greater than that in the third stage. Therefore, the extensible CZM model is set to trilinear, such as... Figure 4 As shown, this is an extended CZM model applicable to the PI-Cu interface in this specific embodiment.

[0059] The trilinear CZM model in this specific embodiment is as follows: Figure 5a As shown, the model is divided into three stages: the first stage is segment OA, in which the cohesive elements are in a linear elastic state; the second stage is segment AB, in which the cohesive elements are damaged and the stiffness decreases; the damage in segment BC continues to expand until the interface fails at point C. Furthermore, based on the fracture curve characteristics of different interfaces, the extended CZM can also be set to a four-linear configuration, such as... Figure 5b As shown, the quadlinear CZM adds a fourth stage CD segment to the trilinear CZM model. Based on the parameters of the trilinear CZM model and the damage coefficient-separation displacement relationship, the damage coefficient is calculated. D With separation displacement δ The corresponding table data is shown in Table 1.

[0060] Table 1- D-δ relation

[0061] IV. Modeling in Finite Element Simulation Tools A finite element three-dimensional geometric model was established for the above PI-Cu interface sample, such as... Figure 6 As shown, the model includes a silicon substrate and a polyimide layer structure, and the pusher direction and boundary conditions are labeled. Cohesive elements are added at the PI-Cu interface. For the first stage of linear elasticity, the first-stage stiffness is input into the finite element simulation tool. K 0 and the first stage interface strength σ 0 is sufficient; for the damage softening stage, in the finite element simulation tool, select "Damage softening law based on displacement" and input the damage coefficients in Table 1 above. D With separation displacement δ The corresponding data is sufficient.

[0062] V. Obtaining Interface Cohesion Parameters First, input any initial set of CZM parameters and perform simulation calculations to obtain the simulation curve. Based on the difference between the simulation curve and the experimental fracture curve, continuously adjust the CZM parameters until they are well-fitted. Figure 7 The figure shows the fitting results of the simulation and experimental curves for the PI-Cu interface sample. Finally, the average of the interface parameters of the 8 parallel samples is taken as the target CZM parameter of the PI-Cu interface under this working condition.

[0063] This specific embodiment achieves accurate simulation of the interface fracture behavior of heterogeneous materials in the package by constructing an extensible cohesive force model and calibrating finite element inversion parameters. It solves the problem that the traditional CZM model cannot adapt to this type of interface fracture, and provides accurate parameter support for the quantitative assessment of package reliability.

[0064] It should be noted that the sequence numbers of the steps in the above embodiments do not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application. In practical applications, all the above possible implementation methods can be arbitrarily combined in a combined manner to form possible embodiments of this application, which will not be described in detail here.

[0065] Based on the modeling methods for heterogeneous material interfaces in a package provided in the above embodiments, and based on the same inventive concept, this application also provides a modeling apparatus for heterogeneous material interfaces in a package.

[0066] Figure 8 This is a structural diagram of a modeling device for heterogeneous material interfaces in an encapsulation provided in an embodiment of this application. Figure 8 As shown, the modeling device for the interface of heterogeneous materials in the package may specifically include a sample preparation module 210, a test calculation module 220, a model construction module 230, a simulation input module 240, and a parameter inversion module 250.

[0067] The sample preparation module 210 is used to prepare interface samples of heterogeneous materials within the package, and the number of interface samples is at least one. The test calculation module 220 is used to perform shear tests on the interface sample, obtain the fracture curve of the interface sample, and calculate the interface fracture energy. Model building module 230 is used to analyze the relationship between load force and displacement in the fracture curve, determine the number of linear stages in the expandable cohesive model, and build the expandable cohesive model. The simulation input module 240 is used to establish the finite element geometric model of the interface sample and input the damage coefficient and separation displacement relationship data of the expandable cohesive model into the finite element geometric model. The parameter inversion module 250 is used to adjust the parameters of the expandable cohesive model through the finite element inversion method until the simulation curve and the fracture curve reach a fitting state, thereby obtaining the target expandable cohesive model parameters of the interface sample.

[0068] This application embodiment provides a possible implementation, wherein the test calculation module 220 is further configured to: Apply aging tests or temperature cycling tests to the interface samples.

[0069] This application embodiment provides a possible implementation, wherein the test calculation module 220 is further configured to: The interface fracture energy is calculated according to the first objective formula, which satisfies the following: (1) In equation (1), Gc Indicates the interfacial fracture energy. P Indicates the magnitude of the load force. A Indicates the contact area between the dielectric material and the metallic material. dδ This represents the length of a small element along the separation displacement path.

[0070] This application embodiment provides a possible implementation, wherein the model building module 230 is further configured to: When the fracture curve shows that the relationship between load force and displacement includes three stages, the expandable cohesive model is set to a trilinear model. The trilinear model includes the linear elastic stage, the damage initiation stage, and the first damage propagation stage; The linear elastic stage adopts the first stage stiffness. K The first-stage interface strength σ0 is used to characterize the stress, while the second-stage stiffness is used during the damage initiation stage. K d The displacement ratio R of the second stage is used to characterize the first damage propagation stage, while the final displacement is used to characterize the second stage. δ f Characterize it.

[0071] This application embodiment provides a possible implementation, wherein the model building module 230 is further configured to: When the fracture curve shows that the relationship between load force and displacement includes four stages, the expandable cohesive force model is set to a four-linear model. The quadlinear model adds a second damage propagation stage to the trilinear model. The linear elastic stage adopts the first stage stiffness. K The first-stage interface strength σ0 is used to characterize the stress, while the second-stage stiffness is used during the damage initiation stage. K d1 The displacement ratio R of the second stage is used to characterize the first damage propagation stage, and the stiffness of the second stage is adopted. K d2 The second stage displacement ratio R' is used to characterize the second damage propagation stage, and the final displacement is used to characterize the second damage propagation stage. δ f Characterize it.

[0072] This application embodiment provides a possible implementation, wherein the simulation input module 240 is further configured to: In the finite element simulation tool, select the option based on displacement-based damage and softening behavior; Import the pre-calculated corresponding data table containing the values ​​of separation displacement and damage coefficient into the finite element simulation tool to define the damage evolution of the cohesive element.

[0073] This application embodiment provides a possible implementation, wherein the parameter inversion module 250 is further configured to: Input the initial parameters of the expandable cohesive force model to perform simulation calculations and obtain the curve of the simulated load force changing with displacement; Compare the differences between the simulated load force versus displacement curve and the fracture curve; Adjust at least one parameter based on the difference, repeat the simulation calculation and comparison adjustment until the overlap between the simulated load force change curve and the fracture curve reaches a preset threshold. The scalable cohesive model parameter that reaches the preset threshold is taken as the target scalable cohesive model parameter.

[0074] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that within the spirit and principles of this application, modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the corresponding technical solutions to leave the protection scope of this application.

Claims

1. A method for modeling interfaces of heterogeneous materials in an encapsulation, characterized in that, The method includes: Prepare at least one interface sample of the heterogeneous material within the encapsulation. Shear tests were conducted on the interface samples to obtain the fracture curves of the interface samples and to calculate the interface fracture energy. The relationship between load force and displacement in the fracture curve is analyzed to determine the number of linear stages in the expandable cohesive model and to construct the expandable cohesive model. A finite element geometric model of the interface sample is established, and the damage coefficient and separation displacement relationship data of the extensible cohesive model are input into the finite element geometric model. The parameters of the expandable cohesive model are adjusted by finite element inversion until the simulation curve and the fracture curve reach a fitting state, thus obtaining the target expandable cohesive model parameters of the interface sample.

2. The method according to claim 1, characterized in that, Before performing the shear test on the interface sample, the method further includes: Apply aging tests or temperature cycling tests to the interface samples.

3. The method according to claim 1, characterized in that, The calculation of the interface fracture energy includes: The interface fracture energy is calculated according to the first objective formula, which satisfies the following: （1） In equation (1), Gc Indicates the interfacial fracture energy. P Indicates the magnitude of the load force. A This indicates the contact area between the dielectric material and the metallic material. dδ This represents the length of a small element along the separation displacement path.

4. The method according to claim 1, characterized in that, The process of determining the number of linear stages in the scalable cohesive model and constructing the scalable cohesive model includes: When the fracture curve shows that the relationship between load force and displacement includes three stages, the expandable cohesive model is set to a trilinear model. The trilinear model includes the linear elastic stage, the damage initiation stage, and the first damage propagation stage; The linear elastic stage adopts the first stage stiffness. K The first-stage interface strength σ0 is used to characterize the stress, while the second-stage stiffness is used during the damage initiation stage. K d The displacement ratio R of the second stage is used to characterize the first damage propagation stage, while the final displacement is used to characterize the second stage. δ f Characterize it.

5. The method according to claim 4, characterized in that, The construction of the scalable cohesion model also includes: When the fracture curve shows that the relationship between load force and displacement includes four stages, the expandable cohesive force model is set to a four-linear model. The quadlinear model adds a second damage propagation stage to the trilinear model. The linear elastic stage adopts the first stage stiffness. K The first-stage interface strength σ0 is used to characterize the stress, while the second-stage stiffness is used during the damage initiation stage. K d1 The displacement ratio R of the second stage is used to characterize the first damage propagation stage, and the stiffness of the second stage is adopted. K d2 The second stage displacement ratio R' is used to characterize the second damage propagation stage, and the final displacement is used to characterize the second damage propagation stage. δ f Characterize it.

6. The method according to claim 4, characterized in that, The relationship between cohesive traction force and separation displacement in the extended cohesive force model satisfies: （2） In equation (2), σ This represents the cohesive traction force at the current separation displacement. δ This indicates the separation displacement of the interface. δ 0 represents the critical displacement at the end of the linear elastic stage and the beginning of the damage initiation stage. δ d This indicates the displacement at the end of the damage initiation stage and the beginning of the damage propagation stage. δ f This represents the final displacement when the interface completely fails and the cohesive traction force drops to 0.

7. The method according to claim 6, characterized in that, The damage coefficient versus separation displacement relationship data of the scalable cohesion model satisfy: （3） In equation (3), D It represents the damage coefficient of the interface, characterizing the degree of degradation of the interface stiffness.

8. The method according to claim 1, characterized in that, The step of inputting the damage coefficient and separation displacement relationship data of the expandable cohesion model into the finite element geometric model includes: In the finite element simulation tool, select the option based on displacement-based damage and softening behavior; Import the pre-calculated corresponding data table containing the values ​​of separation displacement and damage coefficient into the finite element simulation tool to define the damage evolution of the cohesive element.

9. The method according to claim 1, characterized in that, The process of adjusting the parameters of the expandable cohesive model using the finite element inversion method until the simulation curve and the fracture curve reach a fitting state, thereby obtaining the target expandable cohesive model parameters for the interface sample, includes: Input the initial parameters of the expandable cohesive force model to perform simulation calculations and obtain the curve of the simulated load force changing with displacement; Compare the differences between the simulated load force versus displacement curve and the fracture curve; Adjust at least one parameter based on the difference, repeat the simulation calculation and comparison adjustment until the overlap between the simulated load force change curve and the fracture curve reaches a preset threshold. The scalable cohesive model parameter that reaches the preset threshold is taken as the target scalable cohesive model parameter.

10. A modeling apparatus for heterogeneous material interfaces in an encapsulation, characterized in that, The device includes: The sample preparation module is used to prepare interface samples of heterogeneous materials within the package, and the number of interface samples is at least one. The test calculation module is used to perform shear tests on interface samples, obtain the fracture curve of the interface samples, and calculate the interface fracture energy. The model building module is used to analyze the relationship between load force and displacement in the fracture curve, determine the number of linear stages in the expandable cohesive model, and build the expandable cohesive model. The simulation input module is used to establish the finite element geometric model of the interface sample and input the damage coefficient and separation displacement relationship data of the expandable cohesive model into the finite element geometric model. The parameter inversion module is used to adjust the parameters of the expandable cohesive model using the finite element inversion method until the simulation curve and the fracture curve reach a fitting state, thereby obtaining the target expandable cohesive model parameters of the interface sample.

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