Electronic packaging structure in-situ homogenization method, system and medium

Abstract

The invention discloses an in-situ homogenization method and system for an electronic packaging structure and a medium, and belongs to the technical field of microelectronic integration. The method comprises the following steps: carrying out layering, pixelation and unitization preprocessing on a packaging structure, and dividing macroscopic units; an in-situ structure unit is constructed through in-layer boundary expansion and out-layer boundary expansion, and a boundary overrun problem is processed by combining a low-modulus false expansion region; applying multiple groups of displacement / thermal field boundary conditions, and extracting an equivalent stiffness matrix and an anisotropic thermal expansion coefficient of the macroscopic unit through finite element solution; and finally, replacing the macroscopic unit with an equivalent homogeneous material, and constructing a packaging macroscopic model to support high-efficiency-thermal simulation. According to the method, the cross-layer and cross-scale material interaction effect is truly simulated through in-situ boundary expansion, the limitation of periodic boundary condition assumption in traditional homogenization is broken through, the equivalent parameter calculation precision is remarkably improved, and an efficient solution is provided for reliability evaluation of complex electronic packaging.

Description

Technical Field

[0001] The present invention belongs to the field of microelectronic integration technology, and in particular relates to a mechanical-thermal simulation technology of an electronic packaging structure, and specifically relates to an in-situ homogenization method, system and medium for an electronic packaging structure. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.

[0003] The structure of advanced electronic packaging is more complex than traditional packaging. For example, a system-in-package (SiP) integrates multiple chips into a single package, forming an independent device with specific system-level or subsystem-level functionality. Advanced packages typically include components and structures such as multi-layer substrates, redistribution layers (RDLs), microbumping, and through-silicon vias (TSVs). They are constructed from complex materials such as silicon, copper conductors, solder, and resin. During the manufacturing and use of advanced packaging, the mechanical and thermal performance of the package has a critical impact on product manufacturability and reliability. Excessive warpage, for example, can reduce routing accuracy during the packaging process and even lead to wafer / panel cracking and rejection. Excessive thermal deformation can lead to poor soldering on the PCB, such as cold solder joints or short circuits. To reduce product development iterations, shorten time to market, and improve product reliability, the industry primarily uses the finite element method (FEM) to simulate, evaluate, and optimize the mechanical and thermal performance of the package. However, the typical cross-scale characteristics of advanced packaging structures pose significant challenges to mechanical and thermal simulation of packaging. For example, the typical line width / space (L / S) of multi-layer substrate wiring is 12μm, with 14 layers; the typical L / S of RDL is only 2μm, with a layer thickness of 5μm. Given the typical package size of 40-100mm, this spans four to five orders of magnitude. If traditional finite element simulation methods are used, the number of cells and nodes in the generated mesh would be enormous (tens or even hundreds of millions), making simulation inefficient or even infeasible.

[0004] To address these simulation challenges, the industry primarily employs homogenized material equivalence methods, avoiding the need for fine meshing of microstructures and significantly reducing the size of finite element simulation units and nodes. Semi-empirical methods within homogenization, such as the Voigt and Reuss approximations, are based on mixed rules. Since they only provide upper and lower limits for equivalent material parameters, they are used only for rough estimates. Computational homogenization, on the other hand, is an effective method for improving homogenization accuracy. By performing precise finite element modeling of the microscopic representative volume element (RVE), setting "periodic" boundary conditions, extracting simulation results, and calculating the homogenized equivalent material parameters of the RVE, as exemplified by the calculation of equivalent performance parameters for wiring areas of integrated circuit products in patent CN 115713059A, the authors propose a method for calculating the equivalent performance parameters of integrated circuit product wiring areas. However, actual packaging structures generally lack the "periodicity" of composite materials. Consequently, existing boundary condition settings for computational homogenization studies are severely inconsistent with actual practice, and the calculated homogenized material parameters also exhibit significant deviations from actual results. In addition, the paper (W.Qiao et al., "Efficient Prediction of Equivalent Thermo-Mechanical Properties for Embedded Unit Cells in Reliability Simulations of Complex Circuit Wiring Structures Using a Transformer-CNN Model," 2024 25th ICEPT, Tianjin, China, 2024, pp. 1-6, doi: 10.1109 / ICEPT63120.2024.10668535.) adopted an "embedded metapackage (EUC)" method to consider the influence of the wiring structure surrounding the calculated unit on the equivalent material parameters when calculating the equivalent material parameters of the wiring layer. However, the method described in the paper only considers the influence of the surrounding structure of the wiring layer of the calculated unit, and does not consider the influence of structures outside the layer (such as adjacent upper and lower layers). The extracted orthotropic equivalent material constitutive model cannot correctly reflect the anisotropic characteristics of the complex packaging structure. As a result, the mechanical-thermal simulation accuracy of the final packaging structure is obviously insufficient.

[0005] In summary, the existing methods for homogenizing the package structure calculation have obvious discrepancies with the actual situation in setting the boundary conditions of the package unit structure, which seriously affects the accuracy of the homogenization calculation results. Summary of the Invention

[0006] The purpose of the present invention is to propose an in-situ homogenization method, system and medium for electronic packaging structure to address the need for accurately obtaining the equivalent parameters of the homogenized material of the packaging structure in the mechanical-thermal simulation of electronic packaging, so as to solve the problem of low calculation accuracy caused by unreasonable and incomplete calculation unit boundaries in the calculation homogenization of electronic packaging structure; and at the same time, a computer software system is proposed to support the engineering implementation of this method.

[0007] The technical solutions of the present invention are as follows:

[0008] An in-situ homogenization method for an electronic packaging structure, comprising:

[0009] Step S1: preprocessing the electronic packaging structure model; the preprocessing includes layering processing, pixelation processing and unitization processing;

[0010] Step S2: in-situ structural unit modeling; the macro units obtained by the unitization process are subjected to intra-layer boundary expansion and extra-layer boundary expansion one by one to obtain in-situ structural units;

[0011] Step S3: Calculation of homogenized equivalent material parameters: applying boundary conditions to the in-situ structural unit, and extracting the homogenized equivalent material parameters corresponding to the macro units contained in the in-situ structural unit through finite element solution and post-processing of the solution results;

[0012] Step S4: Modeling the package macro model; replacing each macro unit in the package structure model with a rectangular equivalent homogeneous material of the same shape, and using each rectangular equivalent homogeneous material as a FEM finite element unit in the package macro model.

[0013] Furthermore, the layering process includes: performing virtual cutting and layering on the package structure in the thickness direction, and ensuring that the materials of the layers obtained by the cutting are uniform in the thickness direction;

[0014] Pixelation processing includes: pixelating each layer obtained by the layering process according to the pattern formed by different materials, where the size p of a single pixel is 1 / k times the minimum feature size c of the package;

[0015] Unitization processing includes: dividing each layer obtained by pixelation processing into cuboids of the same size, each cuboid contains exactly n×n pixels in the xy plane, and the z direction is the thickness of the layer. These divided cuboids are macro units.

[0016] Furthermore, the intra-layer boundary is expanded to include:

[0017] Taking the macro unit as the center, m pixels are expanded in all directions within the same layer of the unit to obtain a rectangular pixel frame; the pixel frame is the intra-layer expansion area of ​​the macro unit; when the intra-layer expansion area exceeds the range of the packaging structure, the intra-layer boundary expansion requirements are met by adding a low-modulus dummy expansion area at the required position.

[0018] Furthermore, the outer boundary of the layer is extended to include:

[0019] Taking the intra-layer area composed of the macro unit and the intra-layer expansion area as the benchmark, the layered structure is expanded upward and downward by q layers in the thickness direction; the expanded part is the extra-layer expansion area; the projection of the extra-layer expansion area in the thickness direction coincides with the projection of the intra-layer area; when the extra-layer expansion area exceeds the range of the packaging structure, it is satisfied by adding a low-modulus pseudo-expansion area at the required position.

[0020] Furthermore, the macro unit, the intra-layer expansion region, and the extra-layer expansion region together constitute an in-situ structural unit.

[0021] Furthermore, the elastic modulus of the material corresponding to the low modulus pseudo-expansion region is 10 times the lowest elastic modulus of all component materials in the macro unit. -4 ~10 -6 times.

[0022] Furthermore, the step S3 includes:

[0023] Step S31: Divide the in-situ structural unit into FEM grids based on the plane pixels and layers of each layer, and assign the packaging material parameters to the divided finite element units according to the corresponding plane pixels;

[0024] Step S32: applying boundary conditions to different surfaces of the in-situ structural unit, including: applying uniform uniaxial tensile displacement in the x, y, and z directions; applying uniform shear displacement in the xy, xz, and yz directions; and applying a uniform temperature field separately;

[0025] Step S33: performing FEM solutions on the models with the boundary conditions applied to obtain solution results;

[0026] Step S34: extracting the arithmetic mean stress and the arithmetic mean strain of the finite element unit corresponding to the macro unit from the solution results of applying uniaxial tensile displacement and the solution results of applying shear displacement respectively;

[0027] Step S35: Based on the arithmetic mean stress and arithmetic mean strain obtained in step S34, calculate the macro unit equivalent stiffness matrix C eff ;

[0028] Step S36: extracting the arithmetic mean strain of the finite element unit corresponding to the macro unit from the solution result with the uniform temperature field applied;

[0029] Step S37: Calculate the equivalent anisotropic thermal expansion coefficient CTE of the macro unit based on the average strain obtained in step S36 eff .

[0030] Furthermore, the step S4 includes:

[0031] The linear elastic constitutive model parameters of the FEM finite element are set to the equivalent stiffness matrix C calculated by the corresponding macro element eff , the linear thermal expansion coefficient is set to the equivalent anisotropic thermal expansion coefficient CTE calculated for the corresponding macro unit eff .

[0032] The present invention also proposes an in-situ homogenization system for an electronic packaging structure, comprising:

[0033] A pre-processing module, which completes the layering processing, pixelation processing, and unitization processing of the electronic packaging structure and outputs the pre-processed electronic packaging structure model data;

[0034] The in-situ structural unit modeling module completes the intra-layer boundary expansion and extra-layer boundary expansion of all macro units one by one, and outputs the in-situ structural unit model data;

[0035] The homogenized equivalent material parameter calculation module completes the application of boundary conditions on the in-situ structural unit model, extracts the homogenized equivalent material parameters corresponding to the macro units contained in the in-situ structural unit through finite element solution and post-processing of the solution results, and outputs the macro unit equivalent stiffness matrix C eff and the equivalent anisotropic thermal expansion coefficient CTE of the macro unit eff Two sets of parameters;

[0036] The encapsulation macro model module is built to replace each macro unit in the encapsulation structure model with a rectangular equivalent homogeneous material of the same shape, and the parameters of the equivalent homogeneous material are set to the equivalent stiffness matrix C calculated by the corresponding macro unit. eff and equivalent anisotropic thermal expansion coefficient CTE eff , and output the package macro FEM model.

[0037] The present invention further provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the computer program implements the steps of the above-mentioned method for in-situ homogenization of an electronic packaging structure.

[0038] Compared with the existing technology, the beneficial effects of the present invention are:

[0039] (1) By modeling the in-situ structural unit, the stress and strain patterns of the macro-units in the homogenization calculation are made consistent with the actual situation to the greatest extent possible, avoiding the problem that the periodic boundary conditions used in the conventional homogenization method are seriously inconsistent with the actual packaging situation and the calculated homogenized material parameters have obvious deviations from the actual situation;

[0040] (2) A method for calculating the in-situ boundary extension pixel points or extension distance of a macro unit in the x, y, and z directions is given, which better balances the conflict between homogenization calculation accuracy and calculation efficiency;

[0041] (3) A scheme using stiffness matrix and anisotropic thermal expansion coefficient as equivalent constitutive model parameters of macro units is proposed, which can accurately describe the general anisotropy of complex packaging structures and improve the simulation accuracy of the homogenized material equivalent method;

[0042] (4) The displacement boundary loading method adapted to in-situ homogenized finite element calculations, as well as the extraction and calculation method of the equivalent stiffness matrix and anisotropic thermal expansion coefficient of the macro unit, are adopted, which has the advantages of simple boundary setting and fast calculation speed;

[0043] (5) A complete in-situ homogenization method and implementation process for electronic packaging structures are provided, and a computer software system adapted thereto is designed, which provides clear guidance for the engineering implementation of the method of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 The layered processing of the electronic packaging structure according to the present invention is shown;

[0045] Figure 2 The pixelation and unitization process of the present invention is shown;

[0046] Figure 3 The in-situ structural unit modeling method of the present invention is shown;

[0047] Figure 4 The package macro model modeling of the present invention is shown;

[0048] Figure 5 The figure shows the structure of the in-situ homogenization system of the electronic packaging structure according to the present invention.

[0049] Description of the accompanying drawings: 1- packaging substrate; 2- bottom filling glue; 3- solder bump; 4- plastic packaging material; 5- chip; L1~L12- layers obtained by virtual cutting; 201- virtual cutting layer; 202- unitized layer; 203- pixelated layer (taking a macro unit as an example); 301- macro unit; 302- extended area within the layer; 303- macro unit + extended area within the layer; 304- in-situ structural unit. DETAILED DESCRIPTION

[0050] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.

[0051] The features and performance of the present invention are further described in detail below with reference to the embodiments.

[0052] Example 1

[0053] Assume that the xy coordinate axes of the Cartesian coordinate system O-xyz are parallel to the sides of the rectangular circuit substrate, and the thickness direction is z. Based on this coordinate system, the technical solution of this embodiment is described as follows.

[0054] An in-situ homogenization method for an electronic packaging structure, comprising:

[0055] Step S1: preprocessing the electronic packaging structure model; the preprocessing includes layering processing, pixelation processing and unitization processing.

[0056] In this embodiment, the layering process specifically includes: performing virtual cutting and layering on the package structure in the thickness direction, and ensuring that the materials of the layers obtained by the cutting are uniform in the thickness direction;

[0057] Pixelation processing includes: pixelating each layer obtained by the layering process according to the pattern formed by different materials, wherein the size p of a single pixel is 1 / k times the minimum feature size c of the package; wherein k is 2 to 10;

[0058] Unitization processing includes: dividing each layer obtained by pixelation processing into cuboids of the same size, each cuboid contains exactly n×n pixels in the xy plane, and the z direction is the thickness of the layer. These divided cuboids are macro units; wherein n is 10 to 200.

[0059] Step S2: in-situ structural unit modeling; the macro units obtained by the unitization process are subjected to intra-layer boundary expansion and extra-layer boundary expansion one by one to obtain in-situ structural units.

[0060] In this embodiment, specifically, the intra-layer boundary expansion includes:

[0061] Taking the macro unit as the center, m pixels are expanded in all directions within the same layer of the unit (m is 2 to 4 times k) to obtain a rectangular pixel frame; the pixel frame surrounding the unit is the intra-layer expansion area of ​​the macro unit; when the intra-layer expansion area exceeds the range of the packaging structure, a low-modulus dummy expansion area is added at the required position to meet the intra-layer boundary expansion requirements; the elastic modulus of the material corresponding to the low-modulus dummy expansion area is 10 of the lowest elastic modulus of all component materials in the macro unit. -4 ~10 -6 times.

[0062] In this embodiment, specifically, the layer outer boundary expansion includes:

[0063] Taking the intra-layer region composed of the macro unit and the intra-layer extension region as the reference, the layered structure is extended upward and downward by q layers in the thickness direction, and the value of q satisfies that the total thickness of the single-sided extension layer is at least 2 to 4 times the minimum characteristic dimension c; the extended part is the extra-layer extension region; the projection of the extra-layer extension region and the intra-layer region in the thickness direction coincides; when the extra-layer extension region exceeds the range of the packaging structure, a low-modulus dummy extension region is added at the required position to meet the requirement; the elastic modulus of the material corresponding to the low-modulus dummy extension region is 10 times the lowest elastic modulus of all component materials in the macro unit. -4 ~10 -6 times.

[0064] In this embodiment, specifically, the macro unit, the in-layer extension area, and the out-layer extension area together form an in-situ structural unit; the plane pixels of the in-situ structural unit are (n+2m)×(n+2m), and the number of layers is 2q+1.

[0065] Step S3: Calculation of homogenized equivalent material parameters; applying a set of boundary conditions such as displacement field or thermal field to the in-situ structural unit, and extracting the homogenized equivalent material parameters corresponding to the macro units contained in the in-situ structural unit through finite element solution and post-processing of the solution results.

[0066] In this embodiment, specifically, step S3 includes:

[0067] Step S31: Divide the in-situ structural unit into a FEM grid based on the plane pixels and layers of each layer, and the number of divided finite element units is (n+2m)(n+2m)(2q+1), and assign the packaging material parameters to the divided finite element units according to the corresponding plane pixels;

[0068] Step S32: applying boundary conditions to different surfaces of the in-situ structural unit, including: applying uniform unidirectional tensile displacements in the x, y, and z directions, numbered 1-3 respectively; applying uniform shear displacements in the xy, xz, and yz directions, numbered 4-6 respectively; and applying a uniform temperature field with a temperature rise of Δt, numbered 7. It should be noted that uniform tensile displacement or uniform shear displacement means that the displacements of all finite element nodes directly affected by the strain in the direction of displacement application are equal.

[0069] Step S33: performing FEM solutions on the seven groups of models with applied boundary conditions, and numbering the solution results 1 to 7 respectively;

[0070] Step S34: Extract the arithmetic mean stress [σ x , σ y , σ z , τ xy , τ xz , τ yz ] T and the arithmetic mean strain [ε x , ε y , ε z , γ xy , γ xz , γ yz ] T The six solution results give a total of six sets of arithmetic mean stress and arithmetic mean strain;

[0071] Step S35: Based on the arithmetic mean stress and arithmetic mean strain obtained in step S34, calculate the macro unit equivalent stiffness matrix C eff The calculation formula is (the superscript is the number of the above solution):

[0072]

[0073] Step S36: Extract the arithmetic mean strain [ε] of the finite element unit (n×n in total) corresponding to the macro unit from the solution result 7. x , ε y , ε z , γ xy , γ xz , γ yz ] T ;

[0074] Step S37: Calculate the equivalent anisotropic thermal expansion coefficient CTE of the macro unit based on the average strain obtained in step S36 eff (Coefficient of Thermal Expansion, CTE), calculated as follows:

[0075]

[0076] Step S4: Modeling the package macro model; replacing each macro unit in the package structure model with a rectangular equivalent homogeneous material of the same shape, and using each rectangular equivalent homogeneous material as a FEM finite element unit in the package macro model.

[0077] In this embodiment, specifically, step S4 includes:

[0078] The linear elastic constitutive model parameters of the FEM finite element are set to the equivalent stiffness matrix C calculated by the corresponding macro element eff , the linear thermal expansion coefficient is set to the equivalent anisotropic thermal expansion coefficient CTE calculated for the corresponding macro unit eff It should be noted that the packaging macro model constructed based on this step can further carry out mechanical-thermal simulation of the package to obtain the response of the package under external stress, strain, and thermal field conditions.

[0079] Example 2

[0080] See also Figure 5 This embodiment also provides an in-situ homogenization system for an electronic packaging structure, comprising:

[0081] A pre-processing module, which completes the layering processing, pixelation processing, and unitization processing of the electronic packaging structure and outputs the pre-processed electronic packaging structure model data;

[0082] The in-situ structural unit modeling module completes the intra-layer boundary expansion and extra-layer boundary expansion of all macro units one by one, and outputs the in-situ structural unit model data;

[0083] The homogenized equivalent material parameter calculation module completes the application of a set of boundary conditions such as displacement field or thermal field on the in-situ structural unit model, and extracts the homogenized equivalent material parameters corresponding to the macro units contained in the in-situ structural unit through finite element solution and post-processing of the solution results, and outputs the macro unit equivalent stiffness matrix C eff and the equivalent anisotropic thermal expansion coefficient CTE of the macro unit eff Two sets of parameters;

[0084] The encapsulation macro model module is built to replace each macro unit in the encapsulation structure model with a rectangular equivalent homogeneous material of the same shape, and the parameters of the equivalent homogeneous material are set to the equivalent stiffness matrix C calculated by the corresponding macro unit. eff and equivalent anisotropic thermal expansion coefficient CTE eff , and output the package macro FEM model; based on this model, further package force-heat efficient simulation can be carried out.

[0085] Example 3

[0086] This embodiment also proposes a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the steps of the in-situ homogenization method of an electronic packaging structure as described above; however, the computer-readable storage medium of the present invention is not limited to this. In this document, the readable storage medium can be any tangible medium that contains or stores a program, which can be used by or in combination with an instruction execution system, apparatus or device.

[0087] The readable medium can be a readable signal medium or a readable storage medium. The readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof.

[0088] The computer-readable storage medium may include a data signal propagated in baseband or as part of a carrier wave, wherein the readable program code is carried. The data signal propagated may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. The readable storage medium may also be any readable medium other than a readable storage medium, which may send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, device, or component. The program code contained on the readable storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination thereof.

[0089] The program code for performing the operations of the present invention may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, and the like, as well as conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user computing device, partially on the user device, as a stand-alone software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving a remote computing device, the remote computing device may be connected to the user computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0090] Example 4

[0091] To make the technical content of this invention more clear and understandable and practically feasible, the specific implementation of the in-situ homogenization method for the electronic packaging structure proposed in Example 1 is described in detail below with reference to the accompanying drawings.

[0092] In the following embodiments, it is assumed that the xy coordinate axes of the Cartesian coordinate system O-xyz are parallel to the sides of the rectangular circuit substrate, and the thickness direction is set to z.

[0093] (1) Preprocessing of electronic packaging structure model.

[0094] Before starting preprocessing, prepare the package design data file (such as Gerber, GDS and other file formats), including the layout of the package substrate 1, bottom filler 2, solder bumps 3, plastic packaging material 4 and chip 5, etc. Figure 1 shown.

[0095] Preprocessing includes three parts: layer processing, pixel processing, and unit processing.

[0096] First, the layering process is performed to virtually cut and layer the package structure in the thickness direction. Figure 1 The package shown includes a package substrate 1 with five wiring layers and four via layers. Virtual cutting creates nine layers (L1-L9). The underfill 2 and solder bumps 3 together form the tenth layer (L10). The chip and a portion of the molding compound 4 together form the eleventh layer (L11). The molding compound 4 above the chip forms the twelfth layer (L12). All layers are uniform in thickness.

[0097] Then, the pixelation process is performed to transform the pattern formed by each layer according to the different materials obtained by the layering process into pixels. Figure 2In the example, the virtual cutting layer 201 is a wiring layer of the substrate, which is composed of two materials, copper wiring and insulating medium between the wiring layers. The two materials are represented by dark and light patterns respectively. The minimum feature size of the package is the minimum wiring width c = 20μm, so the size of a single pixel is set to p = c × 1 / k = 20 × 1 / 5 = 4μm, where k is 5. Code 1 represents the material copper and code 2 represents the insulating medium. Each pixel obtained by pixelization of this layer is assigned a pixel material code 1 or 2 according to the corresponding material of the pixel location. Figure 2 In the pixelated layer 203, pixels assigned to code 1 are colored dark, while pixels assigned to code 2 are colored light.

[0098] Finally, the unitization process is performed to divide each layer obtained by the pixelization process into cuboids of the same size. These divided cuboids are called macro units. Figure 2 The unitized layer 202 contains 5×5 macro units, each macro unit contains 56×56 pixels, and the thickness of the layer in the z direction is 20 μm. The positions of the macro units in each layer are strictly aligned in the thickness direction.

[0099] (2) In situ structural unit modeling.

[0100] The in-situ structural unit modeling is an operation of performing intra-layer boundary expansion and extra-layer boundary expansion on the macro units obtained by the unitization process one by one to obtain in-situ structural units.

[0101] like Figure 3 As shown, the intra-layer boundary expansion is to expand m pixels (m is 2 to 4 times k) around the macro unit 301 in the same layer of the unit to obtain a rectangular pixel frame. The pixel frame surrounding the unit is the intra-layer expansion area of ​​the macro unit, as shown in FIG. Figure 3 The dark rectangular area shown in 302. In this embodiment, m=3×k=15, so the area extended by the inner boundary of the layer is a rectangular area 303 of 86×86 pixels. When the inner layer extension area exceeds the scope of the package structure, such as the macro unit at the edge of the package, the inner layer boundary extension requirement is met by adding a low modulus dummy extension area at the required position. The elastic modulus of the material set for the low modulus dummy extension area is 10 times the elastic modulus of the insulating medium (6.0GPa). -5 Times, or 60kPa, which is much lower than the actual elastic modulus of the packaging material. The pixel material code corresponding to the low modulus false expansion area is 3.

[0102] The outer boundary expansion of the layer is based on the inner layer area composed of the macro unit and the inner layer expansion area, and expands the layered structure upward and downward by q layers in the thickness direction. In this embodiment, in order to ensure that the total thickness of the single-sided expansion layer is at least 2 to 4 times the minimum feature size c, the thickness of the single-sided expansion layer should be no less than 40 to 80 μm. According to the actual structure of the package, this example expands 2 layers upward and 2 layers downward, such as Figure 3 As shown. The extended part is the outer layer extension area. The outer layer extension area coincides with the projection of the inner layer area in the thickness direction. When the outer layer extension area exceeds the range of the packaging structure, it is satisfied by adding a low modulus dummy extension area at the required position. The elastic modulus of the material set in the low modulus dummy extension area is 10 times the elastic modulus of the insulating medium (6.0GPa). -5 Times, or 60kPa, which is much lower than the actual elastic modulus of the packaging material. The pixel material code corresponding to the low modulus false expansion area is 3.

[0103] The macro unit, the inner layer extension region, and the outer layer extension region together form an in-situ structure unit 304. The in-situ structure unit has a planar pixel size of (n+2m)×(n+2m) and a number of layers of 2q+1. In this embodiment, the in-situ structure has a planar pixel size of 86×86 and a number of layers of 5.

[0104] (3) Calculation of homogenized equivalent material parameters.

[0105] The calculation of the homogenized equivalent material parameters is a process of applying a set of boundary conditions such as displacement field or thermal field on the in-situ structural unit, and extracting the homogenized equivalent material parameters corresponding to the macro units contained in the in-situ structural unit through finite element solution and post-processing of the solution results. The sub-steps of the calculation of the homogenized equivalent material parameters are as follows:

[0106] ① The in-situ structural unit is divided into FEM grids based on the plane pixels and layers of each layer. The number of finite element units divided is (n+2m)(n+2m)(2q+1). In addition, the elastic modulus of the material (copper conductor) of code 1 is set to 120 GPa, Poisson's ratio is 0.33, and thermal expansion coefficient is 17×10 -6 / ℃; the elastic modulus of the material (insulating medium) of code 2 is set to 6.0GPa, Poisson's ratio is 0.25, and thermal expansion coefficient is 35×10 -6 / °C; the elastic modulus of the material of code 3 (low modulus pseudo-expansion zone material) is set to 60 kPa, Poisson's ratio is 0.0, and thermal expansion coefficient is 0. The above material parameters are assigned to the corresponding FEM unit according to the material code of the pixel.

[0107] ② Apply boundary conditions to different surfaces of the in-situ structural unit, including: applying uniform uniaxial tensile displacement in the x, y, and z directions, and applying uniform shear displacement in the xy, xz, and yz directions; and applying a uniform temperature field with a temperature rise of Δt.

[0108] ③ The 7 groups of models with boundary conditions are solved by FEM separately, and the solution results are numbered 1 to 7 respectively;

[0109] ④ In the solution results 1 to 6, the arithmetic mean stress [σ x , σ y , σ z , τ xy , τ xz , τ yz ] T and the arithmetic mean strain [ε x , ε y , ε z , γ xy , γ xz , γ yz ] T The six solution results give a total of six sets of arithmetic mean stress and arithmetic mean strain;

[0110] ⑤ Calculate the equivalent stiffness matrix C of the macro unit eff , the calculation results of a typical macro unit are as follows:

[0111]

[0112] ⑥ Extract the arithmetic mean strain [ε] of the finite element unit (n×n in total) corresponding to the macro unit in solution 7 x , ε y , ε z , γ xy , γ xz , γ yz ] T ;

[0113] ⑦ Calculate the equivalent anisotropic thermal expansion coefficient CTE of the macro unit eff (Coefficient of Thermal Expansion, CTE), the calculation results of a typical macro unit are as follows:

[0114]

[0115] (4) Encapsulation macro model modeling.

[0116] The package macro model modeling is to replace each macro unit in the package structure model with a rectangular parallelepiped equivalent homogeneous material of the same shape, such as Figure 4 A macro unit 301 located at L12 in the package. Each of the cuboid equivalent homogeneous materials is used as a FEM finite element unit in the package macro model. The linear elastic constitutive model parameters of the FEM finite element unit are set to the equivalent stiffness matrix C calculated by the corresponding macro unit. eff , the linear thermal expansion coefficient is set to the equivalent anisotropic thermal expansion coefficient CTE calculated for the corresponding macro unit eff The package macro model constructed based on this step can be used to further carry out mechanical-thermal simulation of the package to obtain the response of the package under external stress, strain, and thermal field conditions.

[0117] Simulations and field measurements have verified that the in-situ homogenization method and software system for electronic packaging structures of this embodiment significantly improves the speed and accuracy of package homogenization calculations. The thermal deformation simulation error of a typical multi-layer substrate package is reduced by 50% compared to calculation methods using periodic boundary conditions and by 30% compared to calculation methods using embedded metapackages.

[0118] The above-described embodiments merely represent specific implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of protection of the present application. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the technical concept of the present application, and all such variations and improvements fall within the scope of protection of the present application.

[0119] This background section is provided to generally present the context of the invention, and the work of the presently named inventors, the work to the extent described in this background section, and aspects of the description in this section that did not constitute prior art at the time of filing are neither explicitly nor implicitly admitted to be prior art to the present invention.

Claims

1. A method for in-situ homogenization of an electronic packaging structure, characterized in that: include: Step S1: preprocessing the electronic packaging structure model; the preprocessing includes layering processing, pixelation processing and unitization processing; Step S2: in-situ structural unit modeling; The macro units obtained by unitization are subjected to intra-layer boundary expansion and extra-layer boundary expansion one by one to obtain in-situ structural units; Step S3: Calculation of homogenized equivalent material parameters: applying boundary conditions to the in-situ structural unit, and extracting the homogenized equivalent material parameters corresponding to the macro units contained in the in-situ structural unit through finite element solution and post-processing of the solution results; Step S4: Modeling the package macro model; replacing each macro unit in the package structure model with a rectangular equivalent homogeneous material of the same shape, and using each rectangular equivalent homogeneous material as a FEM finite element unit in the package macro model.

2. The in-situ homogenization method of an electronic packaging structure according to claim 1, characterized in that: Layering processing includes: performing virtual cutting and layering on the package structure in the thickness direction, and ensuring that the materials of the layers obtained by cutting are uniform in the thickness direction; Pixelation processing includes: pixelating each layer obtained by the layering process according to the pattern formed by different materials, where the size p of a single pixel is 1 / k times the minimum feature size c of the package; Unitization processing includes: dividing each layer obtained by pixelation processing into cuboids of the same size, each cuboid contains exactly n×n pixels in the xy plane, and the z direction is the thickness of the layer. These divided cuboids are macro units.

3. The in-situ homogenization method of an electronic packaging structure according to claim 1, characterized in that: Intra-layer boundary expansion, including: Taking the macro unit as the center, m pixels are expanded in all directions within the same layer of the unit to obtain a rectangular pixel frame; the pixel frame is the intra-layer expansion area of ​​the macro unit; when the intra-layer expansion area exceeds the range of the packaging structure, the intra-layer boundary expansion requirements are met by adding a low-modulus dummy expansion area at the required position.

4. The in-situ homogenization method of an electronic packaging structure according to claim 3, characterized in that: Layer outer boundary extension, including: Taking the intra-layer area composed of the macro unit and the intra-layer expansion area as the benchmark, the layered structure is expanded upward and downward by q layers in the thickness direction; the expanded part is the extra-layer expansion area; the projection of the extra-layer expansion area in the thickness direction coincides with the projection of the intra-layer area; when the extra-layer expansion area exceeds the range of the packaging structure, it is satisfied by adding a low-modulus pseudo-expansion area at the required position.

5. The in-situ homogenization method of an electronic packaging structure according to claim 4, characterized in that: An in-situ structural unit consisting of three parts: a macro unit, an intra-layer expansion area, and an extra-layer expansion area.

6. The in-situ homogenization method for an electronic packaging structure according to claim 4, characterized in that: The elastic modulus of the material corresponding to the low modulus pseudo-expansion region is 10 times the lowest elastic modulus of all component materials in the macro unit. -4 ~10 -6 times.

7. The in-situ homogenization method for an electronic packaging structure according to claim 1, characterized in that: The step S3 includes: Step S31: Divide the in-situ structural unit into FEM grids based on the plane pixels and layers of each layer, and assign the packaging material parameters to the divided finite element units according to the corresponding plane pixels; Step S32: applying boundary conditions to different surfaces of the in-situ structural unit, including: applying uniform uniaxial tensile displacement in the x, y, and z directions; applying uniform shear displacement in the xy, xz, and yz directions; and applying a uniform temperature field separately; Step S33: performing FEM solutions on the models with the boundary conditions applied to obtain solution results; Step S34: extracting the arithmetic mean stress and the arithmetic mean strain of the finite element unit corresponding to the macro unit from the solution results of applying uniaxial tensile displacement and the solution results of applying shear displacement respectively; Step S35: Based on the arithmetic mean stress and arithmetic mean strain obtained in step S34, calculate the macro unit equivalent stiffness matrix C eff ; Step S36: extracting the arithmetic mean strain of the finite element unit corresponding to the macro unit from the solution result with the uniform temperature field applied; Step S37: Calculate the equivalent anisotropic thermal expansion coefficient CTE of the macro unit based on the average strain obtained in step S36 eff .

8. The in-situ homogenization method for an electronic packaging structure according to claim 1, characterized in that: The step S4 comprises: The linear elastic constitutive model parameters of the FEM finite element are set to the equivalent stiffness matrix C calculated by the corresponding macro element eff , the linear thermal expansion coefficient is set to the equivalent anisotropic thermal expansion coefficient CTE calculated for the corresponding macro unit eff .

9. An in-situ homogenization system for electronic packaging structures, characterized in that: include: A pre-processing module, which completes the layering processing, pixelation processing, and unitization processing of the electronic packaging structure and outputs the pre-processed electronic packaging structure model data; The in-situ structural unit modeling module completes the intra-layer boundary expansion and extra-layer boundary expansion of all macro units one by one, and outputs the in-situ structural unit model data; The homogenized equivalent material parameter calculation module completes the application of boundary conditions on the in-situ structural unit model, extracts the homogenized equivalent material parameters corresponding to the macro units contained in the in-situ structural unit through finite element solution and post-processing of the solution results, and outputs the macro unit equivalent stiffness matrix C eff and the equivalent anisotropic thermal expansion coefficient CTE of the macro unit eff Two sets of parameters; The encapsulation macro model module is built to replace each macro unit in the encapsulation structure model with a rectangular equivalent homogeneous material of the same shape, and the parameters of the equivalent homogeneous material are set to the equivalent stiffness matrix C calculated by the corresponding macro unit. eff and equivalent anisotropic thermal expansion coefficient CTE eff , and output the package macro FEM model.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the in-situ homogenization method of an electronic packaging structure according to any one of claims 1 to 8 are implemented.

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