CN114282414A - Method and system for optimal design of warp/weft laying direction of glass fiber cloth for PCB - Google Patents

Abstract

The invention discloses a method and a system for optimally designing the warp/weft laying direction of glass fiber cloth for a PCB (printed Circuit Board), wherein the method comprises the following steps: establishing a geometric model of the multilayer PCB and a mathematical model of pressing and molding the PCB to the welding chip; determining material performance parameters and initial boundary value conditions required by finite element simulation through experimental tests and actual processes; determining the corresponding relation between the warp/weft yarn laying direction and the material direction; respectively obtaining a warping deformation simulation result and an experimental result when the PCB is pressed and molded to a welding chip; and continuously optimizing the physical and chemical performance parameters of the material corresponding to the arrangement direction of the warp/weft yarns of the electronic glass fiber cloth to obtain an optimization scheme for minimizing the warping deformation of the PCB or controlling the arrangement direction of the warp/weft yarns of the corresponding electronic glass fiber cloth according to requirements. The invention can conveniently carry out the numerical simulation of the warping deformation when the warp/weft laying direction of the electronic glass fiber cloth for the PCB influences the press-forming of the PCB to the welding chip.

Description

Method and system for optimal design of warp/weft laying direction of glass fiber cloth for PCB

technical field

The invention relates to the technical field of printed circuit boards, in particular to a method and a system for optimizing the arrangement direction of the warp/weft yarns of glass fiber cloth for PCB.

Background technique

The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

The problem of warpage and deformation of printed circuit boards (Printed Circuit Board, PCB for short, the same below) during manufacturing and service is becoming more and more serious. The dimensional stability of the PCB affects the reliability of the soldering of electronic components on the surface of the PCB. Especially when soldering chips, it is necessary to more strictly control the warpage and deformation of the corresponding soldering area on the surface of the PCB. At this time, the flatness of the PCB in this area is very high. It largely depends on its manufacturing process, therefore, it places high demands on the manufacturing process of the PCB.

According to the degree of rigidity and flexibility, PCB includes rigid board and flexible board. Rigid board cannot be bent and flexed like flexible board when used, and electronic glass fiber cloth is required as a reinforcing material, and its thickness is about 0.5 ~ 7mm , including but not limited to smart phone circuit boards, personal computer circuit boards, home appliance circuit boards, server circuit boards and other circuit boards of different sizes. Referring to Figure 1, the manufacturing process is that the multi-layer copper clad laminate 4 and the prepreg 2 are subjected to a certain temperature and pressure to obtain a semi-finished board, and then the finished board is obtained through drilling, copper plating, etching, solder mask ink treatment and other processes. The function is: Carrier boards for surface soldering electronic components.

Prepreg 2, also known as "PP sheet" or resin sheet, is mainly composed of resin and reinforcing materials. At present, most of the prepregs used in the production of multi-layer printed circuit boards use electronic glass fiber cloth as reinforcing materials; The main function is to bond different layers and act as insulation. The mechanism is that the epoxy resin softens and flows at high temperature, filling the voids between the copper wires, and at the same time curing and cross-linking reaction occurs to form an insoluble and infusible rigid resin. Thus, the double-sided etched copper clad laminates are firmly bonded to form a multi-layer PCB.

The glass fiber cloth for PCB refers to the electronic glass fiber cloth 6, which is formed by orthogonal weaving of electronic-grade glass fiber. The glass fiber is also called E-glass fiber, alkali-free glass fiber or electronic yarn (hereinafter collectively referred to as electronic yarn). Divided into warp yarn and weft yarn, it has good electrical insulation and mechanical properties.

Copper clad laminate 4 refers to a plate-like material made of electronic glass fiber cloth as a reinforcing material, impregnated with resin 5, covered with copper foil on one or both sides, and hot pressed. The full name is copper clad laminate, that is CCL (Copper Clad Laminate), wherein the glass fiber cloth reinforced resin matrix composite material between the double-sided copper foils is called the CCL core board 3 . Before the PCB is pressed and formed, the copper foil is etched according to the designed circuit; after the PCB is pressed and formed, the geometric layer containing copper foil and resin is defined as copper foil/resin hybrid layer 1.

Combined with Figure 2, the factors that affect the direction of the warp and weft of the electronic glass fiber cloth are mainly the material performance parameters of the electronic yarn. According to the national standard "GB/T 18373-2013 E glass fiber cloth for printed boards", the specifications of warp 7 and weft 8 of electronic glass fiber cloth 6 are generally different. Taking commercial code 1080 electronic glass fiber cloth as an example, its specifications The code is EWPC53, E stands for general-purpose glass with good electrical insulation properties, WPC stands for glass fiber cloth for printed boards, 53 represents the thickness of this glass fiber cloth is 53μm, of which the warp yarn density is 59 / 25mm, the weft yarn density It is 46/25mm, the warp and weft are continuous fibers, and the nominal diameter of a single thread is 5μm. The difference in the density of warp and weft causes the elastic modulus and shear mode of electronic glass fiber cloth in the direction of warp and weft. The difference in quantity leads to directional differences in thermal and mechanical properties. It can be seen that the direction of the warp and weft yarns has a direct impact on the performance parameters of the in-plane anisotropic material, and the mismatch of thermal expansion coefficients of glass fiber, resin and copper and the chemical shrinkage of the resin caused by the in-plane anisotropic material performance parameters Factors such as the mismatch between the strain and the mechanical strain of glass fiber and copper, and the asymmetric distribution of the interlayer resin and copper are the root causes of warpage when the PCB is pressed and molded to the soldered chip.

The current measures to reduce the amount of warpage deformation of the PCB from compression molding to welding chips include: placing a release buffer material between the prepregs of the multi-layer circuit board with an asymmetric structure; Copper operation or placement of several copper blocks staggered at intervals; design a CCL inner core board with an asymmetrical structure, and offset the bowing produced by asymmetric circuits during pressing through the reverse bowing during pressing; The residual copper distribution of the structural board is set to roughly mirror the distribution between layers; and so on. The above measures are mainly considered from the material factors. Although these measures all involve the optimization of the in-plane and inter-layer distribution of resin and copper, few of them involve the optimization of the warp/weft laying direction of the electronic-grade fiberglass cloth for the prepreg and CCL core board. Research.

At present, there are few finite element simulation studies on reducing PCB warpage deformation by optimizing the warp/weft laying direction of electronic glass fiber cloth, and there is no specific description of the internal stress history and anisotropic viscoelasticity model of PCB from press molding to welding chips. It does not systematically give the evolution history of the thermal and mechanical properties of the PCB from compression molding to welding chips, and also partially ignores the in-plane non-uniformity and inter-layer asymmetry of the PCB. At the same time, the geometric modeling is too The simplification leads to a large deviation between the numerical simulation results and the experimental results, and the goal of reducing the warpage deformation of the PCB and optimizing the direction of the warp/weft yarn layout of the electronic glass fiber cloth cannot be truly achieved.

SUMMARY OF THE INVENTION

In order to solve the above problems, the present invention proposes a method and system for optimizing the warp/weft laying direction of glass fiber cloth for PCB. With the help of finite element simulation and experimental verification, the warpage deformation of the PCB is minimized or controlled on demand when it is pressed and molded to the welding chip, so as to obtain the best electronic glass fiber cloth. direction, improve the flatness and soldering reliability of PCB when soldering chips.

In some embodiments, the following technical solutions are adopted:

A method for optimizing design of warp/weft laying direction of glass fiber cloth for PCB, comprising:

Build the geometric model of the multi-layer PCB and the mathematical model of the PCB compression molding to the soldered chip;

Determine the material performance parameters and initial boundary value conditions required by the finite element simulation through experimental tests and actual processes; determine the corresponding relationship between the direction of warp/weft yarns and the direction of the material;

Through finite element simulation and experimental verification, respectively, the simulation results and experimental results of the warpage deformation amount when the PCB is pressed and formed to the welding chip are obtained;

Based on the simulation results and experimental results, the material physical and chemical performance parameters corresponding to the warp/weft laying direction of the electronic glass fiber cloth are continuously optimized, and the corresponding electronic glass fiber cloth warp/weft can be obtained to minimize the warp deformation of the PCB or control the corresponding electronic glass fiber cloth as needed. Optimization scheme for the direction of weft yarn placement.

In other embodiments, the following technical solutions are adopted:

An optimized design system for the direction of the warp/weft laying out of glass fiber cloth for PCB, comprising:

Mathematical modeling module, used to establish the geometric model of multilayer PCB and the mathematical model of PCB compression molding to soldered chips;

The parameter setting module is used to determine the material performance parameters and initial boundary value conditions required by the finite element simulation through experimental tests and actual processes; to determine the corresponding relationship between the warp/weft yarn laying direction and the material direction;

The numerical simulation module is used to obtain the simulation results and experimental results of the warpage deformation amount when the PCB is pressed and formed to the welding chip through finite element simulation and experimental verification respectively;

The optimization design module is used to continuously optimize the material physical and chemical performance parameters corresponding to the warp/weft laying direction of the electronic glass fiber cloth based on the simulation results and experimental results, so as to obtain the corresponding parameters that minimize the warpage deformation of the PCB or control it on demand. Optimization scheme of warp/weft laying direction of electronic glass fiber cloth.

In other embodiments, the following technical solutions are adopted:

A terminal device, comprising a processor and a memory, the processor is used to implement each instruction; the memory is used to store a plurality of instructions, and the instructions are suitable for being loaded by the processor and executing the above-mentioned warp/weft laying direction of the glass fiber cloth for PCB Optimization design method.

In other embodiments, the following technical solutions are adopted:

A computer-readable storage medium, wherein a plurality of instructions are stored, and the instructions are suitable for being loaded by a processor of a terminal device and executing the above-mentioned optimal design method for the warp/weft arrangement direction of glass fiber cloth for PCB.

Compared with the prior art, the beneficial effects of the present invention are:

(1) The present invention converts the physical process of the warp/weft laying direction of the electronic glass fiber cloth into a simple setting of the parameters of the mathematical model, so as to conveniently carry out the electronic glass fiber cloth warp/weft laying direction for the PCB to affect the PCB compression molding to welding Numerical simulation of the warpage deformation of the chip, and experimental verification of the simulation results.

(2) The present invention establishes an optimized design system and method for the warp/weft laying direction of electronic glass fiber cloth by means of the finite element simulation technology of the process before PCB compression molding to welding chips, which is conducive to promoting the production process of electronic glass fiber cloth. Refinement, broaden the application prospects of electronic-grade glass fiber cloth in the PCB manufacturing industry.

(3) The present invention provides a solution for reducing the warpage and deformation of the PCB manufacturing process, which is conducive to promoting the PCB manufacturing industry towards the road of high quality, high stability and low cost, and promoting the development of the integrated circuit technology industry. It provides new ideas for reducing warpage deformation in high-density circuit board manufacturing and improving chip soldering quality.

Other features and advantages of additional aspects of the invention will be set forth in part from the description that follows, and in part will become apparent from the description below, or will be learned by practice of the present aspects.

Description of drawings

Figure 1 is a schematic diagram of the interlayer position of the CCL core board, the prepreg, the copper foil/resin hybrid layer in the PCB and the structure of the double-sided etched copper clad laminate;

Fig. 2 is the schematic diagram of warp/weft laying direction of glass fiber cloth for PCB;

Fig. 3 is the flow chart of the optimized design method for the warp/weft laying direction of glass fiber cloth for PCB in the embodiment of the present invention;

4 is the simulation result and the experimental result of the warpage deformation amount when the PCB under the warp/weft laying direction of the electronic glass fiber cloth corresponding to the example (1) of the present invention is press-molded to the welding chip;

5 is the simulation result and the experimental result of the warpage deformation amount when the PCB under the warp/weft laying direction of the electronic glass fiber cloth corresponding to the example (2) of the present invention is press-molded to the welding chip;

6 is the simulation result and the experimental result of the warpage deformation amount when the PCB under the warp/weft laying direction of the electronic glass fiber cloth corresponding to the example (3) of the present invention is press-molded to the welding chip;

7 is the simulation result and the experimental result of the warpage deformation amount when the PCB under the warp/weft laying direction of the electronic glass fiber cloth corresponding to the example (4) of the present invention is press-molded to the welding chip;

Among them, 1. Copper foil/resin hybrid layer; 2. Prepreg; 3. CCL core board; 4. Copper clad laminate; 5. Resin; 6. Electronic glass fiber cloth; 7. Weft yarn; 8. Warp yarn.

Detailed ways

It should be noted that the following detailed description is exemplary and intended to provide further explanation of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

It should be noted that the terminology used herein is for the purpose of describing specific embodiments only, and is not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly dictates otherwise, the singular is intended to include the plural as well, furthermore, it is to be understood that when the terms "comprising" and/or "including" are used in this specification, it indicates that There are features, steps, operations, devices, components and/or combinations thereof.

Example 1

In one or more embodiments, a method for optimizing the warp/weft arrangement direction of glass fiber cloth for PCB is disclosed. First, a geometric model of a multi-layer PCB and a mathematical model of the PCB being pressed and molded to a soldered chip are established, and then an experiment is performed. The material performance parameters and initial boundary value conditions required by the finite element simulation are determined by testing and actual process, and then the material physical and chemical performance parameters corresponding to the warp/weft laying direction of the electronic glass fiber cloth are continuously optimized to form multiple electronic glass fiber cloth warp/weft yarns. An optional solution for the direction of weft yarn laying, so as to obtain the simulation results of the corresponding warpage deformation when the PCB is pressed and formed to the welding chip through finite element simulation. At the same time, the simulation results are verified by experiments and compared with the control group. The plan with a larger value than the control group is discarded, and the plan with a smaller warpage deformation value than the control group is retained and replaced with a new control group. After continuous screening, the PCB warpage deformation amount will be minimized or controlled according to demand The warp/weft laying direction of the electronic glass fiber cloth is the best solution for the optimal design.

In this embodiment, the electronic glass fiber cloth is an orthogonal woven material, and the arrangement of the warp and weft yarns affects the warpage deformation of the PCB when it is pressed and molded to the soldered chip, which is determined by the material of the PCB itself. When the material physical property parameters in the warp and weft axes change, in the face of the external environment of high temperature and high pressure and the complex environment with the resin curing reaction exothermic as the internal heat source, the uneven thermal expansion and contraction in the plane and between layers Residual internal stress caused by strain and resin chemical shrinkage strain will also change, which affects the surface flatness of the PCB when soldering the chip, and also makes the warpage and deformation state of the PCB difficult to predict. This makes it very difficult to observe and predict the warpage deformation of the PCB in real time after changing the warp/weft laying direction of the electronic glass fiber cloth and welding the chip. influences.

Therefore, in this embodiment, the physical process of changing the warp/weft laying direction of the electronic glass fiber cloth is transformed into the parameter setting in the mathematical model, and the finite element simulation method when the PCB is pressed and formed to the welding chip is used to numerically solve the given initial The generalized equation under the boundary value condition is used to obtain the numerical solution of the warpage deformation in the thickness direction when the PCB is pressed and formed to the welding chip and compared with the experimental results, so as to establish the optimal design method of the warp/weft laying direction of the electronic glass fiber cloth for PCB. .

Referring to FIG. 1, the specific optimization design method of this embodiment includes the following processes:

Step (1): establish the geometric model of the multilayer PCB and the mathematical model of the PCB compression molding to the welding chip;

Step (2): determine the material performance parameters and initial boundary value conditions required by the finite element simulation through experimental tests and actual processes; determine the corresponding relationship between the warp/weft yarn laying direction and the material direction;

Among them, according to the material temperature, pressure history and the geometric relationship between the PCB and the press in actual production, the initial conditions and boundary conditions of heat transfer and mechanics required for the finite element simulation and the contact relationship between the PCB and the press are respectively determined, including: The initial temperature, initial pressure, initial displacement of the PCB, and the displacement boundary conditions of the PCB from the stage of pressing and forming to the welding chip, etc.;

Obtain the material performance parameters required for finite element simulation based on experimental tests, including density, specific heat capacity, thermal conductivity, chemical reaction heat release per unit mass, chemical reaction kinetic series, elastic modulus, shear modulus, Poisson's ratio , thermal expansion coefficient, etc.

The above parameters may be deleted, added, replaced or adjusted in different embodiments.

Step (3): through finite element simulation and experimental verification, respectively, obtain the simulation results and experimental results of the warpage deformation amount when the PCB is pressed and formed to the welding chip;

Among them, the process of finite element simulation is: through the finite element software, based on the established model, input the PCB thermal and mechanical performance parameters of the experimental test and the equivalent initial boundary value conditions corresponding to the actual process, and change the mathematical properties of the prepreg and CCL core board. The material performance parameters of the warp and weft axial directions in the model are used to numerically solve the simulation results of the warpage deformation when the PCB is pressed and molded to the soldered chip.

The process of experimental verification is as follows: establish the experimental process of PCB compression molding to welding chips under the same conditions as the finite element simulation, and measure the concave and convex characteristics of the upper surface of the PCB at a specified time point by the shadow moiré method, and then obtain the data through data processing. The warpage measurement results when the PCB is pressed and formed to the welding chip are compared with the simulation results to verify the rationality and feasibility of the optimized design method.

Step (4): Based on the simulation results and experimental results, continuously optimize the material physical and chemical performance parameters corresponding to the warp/weft laying direction of the electronic glass fiber cloth, and obtain the corresponding electronic material that minimizes the warpage deformation of the PCB or controls the corresponding electronic fiberglass cloth as needed. Optimization scheme of warp/weft laying direction of glass fiber cloth.

The specific process is as follows:

(1) After obtaining the warpage deformation A when a certain type of PCB is pressed and formed to the welding chip, only change the arrangement direction of the warp/weft yarn of a certain type of electronic glass fiber cloth, and re-run the finite element simulation and experimental verification; The warpage deformation amount B when the PCB is pressed and formed to the welding chip;

(2) If B>A, discard the warp/weft arranging scheme that obtains the current warpage deformation B; if B<A, replace the warp/weft arranging scheme of the current warpage deformation B with the warp deformation A Warp/Weft Arrangement Scheme;

(3) Continue to change only the warp/weft laying direction of a certain electronic glass fiber cloth, and repeat steps (2)-(3) until traversing all the warp/weft laying directions of the electronic glass fiber cloth of a single model;

(4) Starting from changing the warp/weft laying direction of two types of electronic glass fiber cloth each time, to changing the warp/weft laying direction of all types of electronic glass fiber cloth, the finite element simulation and experimental verification are carried out one by one; get PCB The warpage deformation amount B when the pressure is formed to the welding chip; the method in step (2) is used to continue to compare the warpage deformation amount B and the current value of the warpage deformation amount A, until the PCB pressure forming to the welding chip is obtained. Minimize the amount of warpage deformation or control the corresponding electronic glass fiber cloth warp/weft laying direction as needed.

As a specific embodiment, this example optimizes the design of the warp/weft arrangement direction of the electronic glass fiber cloth in the prepreg and the CCL core board.

With the integrated finite element simulation method of the whole process from PCB compression molding to welding chip, the control variable optimization method is introduced to reduce the interference of many external factors, using computational mathematics, composite material mechanics, numerical heat transfer, anisotropic viscoelasticity, Theoretical knowledge of curing reaction kinetics, etc., establish a mathematical model of the whole process of PCB compression molding, post-processing to welding chips, and numerically simulate the warpage of PCB after changing the mechanical, thermal, physical and chemical performance parameters of CCL core board and prepreg The deformation process, and finally the numerical solution of the PCB warpage deformation is obtained and verified with the experimental results.

In this embodiment, according to each copper foil/resin hybrid layer, prepreg layer and CCL core layer of the PCB, the geometric model of the laminate is established in the graphical interface or geometric modeling software, and then imported into the finite element software, and the establishment includes resin curing. Mathematical models of reaction kinetic equations, anisotropic viscoelastic stress-strain constitutive equations, and material thermal constitutive equations. Among them, the curing reaction kinetic equation is obtained through experimental testing and data fitting. The anisotropic viscoelastic stress-strain constitutive equation and material thermal constitutive equation are known, but they need to be obtained through experimental testing according to the specific material type. Data input as part of the mathematical model building; these equations are available to those skilled in the art based on their current knowledge.

Define the correspondence between the warp axis, weft axis and thickness direction and the prepreg in the mathematical model and the weft axis, warp axis and thickness direction of the CCL core board. In this embodiment, the weft, warp, and thickness directions of the prepreg and the CCL core are numbered 1, 2, and 3, respectively, and correspond to the in-plane weft, warp, and thickness directions of the PCB geometric model. Correspondingly, so that the optimal design of the warp and weft laying directions is transformed into the optimal design of the material physical property parameters corresponding to the warp and weft axes.

Changing the type of electronic glass fiber cloth changes the material performance parameters of the warp and weft axes in the finite element simulation; for changing the direction of the warp and weft of a certain type of prepreg in the PCB, the warp of this type of prepreg is changed during the finite element simulation. Material property parameters in the axial and weft axis.

For example, define the direction of material 2 as the warp axis and the direction of material 1 as the weft axis. If the weft and warp laying directions of the electronic glass fiber cloth are exchanged, the corresponding exchange electronic glass fiber cloth corresponds to the material 1 and 2 directions of the mathematical model. parameters such as elastic modulus, shear modulus, Poisson's ratio, thermal expansion coefficient, chemical shrinkage strain calculation coefficient, etc.; if only the warp yarn type of the electronic glass fiber cloth is changed, only the 2-direction elastic modulus in the mathematical model will be changed. , shear modulus, Poisson's ratio, thermal expansion coefficient, chemical shrinkage strain calculation coefficient and other parameters, while the 1-direction parameters remain unchanged.

Orthotropic treatment of in-plane material performance parameters; from the point of view of material mechanics, elastic modulus, shear modulus, Poisson's ratio, thermal expansion coefficient in two orthogonal directions in the plane and in the out-of-plane normal direction and volume shrinkage can be directly obtained by experimental testing methods, which can be used as the input of orthotropic material performance parameters in the finite element simulation of PCB compression molding to welding chips, which further lays the foundation for the optimal design of the warp and weft laying directions.

Among them, the volume shrinkage rate (hereinafter referred to as the chemical shrinkage rate) is caused by the chemical shrinkage caused by the curing reaction of the resin, and the glass fiber cloth will be subjected to the tensile force of the resin matrix because it does not undergo chemical shrinkage. The composite material of cloth and resin undergoes volume shrinkage, and the difference in the warp and weft modulus of the glass fiber cloth leads to the difference in mechanical strain in the warp/weft direction, which leads to the difference in the warp and weft direction of the volume shrinkage rate, which leads to the change in the warp deformation of the PCB.

The density, specific heat capacity, and thermal conductivity of the prepreg and CCL core board are considered as temperature-dependent isotropic material performance parameters, and the data can be obtained directly through some experimental instruments and test standards.

However, the thickness of the prepreg and CCL core board is very small. For example, the nominal thickness of 1080 electronic glass fiber cloth is 55 μm, and the thickness of the corresponding cured sheet is only 76 μm. For such thin-plate composite materials, the thermal expansion coefficient and chemical shrinkage in the three main axis directions are difficult to pass. The experiment is accurately measured. Therefore, this embodiment provides an anisotropic equivalent processing method for the thermal expansion coefficient and chemical shrinkage rate of the PCB, so as to perform numerical simulation of the warpage deformation when the PCB is press-molded to a soldered chip.

The equivalent processing method of PCB anisotropic thermal expansion coefficient is as follows:

For the thermal expansion coefficients in the two directions in the plane, the average value a of the in-plane thermal expansion coefficient of a certain type of curing sheet and the elastic moduli E1 and E2 in the warp and weft directions are measured through experiments. It is considered that the thermal expansion coefficient is inversely proportional to the elastic modulus, and the thermal expansion coefficients e1 and e2 of the warp and weft axes of this type of curing sheet are calculated respectively. The calculation formula is shown in formula (1):

In the same way, the equivalent thermal expansion coefficients e1 and e2 of the in-plane warp and weft axial directions of different types of prepregs and CCL core boards in the PCB can be calculated. The thermal expansion coefficient e3 in the thickness direction of the PCB.

The equivalent treatment method of PCB anisotropic chemical shrinkage coefficient is as follows:

The unit cell model of the orthogonal woven glass fiber cloth composite material of the prepreg and the CCL core board was established, and the volume shrinkage rate of the composite material caused by the resin curing reaction was measured experimentally. The volume fraction of resin, fiber volume fraction, resin elastic modulus, and fiber elastic modulus in the weft axis are calculated to obtain the equivalent chemical shrinkage coefficients of the weft axis and the warp axis, denoted as ε ₁ , ε ₂ , and then in the composite In the material unit cell, the chemical shrinkage coefficient in the other direction is calculated according to the known chemical shrinkage coefficient in two directions and the total volume shrinkage rate, and the equivalent chemical shrinkage coefficient ε ₃ in the thickness direction is obtained, so that the three main axis directions are (1 and 2 directions are in-plane along the fiber direction, that is, the weft and warp axial directions, and the 3 directions are the thickness direction), the equivalent chemical shrinkage strain can be obtained. It should be noted that when the chemical shrinkage strain of the resin is very small, the mechanical strain of the fiber can be ignored, which simplifies the calculation formula of chemical shrinkage strain. The specific calculation formulas are shown in formulas (2), (3) and (4) respectively:

Among them, E _1f , E _2f , and Em are the modulus and resin modulus of the prepreg and the CCL core in the weft and warp axes, respectively, V _{f is} the volume fraction of fibers in the prepreg and the CCL core, Δv _composite is the overall curing shrinkage of the prepreg measured experimentally; ε _m is the isotropic chemical shrinkage strain of the pure resin, which is related to the volume change rate Δv of the resin, the curing degree Δα and the total volume change rate V _sh after complete curing, ε The calculation formula of _m is shown in formula (5):

The CCL core board is a composite laminate of epoxy resin matrix reinforced by one or more layers of orthogonally woven electronic glass fiber cloth. The resin has been cured before lamination, while the prepreg is a number of layers of orthogonal weaving with the resin not fully cured. The electronic glass fiber cloth reinforced epoxy resin matrix composite laminate. In the PCB, the CCL core board and the prepreg affect the anisotropic material properties of the PCB in-plane and between layers, especially when the electronic glass fiber cloth inside the two are placed orthogonally, the physical performance parameters of the PCB will appear significantly. anisotropy. This is because the elastic modulus of the warp yarn of the electronic glass fiber cloth is slightly larger than the elastic modulus of the weft yarn. Under the condition of the same weaving length, the elastic modulus of the warp yarn axial direction of the glass fiber cloth reinforced epoxy resin composite sheet, The mechanical properties parameters such as shear modulus and tensile strength are higher than those corresponding to the weft axis, while the thermal expansion coefficient is opposite, that is, the thermal expansion coefficient of the composite material in the warp axis is smaller than that in the weft axis. The difference in the performance parameters of warp and weft leads to the difference in warpage deformation of PCBs with different warp and weft arrangement directions of electronic glass fiber cloth in the process of thermal expansion and cold contraction, chemical shrinkage and mechanical rebalancing.

Therefore, changing the warp/weft arranging direction of the PCB electronic glass fiber cloth will lead to differences in the mechanical and thermal properties of the PCB in the warp axis and the weft axis. Key factor.

In this embodiment, the finite element simulation method is integrated in the whole process of PCB compression molding to welding chip, and the control variable optimization method is introduced to reduce the interference of many external factors. Theoretical knowledge of elasticity, curing reaction kinetics, etc., establish the mathematical model of the whole process of PCB compression molding, post-processing to welding chips, and numerically simulate PCB after changing the mechanical, thermal, physical and chemical performance parameters of CCL core board and prepreg Finally, the numerical solution of the warpage deformation of the PCB is obtained and verified with the experimental results.

The integrated finite element simulation of the whole process of PCB compression molding to welding chips, including but not limited to: importing the geometric model of the PCB into the finite element software, mathematically describing the mathematical model with mathematical formulas and a series of constitutive equations, using thermal -Chemical-mechanical multi-physics coupling, quantitatively revealing the evolution law of internal stress and strain of PCB in the process of high temperature and high pressure, thermal cycle, and external force loading, to solve the problem of mutual influence between the physical performance parameters of copper, resin, and glass fiber, using The implicit iterative method of decoupling continuously numerically solves the force balance control equation and the moment balance control equation (these equations are all existing algorithms in the finite element software), thereby quantitatively obtaining copper, The dynamic evolution of thermal expansion and cold contraction strain, resin curing degree, PCB temperature, residual internal stress and chemical shrinkage strain of resin and glass fiber composite system, and the numerical solution of warpage deformation from PCB compression molding to welding chip, At the same time, the experimental results are used for verification, and then for the ideal mechanical properties, warpage deformation and deformation morphology of the ideal PCB, the warp/weft arrangement direction of the electronic glass fiber cloth is optimally designed, thereby improving the production yield of the PCB and reducing the production cost.

It should be noted that the numerical solution of the warpage deformation amount when the PCB is pressed and formed to the welding chip in this embodiment refers to the directionality of the physical property parameters of the material caused by only changing the warp/weft laying direction of the electronic glass fiber cloth. , By establishing the geometric model of the multi-layer PCB and the mathematical model of the PCB compression molding to the welding chip, with the help of computer software and numerical calculation methods, numerically simulate the warpage deformation of the PCB from the compression molding to the welding chip, and post-processing through the software The function is to establish a space rectangular coordinate system with the three coordinate axes of the warp and weft yarns in the PCB plane and the thickness direction as the three coordinate axes, and obtain the relative maximum displacement in the thickness direction of the PCB.

This embodiment does not limit the brand of electronic glass fiber cloth, all electronic glass fiber cloth used for PCB and IC packaging substrates are within the scope of protection of this application; there is no absolute correspondence between the major axis direction of the material involved and the axial direction of the yarn, only Strictly correspond in the determined PCB model, and achieve the goal of optimal design by adjusting the physical and chemical performance parameters of the material.

An example is given below:

Example (1): The room temperature dimension of a multi-layer rigid PCB is 430mm×378mm×2mm, and the number of copper foil/resin mixed layers is 10 layers. The prepreg and CCL core board used to manufacture the product board are three types of electronic glass fibers. The composite material of cloth and epoxy resin, the copper foil is a general-purpose rolled copper foil used in the electronic industry for the manufacture of CCL on the market. is 1080. Among them, the monofilament diameter of 1080 electronic glass fiber cloth warp/weft yarn is 5 μm, and the nominal thickness of gauze is 0.053mm; the monofilament diameter of 2116 electronic glass fiber cloth warp/weft yarn is 7 μm, and the nominal thickness of gauze is 0.094mm; 3313 electronic glass fiber cloth warp / weft yarn The diameter of the monofilament is 6μm, and the nominal thickness of the gauze is 0.084mm; taking this PCB as the research object, the optimization design of the warp/weft laying direction of the electronic glass fiber cloth is carried out, which includes the following processes:

Step 1: According to each copper foil/resin hybrid layer, prepreg layer and CCL core layer of the PCB, establish the geometric model of the laminate in the graphical interface or geometric modeling software, and then import the finite element software to establish the resin curing reaction kinetics Mathematical models such as equations, anisotropic viscoelastic stress-strain constitutive equations, and material thermal constitutive equations;

Step 2: Determine the initial conditions and boundary conditions according to the experimental test and actual lamination process parameters, and unify the corresponding relationship between the warp/weft laying direction and the material direction, that is, the weft axis of all electronic glass fiber cloths is the material 1 direction of the model, The warp axis is the material 2 direction of the model, and the plan number of this warp/weft laying direction is ①;

Step 3: Use the finite element simulation software and the numerical calculation ability of the computer to carry out simulation simulation and experimental verification, and obtain the simulation result A and the experimental result of the warpage deformation amount when the PCB is pressed and formed to the welding chip, as a control group;

Step 4: Only change the warp/weft laying direction of a certain type of electronic glass fiber cloth (such as 1080), re-run the finite element simulation and experimental verification, and obtain the result B of the warpage deformation amount when the PCB is pressed and formed to the welding chip. The scheme number of the warp/weft laying direction is ②;

Step 5: If B>A, discard the current value of B; if B<A, set A=B. Continue to change the warp/weft laying direction of the electronic glass fiber cloth (for example, only change the warp/weft laying direction of the 1080 prepreg and CCL core board electronic glass fiber cloth, the plan number of this warp/weft laying direction is ③), and perform finite element simulation and experimental verification, the simulation results B and experimental results of the warpage deformation amount when the new PCB is pressed and formed to the welding chip are obtained respectively;

Step 6: Repeat step 5 until all the alternatives from changing the warp/weft laying direction of a certain type of electronic glass fiber cloth to changing the warp/weft laying direction of multiple types of electronic glass fiber cloth have results, and the results of these program numbering;

Step 7: Change the warp/weft arrangement direction of the electronic glass fiber cloth for all models (1080/2116/3313) of the prepreg and CCL core board and number them, re-run the finite element simulation and experimental verification, and obtain the PCB compression molding to the welding chip respectively. The simulation result B and the experimental result of the warpage deformation amount at the time, go to step 5;

Step 8: Result B corresponds to the warp/weft laying direction of the electronic glass fiber cloth, which is to minimize the warpage deformation when the PCB is pressed and molded to the soldered chip or to control the corresponding electronic glass fiber cloth warp/weft laying direction as needed.

Through the implementation of the above steps, the warpage deformation results when the PCB corresponding to the warp/weft laying directions of the electronic glass fiber cloth is pressed into the soldered chip are shown in Figure 4. So far, the goal of this optimization design has been achieved, and the corresponding number ⑤ corresponds to The warp/weft laying direction of PCB electronic glass fiber cloth is the optimal solution.

Example (2): The room temperature dimension of a multi-layer rigid PCB is 400mm×350mm×2.2mm, the number of copper foil/resin mixed layers is 8, and the prepreg and CCL core board used to manufacture the product board are three types of electronic glass. It is a composite material of fiber cloth and epoxy resin. The copper foil is a general-purpose rolled copper foil used in the electronic industry to manufacture CCL on the market. 1078. Among them, the monofilament diameter of 2116 electronic glass fiber cloth warp/weft yarn is 7 μm, and the nominal thickness of gauze is 0.094mm; the monofilament diameter of 3313 electronic glass fiber cloth warp / weft yarn is 6 μm, and the nominal thickness of gauze is 0.084mm; 1078 electronic glass fiber cloth warp / weft yarn The diameter of the monofilament is 5μm, and the nominal thickness of the gauze is 0.043mm. Taking the PCB as the research object, the optimization design of the warp/weft laying direction of the electronic glass fiber cloth is carried out, including:

First, according to each copper foil/resin hybrid layer, prepreg layer and CCL core layer of the PCB, the geometric model of the laminate is established in the graphical interface or geometric modeling software, and then imported into the finite element software to establish the resin curing reaction kinetic equation, Mathematical models such as anisotropic viscoelastic stress-strain constitutive equation and material thermal constitutive equation; then determine initial conditions and boundary conditions according to experimental tests and actual lamination process parameters, and unify the warp/weft laying direction and material of electronic glass fiber cloth The corresponding relationship of the directions, that is, the weft axis of all electronic glass fiber cloths is the material 1 direction of the model, and the warp axis is the material 2 direction of the model; The scheme is numbered and corresponding to the parameters in the mathematical model. After the parameters are modified, the finite element simulation software and the numerical computing power of the computer are used to simulate the simulation. At the same time, the experimental verification is carried out to obtain the warpage deformation amount when the PCB is pressed and formed to the welding chip. The simulation results and experimental results are plotted with the amount of warpage deformation as the ordinate and the number as the abscissa (bar chart, line chart and scatter chart are all acceptable), as shown in Figure 5, the electronic glass fiber corresponding to number ⑤ is preferred Warp/Weft lay-out direction.

Example (3): The room temperature dimension of a multi-layer rigid PCB is 350mm×365mm×2.0mm, and the number of copper foil/resin mixed layers is 8 layers. The composite material of fiber cloth and epoxy resin, the copper foil is a general-purpose rolled copper foil used in the electronic industry for the manufacture of CCL on the market. The grade is 1081. Among them, the monofilament diameter of 1081 electronic glass fiber cloth warp/weft yarn is 5 μm, and the nominal thickness of gauze is 0.060 mm; the monofilament diameter of 1678 electronic glass fiber cloth warp/weft yarn is 9 μm, and the nominal thickness of gauze is 0.091 mm; 2313 electronic glass fiber cloth warp yarn The wire diameter is 7μm, the weft monofilament diameter is 5μm, and the nominal thickness of the gauze is 0.084mm. Taking the PCB as the research object, the optimal design of the warp/weft laying direction of the electronic glass fiber cloth is carried out.

Firstly, the laminate geometric model and mathematical model are established according to each copper foil/resin hybrid layer, prepreg layer and CCL core layer of the PCB; then the initial conditions and boundaries required for finite element simulation are determined according to experimental tests and actual lamination process parameters conditions, and unify the corresponding relationship between the warp/weft laying direction and the material direction of the electronic glass fiber cloth. For this embodiment, it is specified that the warp axis of the electronic glass fiber cloth is the material 1 direction of the model, and the weft axis is the model material 2 direction. , and then find all possible solutions for the warp/weft laying direction of the electronic glass fiber cloth according to the grade of glass fiber cloth and number them. After modifying the parameters in the mathematical model, use the finite element simulation software and the numerical calculation ability of the computer to simulate the simulation. , and carry out experimental verification at the same time, and obtain the simulation results and experimental results of the warpage deformation amount when the PCB is pressed and formed to the welding chip. Take the warpage deformation amount as the ordinate and the number as the abscissa to make a broken line graph, as shown in Figure 6 , and preferably the warp/weft laying direction of the electronic glass fiber cloth corresponding to the number ⑤.

Example (4): The room temperature dimension of a multi-layer rigid PCB is 400mm×380mm×2.2mm, and the number of copper foil/resin mixed layers is 8 layers. The composite material of fiber cloth, epoxy resin and cyanic acid resin, the copper foil is a general-purpose rolled copper foil used in the electronic industry to manufacture CCL on the market. The grade of electronic glass fiber cloth is 1065. The monofilament diameter of 1065 electronic glass fiber cloth warp/weft yarn is 5 μm, the nominal thickness of gauze is 0.053mm, the monofilament diameter of 2150 electronic glass fiber cloth warp / weft yarn is 5 μm, the nominal thickness of gauze is 0.075mm, and the 3070 electronic fiberglass cloth has a monofilament diameter of 5 μm. The monofilament diameter of the warp/weft yarn of the glass fiber cloth is 6μm, and the nominal thickness of the gauze is 0.078mm. Taking the PCB as the research object, the optimal design of the warp/weft laying direction of the electronic glass fiber cloth is carried out.

Firstly, the laminate geometric model and mathematical model are established according to each copper foil/resin hybrid layer, prepreg layer and CCL core layer of the PCB; then the initial conditions and boundaries required for finite element simulation are determined according to experimental tests and actual lamination process parameters conditions, and unify the corresponding relationship between the warp/weft laying direction and the material direction of the electronic glass fiber cloth. For this embodiment, it is specified that the weft axis of the electronic glass fiber cloth is the material 1 direction of the model, and the warp axis is the model material 2 direction. , and then find all possible solutions for the warp/weft laying direction of the electronic glass fiber cloth according to the grade of glass fiber cloth and number them. After modifying the parameters in the mathematical model, use the finite element simulation software and the numerical calculation ability of the computer to simulate the simulation. , and carry out experimental verification at the same time, and obtain the simulation results and experimental results of the warpage deformation amount when the PCB is pressed and formed to the welding chip. The warpage deformation amount is taken as the ordinate and the number is the abscissa to make a broken line graph, as shown in Figure 7 , preferably the warp/weft laying direction of the electronic glass fiber cloth corresponding to the number ⑥.

Embodiment 2

In one or more embodiments, a system for optimizing the warp/weft arrangement direction of glass fiber cloth for PCB is disclosed, including:

Mathematical modeling module, used to establish the geometric model of multilayer PCB and the mathematical model of PCB compression molding to soldered chips;

The parameter setting module is used to determine the material performance parameters and initial boundary value conditions required by the finite element simulation through experimental tests and actual processes; to determine the corresponding relationship between the warp/weft yarn laying direction and the material direction;

The numerical simulation module is used to obtain the simulation results and experimental results of the warpage deformation amount when the PCB is pressed and formed to the welding chip through finite element simulation and experimental verification respectively;

The optimization design module is used to continuously optimize the material physical and chemical performance parameters corresponding to the warp/weft laying direction of the electronic glass fiber cloth based on the simulation results and experimental results, and obtain the corresponding parameters that minimize the warpage deformation of the PCB or control it on demand. Optimization scheme of warp/weft laying direction of electronic glass fiber cloth.

The specific implementation of the above modules has been described in the first embodiment, and will not be described in detail here.

Embodiment 3

In one or more embodiments, a terminal device is disclosed, including a server, the server including a memory, a processor, and a computer program stored on the memory and executable on the processor, the processor executing the During the program, the optimal design method for the warp/weft arrangement direction of the glass fiber cloth for PCB in the first embodiment is realized. For brevity, details are not repeated here.

It should be understood that, in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, off-the-shelf programmable gate array FPGA or other programmable logic devices , discrete gate or transistor logic devices, discrete hardware components, etc. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.

The memory may include read-only memory and random access memory and provide instructions and data to the processor, and a portion of the memory may also include non-volatile random access memory. For example, the memory may also store device type information.

In the implementation process, each step of the above-mentioned method can be completed by a hardware integrated logic circuit in a processor or an instruction in the form of software.

Embodiment 4

In one or more embodiments, a computer-readable storage medium is disclosed, in which a plurality of instructions are stored, and the instructions are adapted to be loaded by a processor of a terminal device and execute the PCB glass used in the first embodiment. Optimal design method of fiber cloth warp/weft laying direction.

Although the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, they do not limit the scope of protection of the present invention. Those skilled in the art should understand that on the basis of the technical solutions of the present invention, those skilled in the art do not need to pay creative efforts. Various modifications or deformations that can be made are still within the protection scope of the present invention.

Claims (10)

1. A warp/weft yarn laying direction optimization design method for glass fiber cloth for a PCB is characterized by comprising the following steps:

establishing a geometric model of the multilayer PCB and a mathematical model of pressing and molding the PCB to the welding chip;

determining material performance parameters and initial boundary value conditions required by finite element simulation through experimental tests and actual processes; determining the corresponding relation between the warp/weft yarn laying direction and the material direction;

obtaining a warping deformation simulation result and an experimental result when the PCB is pressed and molded to a welding chip through finite element simulation and experimental verification respectively;

and continuously optimizing the physical and chemical performance parameters of the material corresponding to the arrangement direction of the warp/weft yarns of the electronic glass fiber cloth based on the simulation result and the experimental result to obtain an optimization scheme for minimizing the warping deformation of the PCB or controlling the arrangement direction of the warp/weft yarns of the electronic glass fiber cloth according to the requirement.

2. The method for optimally designing the warp/weft laying direction of the glass fiber cloth for the PCB as claimed in claim 1, wherein the establishing of the geometric model of the multilayer PCB and the mathematical model of the PCB press-fit molding to the welding chip specifically comprises the following steps:

according to each copper foil/resin mixed layer, the prepreg layer and the CCL core layer of the PCB, a geometric model of the laminated plate is established in a graphical interface or geometric modeling software, then finite element software is introduced, and a mathematical model comprising a resin curing reaction kinetic equation, an anisotropic viscoelastic stress strain constitutive equation and a material thermal constitutive equation is established.

3. The method for optimally designing the warp/weft yarn arrangement direction of the glass fiber cloth for the PCB as claimed in claim 1, wherein the step of determining the corresponding relation between the warp/weft yarn arrangement direction and the material direction specifically comprises the following steps:

and respectively corresponding the warp axial direction, the weft axial direction and the thickness direction of the prepreg and the CCL core board in the mathematical model with the in-plane weft axial direction, the warp axial direction and the thickness direction of the PCB geometric model so as to convert the optimal design of the laying direction of the warp and the weft into the optimal design of the material physical property parameters corresponding to the warp axial direction and the weft axial direction.

4. The method for optimally designing the warp/weft laying direction of the glass fiber cloth for the PCB as claimed in claim 1, wherein the warping deformation amount when the PCB is pressed and molded to a welding chip is as follows:

after the directional change of the physical property parameters of the material caused by changing the warp/weft laying direction of the electronic glass fiber cloth is carried out, based on the mathematical model, the warping deformation of the PCB from press-fit molding to chip welding is simulated through a numerical calculation method, and a spatial rectangular coordinate system is established by taking the warp axial direction, the weft axial direction and the thickness direction in the PCB surface as three coordinate axes through data processing, so that the relative maximum displacement in the thickness direction of the PCB is obtained.

5. The method for optimally designing the warp/weft laying direction of the glass fiber cloth for the PCB as claimed in claim 1, wherein the warp deformation simulation result when the PCB is pressed and molded to a welding chip is obtained through finite element simulation, and the method specifically comprises the following steps:

inputting thermal and mechanical property parameters of the PCB and equivalent initial edge value conditions corresponding to an actual process based on the established geometric model of the multilayer PCB and the mathematical model from the PCB press-forming to the welding chip, and changing axial material property parameters of warp yarns and weft yarns of the prepreg and the CCL core board in the mathematical model, thereby numerically solving a warping deformation simulation result from the PCB press-forming to the welding chip.

6. The method for optimally designing the warp/weft laying direction of the glass fiber cloth for the PCB as claimed in claim 1, wherein the experimental verification is carried out to obtain the experimental result of the warping deformation when the PCB is pressed and molded to a welding chip, and the experimental result specifically comprises the following steps:

establishing an experimental process from PCB press-forming to chip welding under the same conditions as finite element simulation, measuring the concave-convex characteristics of the upper surface of the PCB at a set time point by a shadow moire method, and obtaining the actual measurement result of warping when the PCB is press-formed to the chip welding through data processing.

7. The method for optimally designing the warp/weft laying direction of the glass fiber cloth for the PCB as claimed in claim 1, wherein based on the simulation result and the experiment result, the physical and chemical performance parameters of the material corresponding to the warp/weft laying direction of the electronic glass fiber cloth are continuously optimized to obtain an optimization scheme for minimizing the warp deformation of the PCB or controlling the corresponding warp/weft laying direction of the electronic glass fiber cloth as required, and the optimization scheme specifically comprises the following steps:

(1) after the warping deformation A when a PCB of a certain model is pressed and molded to a welding chip is obtained, only the arrangement direction of warp yarns/weft yarns of the electronic glass fiber cloth of the certain model is changed, and finite element simulation and experimental verification are carried out again; obtaining the warping deformation B when the PCB is pressed and molded to a welding chip;

(2) if B is larger than A, abandoning the warp/weft yarn arrangement scheme for obtaining the current warping deformation B; if B is less than A, replacing the warp/weft arrangement scheme of the warp deformation A with the warp/weft arrangement scheme of the current warp deformation B;

(3) continuously changing the arrangement direction of the warp/weft yarns of a certain electronic glass fiber cloth, and repeating the steps (2) - (3) until all the arrangement directions of the warp/weft yarns of the electronic glass fiber cloth of a single model are changed;

(4) from changing the warp/weft yarn arrangement direction of the electronic glass fiber cloth with two types each time to changing the warp/weft yarn arrangement direction of the electronic glass fiber cloth with all types, carrying out finite element simulation and experimental verification one by one again; obtaining the warping deformation B when the PCB is pressed and molded to a welding chip; and (3) continuously comparing the warping deformation amount B with the current warping deformation amount A by adopting the method in the step (2) until the warping deformation amount when the PCB is laminated and molded to the welding chip is minimized or the corresponding warp/weft laying direction of the electronic glass fiber cloth is controlled according to the requirement.

8. A glass fiber cloth warp/weft laying direction optimal design system for a PCB is characterized by comprising:

the mathematical modeling module is used for establishing a geometric model of the multilayer PCB and a mathematical model from the PCB press-fit molding to the welding chip;

the parameter setting module is used for determining material performance parameters and initial boundary value conditions required by finite element simulation through experimental tests and actual processes; determining the corresponding relation between the warp/weft yarn laying direction and the material direction;

the numerical simulation module is used for obtaining a warping deformation simulation result and an experiment result when the PCB is pressed and molded to a welding chip through finite element simulation and experimental verification respectively;

and the optimization design module is used for continuously optimizing the material physical and chemical performance parameters corresponding to the electronic glass fiber cloth warp/weft yarn arrangement direction based on the simulation result and the experiment result to obtain an optimization scheme for minimizing the PCB warping deformation or controlling the corresponding electronic glass fiber cloth warp/weft yarn arrangement direction as required.

9. A terminal device comprising a processor and a memory, the processor being arranged to implement instructions; the memory is used for storing a plurality of instructions, wherein the instructions are suitable for being loaded by the processor and executing the fiberglass cloth warp/weft yarn arrangement direction optimization design method for the PCB according to any one of claims 1 to 7.

10. A computer-readable storage medium having stored therein a plurality of instructions, wherein the instructions are adapted to be loaded by a processor of a terminal device and to execute the method for optimally designing warp/weft lay-up direction of glass fiber cloth for PCB according to any one of claims 1 to 7.

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