KR20090064428A - Method for analyzing fluidity of resin material including particles and fluidity analysis system - Google Patents

Abstract

A technique of analyzing fluid behavior of a resin material including deformation of particles. A fluidity analysis method is characterized by establishing a calculating method in which the results of experiments on the deformation of and load on the particles are received as inputted values, the flow process of a resin material is predicted by a fluid analysis technique, and the flow and particle deformation of the resin material are predicted. Specifically, at a time step, the deformation of particles is determined from the interval between electrodes determined by fluid analysis, the load determined by subtracting the load corresponding to the deformation of the particles from the load to move the electrodes is used as the load to move the electrode at the next time step. With this, the process of flowing of a resin material while particles are deforming is predicted by fluid analysis.

Description

Flow analysis method and flow analysis system of resin material incorporating particles {METHOD FOR ANALYZING FLUIDITY OF RESIN MATERIAL INCLUDING PARTICLES AND FLUIDITY ANALYSIS SYSTEM}

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a flow analysis method and a flow analysis system of a resin material incorporating particles, and particularly includes conductive particles between electrodes in order to connect a semiconductor integrated circuit (IC) used in a device, a liquid crystal, or the like to a substrate. It relates to a three-dimensional flow analysis method when the resin material to be flowed to evaluate conductivity from the number of particles between the electrodes and the amount of deformation of the particles.

As a flow analysis method of a thermosetting material, the analysis programs which can analyze the foaming behavior whose density of a polyurethane foam material decreases with time are described in following patent document 1 and patent document 2.

In Patent Literature 1, the entire foamed material is regarded as a uniform density, and as the density, the density calculated as the elapsed time after exiting the nozzle of the first foamed material from the nozzle which blows out the foamed material in which the foamed raw material is stirred is determined. I use it. Moreover, in patent document 2, in addition to the technique of patent document 1, it is described to perform foam flow analysis of foam material using the function which considered that the density of foam material changes with the change of thickness.

In addition, there is a report example of R. Dudek et al. In Non-Patent Document 1 described below as a method for calculating particle deformation by compressing a resin material having particles embedded therebetween the electrodes. This uses a structural analysis (soft: ABAQUS), inputs the shape of the electrode, the particle and the resin material, the physical properties of the particle and the resin (Young's modulus, Poisson's ratio, linear expansion coefficient), and compresses the particle and resin between the heated electrodes. It is a calculation method.

Patent Document 1: Japanese Patent Application Laid-Open No. 2001-318909

Patent Document 2: Japanese Patent Laid-Open No. 2003-91561

Non-Patent Document 1: F10W Characterization and Thermo-Mechanical Response of Anisotropic Conductive Films 1998 IEEE, (R.Dudek, A.Schubert, S.Meinel, B.Michel (Fraunhofer Institute for Reliability and Microintegration (IZM) Berlin))

<Start of invention>

Problems to be Solved by the Invention

In the case of performing an analysis in which the particles deform between the electrodes while the resin material flows, it is necessary to predict the flow of the resin material using the fluid analysis and also predict the deformation of the particles using the structural analysis. The above-described prior art is a method of predicting particle deformation using structural analysis, but there is a problem in that the flow of resin material and particles, the number of particles sandwiched between electrodes, viscosity change of resin material, exothermic reaction, etc. cannot be taken into consideration.

As described above, the structural analysis cannot accurately predict the flow process of the resin material which changes in viscosity with an exothermic reaction. On the other hand, in the fluid analysis of the phenomenon, it is not possible to accurately calculate the plastic deformation between the electrodes of the particles while the resin material is flowing.

Therefore, an object of the present invention is to calculate the number of particles to be sandwiched between electrodes by calculating the flow behavior of the resin material and the particles by compression between the electrodes. In addition, the object of the present invention is to predict the amount of deformation of the particles based on the load or velocity conditions applied to the electrodes in order to move the electrodes in consideration of the increase in the resin viscosity, the characteristics of the load and displacement of the particles, and the number of particles sandwiched between the electrodes. .

Another object of the present invention is to predict the conductivity between electrodes from the amount of deformation of the particles and the number of particles sandwiched between the electrodes.

Means for solving the problem

In order to achieve the above object, the present invention at least predicts the flow process of the resin material by fluid analysis technology and at the same time inputs at least the viscosity conditions of the resin material, the deformation amount of the particles and the experimental results of the load, and the flow of the resin material. And a calculation method for predicting particle deformation. Specifically, the prediction of the number of particles to be sandwiched between the electrodes is made possible by the prediction of the flow process of the resin material and the particles in consideration of the viscosity change.

In the time step with the fluid analysis, the deformation amount of the particle is obtained from the interval between the electrodes obtained by the fluid analysis, and the load obtained by subtracting the load corresponding to the deformation amount of the particle from the load applied from the outside to move the electrode is obtained. By using it as a load for moving the electrode in the next time step, the deformation amount of the particles to be obtained by the structural analysis is calculated by the fluid analysis, and the resin material flows while the particles are deformed only by the fluid analysis without using the structural analysis. Makes it possible to predict the process.

In addition, by inputting the relationship between the amount of deformation of the particle and the conductivity, it is possible to predict the conductivity between the electrodes from the maximum amount of deformation of the particle and the number of particles sandwiched between the substrates.

Effect of the Invention

As described above, the analysis technique of the present invention can predict the number of particles and the amount of deformation of the particles sandwiched between the electrodes of the chip and the substrate. In addition, the analysis can be optimized for the factors in which the shape of the particles and the electrode, the physical properties such as the elastic modulus of the particles, the molding process conditions such as the load applied to the electrode, and the like are complicated.

In addition, it is not realistic to carry out experimental examination in order to optimize these factors because of the high cost and the long development period.

BRIEF DESCRIPTION OF THE DRAWINGS It is a schematic diagram which shows the shaping | molding process of a semiconductor integrated circuit (IC) and a board | substrate using the resin material containing the electroconductive particle used as the analysis object.

2 is a hardware configuration diagram for performing flow analysis.

Fig. 3 is a flowchart of calculation in which the movement of the semiconductor integrated circuit (IC) 3 and the electrode of Embodiment 1 of the present invention is pressure controlled.

4 is a flowchart of a calculation in which the movement of the semiconductor integrated circuit (IC) 3 and the electrode of Embodiment 2 of the present invention is pressure-controlled from speed.

It is an example of analysis (one layer resin) of the pressure control of the electrode of Example 1 or 2 of this invention.

6 is an analysis example (two-layer resin) of pressure control of the electrode of Example 1 or 2 of the present invention.

Fig. 7 is a flowchart of the analysis for predicting the conductivity of the third embodiment of the present invention (calculation in which the movement of the semiconductor integrated circuit (IC) 3 and the electrodes is under pressure control).

Fig. 8 is a flowchart of the analysis for predicting the conductivity of the fourth embodiment of the present invention (calculation in which the movement of the semiconductor integrated circuit (IC) 3 and the electrodes is pressure controlled from the speed).

FIG. 9: is a figure which shows the relationship of the "deformation amount when a load is applied per one of particle | grains 1" input.

It is a figure which shows the relationship of the "inversion amount of arbitrary allowance of particle | grains, and electroconductivity between the electrode of a semiconductor integrated circuit (IC) and the electrode of a board | substrate" inputted.

FIG. 11: is a schematic diagram which shows the shaping | molding process of a semiconductor integrated circuit (IC) and a board | substrate using the resin material containing the electroconductive particle used as the analysis object.

It is a hardware block diagram which performs a flow analysis.

Fig. 13 is a flowchart of calculation in which the movement of the semiconductor integrated circuit (IC) 3 and the electrode of the fifth embodiment of the present invention is pressure controlled.

Fig. 14 is a flowchart of calculation in which the movement of the semiconductor integrated circuit (IC) 3 and the electrode of the sixth embodiment of the present invention is pressure controlled from the speed.

It is an example of analysis (one layer resin) of the pressure control of the electrode of Example 5 or 6 of this invention.

It is an example of analysis (two-layer resin) of the pressure control of the electrode of Example 5 or 6 of this invention.

Fig. 17 is a flowchart of the analysis for predicting the conductivity of the seventh embodiment of the present invention (calculation in which the movement of the semiconductor integrated circuit (IC) 3 and the electrodes are under pressure control).

It is a figure which shows the relationship of the "deformation amount when a load is applied per one of particle | grains 1 which considered temperature" input.

FIG. 19 is a diagram showing a relationship between the input "deformation amount of arbitrary allowance of particles and conductivity between an electrode of a semiconductor integrated circuit (IC) and an electrode of a substrate".

FIG. 20 is a result of structural analysis using the coordinates of the particles 1 of the connecting portion sandwiched between the electrodes 4 and the moving speed of the electrodes 4 as input conditions.

FIG. 21 is a diagram showing a relationship between "contact area of particles and conductivity between electrodes of a semiconductor integrated circuit (IC) and electrodes of a substrate".

<Description of the code>

1: Particle

2: resin material

3: semiconductor integrated circuit (IC)

4: electrode

5: substrate

6: calculating device

7: calculating device

8: LAN

9: display device

10: recording device

11: Resin material of the second layer

Best Mode for Carrying Out the Invention

EMBODIMENT OF THE INVENTION Hereinafter, embodiment which concerns on this invention is described, referring an accompanying drawing.

Example 1

[Pressure Control of Moving Electrode]

First, the shaping | molding process used as an analysis object is demonstrated using FIG. In the initial state (1-a), the resin material 2 including the conductive particles 1 is disposed between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5. Installed in In the molding step, the semiconductor integrated circuit (IC) 3 to which the heat is applied is moved in the direction of the substrate 5 to compress the resin material 2 including the particles 1 to contain the particles 1. The resin material 2 flows.

At this time, the contact of the electrode 4 of the semiconductor integrated circuit (IC) 3 and the resin material 2 causes the temperature of the resin material 2 to change, while generating a viscosity change accompanying the temperature change, The resin material 2 flows while being compressed with the particles 1. In addition, when the space | interval of the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the board | substrate 5 becomes smaller than the diameter of the particle | grains 1, the particle | grains interposed between the electrodes 4 ( 1) is compressed while deforming.

When the movement of the semiconductor integrated circuit (IC) 3 is completed (1-b), the semiconductor integrated circuit (IC) 3 and the substrate are moved by the conductivity of the particles 1 sandwiched between the electrodes 4. It is possible to transmit the electrical signal between (5). Here, the contact area of the particle 1 and the electrode 4 is determined by the deformation amount of the particle 1, and the conductivity between the semiconductor integrated circuit (IC) 3 and the substrate 5 is determined by this contact area. Is determined. In addition, conductivity is evaluated by the current flowing when a constant voltage is applied between the electrodes 4. Here, the amount of deformation of the particles 1 is the ability of the device to apply a load from the upper portion of the semiconductor integrated circuit (IC) 3, the amount of deformation of the particles 1 when the load is applied, the amount of the particles 1 sandwiched between the electrodes It is determined by the number and the viscosity change of the resin material (2).

[Configuration of Analysis System]

Next, the analysis system used in order to predict the flow process of the resin material 2 accompanying particle | grain 1 deformation | transformation is demonstrated. The analysis system is a hardware configuration shown in Fig. 2 and functions by executing software having the flows of Figs. 3, 4, 7, and 8 described later.

Specifically, a calculation device 7 including a calculation device 6, a recording device 10 (hard disk, MO, etc.), a LAN 8 connecting these two calculation devices, and a calculation device 7 are provided. The display apparatus 9 provided is provided. Moreover, it can also be comprised so that the CAD data created with the calculation device 6 may be transmitted to the calculation device 7 via LAN8. The CAD data transferred to the calculation device 7 may be recorded and used on the recording device 10 (hard disk, MO, etc.) of the calculation device 7. The calculation device 7 executes calculation in accordance with the flowcharts shown in Figs. 3, 4, 7, 8, records the result in the recording device 10, and then displays the result in the display device 9. Although not shown, the calculation devices 6 and 7 are naturally provided with input devices such as a keyboard and a mouse.

[Flowchart]

Next, the process of an analysis program is demonstrated according to the flowchart of FIG. First, in the model shape creation step 1001, the analysis target model specified by the operator through the input device, that is, the electrode of the analysis target, the shape of the resin material including the initial particles, and the resin material including the particles can flow. The data of the space is read from the storage device 10.

Next, in step 1002 of the three-dimensional solid element creation, the shape of the data read in the model shape creation step 1001 is decomposed into a plurality of specific spaces (finite elements of the three-dimensional solid), and shape data of each finite element is created. .

Next, in the physical property value input step 1003, the density, the thermal conductivity, the specific heat, the exothermic equation (Equation 7) to (Equation 11), the viscosity equations (Equation 12) to (Equation 15), which are physical properties of the material to be analyzed The display prompting the operator to input the arrangement, the density, the diameter of the particle 1, and the deformation amount when a load is applied to each of the particle 1 is performed, and these data are received from the input device. In addition, A: reaction rate, t: time, T: temperature, dA / dt: reaction rate, X1, X2: coefficients as a function of temperature, N, M, Xa, Ea, Xb, Eb: material-specific coefficients, Q : Calorific value until arbitrary time, Qo: total calorific value until the end of reaction, dQ / dt: exothermic rate, η: viscosity, η ₀ : initial viscosity, t: hour, t ₀ : gelation time, T: temperature, a, b , d, e, f, g: material constants.

Next, in boundary condition and molding condition input step 1004, a display prompting the operator to input the pressure applied to the semiconductor integrated circuit (IC) 3 and the upper portion of the electrode 4 is performed, and the data is input from the input device. Receive. Here, the semiconductor integrated circuit (IC) 3 and the electrode from the pressure applied to the upper portion of the semiconductor integrated circuit (IC) 3 and the electrode 4 received and the area of the upper portion of the semiconductor integrated circuit (IC) 3. The load F applied to the upper part of (4) is computed.

Next, the instruction of analysis start from an operator and the initial time increment are received. In addition, the analysis increases the minute time and calculates the change for each time step, and the time increase represents the interval of the time step.

In step 1005, based on this instruction, continuous equations (1) and Nabi Stokes' equations (2) to (4) and energy conservation equations (5) stored in the recording apparatus are called, and the input is received so far. In addition, the initial time increase, the pressure applied to the semiconductor integrated circuit (IC) 3 and the upper portion of the electrode 4, the density of the resin material, the specific heat, the thermal conductivity, the exothermic (Equation 7) to (11), Substituting the viscosity equations (Equations 12) to (15) calculates the speed, pressure, temperature and viscosity associated with the flow of the resin material 2 and the particles 1 by compression of the electrode. The result of the calculation is stored in the storage device in correspondence with the position of the finite element.

Where P; Density, u; Velocity in the X direction, υ; Velocity in the Y direction, ω; Z direction speed, T; Temperature, P; Pressure, t; time, η; Viscosity, Cp; Constant pressure specific heat, β; Coefficient of volume expansion, λ; The thermal conductivity is shown.

Next, in step 1006, it is determined whether the interval between the electrodes 4 is larger than the diameter of the particles. Here, when the space | interval between the electrodes 4 becomes equal to the diameter (phi) D of the particle | grains 1, in step 1007, the number N of the particle | grains 1 of the connection part inserted between the electrodes 4 is output. .

From the next step 1008, the flow process of the resin material 2 with the deformation | transformation of the particle | grains 1 is calculated. In the first step 1008 that calculates the flow process of the resin material 2 with the deformation of the particles 1, the deformation of the particles 1 is ignored and the resin in the moving direction of the electrode 4 is ignored. After calculating the movement amount (= deformation amount of particle 1) ΔH1 of the material 2, it is determined from the input `` deformation amount when a load is applied to one particle 1 '' to the deformation amount ΔH1 of the particle 1. By this, the load ΔF1 applied to each particle 1 is calculated. Here, an example of the relationship of the "deformation amount when a load is applied per one of particle | grains 1" which was input is shown in FIG.

In the next second step 1009, the load FJ2 applied to the upper portion of the semiconductor integrated circuit (IC) 3 and the electrode 4 is determined per one of the particles 1 obtained in step 1008 from the set value F. The calculation using the difference (FJ2 = FN × ΔF1) obtained by the product of the number of particles N sandwiched between the applied load ΔF1 and the electrode determined in step 1007 is performed (step 1010). After calculating the movement amount DELTA H2 (= strain amount of particle | grains 1) of the resin material 2 by the movement of the electrode 4 when this load FJ2 is applied, the particle | grain 1 is changed by the strain amount DELTA H2 of the particle | grains 1; The load ΔF2 applied to the unit is calculated, and FJ3 = FN × ΔF2 is used as the load condition applied to the semiconductor integrated circuit (IC) 3 in the calculation of the next time step.

In step 1011, the calculations of steps 1008 to 1010 are repeated, and in the M-th step, the deformation amount ΔH (M) of the particles 1 and the load ΔF (M) applied to each particle are calculated, Particles sandwiched between the load ΔF (M) applied to one particle 1 from the load set value F applied to the semiconductor integrated circuit (IC) 3 and the upper portion of the electrode 4 and the electrode obtained in step 1007 (F-NXΔF (M) ≤ 0), or the load F applied to the electrode until the value obtained by the product of the number N becomes 0 or less due to the increase in the viscosity of the resin material (gelling viscosity) The amount of deformation of the particles 1 and the flow behavior of the resin material 2 are calculated until they cannot be moved or the interval between the electrodes 4 becomes zero (step 1012).

In step 1013, the determination procedure of zero convergence that performs the convergence determination of the calculation is made as a procedure to determine the case within the range against the pressure and the predetermined pressure range. If no procedure is taken, the process returns to any one of steps 1001 to 1004. At this time, the operator is prompted for input to determine which step to return to.

In step 1014, proper determination of particle deformation is performed. Here, it is determined whether the amount of deformation of the particles is within the range of the prescribed value, and when outside the prescribed range, the process returns to any one of steps 1001 to 1004. At this time, it is determined in step 1013 that the operator is prompted for input to determine which step to return, and after determining that the particle deformation is appropriate in step 1014, the calculation ends in step 1015.

In addition, although the example of the relationship of the deformation amount when the load per one of particle | grains 1 was applied as an input condition in step 1003 was demonstrated, the deformation amount (or strain rate) when the load per several pieces of particle | grains 1 is applied. It is assumed that the relationship between and the relationship between the stress applied to the particle 1 and the amount of deformation (or strain) can be input. In addition, the exothermic expression is not limited to the formulas (7) to (11), and any function including the reaction rate of the resin material (2) can be used.

In addition, a viscosity formula is not limited to (12)-(15), The arbitrary functions containing the temperature or reaction rate of the resin material (2) can be used. In addition, the procedure determination can use arbitrary determination methods. In addition, not only three-dimensional analysis but also two-dimensional analysis may be performed. In addition, it is assumed that the above calculation can be performed using the finite element method, the finite volume method, or the finite difference method.

Example 2

[Switching from Electrode Speed to Pressure Control]

Next, the process of an analysis program is demonstrated according to the flowchart of FIG. First, in the model shape preparation step 2001, the analysis target model specified by the operator through the input device, that is, the electrode of the analysis target, the shape of the resin material including the initial particles, and the resin material including the particles can flow. The data of the space is read from the storage device 10.

Next, in step 2002 of creating the three-dimensional solid element, the shape of the data read in the model shape creation step 2001 is decomposed into a plurality of specific spaces (finite elements of the three-dimensional solid), and shape data of each finite element is created. .

Next, in the physical property value input step 2003, the density, the thermal conductivity, the specific heat, the exothermic equations (Equation 7) to (Equation 7) to (Equation 7), the viscosity equations (Equation 12) to (Equation 15), which are physical properties of the material to be analyzed, The display prompting the operator to input the arrangement, the density, the diameter of the particle 1, and the deformation amount when a load is applied to each of the particle 1 is performed, and these data are received from the input device.

Next, in the boundary condition and molding condition input step 2004, the moving speed Vd of the semiconductor integrated circuit (IC) 3 and the electrode 4 and the semiconductor integrated circuit (IC) 3 and the electrode 4 are placed on top. The display prompts the operator to input the maximum pressure to be applied, and receives data from the input device.

Here, the semiconductor integrated circuit (IC) 3 is formed from the maximum pressure applied to the upper portion of the semiconductor integrated circuit (IC) 3 and the electrode 4 received and the area of the upper portion of the semiconductor integrated circuit (IC) 3. And the maximum load Fmax applied to the upper portion of the electrode 4.

Next, the instruction of analysis start from an operator and the initial time increment are received. In step 2005, based on this instruction, continuous equations (1) stored in the recording device, Nabi Stokes's equations (2) to (4), and an energy conservation equation (5) are called, and the input is received so far. In addition, the initial time increase, the pressure applied to the semiconductor integrated circuit (IC) 3 and the upper portion of the electrode 4, the density of the resin material, the specific heat, the thermal conductivity, the exothermic (Equation 7) to (11), Substituting the viscosity equations (Equations 12) to (15) calculates the speed, pressure, temperature and viscosity associated with the flow of the resin material 2 and the particles 1 by compression of the electrode. The result of the calculation is stored in the storage device in correspondence with the position of the finite element.

Next, in step 2006, it is judged whether the space | interval between the electrodes 4 is larger than the diameter of a particle | grain. Here, when the space | interval between the electrodes 4 becomes equal to the diameter (phi) D of the particle | grains 1, in step 2007, the number N of the particle | grains 1 of the connection part inserted between the electrodes 4 is output. .

From next step 2008, the flow process of the resin material 2 with deformation of the particle | grains 1 is calculated. In step 2008, when the amount of movement of the resin material 2 in the movement direction of the electrode 4 (= deformation amount of the particle 1) ΔH is calculated, a load is applied to one of the particles 1 input. The load ΔF applied to one particle 1 is calculated from the deformation amount ΔH of the particle 1 from the deformation amount of, and the load FR = N × ΔF applied to the particle 1 is calculated. In addition, the load FJ applied to resin is computed as a product of "the contact area of the electrode 4 to move and the resin material 2", and the "pressure of the resin material 2 of a contact part."

Here, an example of the relationship of the "deformation amount when a load is applied per one of particle | grains 1" which was input is shown in FIG. Here, whether the maximum load Fmax applied to the upper portion of the semiconductor integrated circuit (IC) 3 and the electrode 4 in step 2009 is greater than the sum of the load FJ applied to the resin material 2 and the load FR applied to the particles. Is determined (Fmax≥FJ1 + FR1).

Here, when Fmax <FJ1 + FR1, even if the maximum load Fmax is applied, the set moving speed Vd of the electrode 4 cannot be realized. Therefore, as a control method of the movement of the electrode 4, it switches to control when the maximum load Fmax is applied instead of control of the speed Vd.

That is, calculations of steps 1008 to 1011 shown in FIG. 3 are performed to calculate the deformation of the particles 1 and the flow process of the resin material 2.

Here, the load ΔF (M) applied to one particle 1 from the load set value F applied to the upper portion of the semiconductor integrated circuit (IC) 3 and the electrode 4 is sandwiched between the electrode and the electrode obtained in step 1007. When the value determined by the product of the number of particles N losing becomes 0 or less (FN x ΔF (M) ≤ 0), or the load F applied to the electrode is increased by the increase in the viscosity of the resin material (gelling viscosity). The amount of deformation of the particles 1 and the flow behavior of the resin material 2 are calculated until they cannot be moved or until the interval between the electrodes 4 becomes zero.

In addition, in step 2009, when Fmax≥FJ1 + FR1, until the load F applied to an electrode becomes impossible to move an electrode by the rise of the viscosity of a resin material (gelling viscosity), or between electrodes 4 The calculation of step 2008 and the determination of step 2009 are repeated until the interval of 0 becomes zero.

Here, in step 2012, the procedure for the calculation is determined. The procedure for judging the procedure determines the case where the procedure is within the range against the pressure and the predetermined pressure range. If no procedure is taken, the process returns to any one of steps 2001 to 2004. At this time, the operator is prompted for input to determine which step to return to.

In step 2013, appropriate determination of particle deformation is performed. Here, it is determined whether the amount of deformation of the particles is within the range of the prescribed value, and if outside the prescribed range, the process returns to any one of steps 2001 to 2004. At this time, the operator is prompted for input to determine which step to return to.

It is determined in step 2012 that the calculation has been performed, and in step 2013 it is determined that the particle deformation is appropriate, and then the calculation is terminated in step 2014.

In addition, although the example of the relationship of the deformation amount when the load per one of the particles 1 was applied as an input condition in Step 2003 was demonstrated, the deformation amount (or strain rate) when the load per several pieces of the particle 1 is applied. ), And the relationship between the stress applied to the particles 1 and the amount of deformation (or strain) can be input.

In addition, the exothermic expression is not limited to the formulas (7) to (11), and any function including the reaction rate of the resin material (2) can be used. In addition, a viscosity formula is not limited to (12)-(15), The arbitrary functions containing the temperature or reaction rate of the resin material (2) can be used.

In addition, the procedure determination can use arbitrary determination methods. In addition, not only three-dimensional analysis but also two-dimensional analysis may be performed. In addition, it is assumed that the above calculation can be performed using the finite element method, the finite volume method, or the finite difference method.

[Analysis example of pressure control of electrode (one layer resin)]

Here, an example (two-dimensional analysis) of an analysis example is shown in FIG. In the initial state, a resin material 2 comprising conductive particles 1 is provided between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5. . Here, it is assumed that the resin material (2) has an initial temperature of 30 ° C. and uses exothermic formulas (7) to (11) and viscosity formulas (12) to (15). In addition, the values of the constants, densities, thermal conductivity, specific heat values, diameters of the particles (φD), and densities of the exothermic formulas (7) to (11) and the viscosity formulas (12) to (15) Is shown in Table 1.

In addition, the temperature of the semiconductor integrated circuit (IC) 3 is set to be constant (185 ° C.), and the resin material 2 including the particles 1 is moved by applying a pressure of 5 MPa in the direction of the substrate 5. By compressing, the resin material 2 including the particle 1 is made to flow. At this time, the contact of the electrode 4 of the semiconductor integrated circuit (IC) 3 and the resin material 2 causes the temperature of the resin material 2 to change, while generating a viscosity change accompanying the temperature change, The process by which the resin material 2 flows while being compressed with the particles 1 can be calculated.

In addition, when the space | interval of the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the board | substrate 5 becomes smaller than the diameter of the particle | grains 1, particle | grains 1 and an electrode ( The contact of 4) is not calculated. That is, in the analysis, when the particles 1 are in contact with the particles 1 and the electrode 4, the resin material 2 is set by setting the particles 1 to exit the electrode 4 or the like. Only the liquidity is calculated. At this time, the pressure applied from the upper portion of the semiconductor integrated circuit (IC) 3 is not 5 MPa, which is the set value, but the particles 1 are obtained from the load obtained by multiplying the set pressure and the area, as shown in the flowchart of FIG. Use the value obtained by subtracting the load corresponding to the deformation of.

As a result of this calculation, the resin viscosity becomes large and the semiconductor integrated circuit (IC) 3 and the electrode 4 cannot be moved even when a load is applied, and the analysis ends. At this time, the deformation amount of the particle 1 can be calculated | required from the space | interval between electrodes. In addition, strain amount D of particle | grains can be calculated | required by (Equation 6).

Here, D: diameter of particle | grains 1, D1: space | interval of the board | substrate 4 after completion | finish of analysis is shown. In addition, although the case where the movement of the electrode 4 is controlled by the pressure was shown above, this invention is not limited only to this, As shown by the flowchart of FIG. 4, the movement of an electrode from a speed to a pressure is shown. It is also possible to control. In addition, although the heat conduction calculation in particle | grains is not performed here, the heat conduction calculation in particle | grains can also be performed by input of the specific heat of a particle | grain, thermal conductivity, the heat transfer rate of a resin material, and particle | grains.

[Analysis example of pressure control of electrode (two-layer resin)]

6 shows an example of an analysis example (two-dimensional analysis) in which a resin material is divided into two layers.

In an initial state, the resin material of the two-layered structure containing the resin material 11 from which the physical property containing the particle | grains 1 differs in the upper part of the resin material 2 containing the particle | grains 1 which have electroconductivity, It is provided between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the board | substrate 5. Here, it is assumed that the resin material (2) has an initial temperature of 30 ° C. and uses exothermic formulas (7) to (11) and viscosity formulas (12) to (15). In addition, the values of the constants, densities, thermal conductivity, specific heat values, diameters of the particles (φD), and densities of the exothermic formulas (7) to (11) and the viscosity formulas (12) to (15) For the resin material 2 and the particle 1 of the first layer, the values of Table 1 were used, and the values of the resin material 11 and the particle 1 of the second layer were shown in Table 2.

TABLE 1

Here, the temperature of the semiconductor integrated circuit (IC) 3 is set constant (185 ° C.), and is moved by applying a pressure of 5 MPa in the direction of the substrate 5 to compress the resin materials 2 and 11. , The resin materials (2) and (11) containing the particles (1) are made to flow. At this time, the contact between the electrodes 4 of the semiconductor integrated circuit (IC) 3 and the resin materials 2 and 11 changes the temperature of the resin materials 2 and 11, resulting in a change in temperature. It is possible to calculate the process by which the resin materials (2), (11) flow while being compressed with the particles (1) while generating the accompanying viscosity change.

In addition, when the space | interval of the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the board | substrate 5 becomes smaller than the diameter of the particle | grains 1, particle | grains 1 and an electrode ( The contact of 4) is not calculated. That is, in the analysis, when the particles 1 are in contact with the particles 1 and the electrode 4, the resin material 2 is set by setting the particles 1 to exit the electrode 4 or the like. And (11) calculate the fluidity. At this time, the pressure applied from the upper portion of the semiconductor integrated circuit (IC) 3 is not 5 MPa, which is the set value, but the particles 1 are obtained from the load obtained by multiplying the set pressure and the area, as shown in the flowchart of FIG. Use the value obtained by subtracting the load corresponding to the deformation of.

As a result of this calculation, the resin viscosity becomes large, and even if a load is applied, the semiconductor integrated circuit (IC) 3 and the electrode 4 cannot be moved, and the analysis ends. At this time, the deformation amount of the particle 1 can be calculated | required from the space | interval between electrodes. In addition, strain amount D of particle | grains 1 can be calculated | required by (Equation 6).

[Equation 6]

Here, D: diameter of particle | grains 1, D1: space | interval of the board | substrate 4 after completion | finish of analysis is shown. In addition, although the case where the movement of the electrode 4 is controlled by the pressure was shown above, this invention is not limited only to this, As shown by the flowchart of FIG. 4, the movement of an electrode from a speed to a pressure is shown. It is also possible to control. In addition, although the heat conduction calculation in particle | grains is not performed here, the heat conduction calculation in particle | grains can also be performed by input of the specific heat of a particle | grain, thermal conductivity, the heat transfer rate of a resin material, and particle | grains. In addition, although the example of the analysis in which the particle | grains 1 are contained in the resin material 11 of the abnormal day was shown above, this invention is not limited only to this, The particle | grain 1 is contained in the resin material 11 of the abnormal day. It is also assumed that the analysis can be performed in a state where it is not possible.

Example 3

Prediction of Conductivity (Pressure Control of Electrode Movement)

7 is a flowchart for predicting the conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 of Embodiment 3 of the present invention. Here, the conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 is predicted by the input of the relationship between the particle deformation amount and the conductivity obtained in the flowchart of FIG. 3. First, in the model shape creation step 3001, the analysis target model specified by the operator through the input device, that is, the electrode of the analysis target, the shape of the resin material including the initial particles, and the resin material including the particles can flow. The data of the space is read from the storage device 10.

Next, in step 3002 of three-dimensional solid element creation, the shape of the data read in model shape creation step 1001 is decomposed into a plurality of specific spaces (finite elements of three-dimensional solids), and shape data of each finite element is created. .

Next, in the physical property value input step 3003, the density, the thermal conductivity, the specific heat, the exothermic type (Equation 7) to (Equation 7) to (Equation 7), the viscosity equations (Equation 12) to (Equation 15), which are the physical property values of the material to be analyzed, The display prompting the operator to input the arrangement, the density, the diameter of the particle 1, and the deformation amount when a load is applied to each of the particle 1 is performed, and these data are received from the input device.

Next, in the boundary condition and molding condition input step 3004, a display prompting the operator to input the pressure applied to the semiconductor integrated circuit (IC) 3 and the upper portion of the electrode 4 is performed, and data is input from the input device. Accept. Here, the semiconductor integrated circuit (IC) 3 and the electrode from the pressure applied to the upper portion of the semiconductor integrated circuit (IC) 3 and the electrode 4 received and the area of the upper portion of the semiconductor integrated circuit (IC) 3. The load F applied to the upper part of (4) is computed.

Next, the instruction of analysis start from an operator and the initial time increment are received. In step 3005, the continuous equations (1) stored in the recording device, the butterfly Stokes equations (2) to (4), and the energy conservation equation (5) are called up based on this instruction, and the input is accepted so far. In addition, the initial time increase, the pressure applied to the semiconductor integrated circuit (IC) 3 and the upper portion of the electrode 4, the density of the resin material, the specific heat, the thermal conductivity, the exothermic (Equation 7) to (11), Substituting the viscosity equations (Equations 12) to (15) calculates the speed, pressure, temperature and viscosity associated with the flow of the resin material 2 and the particles 1 by compression of the electrode. The result of the calculation is stored in the storage device in correspondence with the position of the finite element.

Next, in step 3006, a determination is made as to whether or not the interval between the electrodes 4 is larger than the diameter of the particles. Here, when the space | interval between the electrodes 4 becomes equal to the diameter (phi) D of the particle | grains 1, in step 3007, the number N of the particle | grains 1 of the connection part inserted between the electrodes 4 is output. .

The following steps 1008 to 1015 are calculation methods shown in the flowchart of FIG. 3, and the deformation amount of the particles is output in step 3008. In step 3009, the deformation amount of the arbitrary allowance of the particles 1 and the conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 are input. In addition, electroconductivity is made into the electric current value I when the arbitrary voltage is applied between electrodes. Here, the number N sandwiched between the electrodes 4 of the particles 1 is calculated in step 3007, and the deformation amount of the particles 1 is determined in step 3008.

Here, an example of the relationship between the input "deformation amount of arbitrary allowance of the particle 1 and the electroconductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the board | substrate 5" is shown in FIG. Indicated. In addition, as the representative value of arbitrary numbers of the particle | grains 1 here, the case of N1, N2, N3 is shown, In step 3007, the number N of the particle | grains 1 of the connection part inserted between the electrodes 4 is N1. In the case of other than N2 and N3, the value can be obtained by interpolation or extrapolation.

Here, in step 3010, the electroconductivity per particle is calculated from the deformation amount of the particle 1 obtained in step 3008, and the semiconductor integrated circuit is calculated from the electroconductivity per particle and the number of particles between the electrode 4 obtained in step 3007. (IC) The conductivity between the electrode 4 of the substrate 3 and the electrode 4 of the substrate 5 is calculated.

Next, a calculation procedure is determined in step 3011. The procedure for judging the procedure determines the case where the procedure is within the range against the pressure and the predetermined pressure range. In the case of no procedure, the process returns to any one of steps 3001 to 3004. At this time, the operator is prompted for input to determine which step to return to.

In step 3012, proper determination of conductivity is performed. Here, it is determined whether the conductivity is within the range of the prescribed value, and when it is outside the prescribed range, the process returns to any one of steps 3001 to 3004. At this time, the operator is prompted for input to determine which step to return to.

It is determined in step 3011 that the calculation has been performed, and after determining that the particle deformation is appropriate in step 3012, the calculation ends in step 3013. In addition, "the amount of deformation of the arbitrary allowance of the particle | grains 1 and the electroconductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the board | substrate 5" input in step 3009 is "particle ( The contact area between the particle 1 and the electrode 4 and the semiconductor integrated circuit (IC) 3 obtained from the relationship between the deformation amount of the arbitrary allowance of 1) and the contact area between the particle 1 and the electrode 4. Conductivity between the electrode 4 and the electrode 4 of the substrate 5 can be input. In addition, although electroconductivity was made into the electric current value at the time of applying arbitrary voltage between electrodes, this invention is not limited only to this, The resistance value between electrodes, etc. can be used.

Example 4

Prediction of Conductivity (Speed of Electrode Movement to Pressure Control)

Fig. 8 shows a flowchart for predicting the conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 of Embodiment 4 of the present invention. Here, the conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 is predicted by the input of the relationship between the particle deformation amount and the conductivity obtained in the flowchart of FIG. 4.

First, in the model shape creation step 4001, the analysis target model specified by the operator via the input device, that is, the electrode of the analysis target, the shape of the resin material including the initial particles, and the resin material including the particles can flow. The data of the space is read from the storage device 10.

Next, in step 4002 of the three-dimensional solid element creation, the shape of the data read in the model shape creation step 4001 is decomposed into a plurality of specific spaces (finite elements of the three-dimensional solid), and shape data of each finite element is created. .

Next, in the physical property value input step 4003, the density, the thermal conductivity, the specific heat, the exothermic type (Equation 7) to (Equation 7) to (Equation 7), the viscosity equations (Equation 12) to (Equation 15), which are the physical property values of the material to be analyzed The display prompts the operator to input the density of the particle, the diameter, and the amount of deformation when a load is applied to one of the particles 1, and receives these data from the input device.

Next, in the boundary condition and molding condition input step 4004, the moving speed Vd of the semiconductor integrated circuit (IC) 3 and the electrode 4 and the upper portion of the semiconductor integrated circuit (IC) 3 and the electrode 4 are shown. The display prompts the operator to input the maximum pressure to be applied, and receives data from the input device. Here, the semiconductor integrated circuit (IC) 3 is formed from the maximum pressure applied to the upper portion of the semiconductor integrated circuit (IC) 3 and the electrode 4 received and the area of the upper portion of the semiconductor integrated circuit (IC) 3. And the maximum load Fmax applied to the upper portion of the electrode 4.

Next, the instruction of analysis start from an operator and the initial time increment are received. In step 4005, based on this instruction, continuous equations (1) stored in the recording device, Nabi Stokes' equations (2) to (4), and an energy conservation equation (5) are called, and the input is received until now. In addition, the initial time increase, the pressure applied to the semiconductor integrated circuit (IC) (3) and the upper portion of the electrode (4), the density of the resin material, the specific heat, the thermal conductivity, the heating type (1), the viscosity formula (2) by substituting The velocity, pressure, temperature and viscosity accompanying the flow of the resin material 2 and the particles 1 by the compression of the electrode are calculated. The result of the calculation is stored in the storage device in correspondence with the position of the finite element.

Next, in step 4006, it is judged whether the space | interval between the electrodes 4 is larger than the diameter of a particle | grain. Here, when the space | interval between the electrodes 4 becomes equal to the diameter (phi) D of the particle | grains 1, in step 4007, the number N of the particle | grains 1 of the connection part inserted between the electrodes 4 is output. .

Steps 2008 to 2014 are calculation methods shown in the flowchart of FIG. 4, and the deformation amount of the particles is output in step 4008. In step 4009, the deformation amount of the arbitrary allowance of the particles 1 and the conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 are input. In addition, electroconductivity is made into the electric current value I when the arbitrary voltage is applied between electrodes. Here, the number N sandwiched between the electrodes 4 of the particles 1 is calculated in step 4007, and the deformation amount of the particles 1 is determined in step 4008. Here, an example of the relationship between the input "deformation amount of arbitrary allowance of the particle 1 and the electroconductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the board | substrate 5" is shown in FIG. Indicated. In addition, as the representative value of arbitrary numbers of the particle | grains 1 here, the case of N1, N2, N3 is shown, In step 4007, the number N of the particle | grains 1 of the connection part inserted between the electrodes 4 is N1. In the case of other than N2 and N3, the value can be obtained by interpolation or extrapolation.

Here, in step 4010, the conductivity per particle is calculated from the deformation amount of the particle 1 obtained in step 4008, and from the conductivity between the particle and the number of particles between the electrode 4 obtained in step 4007, the semiconductor integrated circuit ( IC) The conductivity between the electrode 4 of the 3 and the electrode 4 of the substrate 5 is calculated.

Next, a calculation procedure is determined in step 4011. The procedure for judging the procedure determines the case where the procedure is within the range against the pressure and the predetermined pressure range. In the case of no procedure, the process returns to any one of steps 4001 to 4004. At this time, the operator is prompted for input to determine which step to return to.

In step 4012, the conductivity is appropriately determined. Here, it is determined whether the conductivity is within the range of the prescribed value, and when outside the prescribed range, the process returns to any one of steps 4001 to 4004. At this time, the operator is prompted for input to determine which step to return to.

It is determined in step 4011 that the calculation has been performed, and after determining that the particle deformation is appropriate in step 4012, the calculation ends in step 4013.

In addition, "the amount of deformation of the arbitrary allowance of the particle | grains 1 and the electroconductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the board | substrate 5" input in step 4009 is "particle ( The contact area between the particle 1 and the electrode 4 and the semiconductor integrated circuit (IC) 3 obtained from the relationship between the deformation amount of the arbitrary allowance of 1) and the contact area between the particle 1 and the electrode 4. Conductivity between the electrode 4 and the electrode 4 of the substrate 5 can be input. In addition, although electroconductivity was made into the electric current value at the time of applying arbitrary voltage between electrodes, this invention is not limited only to this, The resistance value between electrodes, etc. can be used.

Example 5

[Pressure Control of Moving Electrode]

First, the shaping | molding process used as an analysis object is demonstrated using FIG. In the initial state (1-a), the resin material 2 including the conductive particles 1 is disposed between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5. Installed in In the molding step, the semiconductor integrated circuit (IC) 3 to which the heat is applied is moved in the direction of the substrate 5 to compress the resin material 2 including the particles 1 to contain the particles 1. The resin material 2 flows.

At this time, the contact of the electrode 4 of the semiconductor integrated circuit (IC) 3 and the resin material 2 causes the temperature of the resin material 2 to change, while generating a viscosity change accompanying the temperature change, The resin material 2 flows while being compressed with the particles 1. In addition, when the space | interval of the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the board | substrate 5 becomes smaller than the diameter of the particle | grains 1, the particle | grains interposed between the electrodes 4 ( 1) is compressed while deforming.

When the movement of the semiconductor integrated circuit (IC) 3 is completed (1-b), the semiconductor integrated circuit (IC) 3 and the substrate are moved by the conductivity of the particles 1 sandwiched between the electrodes 4. It is possible to transmit the electrical signal between (5). Here, the contact area of the particle 1 and the electrode 4 is determined by the deformation amount of the particle 1, and the conductivity between the semiconductor integrated circuit (IC) 3 and the substrate 5 is determined by this contact area. do.

In addition, conductivity is evaluated by the current flowing when a constant voltage is applied between the electrodes 4. Here, the amount of deformation of the particles 1 is the ability of the device to apply a load from the upper portion of the semiconductor integrated circuit (IC) 3, the amount of deformation of the particles 1 when the load is applied, the amount of the particles 1 sandwiched between the electrodes It is determined by the number and the viscosity change of the resin material (2).

[Configuration of Analysis System]

Next, the analysis system used in order to predict the flow process of the resin material 2 accompanying particle | grain 1 deformation | transformation is demonstrated. The analysis system is a hardware configuration shown in FIG. 12 and functions by executing software having the flows of FIGS. 13, 14 and 17 described later.

Specifically, a calculation device 7 including a calculation device 6, a recording device 10 (hard disk, MO, etc.), a LAN 8 connecting these two calculation devices, and a calculation device 7 are provided. The display apparatus 9 provided is provided. Moreover, it can also be comprised so that the CAD data created with the calculation device 6 may be transmitted to the calculation device 7 via LAN8. The CAD data transferred to the calculation device 7 may be recorded and used on the recording device 10 (hard disk, MO, etc.) of the calculation device 7.

The calculation device 7 executes calculation in accordance with the flowcharts shown in Figs. 13, 4, 7, 8, records the result in the recording device 10, and then displays the result in the display device 9. Although not shown, the calculation devices 6 and 7 are naturally provided with input devices such as a keyboard and a mouse.

[Flowchart]

Next, the processing of the analysis program will be described according to the flowchart of FIG. 13. First, in the model shape creation step 1001, the analysis target model specified by the operator through the input device, that is, the electrode of the analysis target, the shape of the resin material including the initial particles, and the resin material including the particles can flow. The data of the space is read from the storage device 10.

Next, in step 1002 of the three-dimensional solid element creation, the shape of the data read in the model shape creation step 1001 is decomposed into a plurality of specific spaces (finite elements of the three-dimensional solid), and shape data of each finite element is created. .

Next, in the physical property value input step 1003, the density, the thermal conductivity, the specific heat, the exothermic equation (Equation 7) to (Equation 11), the viscosity equations (Equation 12) to (Equation 15), which are physical properties of the material to be analyzed The display prompting the operator to input the arrangement, the density, the diameter of the particle 1, and the deformation amount when a load is applied to each of the particle 1 is performed, and these data are received from the input device. In addition, A: reaction rate, t: time, T: temperature, dA / dt: reaction rate, X1, X2: coefficients as a function of temperature, N, M, Xa, Ea, Xb, Eb: material-specific coefficients, Q : Calorific value until arbitrary time, Qo: total calorific value until the end of reaction, dQ / dt: exothermic rate, η: viscosity, η ₀ : initial viscosity, t: hour, t _O : gelation time, T: temperature, a, b , d, e, f, g: material constants.

[Equation 1]

[Equation 2]

[Equation 3]

[Equation 4]

[Equation 5]

[Equation 6]

[Equation 7]

[Equation 8]

[Equation 9]

Next, in boundary condition and molding condition input step 1004, a display prompting the operator to input the pressure applied to the semiconductor integrated circuit (IC) 3 and the upper portion of the electrode 4 is performed, and the data is input from the input device. Receive. Here, the semiconductor integrated circuit (IC) 3 and the electrode from the pressure applied to the upper portion of the semiconductor integrated circuit (IC) 3 and the electrode 4 received and the area of the upper portion of the semiconductor integrated circuit (IC) 3. The load F applied to the upper part of (4) is computed.

Next, the instruction of an analysis start from an operator, the initial time increment, and the analysis end time tend are received. In addition, the analysis calculates the change for each time step by increasing the minute time, and the time increase represents the interval of the time step.

In step 1005, based on this instruction, continuous equations (1) and Nabi Stokes' equations (2) to (4) and energy conservation equations (5) stored in the recording apparatus are called, and the input is received so far. In addition, the initial time increase, the pressure applied to the semiconductor integrated circuit (IC) 3 and the upper portion of the electrode 4, the density of the resin material, the specific heat, the thermal conductivity, the exothermic (Equation 7) to (11), Substituting the viscosity equations (Equations 12) to (15) calculates the speed, pressure, temperature and viscosity associated with the flow of the resin material 2 and the particles 1 by compression of the electrode. The result of the calculation is stored in the storage device in correspondence with the position of the finite element.

Where P; Density, u; Velocity in the X direction, υ; velocity in y direction, ω; Z direction speed, T; Temperature, P; Pressure, t; time, η; Viscosity, Cp; Constant pressure specific heat, β; Coefficient of volume expansion, λ; The thermal conductivity is shown.

[Equation 10]

[Equation 11]

[Equation 12]

[Equation 13]

[Equation 14]

Next, in step 1006, a determination is made as to whether the time in the analysis is shorter than the set analysis end time tend, and when the determination is no, the analysis is terminated through a procedure for determining the calculation and the like, and when the determination is yes, The determination proceeds to step 1007.

In step 1007, it is determined whether the interval between the electrodes 4 is larger than the diameter of the particles. Here, when the space | interval between the electrodes 4 becomes equal to the diameter (phi) D of the particle | grains 1, in step 1008, the number N of the particle | grains 1 of the connection part inserted between the electrodes 4 is output. .

From the next step 1009, the flow process of the resin material 2 with the deformation of the particles 1 is calculated. In the first step 1009 of calculating the flow process of the resin material 2 with the deformation of the particles 1, the deformation of the particles 1 is ignored and the resin in the moving direction of the electrode 4 is ignored. After calculating the movement amount (= deformation amount of particle 1) ΔH1 of the material 2, it is determined from the input `` deformation amount when a load is applied to one particle 1 '' to the deformation amount ΔH1 of the particle 1. By this, the load ΔF1 applied to each particle 1 is calculated. Here, an example of the relationship of the "deformation amount when a load is applied per one of particle | grains 1 which considered temperature change" was shown in FIG. Here, T1, T2, and T3 represent temperature conditions, and let T1> T2> T3.

In the next second step 1010, the load FJ2 applied to the upper portion of the semiconductor integrated circuit (IC) 3 and the electrode 4 is applied to one of the particles 1 obtained in step 1009 from the set value F. Calculation using the difference (FJ2 = FN × ΔF1) obtained by the product of the load ΔF1 losing and the number of particles N sandwiched between the electrodes obtained in step 1008 is performed (step 1011).

After calculating the movement amount DELTA H2 (= strain amount of particle | grains 1) of the resin material 2 by the movement of the electrode 4 when this load FJ2 is applied, the particle | grain 1 is changed by the strain amount DELTA H2 of the particle | grains 1; The load ΔF2 applied to the unit is calculated, and FJ3 = FN × ΔF2 is used as the load condition applied to the semiconductor integrated circuit (IC) 3 in the calculation of the next time step.

In step 1012, the calculations in steps 1009 to 1011 are repeated, and in the M-th step, the deformation amount ΔH (M) of the particles 1 and the load ΔF (M) applied to each particle are calculated, The amount of deformation of the particles 1 and the flow behavior of the resin material 2 are calculated (step 1012).

In step 1013, it is determined whether the interval between the electrodes 4 is larger than zero or the time in the analysis is shorter than the set analysis end time tend, and when the determination is no, the analysis is performed through the procedure of determining the calculation or the like. If the determination is YES, the flow proceeds to the determination of step 1014.

In step 1014, the load ΔF (M) applied per one particle 1 from the load set value F applied to the upper portion of the semiconductor integrated circuit (IC) 3 and the electrode 4 and the electrode obtained in step 1008. It is determined whether the value obtained by subtracting the value obtained by the product of the particle number N sandwiched between is 0 or less (FN × ΔF (M) ≦ 0). If the determination is no, the calculation is repeated in step 1012. If the determination is yes, then in step 1015, the resin temperature is calculated using the energy equation 5 in the state where the movement speed of the electrode is zero.

Next, a determination is made as to whether the time in the analysis in step 1016 is shorter than the set analysis end time tend, and when the determination is YES, the repetition calculation in step 1012 is performed.

Here, as shown in FIG. 18, when the relationship between the compressive load and the particle deformation amount input in step 1004 uses the physical properties in consideration of temperature dependence, even if the same particle deformation amount ΔH is caused by the increase in the resin temperature calculated in step 1015d. Since the compressive load ΔF (M) becomes small, in step 1014, when the determination of F-NXΔF (M) ≦ 0 becomes no, the movement speed of the electrode in step 1012 is calculated to be nonzero. Is done.

In addition, the temperature shown in FIG. 18 can use the resin temperature of the arbitrary place calculated | required by analysis. For example, temperatures, such as the average value of the resin temperature between the electrodes 4 computed by the calculation of the flow process of 1012, the resin temperature of the particle 1 vicinity, etc. can be used.

Here, when the determination in step 1016 is no,

In step 1017, the procedure for the calculation is determined. The procedure for judging the procedure determines the case where the procedure is within the range against the pressure and the predetermined pressure range. If no procedure is taken, the process returns to any one of steps 1001 to 1004. At this time, the operator is prompted for input to determine which step to return to.

In step 1018, appropriate determination of particle deformation is performed. Here, it is determined whether the amount of deformation of the particles is within the range of the prescribed value, and when outside the prescribed range, the process returns to any one of steps 1001 to 1004. At this time, it is determined in step 1017 that the operator is prompted for input to determine which step to return, and after determining that the particle deformation is appropriate in step 1018, the calculation ends in step 1019.

In addition, although the example of the relationship of the deformation amount when the load per one of the particles 1 was applied as an input condition in step 1003 was demonstrated, the deformation amount (or strain rate) when the load per several pieces of the particle 1 is applied. ), And the relationship between the stress applied to the particles 1 and the amount of deformation (or strain) can be input. In addition, the exothermic expression is not limited to the formulas (7) to (11), and any function including the reaction rate of the resin material (2) can be used.

In addition, a viscosity formula is not limited to (12)-(15), The arbitrary functions containing the temperature or reaction rate of the resin material (2) can be used. In addition, the procedure determination can use arbitrary determination methods. In addition, not only three-dimensional analysis but also two-dimensional analysis may be performed. In addition, it is assumed that the above calculation can be performed using the finite element method, the finite volume method, or the finite difference method.

Example 6

[Switching from Electrode Speed to Pressure Control]

Next, the processing of the analysis program will be described according to the flowchart of FIG. First, in the model shape preparation step 2001, the analysis target model specified by the operator through the input device, that is, the electrode of the analysis target, the shape of the resin material including the initial particles, and the resin material including the particles can flow. The data of the space is read from the storage device 10.

Next, in step 2002 of creating the three-dimensional solid element, the shape of the data read in the model shape creation step 2001 is decomposed into a plurality of specific spaces (finite elements of the three-dimensional solid), and shape data of each finite element is created. .

Next, in the physical property value input step 2003, the density, the thermal conductivity, the specific heat, the exothermic equations (Equation 7) to (Equation 7) to (Equation 7), the viscosity equations (Equation 12) to (Equation 15), which are physical properties of the material to be analyzed, The display prompting the operator to input the arrangement, the density, the diameter of the particle 1, and the deformation amount when a load is applied to each of the particle 1 is performed, and these data are received from the input device.

Next, in the boundary condition and molding condition input step 2004, the initial moving speed Vd of the semiconductor integrated circuit (IC) 3 and the electrode 4 and the upper portion of the semiconductor integrated circuit (IC) 3 and the electrode 4 are shown. A display is urged to prompt the operator to input the maximum pressure applied to the data, and the data is received from the input device.

Here, the semiconductor integrated circuit (IC) 3 is formed from the maximum pressure applied to the upper portion of the semiconductor integrated circuit (IC) 3 and the electrode 4 received and the area of the upper portion of the semiconductor integrated circuit (IC) 3. And the maximum load Fmax applied to the upper portion of the electrode 4.

Next, the instruction of an analysis start from an operator, the initial time increment, and the analysis end time tend are received. In step 2005, based on this instruction, continuous equations (1) stored in the recording device, Nabi Stokes's equations (2) to (4), and an energy conservation equation (5) are called, and the input is received so far. In addition, the initial time increase, the pressure applied to the semiconductor integrated circuit (IC) 3 and the upper portion of the electrode 4, the density of the resin material, the specific heat, the thermal conductivity, the exothermic (Equation 7) to (11), Substituting the viscosity equations (Equations 12) to (15) calculates the speed, pressure, temperature and viscosity associated with the flow of the resin material 2 and the particles 1 by compression of the electrode. The result of the calculation is stored in the storage device in correspondence with the position of the finite element.

Next, in step 2006, a determination is made as to whether the time in the analysis is shorter than the set analysis end time tend, and when the determination is no, the analysis is terminated through a procedure for determining the calculation, and when the determination is YES, Proceed to step 2007.

In step 2007, the load FJ applied to the resin when the electrode is moved at the initial moving speed Vd input in step 2004 is defined as "the contact area between the moving electrode 4 and the resin material 2" and the "contact part." It calculates as a product of the "pressure of the resin material (2)".

In step 2008, the maximum load Fmax applied to the upper portion of the electrode 4 is compared with the FJ determined in step 2007, and if Fmax> FJ, the calculation is made in which the electrode moves at the initial moving speed Vd input in step 2004 in step 2009. If it is not Fmax> FJ, it switches to pressure control and calculates the movement of the electrode when the maximum load Fmax is applied to the upper part of the electrode 4.

In step 2010, it is determined whether the interval between the electrodes 4 is larger than the diameter of the particles. When the distance between the electrodes 4 is larger than the diameter of the particles, the process returns to step 2005 and the calculation is repeated. When the distance between the electrodes 4 is equal to the diameter φD of the particles 1, FIG. The calculation of steps 1008 to 1016 shown in 13 is performed.

In step 2012, the procedure for the calculation is determined. The procedure for judging the procedure determines the case where the procedure is within the range against the pressure and the predetermined pressure range. If no procedure is taken, the process returns to any one of steps 2001 to 2004. At this time, the operator is prompted for input to determine which step to return to.

In step 2013, appropriate determination of particle deformation is performed. Here, it is determined whether the amount of deformation of the particles is within the range of the prescribed value, and if outside the prescribed range, the process returns to any one of steps 2001 to 2004. At this time, it is determined in step 2012 that the operator is prompted to input and decides which step to return to, and after determining that the particle deformation is appropriate in step 2013, the calculation ends in step 2014.

In addition, although the example of the relationship of the deformation amount when the load per one of the particles 1 was applied as an input condition in Step 2003 was demonstrated, the deformation amount (or strain rate) when the load per several pieces of the particle 1 is applied. ), And the relationship between the stress applied to the particles 1 and the amount of deformation (or strain) can be input.

In addition, the exothermic expression is not limited to the formulas (7) to (11), and any function including the reaction rate of the resin material (2) can be used. In addition, a viscosity formula is not limited to (12)-(15), The arbitrary functions containing the temperature or reaction rate of the resin material (2) can be used.

In addition, the procedure determination can use arbitrary determination methods. In addition, not only three-dimensional analysis but also two-dimensional analysis may be performed. In addition, it is assumed that the above calculation can be performed using the finite element method, the finite volume method, or the finite difference method.

[Analysis example of pressure control of electrode (one layer resin)]

Here, an example (two-dimensional analysis) of an analysis example is shown in FIG. In the initial state, a resin material 2 comprising conductive particles 1 is provided between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5. . Here, it is assumed that the resin material (2) has an initial temperature of 30 ° C. and uses exothermic formulas (7) to (11) and viscosity formulas (12) to (15). In addition, the values of the constants, densities, thermal conductivity, specific heat values, diameters of the particles (φD), and densities of the exothermic formulas (7) to (11) and the viscosity formulas (12) to (15) Is shown in Table 1.

TABLE 1

In addition, the temperature of the semiconductor integrated circuit (IC) 3 is set to be constant (185 ° C.), and the resin material 2 including the particles 1 is moved by applying a pressure of 5 MPa in the direction of the substrate 5. By compressing, the resin material 2 including the particle 1 is made to flow. At this time, the contact of the electrode 4 of the semiconductor integrated circuit (IC) 3 and the resin material 2 causes the temperature of the resin material 2 to change, while generating a viscosity change accompanying the temperature change, The process by which the resin material 2 flows while being compressed with the particles 1 can be calculated.

In addition, when the space | interval of the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the board | substrate 5 becomes smaller than the diameter of the particle | grains 1, particle | grains 1 and an electrode ( The contact of 4) is not calculated. That is, in the analysis, when the particles 1 are in contact with the particles 1 and the electrode 4, the resin material 2 is set by setting the particles 1 to exit the electrode 4 or the like. Only the liquidity is calculated.

At this time, the pressure applied from the upper portion of the semiconductor integrated circuit (IC) 3 is not 5 MPa, which is a set value, but as shown in the flowchart of FIG. 13, the relationship between the deformation amount of the particles and the compressive load shown in FIG. The value obtained by subtracting the load obtained from the number of particles inserted between the electrodes from the load obtained by the product of the set pressure and the area is used.

As a result of this calculation, when the load applied from the upper part of the electrode and the compressive load required to deform the particles become equal, the movement speed of the electrode becomes zero, and the temperature calculation of the resin not involving electrode movement is performed. Here, when the resin temperature is high, since the compressive load required to deform the particles is reduced as shown in Fig. 18, calculation with the electrode movement is performed again.

Here, the temperature shown in FIG. 18 can use the temperature of arbitrary place calculated | required by analysis. For example, temperature, such as the average value of the resin temperature between the electrodes 4 calculated by the calculation of the flow process of 1012 shown in FIG. 13, the resin temperature of the particle 1 vicinity, etc. can be used. In addition, although the thermal conductivity calculation in particle | grains is not performed here, thermal conductivity calculation in particle | grains can also be calculated by input of the specific heat of a particle | grain, thermal conductivity, the heat transfer rate of resin material and particle | grains, and the temperature of the arbitrary position of the particle | grains calculated | required by this heat transfer calculation. May be used as the temperature shown in FIG. 18.

Thereafter, the analysis ends at the set analysis end time. At this time, the deformation amount of the particle 1 can be calculated | required from the space | interval between electrodes. In addition, strain amount D of particle | grains can be calculated | required by (Equation 6).

[Equation 15]

Here, D: diameter of particle | grains 1, D1: space | interval of the board | substrate 4 after completion | finish of analysis is shown. In addition, although the case where the movement of the electrode 4 is controlled by the pressure was shown above, this invention is not limited only to this, As shown by the flowchart of FIG. 14, the movement of an electrode from a speed to a pressure is shown. It is also possible to control.

[Analysis example of pressure control of electrode (two-layer resin)]

Here, an example of the analysis example (two-dimensional analysis) by which resin material is divided into two layers is shown in FIG.

In the initial state, the resin material of the two-layer structure including the resin material 11 having different physical properties including the particles 1 on the upper portion of the resin material 2 containing the conductive particles 1 And an electrode 4 of the semiconductor integrated circuit (IC) 3 and an electrode 4 of the substrate 5. Here, it is assumed that the resin material (2) has an initial temperature of 30 ° C. and uses exothermic formulas (7) to (11) and viscosity formulas (12) to (15). In addition, the values of the constants, densities, thermal conductivity, specific heat values, diameters of the particles (φD), and densities of the exothermic formulas (7) to (11) and the viscosity formulas (12) to (15) For the resin material 2 and the particle 1 of the first layer, the values of Table 1 were used, and the values of the resin material 11 and the particle 1 of the second layer were shown in Table 2.

TABLE 1

TABLE 2

Here, the temperature of the semiconductor integrated circuit (IC) 3 is set constant (185 ° C.), and is moved by applying a pressure of 5 MPa in the direction of the substrate 5 to compress the resin materials 2 and 11. , The resin materials (2) and (11) containing the particles (1) are made to flow. At this time, the contact between the electrodes 4 of the semiconductor integrated circuit (IC) 3 and the resin materials 2 and 11 changes the temperature of the resin materials 2 and 11, resulting in a change in temperature. It is possible to calculate the process by which the resin materials (2), (11) flow while being compressed with the particles (1) while generating the accompanying viscosity change.

In addition, when the space | interval of the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the board | substrate 5 becomes smaller than the diameter of the particle | grains 1, particle | grains 1 and an electrode ( The contact of 4) is not calculated. That is, in the analysis, when the particles 1 are in contact with the particles 1 and the electrode 4, the resin material 2 is set by setting the particles 1 to exit the electrode 4 or the like. And (11) calculate the fluidity.

At this time, the pressure applied from the upper portion of the semiconductor integrated circuit (IC) 3 is not 5 MPa, which is a set value, but as shown in the flowchart of FIG. 13, the relationship between the deformation amount of the particles and the compressive load shown in FIG. The value obtained by subtracting the load obtained from the number of particles inserted between the electrodes from the load obtained by the product of the set pressure and the area is used.

As a result of this calculation, when the load applied from the upper part of the electrode and the compressive load required to deform the particles become equal, the movement speed of the electrode becomes zero, and the temperature calculation of the resin not involving electrode movement is performed. Here, when the resin temperature is high, since the compressive load required to deform the particles is reduced as shown in Fig. 18, calculation with the electrode movement is performed again.

Here, the temperature shown in FIG. 18 can use the temperature of arbitrary place calculated | required by analysis. For example, temperatures, such as the average value of the resin temperature between the electrodes 4 computed by the calculation of the flow process of 1012, the resin temperature of the particle 1 vicinity, etc. can be used. In addition, although the thermal conductivity calculation in particle | grains is not performed here, thermal conductivity calculation in particle | grains can also be calculated by input of the specific heat of a particle | grain, thermal conductivity, the heat transfer rate of resin material and particle | grains, and the temperature of the arbitrary position of the particle | grains calculated | required by this heat transfer calculation. May be used as the temperature shown in FIG. 18.

Thereafter, the analysis ends at the set analysis end time. At this time, the deformation amount of the particle 1 can be calculated | required from the space | interval between electrodes. In addition, strain amount D of particle | grains can be calculated | required by (Equation 6).

[Equation 6]

Here, D: diameter of particle | grains 1, D1: space | interval of the board | substrate 4 after completion | finish of analysis is shown. In addition, although the case where the movement of the electrode 4 is controlled by the pressure was shown above, this invention is not limited only to this, As shown by the flowchart of FIG. 14, the movement of an electrode from a speed to a pressure is shown. It is also possible to control. In addition, although the heat conduction calculation in particle | grains is not performed here, the heat conduction calculation in particle | grains can also be performed by input of the specific heat of a particle | grain, thermal conductivity, the heat transfer rate of a resin material, and particle | grains.

In addition, although the example of the analysis in which the particle | grains 1 are contained in the resin material 11 of the abnormal day was shown above, this invention is not limited only to this, The particle | grain 1 is contained in the resin material 11 of the abnormal day. It is also assumed that the analysis can be performed in a state where it is not possible.

Example 7

[Predicting Conductivity, Main Force of Particle Coordinates (Control of Pressure of Electrode Movement)]

FIG. 17 is a flowchart for predicting the conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 of the seventh embodiment of the present invention.

Here, the conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 is predicted by the input of the relationship between the particle deformation amount and the conductivity obtained by the flowchart of FIG. 13. First, in the model shape creation step 3001, the analysis target model specified by the operator through the input device, that is, the electrode of the analysis target, the shape of the resin material including the initial particles, and the resin material including the particles can flow. The data of the space is read from the storage device 10.

Next, in step 3002 of three-dimensional solid element creation, the shape of the data read in model shape creation step 1001 is decomposed into a plurality of specific spaces (finite elements of three-dimensional solids), and shape data of each finite element is created. .

Next, in the physical property value input step 3003, the density, the thermal conductivity, the specific heat, the exothermic type (Equation 7) to (Equation 7) to (Equation 7), the viscosity equations (Equation 12) to (Equation 15), which are the physical property values of the material to be analyzed, Arrangement, density, diameter of the particle 1, the amount of deformation when a load is applied to one of the particles 1, the amount of deformation of any allowance of the particles 1 and the electrode 4 of the semiconductor integrated circuit (IC) 3 The display prompts the operator to input the conductivity between the electrode 4 and the electrode 4 of the substrate 5, and receives these data from the input device.

Next, in boundary condition and molding condition input step 3004, a display prompting the operator to input the pressure applied to the semiconductor integrated circuit (IC) 3 and the upper portion of the electrode 4 is performed, and the data is input from the input device. Receive. Here, the semiconductor integrated circuit (IC) 3 and the electrode from the pressure applied to the upper portion of the semiconductor integrated circuit (IC) 3 and the electrode 4 received and the area of the upper portion of the semiconductor integrated circuit (IC) 3. The load F applied to the upper part of (4) is computed.

Next, the instruction of an analysis start from an operator, the initial time increment, and the analysis end time tend are received. In step 3005, the continuous equations (1) stored in the recording device, the butterfly Stokes equations (2) to (4), and the energy conservation equation (5) are called up based on this instruction, and the input is accepted so far. In addition, the initial time increase, the pressure applied to the semiconductor integrated circuit (IC) 3 and the upper portion of the electrode 4, the density of the resin material, the specific heat, the thermal conductivity, the exothermic (Equation 7) to (11), Substituting the viscosity equations (Equations 12) to (15) calculates the speed, pressure, temperature and viscosity associated with the flow of the resin material 2 and the particles 1 by compression of the electrode. The result of the calculation is stored in the storage device in correspondence with the position of the finite element.

Next, in step 3006, a determination is made as to whether the time in the analysis is shorter than the set analysis end time tend, and when the determination is no, the analysis is terminated through the procedure of determining the calculation, and when the determination is yes, Proceed to the determination of 3007.

In step 3007, it is determined whether the interval between the electrodes 4 is larger than the diameter of the particles. When the distance between the electrodes 4 is larger than the diameter of the particles, the process returns to step 3005 and the calculation is repeated. When the distance between the electrodes 4 is equal to the diameter φD of the particles 1, the step is performed. In 3008, the number N of the particles 1 of the connecting portion sandwiched between the electrodes 4 or the coordinates of the particles 1 of the connecting portion sandwiched between the electrodes 4 are output. Next, calculations of steps 1008 to 1016 shown in FIG. 13 are performed.

Next, the deformation | transformation amount of particle | grains and the moving speed of the electrode 4 calculated | required by the fluid analysis are output in step 3010. In step 3011, the deformation amount of the particles 1 output in step 3010, the deformation amount of the arbitrary allowance of the particles 1 input in step 3003, the electrode 4 and the substrate 5 of the semiconductor integrated circuit (IC) 3 The conductivity per one particle is calculated from the conductivity between the electrodes 4 of the electrodes), and the electrode of the semiconductor integrated circuit (IC) 3 is obtained from the conductivity per one particle and the number of particles between the electrodes 4 obtained in step 3008. The conductivity between (4) and the electrode 4 of the board | substrate 5 is computed.

In addition, electroconductivity is made into the electric current value I when the arbitrary voltage is applied between electrodes. Here, an example of the relationship between the input "deformation amount of arbitrary allowance of the particle 1 and the electroconductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the board | substrate 5" is shown in FIG. Shown. In addition, as the representative number of arbitrary numbers of the particle | grains 1 here, the case of N1, N2, N3 is shown, In step 3008, the number N of the particle | grains 1 of the connection part inserted between the electrodes 4 is N1, When it is other than N2 and N3, a value can be calculated | required by interpolation and extrapolation.

Here, in step 3012, the procedure for determining the calculation is performed. The procedure for judging the procedure determines the case where the procedure is within the range against the pressure and the predetermined pressure range. In the case of no procedure, the process returns to any one of steps 3001 to 3004. At this time, the operator is prompted for input to determine which step to return to.

In step 3013, appropriate determination of particle deformation is performed. Here, it is determined whether the amount of deformation of the particles is within the range of the prescribed value, and if outside the prescribed range, the process returns to any one of steps 3001 to 3004. At this time, the operator is prompted for input to determine which step to return to.

After it is determined in step 3012 that the calculation has been performed, and in step 3013 it is determined that the particle deformation is appropriate, the calculation is terminated in step 3014. In addition, "the amount of deformation of the arbitrary allowance of the particle | grains 1 and the electroconductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the board | substrate 5" input in step 3003 is "particle ( The contact area between the particle 1 and the electrode 4 and the semiconductor integrated circuit (IC) 3 obtained from the relationship between the deformation amount of the arbitrary allowance of 1) and the contact area between the particle 1 and the electrode 4. Conductivity between the electrode 4 and the electrode 4 of the substrate 5 can be input. In addition, although electroconductivity was made into the electric current value at the time of applying arbitrary voltage between electrodes, this invention is not limited only to this, The resistance value between electrodes, etc. can be used.

Here, the coordinates of the particles 1 sandwiched between the electrodes 4 output in step 3008 and the moving speed of the electrode 4 output in step 3010 can be used as input conditions for structural analysis. In addition, the coordinate of the output particle 1 shall output the arbitrary position of the particle 1, and here it shall output the coordinate of the center of the particle 1.

For structural analysis using input conditions (coordinates of particles 1 sandwiched between electrodes 4 and electrode 4 moving speeds) and physical properties of particles (elastic modulus, density, Poisson's ratio, etc.) output by the calculation of this fluid As a result, as shown in FIG. 20, the deformation | transformation form when the particle | grain 1 in which the coordinate was input is compressed to the board | substrate 5 which made the velocity of the electrode 4 into an input value, and the contact of particle | grains 1 and an electrode is carried out. The area can be found by analysis.

Moreover, electroconductivity can also be computed from the contact area of the particle 1 and electrode computed in FIG. 20 using the relationship of the contact area and electroconductivity of the particle 1 and electrode 4 shown in FIG.

Claims (24)

(1) data of a convex substrate as an analysis target, a shape of a resin material including initial particles, and a space in which a resin material containing particles can flow are acquired from a storage device into a calculation device; (2) decomposing into three-dimensional solid elements based on the data; (3) Input at least the density of the resin material, the thermal conductivity, the specific heat, the viscosity, the external dimensions of the particles, the density, the load-displacement relationship per particle, and the external load F applied to the convex substrate. , (4) The change of the resin temperature is calculated by the contact of the convex substrate and the resin material by arithmetic processing of a continuous equation, a butterfly Stokes equation, and an energy conservation equation based on the three-dimensional solid element. Calculate the flow of resin material is compressed with the particles by the movement of the convex substrate, (5) At the time when the space | interval between the convex-shaped board | substrate after compression becomes equal to the diameter of particle | grains, the output calculation of the number N of particle | grains interposed between the convex-shaped board | substrates, (6) After the time when the gap between the convex substrates after the compression of the above (5) becomes equal to the diameter of the particles, the load applied to the convex substrate is ignored. From the load F input in (3), between the convex-shaped substrate and the load-displacement relationship per particle input in (3) above, and the convex substrate obtained in (5) above. Calculating a process of flowing the resin material and the particles by compressing the resin material containing the particles into the substrate having the convex shape from two directions, using a value obtained by subtracting the load obtained by multiplying by the number N of particles to be inserted into the substrate. The flow analysis method of the resin material which embedded the particle | grains characterized by the above-mentioned. (1) data of a convex substrate as an analysis target, a shape of a resin material including initial particles, and a space in which a resin material containing particles can flow are acquired from a storage device into a calculation device; (2) decomposing into three-dimensional solid elements based on the data; (3) input at least the density of the resin material, the thermal conductivity, the specific heat, the viscosity, the density of the particles, the external dimensions, and the load-displacement relationship per one particle, (4) Input the moving speed Vd of the convex substrate and the maximum load Fmax from the outside applied to the convex substrate, (5) The change of the resin temperature is calculated by the contact of the convex substrate and the resin material by arithmetic processing of the continuous equation, the butterfly Stokes equation and the energy conservation equation based on the three-dimensional solid element, Calculate the flow of the resin material as it is compressed with the particles by the moving speed Vd of the convex substrate, (6) After the time when the gap between the convex substrates after compression becomes equal to the diameter of the particles, the number of particles N sandwiched between the convex substrates is output-calculated, (7) After the time when the gap between the convex substrates after compression of the above (6) becomes equal to the diameter of the particles, the contact between the convex substrate and the particles is ignored, and from the movement amount of the convex substrate After calculating the deformation amount ΔH of the particles, the load ΔF applied to each particle is calculated based on the deformation amount ΔH of the particles from the load-displacement relationship applied to each particle input in the above (4), and the particles Calculate the load (FR = NXΔF) applied to the resin, and the load FJ applied to the resin by the substrate having the moving convex shape, and the resin pressure of the contact area and the portion of the moving convex substrate and the resin. Calculated as the product of (8) If the maximum load Fmax from the outside applied to the input convex substrate is equal to or greater than the sum of the load FJ applied to the resin and the load FR applied to the particles (Fmax ≧ FJ + FR), the substrate having the convex shape If the maximum load Fmax from the outside applied to the substrate with the input convex shape is smaller than the load FJ applied to the resin and the load FR applied to the particles (Fmax <FJ + FR), The boundary condition of the substrate movement with the shape is converted into a load from the outside (maximum load Fmax) applied to the substrate with the convex shape, and the resin material containing particles is compressed into the substrate with the convex shape from two directions. A flow analysis method for a resin material having particles embedded therein, wherein the step of flowing the material and particles is calculated. The method according to claim 1 or 2, wherein the input method of the relationship between the load and the displacement applied to the particles includes the relationship between the load and the displacement applied to any number of particles or the stress applied to any number of particles. The flow analysis method of the resin material which embedded the particle | grains which inputs the relationship of a strain rate. The particle | grains of Claim 1 or 2 which electroconductivity between the convex-shaped board | substrate is output-calculated by inputting the relationship of the particle | grain number of a connection part, strain, and electroconductivity, and particle | grains are electroconductive. Flow analysis method of the embedded resin material. The conductivity between the convex substrates according to claim 1 or 2, wherein the particles are conductive and input the relationship between the number of particles in the connection portion and the contact area of the substrate with the convex shape and the conductivity. The flow analysis method of the resin material which embedded the particle | grains characterized by calculating. The resin material containing particle | grains of Claim 1 or 2 characterized by inputting the exothermic reaction formula of a resin material, the viscosity formula which is a function containing a resin temperature, and outputting the flow process of a resin material and particle | grains. Flow analysis method. The resin material according to claim 1 or 2, wherein the resin material is formed of two or more layers having different physical properties, particles are disposed in one or more layers of resin, and are functions including an exothermic reaction formula of two or more layers of resin and a resin temperature. A flow analysis method for a resin material having particles embedded therein, wherein a viscosity formula is input and a flow process of two or more layers of resins and particles is output. The flow analysis method of the resin material containing particle | grains of Claim 1 or 2 whose convex-shaped board | substrate is a semiconductor integrated circuit provided with an electrode, and a board | substrate provided with an electrode. (1) an input unit for acquiring data of a convex substrate to be analyzed, a shape of a resin material including initial particles, and a space in which a resin material including particles can flow from a storage device to a calculation device; (2) a processing unit which performs decomposition processing into three-dimensional solid elements based on the data, (3) input at least the density of the resin material, the thermal conductivity, the specific heat, the viscosity, the external dimensions of the particles, the density, the load-displacement relationship per particle, and the external load F applied to the convex substrate; Input, (4) The change of the resin temperature is calculated by the contact of the convex substrate and the resin material by arithmetic processing of a continuous equation, a butterfly Stokes equation, and an energy conservation equation based on the three-dimensional solid element. Computation unit for calculating the flow of the resin material is compressed with the particles by the movement of the substrate having a convex shape, (5) an output unit for output-calculating the number N of particles sandwiched between the convex substrates at a time when the gap between the convex substrates after compression becomes equal to the diameter of the particles; (6) After the time when the gap between the convex substrates after the compression of (5) becomes equal to the diameter of the particles, the contact between the convex substrate and the particles is ignored and applied to the convex substrate. From the load F input in said (3), the load-displacement relationship exerted per particle | grains input in said (3) from the clearance gap between board | substrates with a convex shape, and the convex shape calculated | required in said (5) The resin material and the particles are made to flow by compressing the resin material containing the particles from the two directions into the convex substrate from the two directions by using a value obtained by subtracting the load obtained by the product of the number N of particles sandwiched between the substrates. Computation unit calculating the process The flow analysis system of the resin material which embedded the particle | grains characterized by the above-mentioned. (1) an input unit for acquiring data of a convex substrate to be analyzed, a shape of a resin material including initial particles, and a space in which a resin material including particles can flow from a storage device to a calculation device; (2) a processing unit which performs decomposition processing into three-dimensional solid elements based on the data, (3) an input unit for inputting at least the density of the resin material, the thermal conductivity, the specific heat, the viscosity, the density of the particles, the external dimensions, and the load-displacement relationship per one particle, (4) an input unit for inputting a moving speed Vd of a substrate having a convex shape and a maximum load Fmax from the outside applied to the substrate having a convex shape, (5) The change of the resin temperature is calculated by the contact of the convex substrate and the resin material by arithmetic processing of the continuous equation, the butterfly Stokes equation and the energy conservation equation based on the three-dimensional solid element, An operation unit for calculating a process of flowing the resin material together with the particles by the moving speed Vd of the substrate having the convex shape, (6) an output calculation unit that outputs and calculates the number N of particles sandwiched between the convex substrates after a time when the gap between the convex substrates after compression is equal to the diameter of the particles; (7) After the time when the gap between the convex substrates after the compression of (6) becomes equal to the diameter of the particles, the contact direction of the convex substrate and the particles is ignored, ignoring the contact between the convex substrate and the particles. The load applied to each particle by the deformation amount ΔH of the particles from the load-displacement relational expression applied to each particle input in the above (4) after calculating the deformation amount ΔH of the particles from the movement amount of the resin material in ΔF is calculated, the load (FR = NXΔF) applied to the particles is calculated, and the load FJ applied to the resin by the substrate having the moving convex shape is determined between the moving convex substrate and the resin. A calculation unit that calculates the product of the contact area and the resin pressure of the part; (8) If the maximum load Fmax from the outside applied to the input convex substrate is equal to or greater than the sum of the load FJ applied to the resin and the load FR applied to the particles (Fmax≥FJ + FR), the convex shape is present. If the substrate is controlled at the moving speed Vd and the maximum load Fmax from the outside applied to the input convex substrate is smaller than the load FJ applied to the resin and the load FR applied to the particles (Fmax <FJ + FR), By changing the boundary condition of the convex substrate movement to the load from the outside (maximum load Fmax) applied to the convex substrate, compressing the resin material containing the particles from the two directions to the convex substrate, Computation unit for calculating the process of flowing the resin material and particles The flow analysis system of the resin material which embedded the particle | grains characterized by the above-mentioned. (1) data of a convex substrate as an analysis target, a shape of a resin material including initial particles, and a space in which a resin material containing particles can flow are acquired from a storage device into a calculation device; (2) decomposing into three-dimensional solid elements based on the data; (3) Input at least the density of the resin material, the thermal conductivity, the specific heat, the viscosity, the external dimensions of the particles, the density, the load-displacement relationship per particle, and the external load F applied to the convex substrate. , (4) The change of the resin temperature is calculated by the contact of the convex substrate and the resin material by arithmetic processing of a continuous equation, a butterfly Stokes equation, and an energy conservation equation based on the three-dimensional solid element. Calculate the flow of resin material is compressed with the particles by the movement of the convex substrate, (5) At the time when the space | interval between the convex-shaped board | substrate after compression becomes equal to the diameter of particle | grains, the output calculation of the number N of particle | grains interposed between the convex-shaped board | substrates, (6) After the time when the gap between the convex substrates after the compression of the above (5) becomes equal to the diameter of the particles, the load applied to the convex substrate is ignored. From the load F input in (3), between the convex-shaped substrate and the load-displacement relationship per particle input in (3) above, and the convex substrate obtained in (5) above. Using the value obtained by subtracting the load obtained by multiplying by the number N of particles to be inserted into, the process of compressing the resin material containing the particles into a substrate having a convex shape from two directions is included. Flow analysis method of the made resin material. (1) data of a convex substrate as an analysis target, a shape of a resin material including initial particles, and a space in which a resin material containing particles can flow are acquired from a storage device into a calculation device; (2) decomposing into three-dimensional solid elements based on the data; (3) Load-displacement relation considering at least density of resin material, thermal conductivity, specific heat, viscosity, external dimension of particle, density, temperature change per particle, load from outside applied to convex substrate Type F, (4) The change of the resin temperature is calculated by the contact of the convex substrate and the resin material by arithmetic processing of a continuous equation, a butterfly Stokes equation, and an energy conservation equation based on the three-dimensional solid element. Calculate the flow of resin material is compressed with the particles by the movement of the convex substrate, (5) At the time when the space | interval between the convex-shaped board | substrate after compression becomes equal to the diameter of particle | grains, the output calculation of the number N of particle | grains interposed between the convex-shaped board | substrates, (6) After the time when the gap between the convex substrates after the compression of the above (5) becomes equal to the diameter of the particles, the load applied to the convex substrate is ignored. From the load F input in (3), the load-displacement relationship in consideration of the temperature change applied to each particle input in the above (3) from the gap between the convex substrates and the convex shape obtained in the above (5). Using the value obtained by subtracting the load obtained by the product of the number of particles N sandwiched between the substrates with the substrate, and calculating the process of compressing the resin material containing the particles into the substrate having the convex shape from two directions, (7) The load F input in the above (3) is If the load is greater than the load determined by the product of the load-displacement relationship per particle input in the above (3) and the number of particles N sandwiched between the convex substrates obtained in the above (5), Repeating the process of compressing the resin material containing the particles of the above (6) into the convex substrate from two directions, The load F input in the above (3), If it becomes equal to the load determined by the product of the load-displacement relationship per one particle input in the above (3) and the number N of particles sandwiched between the convex substrates obtained in the above (5), The movement speed of the electrode is set to 0, the temperature calculation of the resin material using the energy equation is performed, and the load-displacement relationship applied to each particle input in the above (3) is changed by the temperature rise, The load F input in the above (3) is a relationship between the load-displacement relationship applied to each particle input in the above (3) and the number N of particles sandwiched between the convex substrates obtained in the above (5). If it is greater than the load determined by the product, By repeatedly calculating the process of compressing the resin material containing the particles of the above (6) into the convex substrate from two directions, the step of flowing the resin material and the particles is calculated. Method of flow analysis of resin materials. (1) data of a convex substrate as an analysis target, a shape of a resin material including initial particles, and a space in which a resin material containing particles can flow are acquired from a storage device into a calculation device; (2) decomposing into three-dimensional solid elements based on the data; (3) input the load-displacement relationship considering at least the density of the resin material, the thermal conductivity, the specific heat, the viscosity, the density of the particles, the external dimensions, and the temperature change applied to each particle, (4) Input the moving speed Vd of the convex substrate and the load F from the outside applied to the convex substrate, (5) The change of the resin temperature is calculated by the contact of the convex substrate and the resin material by arithmetic processing of the continuous equation, the butterfly Stokes equation and the energy conservation equation based on the three-dimensional solid element, Calculate the flow of the resin material as it is compressed with the particles by the moving speed Vd of the convex substrate, (6) The load F applied to the resin by the moving convex substrate is calculated as the product of the contact area of the moving convex substrate and the resin and the resin pressure, and the load F input in the above (4). Has a relationship with FJ, If F≥FJ, the electrode calculates a process of moving at the moving speed Vd of the substrate having the convex shape input in the above (4), If F <FJ, the electrode is compressed by the load F input in the above (4) to calculate the moving process, (7) After the time when the gap between the convex substrates after compression becomes equal to the diameter of the particles, the number of particles N sandwiched between the convex substrates is output calculated. (8) After the time when the gap between the convex substrates after compression of the above (7) becomes equal to the diameter of the particles, the load applied to the convex substrate is ignored, ignoring the contact between the electrode and the particles. From the load F input in (4), the load-displacement relationship in consideration of the temperature change applied to each particle input in the above (3) from the gap between the convex substrates and the convex shape obtained in the above (7). Using the value obtained by subtracting the load obtained by the product of the number of particles N sandwiched between the substrates with the substrate, and calculating the process of compressing the resin material containing the particles into the substrate having the convex shape from two directions, (9) The load F input in the above (4) is If the load is greater than the load determined by the product of the load-displacement relationship per particle input in the above (3) and the number of particles N sandwiched between the convex substrates obtained in the above (7), Repeating the process of compressing the resin material containing the particles of the above (8) into the convex substrate from two directions, The load F input in the above (4), If it becomes equal to the load determined by the product of the load-displacement relationship per particle input in the above (3) and the number of particles N sandwiched between the convex substrates obtained in the above (7), The movement speed of the electrode is set to 0, the temperature calculation of the resin material using the energy equation is performed, and the load-displacement relationship applied to each particle input in the above (3) is changed by the temperature rise, The load F input in the above (4) is between the load-displacement relationship applied to each particle input in the above (3) and the mouth embroidery N sandwiched between the convex substrates obtained in the above (7). If it is greater than the load determined by the product, By repeatedly calculating the process of compressing the resin material containing the particles of the above (8) into the substrate having the convex shape from two directions, the step of flowing the resin material and particles is calculated. Method of flow analysis of resin materials. The method according to any one of claims 11 to 13, wherein as a method for inputting the relationship between the load and the displacement applied to the particles, the relationship considering the temperature change of the load and the displacement applied to any number of particles or any number A flow analysis method for a resin material having particles embedded therein, wherein a relationship in which the stress applied to the particles and the temperature change of the strain are considered is input. The method according to claim 14, wherein in consideration of the temperature change of the load and the displacement applied to the particles, The temperature uses the average value of the resin temperature between board | substrates calculated | required by analysis, or the resin temperature of arbitrary places between board | substrates, The flow analysis method of the resin material which embedded the particle | grains. The method according to any one of claims 11 to 13, The particle | grains which input the relationship of the deformation amount in consideration of the temperature change of Claim 14 have electroconductivity, and input the relationship between the number of particle | grains of a connection part, a strain, and electroconductivity, and output-calculates the electroconductivity between convex-shaped board | substrates, It is characterized by the above-mentioned. The flow analysis method of the resin material which embedded the particle | grains. The method according to any one of claims 11 to 13, The particle | grains which input the relationship of the deformation amount in consideration of the temperature change of Claim 14 have electroconductivity, and input the relationship of the contact area of the board | substrate with a particle number of a connection part, and a particle | convex shape, and electroconductivity, Output calculation of the electroconductivity between board | substrates, The flow analysis method of the resin material which embedded the particle | grains. The method according to any one of claims 11 to 13, The resin material is formed of two or more layers having different physical properties, and particles in which the relationship of the deformation amount in consideration of the temperature change according to claim 4 is input are arranged in one or more layers of resin, and the exothermic reaction formula and the resin temperature of the two or more layers of resins. A flow analysis method for a resin material having particles embedded therein, wherein a viscosity formula that is a function including a is input to output a flow process of two or more layers of resins and particles. The method according to any one of claims 11 to 13, The flow analysis method of the resin material which embedded the particle | grains characterized by outputting the position of the particle | grains interposed between the computed electrodes. The position of the particle | grains interposed between the board | substrate output by the moving speed of the electrode computed by the flow analysis method of the resin material which embedded the particle in any one of Claims 11-13, and the calculation method of Claim 18. The structural method is performed as an input condition, and the amount of deformation of the particles, the shape of deformation of the particles, or the contact area between the particles and the electrode is calculated. The amount of deformation of the particles calculated by the calculation method according to claim 20 or the contact area between the particles and the electrode, Conductivity calculation of the conductivity between the convex substrates is performed by using the relationship between the particle number of the connection part and the strain and the conductivity, or the relationship between the particle number of the connection part and the contact area and conductivity of the particle and the convex substrate. The calculation method of the resin material which made the particle | grains embedding. (1) an input unit for acquiring data of a convex substrate to be analyzed, a shape of a resin material including initial particles, and a space in which a resin material including particles can flow from a storage device to a calculation device; (2) a processing unit which performs decomposition processing into three-dimensional solid elements based on the data, (3) Input at least the density of the resin material, the thermal conductivity, the specific heat, the viscosity, the external dimensions of the particles, the density, the load-displacement relationship per particle, and the external load F applied to the convex substrate. Input unit, (4) The change of the resin temperature is calculated by the contact of the convex substrate and the resin material by arithmetic processing of a continuous equation, a butterfly Stokes equation, and an energy conservation equation based on the three-dimensional solid element. Computation unit for calculating the flow of the resin material is compressed with the particles by the movement of the substrate having a convex shape, (5) an output unit for output-calculating the number N of particles sandwiched between the convex substrates at a time when the gap between the convex substrates after compression becomes equal to the diameter of the particles; (6) After the time when the gap between the convex substrates after the compression of the above (5) becomes equal to the diameter of the particles, the load applied to the convex substrate is ignored. From the load F input in (3), between the convex-shaped substrate and the load-displacement relationship per particle input in (3) above, and the convex substrate obtained in (5) above. A calculation unit that calculates a process of compressing the resin material containing the particles into a convex-shaped substrate from two directions using a value obtained by subtracting the load obtained by multiplying by the number N of particles to be inserted into the substrate. It is provided, The flow analysis system of the resin material which embedded the particle | grains. (1) an input unit for acquiring data of a convex substrate to be analyzed, a shape of a resin material including initial particles, and a space in which a resin material including particles can flow from a storage device to a calculation device; (2) a processing unit which performs decomposition processing into three-dimensional solid elements based on the data, (3) Load-displacement relation considering at least density of resin material, thermal conductivity, specific heat, viscosity, external dimension of particle, density, temperature change per particle, load from outside applied to convex substrate An input for inputting F, (4) The change of the resin temperature is calculated by the contact of the convex substrate and the resin material by arithmetic processing of a continuous equation, a butterfly Stokes equation, and an energy conservation equation based on the three-dimensional solid element. Computation unit for calculating the flow of the resin material is compressed with the particles by the movement of the substrate having a convex shape, (5) an output unit for output-calculating the number N of particles sandwiched between the convex substrates at a time when the gap between the convex substrates after compression becomes equal to the diameter of the particles; (6) After the time when the gap between the convex substrates after the compression of the above (5) becomes equal to the diameter of the particles, the load applied to the convex substrate is ignored. From the load F input in (3), the load-displacement relationship in consideration of the temperature change applied to each particle input in the above (3) from the gap between the convex substrates and the convex shape obtained in the above (5). An arithmetic unit that calculates a process of compressing a resin material containing particles into a substrate having a convex shape from two directions, using a value obtained by subtracting the load obtained by multiplying by the number N of particles sandwiched between the substrates; (7) The load F input in the above (3) is If the load is greater than the load determined by the product of the load-displacement relationship per particle input in the above (3) and the number of particles N sandwiched between the convex substrates obtained in the above (5), Repeating the process of compressing the resin material containing the particles of the above (6) into the convex substrate from two directions, The load F input in the above (3), If it becomes equal to the load determined by the product of the load-displacement relationship per one particle input in the above (3) and the number N of particles sandwiched between the convex substrates obtained in the above (5), The movement speed of the electrode is set to 0, the temperature calculation of the resin material using the energy equation is performed, and the load-displacement relationship applied to each particle input in the above (3) is changed by the temperature rise, The load F input in the above (3) is a relationship between the load-displacement relationship applied to each particle input in the above (3) and the number N of particles sandwiched between the convex substrates obtained in the above (5). If it is greater than the load determined by the product, And a calculation unit for calculating a step of flowing the resin material and particles by repeatedly calculating the resin material containing the particles of the above (6) into a convex substrate from two directions. Flow analysis method of resin material incorporating particles. (1) an input unit for acquiring data of a convex substrate to be analyzed, a shape of a resin material including initial particles, and a space in which a resin material including particles can flow from a storage device to a calculation device; (2) decomposing into three-dimensional solid elements based on the data; (3) an input unit for inputting a load-displacement relationship in consideration of at least the density of the resin material, the thermal conductivity, the specific heat, the viscosity, the density of the particles, the external dimensions, and the temperature change applied to each particle, (4) an input unit for inputting a moving speed Vd of a substrate having a convex shape and a maximum load Fmax from the outside applied to the substrate having a convex shape, (5) The change of the resin temperature is calculated by the contact of the convex substrate and the resin material by arithmetic processing of the continuous equation, the butterfly Stokes equation and the energy conservation equation based on the three-dimensional solid element, An operation unit for calculating a process of flowing the resin material together with the particles by the moving speed Vd of the substrate having the convex shape, (6) The maximum load input in (4) above by calculating the load FJ applied to the resin by the moving convex substrate as the product of the contact area of the moving convex substrate and the resin and the resin pressure. The relationship between Fmax and FJ, If Fmax≥FJ, the electrode calculates the process of moving at the moving speed Vd of the convex substrate input in (4) above, If Fmax <FJ, the electrode is compressed by the load Fmax input in the above (4) to calculate the moving process, (7) an output unit for output-calculating the number N of particles sandwiched between the convex substrates after a time when the gap between the convex substrates after compression is equal to the diameter of the particles; (8) After the time when the gap between the convex substrates after compression of the above (7) becomes equal to the diameter of the particles, the load applied to the convex substrate is ignored, ignoring the contact between the electrode and the particles. From the load Fmax input in (4), the load-displacement relationship in consideration of the temperature change applied to each particle input in the above (3) from the gap between the convex substrates and the convex shape obtained in the above (7). An arithmetic unit for calculating a process of compressing the resin material containing the particles into the substrate having the convex shape from two directions, using a value obtained by subtracting the load obtained by the product of the number N of particles sandwiched between the substrates; (9) The load Fmax input in the above (4) is If the load is greater than the load determined by the product of the load-displacement relationship per particle input in the above (3) and the number of particles N sandwiched between the convex substrates obtained in the above (7), Repeatedly calculating the process of compressing the resin material containing the particles of the above (8) into the substrate having the convex shape from two directions, The load Fmax input in said (4) is If it becomes equal to the load determined by the product of the load-displacement relationship per particle input in the above (3) and the number of particles N sandwiched between the convex substrates obtained in the above (7), The movement speed of the electrode is set to 0, the temperature calculation of the resin material using the energy equation is performed, and the load-displacement relationship applied to each particle input in the above (3) is changed by the temperature rise, The load Fmax input in the above (4) is equal to the load-displacement relationship applied to each particle input in the above (3) and the number N of particles sandwiched between the convex substrates obtained in the above (7). If it is greater than the load determined by the product, It is provided with a calculating part which calculates the process of flowing a resin material and particle | grains by repeating calculating the process of compressing the resin material containing the particle | grains of said (8) to a board | substrate with a convex shape from two directions, Flow analysis system of resin material containing particles.

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