JPWO2008044571A1 - Flow analysis method and flow analysis system for resin material containing particles - Google Patents

Abstract

Establish analysis technology of flow behavior of resin materials with particle deformation. The present invention is characterized by realizing a calculation method for predicting the flow of resin material and the deformation of the resin material at the same time as predicting the flow process of the resin material by the fluid analysis technique using the experimental results of the deformation amount and load of the particle as input values. Specifically, in a certain time step, the amount of deformation of the particle is determined from the distance between the electrodes determined by fluid analysis, and the load corresponding to the amount of deformation of the particle is subtracted from the load for moving the electrode. Is used as a load for moving the electrode of the next time step, it becomes possible to predict the process of flowing the resin material while the particles are deformed by analyzing the fluid.

Description

  The present invention relates to a flow analysis method and flow analysis system for a resin material in which particles are contained, and in particular, to connect a semiconductor integrated circuit (IC) used in a device, a liquid crystal, etc. The present invention relates to a three-dimensional flow analysis method for evaluating conductivity from the number of particles between electrodes and the amount of deformation of particles by flowing a resin material containing particles.

As a flow analysis method for thermosetting materials, Patent Literature 1 and Patent Literature 2 describe analysis programs that can analyze foaming behavior in which the density of a polyurethane foam material decreases with time.
In Patent Document 1, the entire foamed material is regarded as a uniform density, and the density is calculated by the elapsed time from the exit of the first foamed material nozzle that ejects the foamed material obtained by stirring the foaming material. Density is used. Patent Document 2 describes that in addition to the technique of Patent Document 1, foam flow analysis of a foam material is performed using a function that takes into account that the density of the foam material changes due to wall thickness variation.

Further, as a technique for calculating the deformation of a particle by compressing a resin material in which particles are contained between the electrodes, R. There is a report by Dudek et al. This is based on the structure analysis (software: ABAQUS) and the electrode, particle and resin material shapes, particle and resin physical properties (Young's modulus, Boisson's ratio, linear expansion coefficient) are input, and the particles between heated electrodes And a calculation method for compressing the resin.
JP 2001-318909 A JP 2003-91561 A 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))

  When performing an analysis in which the particles are deformed between the electrodes while the resin material is flowing, 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 prior art is a method for predicting particle deformation using structural analysis. However, it is necessary to consider the flow state of the resin material and particles, the number of particles sandwiched between the electrodes, the viscosity change of the resin material, the exothermic reaction, and the like. There is a problem that cannot be done.

Thus, in the structural analysis, it is impossible to accurately predict the flow process of the resin material that changes in viscosity with an exothermic reaction. On the other hand, in the current fluid analysis, the plastic deformation between the electrodes of the particles cannot be accurately calculated while the resin material flows.

  Accordingly, an object of the present invention is to calculate the flow behavior of a resin material and particles by compression between electrodes, and obtain the number of particles sandwiched between the electrodes. In addition, the amount of deformation of the particle is predicted by the load applied to the electrode or the speed condition in order to move the electrode in consideration of the increase in resin viscosity, the characteristics of the load and displacement of the particle, and the number of particles sandwiched between the electrodes. The purpose is to do.

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.

  In order to achieve the above object, the present invention predicts the flow process of an embryo material by a fluid analysis technique using at least the viscosity condition of the resin material, the experimental result of the deformation amount and the load of the particle as input values, and at the same time, It is characterized by realizing a calculation method for predicting flow and particle deformation. Specifically, the number of particles sandwiched between the electrodes can be predicted by predicting the flow process of the resin material and the particles in consideration of the viscosity change.

  Also, in a certain time step of fluid analysis, the amount of particle deformation is obtained from the distance between the electrodes obtained by fluid analysis, and the load corresponding to the amount of particle deformation is subtracted from the load applied from the outside to move the electrode. By using the calculated load as the load for moving the electrode at the next time step, the amount of deformation of the particles to be determined in the structural analysis is calculated by the fluid analysis. It is possible to predict a process in which the resin material flows while the particles are deformed.

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

  As described above, the analysis technique of the present invention can predict the number of particles sandwiched between the electrodes of the chip and the substrate and the amount of deformation of the particles. Analytical optimization of factors that interact with each other in a complex manner such as initial shape such as thickness, particle and electrode shape, physical properties such as particle elastic modulus, and molding process conditions such as load applied to the electrode I can do it.

In order to optimize these factors, it is not practical to conduct an experimental study because it increases the cost and the development period.

FIG. 1 is a schematic diagram showing a molding process of a semiconductor integrated circuit (IC) using a resin material containing conductive particles to be analyzed and a substrate. FIG. 2 is a hardware configuration diagram for performing flow analysis. FIG. 3 is a flowchart of the calculation in which the movement of the semiconductor integrated circuit (IC) 3 and the electrode according to the first embodiment of the present invention is pressure control. FIG. 4 is a flowchart of a calculation in which the movement of the semiconductor integrated circuit (IC) 3 and the electrodes according to the second embodiment of the present invention is controlled from the speed. FIG. 5 is an analysis example (single layer resin) of pressure control of the electrode of Example 1 or 2 of the present invention. FIG. 6 is an analysis example (double-layer resin) of pressure control of the electrode of Example 1 or 2 of the present invention. FIG. 7 is a flowchart of an analysis for predicting conductivity according to the third embodiment of the present invention (calculation in which the movement of the semiconductor integrated circuit (IC) 3 and the electrode is 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 electrode is pressure control from the speed). FIG. 9 is a diagram showing the relationship of the input “deformation amount when a load is applied per particle 1”. FIG. 10 is a graph showing the relationship between the “deformation amount per arbitrary number of particles and the conductivity between the electrode of the semiconductor integrated circuit (IC) and the electrode of the substrate”. It is a schematic diagram showing a molding process of a semiconductor integrated circuit (IC) using a resin material containing conductive particles to be analyzed and a substrate. It is a hardware block diagram which performs a flow analysis. It is a flowchart of the calculation by which the movement of the semiconductor integrated circuit (IC) 3 and electrode of Example 5 of this invention becomes pressure control. It is a flowchart of the calculation from which the movement of the semiconductor integrated circuit (IC) 3 and electrode of Example 6 of this invention becomes pressure control from speed. It is an analysis example (single layer resin) of the pressure control of the electrode of Example 5 or 6 of the present invention. It is an analysis example (double-layer resin) of the pressure control of the electrode of Example 5 or 6 of the present invention. It is a flowchart (calculation by which movement of the semiconductor integrated circuit (IC) 3 and an electrode becomes pressure control) of the analysis which estimates the electroconductivity of Example 7 of this invention. It is a figure which shows the relationship of the input "the amount of deformation | transformation when a load is added per particle | grain 1 which considered temperature". It is a figure which shows the relationship between the input "the deformation | transformation amount per arbitrary number of particle | grains, and the electroconductivity between the electrode of a semiconductor integrated circuit (IC), and a substrate. It is the result of the structural analysis which made the input condition the coordinate of the particle | grains 1 of the connection part pinched | interposed between the electrodes 4, and the moving speed of the electrode 4. FIG. It is a figure which shows the relationship between "the contact area of particle | grains, and the electroconductivity between the electrode of a semiconductor integrated circuit (IC), and a substrate."

Explanation of symbols

1 Particle 2 Resin Material 3 Semiconductor Integrated Circuit (IC)
4 Electrode 5 Substrate 6 Calculator 7 Calculator 8 LAN
9 Display device 10 Recording device 11 Second layer resin material

  Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[Moving electrode pressure control]
First, the forming process to be analyzed will be described with reference to FIG. In the initial state (1-a), the resin material 2 containing the conductive particles 1 is placed between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5. In the molding step, the semiconductor integrated circuit (IC) 3 to which heat is applied is moved in the direction of the substrate 5 and the resin material 2 containing the particles 1 is compressed, whereby the resin material 2 containing the particles 1 flows.

  At this time, the temperature of the resin material 2 changes due to the contact between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the resin material 2, and the resin material 2 is compressed together with the particles 1 while the viscosity changes due to the temperature change. To flow. When the distance between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 becomes smaller than the diameter of the particle 1, the particle 1 sandwiched between the electrodes 4 is compressed while being deformed.

  When the movement of the semiconductor integrated circuit (IC) 3 is completed (1-b), an electrical signal is transmitted between the semiconductor integrated circuit (IC) 3 and the substrate 5 by the conductivity of the particles 1 sandwiched between the electrodes 4. It becomes possible. Here, the contact area between 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. The conductivity is evaluated by a current that flows when a constant voltage is applied between the electrodes 4. Here, the deformation amount of the particles 1 is the ability of the device to apply a load from the upper part of the semiconductor integrated circuit (IC) 3, the deformation amount of the particles 1 when the load is applied, the number of particles 1 sandwiched between the electrodes, the resin It depends on the viscosity change of material 2.

[Configuration of analysis system]
Next, an analysis system used for predicting the flow process of the resin material 2 accompanying the deformation of the particles 1 will be described. The analysis system functions by executing software having the hardware configuration shown in FIG. 2 and having the flows of FIGS. 3, 4, 7, and 8 to be described later.

  Specifically, it includes a computing device 6, a computing device 7 provided with a recording device 10 (hard disk, MO, etc.), a LAN 8 connecting these two computing devices, and a display device 9 provided in the computing device 7. Further, the CAD data created by the calculation device 6 may be transferred to the calculation device 7 via the LAN 8. The CAD data transferred to the computing device 7 can be recorded on the recording device 10 (hard disk, MO, etc.) of the computing device 7 for use. The calculation device 7 executes calculation according to the flowcharts shown in FIGS. 3, 4, 7, and 8, records the result in the recording device 10, and displays the result on 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 along 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 to be analyzed, the shape of the resin material including the initial particles, and the space in which the resin material including the particles can flow is obtained. Data is read from the storage device 10.

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

Next, in the physical property value input step 1003, density, thermal conductivity, specific heat, exothermic equations (Equation 7) to (Equation 11), viscosity equations (Equation 12) to (Equation 15) which are physical property values of the material to be analyzed. ), A display prompting the operator to input the arrangement, density, diameter, and deformation amount when a load is applied to each particle 1 and accepts these data from the input device. A: reaction rate, t: time, T: temperature, dA / dt: reaction rate, X1, X2: coefficient as a function of temperature, N, M, Xa, Ea, Xb, Eb: material specific coefficient, Q: calorific value up to an arbitrary time, Qo: total calorific value until the end of reaction, dQ / dt: exothermic rate, no: viscosity, no 0: initial viscosity, t: time, tO: gelation time, T: temperature A, b, d, e, f, g: Constants specific to the material.

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

  Next, an analysis start instruction and an initial time increment from the operator are received. In the analysis, a minute time is increased and a change for each time step is calculated. The time increment indicates a time step interval.

  In step 1005, based on this instruction, the continuous equation (1), Napier Stokes equations (2) to (4), and energy conservation equation (5) stored in the recording device are called and the input has been accepted so far. In addition, initial time increment, pressure applied to the top of the semiconductor integrated circuit (IC) 3 and the electrode 4, density of resin material, specific heat, thermal conductivity, exothermic formula (formula 7) to (formula 11), viscosity formula (formula 12) to (Equation 15) are substituted, and the velocity, pressure, temperature and viscosity associated with the flow of the resin material 2 and the particles 1 due to compression of the electrode are calculated. The calculation result is stored in the storage device in association with the position of the finite element.

Here, P: density, u: velocity in the X direction, U: velocity in the y direction, ∽: velocity in the Z direction, T: temperature, P; pressure, t; time, no; viscosity, Cp: specific heat at constant pressure, β: volume expansion Coefficient, input; indicates thermal conductivity.

  Next, in step 1006, it is determined whether the distance between the electrodes 4 is larger than the diameter of the particles. Here, when the distance between the electrodes 4 becomes equal to the diameter (φD) of the particles 1, the number N of particles 1 at the connection portion sandwiched between the electrodes 4 is output in Step 1007.

  From the next step 1008, the flow process of the resin material 2 accompanied by the deformation of the particles 1 is calculated. In the first step (1008) for calculating the flow process of the resin material 2 accompanied by the deformation of the particles 1, the deformation of the particles 1 is ignored, and the movement amount of the resin material 2 in the moving direction of the electrode 4 (= the particle 1) After calculating (deformation amount) ΔHl, the load ΔFl applied per particle 1 by the deformation amount ΔHl of particle 1 from the input “deformation amount when load is applied per particle 1”. Is calculated. Here, FIG. 9 shows an example of the relationship of the inputted “deformation amount when a load is applied per particle 1”.

  In the next second step (1009), the load FJ2 applied to the upper portions of the semiconductor integrated circuit (IC) 3 and the electrode 4 is the load Δ applied per particle 1 obtained in step 1008 from the set value F. Calculation is performed using the difference between the values obtained by the product of Fl and the number N of particles sandwiched between the electrodes obtained in Step 1007 (FJ2 = F−N × ΔFl) (Step 1010). After calculating the movement amount ΔH2 of the resin material 2 due to the movement of the electrode 4 when the load FJ2 is applied (= deformation amount of the particle 1), the load applied per particle by the deformation amount ΔH2 of the particle 1 ΔF2 is calculated, and FJ3 = F−N × ΔF2 is set as a load condition applied to the semiconductor integrated circuit (IC) 3 in the calculation of the next time step.

  In Step 1011, the calculations in Steps 1008 to 1010 are repeated. In the Mth step, the deformation amount ΔH (M) of the particle 1 and the load ΔF (M) applied to each particle are calculated, and the semiconductor integrated circuit ( IC) A value obtained by multiplying the load ΔF (M) applied per particle 1 from the load setting value F applied to the upper part of the electrode 3 and the electrode 4 and the number N of particles sandwiched between the electrodes obtained in Step 1007 Until F becomes less than or equal to 0 (F−NXΔF (M) ≦ 0), or until the load F applied to the electrodes becomes unable to move due to an increase in the viscosity of the resin material (gel viscosity), or between the electrodes 4 Until the interval becomes zero, the deformation amount of the particles 1 and the flow behavior of the resin material 2 are calculated (step 1012).

  In step 1013, the zero convergence determination method for determining the convergence of the calculation compares the pressure with a predetermined pressure range and determines that the pressure is within the range as convergence. If it does not converge, the process returns to one of steps 1001 to 1004. At this time, the operator is prompted to input and a step to be returned is determined.

  In step 1014, the appropriateness of particle deformation is determined. Here, it is determined whether the deformation amount of the particles is within the specified value range, and if it is outside the specified range, the process returns to one of steps 1001 to 1004. At this time, the operator is prompted to input, and it is determined that the calculation has converged in Step 1013 for determining which step to return to. After it is determined in Step 1014 that the particle deformation is appropriate, the calculation is terminated in Step 1015. .

  In addition, although the example of the relationship of the deformation amount when a load is applied per particle 1 is shown as the input condition in step 1003, the deformation amount when a load per particle 1 is applied (or It is possible to input the relationship between the deformation rate) and the relationship between the stress applied to the particles 1 and the amount of deformation (or the deformation rate). Further, the exothermic equation is not limited to (Equation 7) to (Equation 11), and any function including the reaction rate of the resin material 2 can be used.

  The viscosity formula is not limited to (Formula 12) to (Formula 15), and any function including the temperature or reaction rate of the embryo material 2 can be used. In addition, an arbitrary determination method can be used for convergence determination. It is assumed that not only three-dimensional analysis but also two-dimensional analysis can be performed. The above calculation can be performed using the finite element method, the finite volume method, or the finite difference method.

[Switching from electrode speed to pressure control]
Next, the processing of the analysis program will be described along the flowchart of FIG. First, in the model shape creation step 2001, the analysis target model specified by the operator via the input device, that is, the electrode to be analyzed, the shape of the resin material including the initial particles, and the space in which the resin material including the particles can flow is obtained. Data is read from the storage device 10.

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

  Next, in the physical property value input step 2003, density, thermal conductivity, specific heat, exothermic equation (Equation 7) to (Equation 11), viscosity equation (Equation 12) to (Equation 15) which are physical property values of the material to be analyzed. ), A display prompting the operator to input the arrangement, density, diameter, and deformation amount when a load is applied to each particle 1 and accepts these data from the input device.

  Next, in the boundary condition / molding condition input step 2004, the moving speed Vd of the semiconductor integrated circuit (IC) 3 and the electrode 4 and the maximum pressure applied to the upper part of the semiconductor integrated circuit (IC) 3 and the electrode 4 are input. And prompting the operator to receive data from the input device.

  Here, from the received maximum pressure applied to the upper part of the semiconductor integrated circuit (IC) 3 and the electrode 4 and the area of the upper part of the semiconductor integrated circuit (IC) 3, it is added to the upper part of the semiconductor integrated circuit (IC) 3 and the electrode 4. The maximum load Fmax that can be obtained is calculated.

  Next, an analysis start instruction and an initial time increment from the operator are received. In step 2005, based on this instruction, the continuous equation (1), Napier Stokes equations (2) to (4), and energy conservation equation (5) stored in the recording device are called and the input has been accepted so far. In addition, initial time increment, pressure applied to the top of the semiconductor integrated circuit (IC) 3 and the electrode 4, density of the seed material, specific heat, thermal conductivity, exothermic formula (formula 7) to (formula 11), viscosity formula ( Substituting equations (12) to (15), the velocity, pressure, temperature and viscosity associated with the flow of the embryo material 2 and the particles 1 due to compression of the electrodes are calculated. The calculation result is stored in the storage device in association with the position of the finite element.

  Next, in step 2006, it is determined whether the distance between the electrodes 4 is larger than the diameter of the particles. Here, when the distance between the electrodes 4 becomes equal to the diameter (φD) of the particles 1, the number N of particles 1 at the connection portion sandwiched between the electrodes 4 is output in step 2007.

  From the next step 2008, the flow process of the resin material 2 accompanied by the deformation of the particles 1 is calculated. In step 2008, after calculating the movement amount of the resin material 2 in the movement direction of the electrode 4 (= deformation amount of the particle 1) ΔH, the particle is calculated from the deformation amount when a load is applied to each of the input particles 1. A load ΔF applied to each particle 1 is calculated based on a deformation amount ΔH of 1, and a load FR = N × ΔF applied to the particle 1 is calculated. Further, the load FJ applied to the resin is calculated as a product of “the contact area between the moving electrode 4 and the resin material 2” and “the pressure of the resin embryo 2 at the contact portion”.

  Here, FIG. 9 shows an example of the relationship of the inputted “deformation amount when a load is applied per particle 1”. Here, in step 2009, it is determined whether the maximum load Fmax applied to the tops of the semiconductor integrated circuit (IC) 3 and the electrode 4 is greater than the sum of the load FJ applied to the embryo material 2 and the load FR applied to the particles. (Fmax ≧ FJl + FRl) is performed.

Here, when Fmax <FJl + FR1, the set moving speed Vd of the electrode 4 cannot be realized even when the maximum load Fmax is applied. Therefore, the control method of the movement of the electrode 4 is switched to the control when the maximum load Fmax is applied instead of the control of the speed Vd.
That is, the calculation in steps 1008 to 1011 shown in FIG. 3 is performed, and the deformation process of the particles 1 and the flow process of the resin material 2 are calculated.

  Here, the load ΔF (M) applied per particle 1 from the load setting value F applied to the upper part of the semiconductor integrated circuit (IC) 3 and the electrode 4 and the number of particles sandwiched between the electrodes determined in step 1007 When the value obtained by the product of N becomes 0 or less (F−N × ΔF (M) ≦ 0), or the load F applied to the electrode increases due to the increase in the viscosity of the resin material (gel viscosity). The deformation amount of the particles 1 and the flow behavior of the resin material 2 are calculated until they cannot move or until the interval between the electrodes 4 becomes zero.

  In step 2009, when Fmax ≧ FJl + FR1, the load F applied to the electrodes cannot be moved due to the increase in the viscosity of the resin material (gel viscosity), or the interval between the electrodes 4 becomes zero. Until it is, the calculation in step 2008 and the determination in step 2009 are repeated.

  Here, in step 2012, calculation convergence is determined. The convergence determination method compares the pressure with a predetermined pressure range, and determines that the pressure is within the range as convergence. If it does not converge, the process returns to one of steps 2001 to 2004. At this time, the operator is prompted to input and a step to be returned is determined.

  In step 2013, the appropriateness of particle deformation is determined. Here, it is determined whether the deformation amount of the particles is within a specified value range, and if it is outside the specified range, the process returns to one of steps 2001 to 2004. At this time, the operator is prompted to input and a step to be returned is determined.

  In step 2012, it is determined that the calculation has converged. In step 2013, it is determined that the particle deformation is appropriate. In step 2014, the calculation is terminated.

  In addition, although the example of the relationship of the deformation amount when a load is applied per particle 1 is shown as the input condition in step 2003, the deformation amount when a load per particle 1 is applied (or It is possible to input the relationship between the deformation rate) and the relationship between the stress applied to the particles 1 and the amount of deformation (or the deformation rate).

  Further, the exothermic equation is not limited to (Equation 7) to (Equation 11), and any function including the reaction rate of the resin material 2 can be used. The viscosity formula is not limited to (Formula 12) to (Formula 15), and any function including the temperature or the reaction rate of the resin material 2 can be used.

  The convergence determination can use any determination method. Further, not only three-dimensional analysis but also two-dimensional analysis can be performed. The above calculation can be performed using the finite element method, the finite volume method, or the finite difference method.

[Analysis example of electrode pressure control (single layer resin)]
Here, FIG. 5 shows an example of analysis (two-dimensional analysis). In an initial state, a resin material 2 containing conductive particles 1 is placed between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5. Here, the embryo material 2 has an initial temperature of 30 ° C., and the exothermic equations (Equation 7) to (Equation 11) and the viscosity equations (Equation 12) to (Equation 15) are used. The constant value, density, thermal conductivity, specific heat value, particle diameter (φD), and density of the exothermic formulas (Formula 7) to (Formula 11) and viscosity formulas (Formula 12) to (Formula 15) are shown. It is shown in 1.

  Further, the temperature of the semiconductor integrated circuit (IC) 3 is set to be constant (185 ° C.), moved by applying a pressure of 5 MPa in the direction of the substrate 5, and the resin material 2 including the particles 1 is compressed, whereby the particles 1 are compressed. The containing embryo material 2 is flowed. At this time, the temperature of the resin material 2 changes due to the contact between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the resin material 2, and the resin material 2 is compressed together with the particles 1 while the viscosity changes due to the temperature change. Calculate the flow process.

  When the distance between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 becomes smaller than the diameter of the particle 1, the calculation of the contact between the particle 1 and the electrode 4 is not performed in the analysis. That is, in the analysis, when the particles 1 are in contact with each other, and when the particles 1 and the electrode 4 are in contact with each other, the fluidity of only the resin material 2 is calculated by setting such that the particles 1 pass through the electrode 4. At this time, the pressure applied from the upper part of the semiconductor integrated circuit (IC) 3 is not the set value of 5 MPa, but the deformation amount of the particles 1 from the load obtained by the product of the set pressure and the area as shown in the flowchart of FIG. The value obtained by subtracting the load corresponding to is used.

As a result of this calculation, the resin viscosity increases, 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 obtained from the interval between the electrodes. In addition, the deformation amount ΔD of the particles can be obtained by (Expression 6).

  Here, D: the diameter of the particle 1 and Dl: the distance between the substrates 4 after the analysis is completed. In the above, the case where the movement of the electrode 4 is controlled by the pressure is shown. However, the present invention is not limited to this, and the movement of the electrode is changed from speed to pressure as shown in the flowchart of FIG. It is also possible to control. In addition, although the heat conduction calculation within the particle is not performed here, the heat conduction calculation within the particle can also be performed by inputting the specific heat of the particle, the heat conductivity, the heat transfer coefficient between the resin material and the particle, and the like.

[Analysis example of electrode pressure control (two-layer resin)]
Here, FIG. 6 shows an example of an analysis example (two-dimensional analysis) in which the resin material is divided into two layers.

In an initial state, a resin material having a two-layer structure made of a resin material 11 having different physical property values including particles 1 is formed on the resin material 2 including the conductive particles 1, and the electrode 4 of the semiconductor integrated circuit (IC) 3. And between the electrodes 4 of the substrate 5. Here, the resin material 2 has an initial temperature of 30 ° C., and the exothermic formulas (Formula 7) to (Formula 11) and the viscosity formulas (Formula 12) to (Formula 15) are used. In addition, regarding the constant value, density, thermal conductivity, specific heat value, particle diameter (φD), and density of the exothermic formulas (Formula 7) to (Formula 11) and the viscosity formulas (Formula 12) to (Formula 15), The resin material 2 and particle 1 in the first layer use the values in Table 1, and the values of the embryo material 11 and particles 1 in the second layer are shown in Table 2.

  Here, the temperature of the semiconductor integrated circuit (IC) 3 is set to be constant (185 ° C.), moved by applying a pressure of 5 MPa in the direction of the substrate 5, and the resin materials 2 and 11 are compressed to include the particles 1. Resin materials 2 and 11 are caused to flow. At this time, due to the contact between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the resin materials 2 and 11, the temperature of the tree material 2 and 11 is changed, and the viscosity change due to the temperature change is generated, while the resin material 2 and 11 is changed. It is possible to calculate the process of flowing while being compressed together with the particles 1.

  When the distance between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 becomes smaller than the diameter of the particle 1, the calculation of the contact between the particle 1 and the electrode 4 is not performed in the analysis. That is, in the analysis, when the particles 1 are in contact with each other, and when the particles 1 and the electrode 4 are in contact with each other, the fluidity of only the resin materials 2 and 11 is calculated by setting such that the particles 1 pass through the electrode 4. . At this time, the pressure applied from the upper part of the semiconductor integrated circuit (IC) 3 is not the set value of 5 MPa, but the deformation amount of the particles 1 from the load obtained by the product of the set pressure and the area as shown in the flowchart of FIG. The value obtained by subtracting the load corresponding to is used.

As a result of this calculation, the viscosity of the embryo increases, 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 obtained from the interval between the electrodes. The deformation amount ΔD of the particles 1 can be obtained by (Expression 6).

  Here, D: the diameter of the particle 1 and Dl: the distance between the substrates 4 after the analysis is completed. In the above, the case where the movement of the electrode 4 is controlled by the pressure is shown. However, the present invention is not limited to this, and the movement of the electrode is changed from speed to pressure as shown in the flowchart of FIG. It is also possible to control. In addition, although the heat conduction calculation within the particle is not performed here, the heat conduction calculation within the particle can also be performed by inputting the specific heat of the particle, the heat conductivity, the heat transfer coefficient between the resin material and the particle, and the like. In addition, although the example of the analysis in which the particle 1 is included in the resin material 11 of the two-phase day has been described above, the present invention is not limited to this, and the resin material 11 of the two-phase day includes the particle 1. It is also possible to perform analysis in a state where

[Prediction of conductivity (pressure control for electrode movement)]
FIG. 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 according to the third 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 based on the input of the relationship between the particle deformation amount and the conductivity obtained in the flowchart of FIG. First, in the model shape creation step 3001, the analysis target model specified by the operator through the input device, that is, the electrode to be analyzed, the shape of the resin material including the initial particles, and the space in which the resin material including the particles can flow is obtained. Data is read from the storage device 10.

  Next, in step 3002 for creating a three-dimensional solid element, the shape of the data read in the model shape creating step 1001 is decomposed into a plurality of specific spaces (three-dimensional solid finite elements) to create shape data for each finite element. .

  Next, in the physical property value input step 3003, the density, thermal conductivity, specific heat, exothermic equation (Equation 7) to (Equation 11), viscosity equation (Equation 12) to (Equation) which are the physical property values of the material to be analyzed. 15) A display prompting the operator to input the arrangement, density, diameter, and deformation amount when a load is applied to each particle 1 is received, and these data are received from the input device.

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

  Next, an analysis opening instruction from the operator and an initial time increment are received. In step 3005, based on this instruction, the continuous equation (1), Napier Stokes equations (2) to (4), and the energy conservation equation (5) stored in the recording device are called and the input has been accepted so far. In addition, initial time increment, pressure applied to the top of the semiconductor integrated circuit (IC) 3 and the electrode 4, density of the seed material, specific heat, thermal conductivity, exothermic formula (formula 7) to (formula 11), viscosity formula ( Substituting Equations 12) to 15 to calculate the velocity, pressure, temperature, and viscosity associated with the flow of the resin material 2 and the particles 1 due to compression of the electrodes. The calculation result is stored in the storage device in association with the position of the finite element.

  Next, in step 3006, it is determined whether the distance between the electrodes 4 is larger than the diameter of the particles. Here, when the distance between the electrodes 4 becomes equal to the diameter (φD) of the particles 1, the number N of particles 1 at the connection portion sandwiched between the electrodes 4 is output in Step 3007.

  The next steps 1008 to 1015 are the calculation method 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 per arbitrary number of 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. The conductivity is a current value I when an arbitrary voltage is applied between the 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 obtained in step 3008.

  Here, FIG. 10 shows an example of the relationship between the input “deformation amount per arbitrary number of particles 1 and conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5”. Here, Nl, N2, and N3 are shown as representative values of an arbitrary number of particles 1, and in step 3007, the number of particles 1 in the connection portion sandwiched between the electrodes 4 is other than Nl, N2, and N3. In this case, the value can be obtained by interpolation and extrapolation.

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

  Next, at step 3011, the convergence of the calculation is determined. Convergence is determined by comparing pressure with a pre-determined pressure range and determining that it is within the range as convergence. If it does not converge, the process returns to one of steps 3001 to 3004. At this time, the operator is prompted to input and a step to be returned is determined.

  In step 3012, the appropriateness of conductivity is determined. Here, it is determined whether or not the conductivity is within the specified value range, and if it is outside the specified range, the process returns to any of steps 3001 to 3004. At this time, the operator is prompted to input and a step to be returned is determined.

  In step 3011, it is determined that the calculation has converged. In step 3012, it is determined that the particle deformation is appropriate. In step 3013, the calculation ends. The “deformation amount per arbitrary number of particles 1 and the conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5” input in step 3009 are “per number of particles 1. “The contact area between the particle 1 and the electrode 4 and the conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 obtained from the relationship between the deformation amount and the contact area between the particle 1 and the electrode 4”. "Can also be entered. In addition, although the electrical conductivity is a current value when an arbitrary voltage is applied between the electrodes, the present invention is not limited to this, and a resistance value between the electrodes can be used.

[Prediction of conductivity (speed of electrode movement ~ pressure control)]
FIG. 8 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 according to the fourth 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 based on the input of the relationship between the particle deformation amount and the conductivity obtained in the flowchart of FIG.

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

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

  Next, in the physical property value input step 4003, density, thermal conductivity, specific heat, exothermic equations (Equation 7) to (Equation 11), viscosity equations (Equation 12) to (Equation) that are physical property values of the material to be analyzed. 15) A display prompting the operator to input the deformation density when a load is applied to each particle density, diameter, and particle 1 is received, and these data are received from the input device.

  Next, in the boundary condition / molding condition input step 4004, the moving speed Vd of the semiconductor integrated circuit (IC) 3 and the electrode 4 and the maximum pressure applied to the upper part of the semiconductor integrated circuit (IC) 3 and the electrode 4 are input. And prompting the operator to receive data from the input device. Here, from the received maximum pressure applied to the upper part of the semiconductor integrated circuit (IC) 3 and the electrode 4 and the area of the upper part of the semiconductor integrated circuit (IC) 3, it is added to the upper part of the semiconductor integrated circuit (IC) 3 and the electrode 4. The maximum load Fmax that can be obtained is calculated.

  Next, an analysis start instruction and an initial time increment from the operator are received. In step 4005, based on this instruction, the continuous equation (1), Napier Stokes equations (2) to (4), and energy conservation equation (5) stored in the recording device are called and the input has been accepted so far. Further, the initial time increment, the pressure applied to the top of the semiconductor integrated circuit (IC) 3 and the electrode 4, the density of the resin material, the specific heat, the thermal conductivity, the exothermic formula (1), and the viscosity formula (2) are substituted, and the electrode The velocity, pressure, temperature and viscosity accompanying the flow of the resin material 2 and the particles 1 due to the compression of are calculated. The calculation result is stored in the storage device in association with the position of the finite element.

  Next, in step 4006, it is determined whether the distance between the electrodes 4 is larger than the particle diameter. Here, when the distance between the electrodes 4 becomes equal to the diameter (φD) of the particles 1, the number N of particles 1 at the connection portion sandwiched between the electrodes 4 is output in Step 4007.

  The next steps 2008 to 2014 are the calculation method shown in the flowchart of FIG. 4, and the deformation amount of the particles is output at step 4008. In step 4009, the deformation amount per arbitrary number of 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. The conductivity is a current value I when an arbitrary voltage is applied between the 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 obtained in step 4008. Here, FIG. 10 shows an example of the relationship between the input “deformation amount per arbitrary number of particles 1 and conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5”. Here, Nl, N2, and N3 are shown as representative values of an arbitrary number of particles 1, and in step 4007, the number of particles 1 at the connecting portion sandwiched between the electrodes 4 is other than Nl, N2, and N3. In this case, the value can be obtained by interpolation and extrapolation.

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

  Next, in step 4011, calculation convergence is determined. The convergence determination method compares the pressure with a predetermined pressure range, and determines that the pressure is within the range as convergence. If not converged, the process returns to one of steps 4001 to 4004. At this time, the operator is prompted to input and a step to be returned is determined.

  In step 4012, the appropriateness of conductivity is determined. Here, it is determined whether or not the conductivity is within a specified value range. If the conductivity is outside the specified range, the process returns to any of steps 4001 to 4004. At this time, the operator is prompted to input and a step to be returned is determined.

In step 4011, it is determined that the calculation has converged. In step 4012, it is determined that the particle deformation is appropriate. In step 4013, the calculation ends.
The “deformation amount per arbitrary number of particles 1 and the conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5” input in step 4009 is “per arbitrary number of particles 1. “The contact area between the particle 1 and the electrode 4 and the conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 obtained from the relationship between the deformation amount and the contact area between the particle 1 and the electrode 4”. "Can also be entered. In addition, although the electrical conductivity is a current value when an arbitrary voltage is applied between the electrodes, the present invention is not limited to this, and a resistance value between the electrodes can be used.

[Moving electrode pressure control]
First, the forming process to be analyzed will be described with reference to FIG. In the initial state (1-a), the resin material 2 containing the conductive particles 1 is placed between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5. In the molding step, the semiconductor integrated circuit (IC) 3 to which heat is applied is moved in the direction of the substrate 5 and the resin material 2 containing the particles 1 is compressed, whereby the resin material 2 containing the particles 1 flows.

  At this time, the temperature of the resin material 2 changes due to the contact between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the resin material 2, and the resin material 2 is compressed together with the particles 1 while the viscosity changes due to the temperature change. To flow. When the distance between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 becomes smaller than the diameter of the particle 1, the particle 1 sandwiched between the electrodes 4 is compressed while being deformed.

  When the movement of the semiconductor integrated circuit (IC) 3 is completed (1-b), an electrical signal is transmitted between the semiconductor integrated circuit (IC) 3 and the substrate 5 by the conductivity of the particles 1 sandwiched between the electrodes 4. It becomes possible. Here, the contact area between 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.

  The conductivity is evaluated by a current that flows when a constant voltage is applied between the electrodes 4. Here, the deformation amount of the particles 1 is the ability of the device to apply a load from the upper part of the semiconductor integrated circuit (IC) 3, the deformation amount of the particles 1 when the load is applied, the number of particles 1 sandwiched between the electrodes, the resin It depends on the viscosity change of material 2.

[Configuration of analysis system]
Next, an analysis system used for predicting the flow process of the resin material 2 accompanying the deformation of the particles 1 will be described. The analysis system functions by executing software having the hardware configuration shown in FIG. 12 and having the flows of FIGS.

  Specifically, it includes a computing device 6, a computing device 7 provided with a recording device 10 (hard disk, MO, etc.), a LAN 8 connecting these two computing devices, and a display device 9 provided in the computing device 7. Further, the CAD data created by the calculation device 6 may be transferred to the calculation device 7 via the LAN 8. The CAD data transferred to the computing device 7 can be recorded on the recording device 10 (hard disk, MO, etc.) of the computing device 7 for use.

  The calculation device 7 performs calculations according to the flowcharts shown in FIGS. 13, 4, 7, and 8, records the results in the recording device 10, and displays the results on 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 along 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 to be analyzed, the shape of the resin material including the initial particles, and the space in which the resin material including the particles can flow is obtained. Data is read from the storage device 10.

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

Next, in the physical property value input step 1003, density, thermal conductivity, specific heat, exothermic equations (Equation 7) to (Equation 11), viscosity equations (Equation 12) to (Equation 15) which are physical property values of the material to be analyzed. ), A display prompting the operator to input the arrangement, density, diameter, and deformation amount when a load is applied to each particle 1 and accepts these data from the input device. A: reaction rate, t: time, T: temperature, dA / dt: reaction rate, X1, X2: coefficient as a function of temperature, N, M, Xa, Ea, Xb, Eb: material specific coefficient, Q: calorific value up to an arbitrary time, Qo: total calorific value until the end of reaction, dQ / dt: exothermic rate, η: viscosity, η0: initial viscosity, t: time, tO: gelation time, T: temperature, a, b, d, e, f, g: Constants specific to the material.

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

  Next, an analysis start instruction, an initial time increment and an analysis end time tend are received from the operator. In the analysis, a minute time is increased and a change for each time step is calculated. The time increment indicates a time step interval.

  In step 1005, based on this instruction, the continuous equation (1), Napier Stokes equations (2) to (4), and energy conservation equation (5) stored in the recording device are called and the input has been accepted so far. In addition, initial time increment, pressure applied to the top of the semiconductor integrated circuit (IC) 3 and the electrode 4, density of resin material, specific heat, thermal conductivity, exothermic formula (formula 7) to (formula 11), viscosity formula (formula 12) to (Equation 15) are substituted, and the velocity, pressure, temperature and viscosity associated with the flow of the resin material 2 and the particles 1 due to compression of the electrode are calculated. The calculation result is stored in the storage device in association with the position of the finite element.

Here, P: density, u: velocity in the X direction, v: velocity in the y direction, ω: velocity in the Z direction, T: temperature, P: pressure, t; time, η; viscosity, Cp: constant pressure specific heat, β: volume expansion Coefficient, λ; indicates thermal conductivity.

  Next, in step 1006, it is determined whether or not the analysis time is shorter than the set analysis end time tend. If the determination is NO, the analysis is terminated through calculation convergence determination or the like. If the determination is YES, The process proceeds to step 1007 for determination.

  In step 1007, it is determined whether the distance between the electrodes 4 is larger than the particle diameter. Here, when the distance between the electrodes 4 becomes equal to the diameter (φD) of the particles 1, the number N of particles 1 at the connection portion sandwiched between the electrodes 4 is output in step 1008.

  From the next step 1009, the flow process of the resin material 2 accompanied by the deformation of the particles 1 is calculated. In the first step (1009) for calculating the flow process of the resin material 2 accompanied by the deformation of the particle 1, the deformation of the particle 1 is ignored, and the movement amount of the resin material 2 in the movement direction of the electrode 4 (= the particle 1) After calculating (deformation amount) ΔHl, the load ΔFl applied per particle 1 by the deformation amount ΔHl of particle 1 from the input “deformation amount when load is applied per particle 1”. Is calculated. Here, FIG. 18 shows an example of the relationship of the inputted “deformation amount when a load is applied per particle 1 in consideration of temperature change”. Here, T1, T2, and T3 represent temperature conditions, and 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 the load Δ applied per particle 1 obtained in step 1009 from the set value F. Calculation is performed using the difference between the values obtained by the product of Fl and the number N of particles sandwiched between the electrodes obtained in Step 1008 (FJ2 = F−N × ΔFl) (Step 1011).

  After calculating the movement amount ΔH2 of the resin material 2 due to the movement of the electrode 4 when the load FJ2 is applied (= deformation amount of the particle 1), the load applied per particle by the deformation amount ΔH2 of the particle 1 ΔF2 is calculated, and FJ3 = F−N × ΔF2 is set as a 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. In the Mth step, the deformation amount ΔH (M) of the particle 1 and the load ΔF (M) applied to each particle are calculated, and the deformation of the particle 1 is calculated. The amount 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 0 or shorter than the set analysis end time tend in the analysis time. If the determination is NO, the analysis is performed through a calculation convergence determination or the like. If the determination is YES, the process proceeds to the determination of step 1014.

  In step 1014, the load ΔF (M) applied to each particle 1 from the load set value F applied to the upper part of the semiconductor integrated circuit (IC) 3 and the electrode 4 is sandwiched between the electrode obtained in step 1008. It is determined whether the value obtained by subtracting the value obtained by the product of the number of particles N is 0 or less (FN−ΔF (M) ≦ 0). If the determination is NO, the calculation of step 1012 is repeated. If the determination is YES, the resin temperature is calculated in step 1015 using the energy equation (5) when the electrode moving speed is zero. Do.

Next, in step 1016, it is determined whether or not the analysis time is shorter than the set analysis end time tend. If the determination is YES, step 1012 is repeatedly calculated.
Here, as shown in FIG. 18, the relationship between the compressive load input in step 1004 and the amount of particle deformation is equal to the increase in the resin temperature calculated in step 1015 when the physical property value considering the temperature dependence is used. Since the compression load ΔF (M) is small even with the particle deformation amount ΔH, if the determination of F−NXΔF (M) ≦ 0 is NO in step 1014, the moving speed of the electrode in step 1012 is 0. Do not calculate.

  Moreover, the resin temperature of the arbitrary places calculated | required by analysis can be used for the temperature shown in FIG. For example, an average value of the resin temperature between the electrodes 4 calculated by calculation of the flow process of 1012, a temperature such as the resin temperature in the vicinity of the particles 1 can be used.

Here, if the determination in step 1016 is NO,
In step 1017, calculation convergence is determined. The convergence determination method compares the pressure with a predetermined pressure range, and determines that the pressure is within the range as convergence. If it does not converge, the process returns to one of steps 1001 to 1004. At this time, the operator is prompted to input and a step to be returned is determined.

  In step 1018, the appropriateness of particle deformation is determined. Here, it is determined whether the deformation amount of the particles is within the specified value range, and if it is outside the specified range, the process returns to one of steps 1001 to 1004. At this time, the operator is prompted to input, and it is determined that the calculation has converged in step 1017 for determining which step to return to. After it is determined in step 1018 that the particle deformation is appropriate, the calculation is terminated in step 1019. .

  In addition, although the example of the relationship of the deformation amount when a load is applied per particle 1 is shown as the input condition in step 1003, the deformation amount when a load per particle 1 is applied (or It is possible to input the relationship between the deformation rate) and the relationship between the stress applied to the particles 1 and the amount of deformation (or the deformation rate). Further, the exothermic equation is not limited to (Equation 7) to (Equation 11), and any function including the reaction rate of the resin material 2 can be used.

  The viscosity formula is not limited to (Formula 12) to (Formula 15), and any function including the temperature or reaction rate of the embryo material 2 can be used. The convergence determination can use any determination method. Further, not only three-dimensional analysis but also two-dimensional analysis can be performed. The above calculation can be performed using the finite element method, the finite volume method, or the finite difference method.

[Switching from electrode speed to pressure control]
Next, the processing of the analysis program will be described along the flowchart of FIG. First, in the model shape creation step 2001, the analysis target model specified by the operator via the input device, that is, the electrode to be analyzed, the shape of the resin material including the initial particles, and the space in which the resin material including the particles can flow is obtained. Data is read from the storage device 10.

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

  Next, in the physical property value input step 2003, density, thermal conductivity, specific heat, exothermic equation (Equation 7) to (Equation 11), viscosity equation (Equation 12) to (Equation 15) which are physical property values of the material to be analyzed. ), A display prompting the operator to input the arrangement, density, diameter, and deformation amount when a load is applied to each particle 1 and accepts these data from the input device.

  Next, in the boundary condition / molding condition input step 2004, the initial moving speed Vd of the semiconductor integrated circuit (IC) 3 and the electrode 4 and the maximum pressure applied to the upper part of the semiconductor integrated circuit (IC) 3 and the electrode 4 are input. As described above, a display prompting the operator is performed, and data is received from the input device.

  Here, from the received maximum pressure applied to the upper part of the semiconductor integrated circuit (IC) 3 and the electrode 4 and the area of the upper part of the semiconductor integrated circuit (IC) 3, it is added to the upper part of the semiconductor integrated circuit (IC) 3 and the electrode 4. The maximum load Fmax that can be obtained is calculated.

  Next, an analysis start instruction, an initial time increment, and an analysis end time tend are received from the operator. In step 2005, based on this instruction, the continuous equation (1), Napier Stokes equations (2) to (4), and energy conservation equation (5) stored in the recording device are called and the input has been accepted so far. In addition, initial time increment, pressure applied to the top of the semiconductor integrated circuit (IC) 3 and the electrode 4, density of the seed material, specific heat, thermal conductivity, exothermic formula (formula 7) to (formula 11), viscosity formula ( Substituting equations (12) to (15), the velocity, pressure, temperature and viscosity associated with the flow of the embryo material 2 and the particles 1 due to compression of the electrodes are calculated. The calculation result is stored in the storage device in association with the position of the finite element.

  Next, in step 2006, it is determined whether or not the analysis time is shorter than the set analysis end time tend. If the determination is NO, the analysis is terminated through calculation convergence determination, and if the determination is YES, The process proceeds to step 2007.

  In step 2007, when the electrode is moved at the initial moving speed Vd input in step 2004, the load FJ applied to the resin is expressed as “the contact area between the moving electrode 4 and the resin material 2” and “the resin tree of the contact portion”. Calculated as the product of “pressure of 2”.

  In step 2008, the maximum load Fmax applied to the upper part of the electrode 4 is compared with the FJ obtained in step 2007. If Fmax> FJ, the calculation is performed in which the electrode moves at the initial moving speed Vd input in step 2004 in step 2009. If Fmax> FJ, the control is switched to pressure control, and the movement of the electrode when the maximum load Fmax is applied to the upper part of the electrode 4 is calculated.

  In step 2010, it is determined whether the distance 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 particle, the process returns to step 2005 and the calculation is repeated. When the distance between the electrodes 4 becomes equal to the diameter (φD) of the particle 1, it is shown in FIG. Steps 1008 to 1016 are calculated.

  At step 2012, calculation convergence is determined. The convergence determination method compares the pressure with a predetermined pressure range, and determines that the pressure is within the range as convergence. If it does not converge, the process returns to one of steps 2001 to 2004. At this time, the operator is prompted to input and a step to be returned is determined.

  In step 2013, the appropriateness of particle deformation is determined. Here, it is determined whether the deformation amount of the particles is within a specified value range, and if it is outside the specified range, the process returns to one of steps 2001 to 2004. At this time, the operator is prompted to input, and it is determined that the calculation has converged in step 2012 for determining which step to return to. After it is determined in step 2013 that the particle deformation is appropriate, the calculation is terminated in step 2014. .

  In addition, although the example of the relationship of the deformation amount when a load is applied per particle 1 is shown as the input condition in step 2003, the deformation amount when a load per particle 1 is applied (or It is possible to input the relationship between the deformation rate) and the relationship between the stress applied to the particles 1 and the amount of deformation (or the deformation rate).

  Further, the exothermic equation is not limited to (Equation 7) to (Equation 11), and any function including the reaction rate of the resin material 2 can be used. The viscosity formula is not limited to (Formula 12) to (Formula 15), and any function including the temperature or the reaction rate of the resin material 2 can be used.

  The convergence determination can use any determination method. Further, not only three-dimensional analysis but also two-dimensional analysis can be performed. The above calculation can be performed using the finite element method, the finite volume method, or the finite difference method.

[Analysis example of electrode pressure control (single layer resin)]
Here, FIG. 15 shows an example of analysis (two-dimensional analysis). In an initial state, a resin material 2 containing conductive particles 1 is placed between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5. Here, the embryo material 2 has an initial temperature of 30 ° C., and the exothermic equations (Equation 7) to (Equation 11) and the viscosity equations (Equation 12) to (Equation 15) are used. The constant value, density, thermal conductivity, specific heat value, particle diameter (φD), and density of the exothermic formulas (Formula 7) to (Formula 11) and viscosity formulas (Formula 12) to (Formula 15) are shown. It is shown in 1.

  Further, the temperature of the semiconductor integrated circuit (IC) 3 is set to be constant (185 ° C.), moved by applying a pressure of 5 MPa in the direction of the substrate 5, and the resin material 2 including the particles 1 is compressed, whereby the particles 1 are compressed. The containing embryo material 2 is flowed. At this time, the temperature of the resin material 2 changes due to the contact between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the resin material 2, and the resin material 2 is compressed together with the particles 1 while the viscosity changes due to the temperature change. Calculate the flow process.

  When the distance between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 becomes smaller than the diameter of the particle 1, the calculation of the contact between the particle 1 and the electrode 4 is not performed in the analysis. That is, in the analysis, when the particles 1 are in contact with each other, and when the particles 1 and the electrode 4 are in contact with each other, the fluidity of only the resin material 2 is calculated by setting such that the particles 1 pass through the electrode 4.

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

  As a result of this calculation, if the load applied from the upper part of the electrode is equal to the compressive load required to deform the particles, the electrode moving speed becomes 0, and the resin temperature calculation without electrode movement is performed. Here, as the resin temperature increases, the compressive load required to deform the particles decreases as shown in FIG. 18, so that the calculation involving the electrode movement is performed again.

  Here, as the temperature shown in FIG. 18, the temperature at an arbitrary place obtained by analysis can be used. For example, an average value of the resin temperature between the electrodes 4 calculated by calculation of the flow process 1012 shown in FIG. In addition, although the heat conduction calculation within the particle is not performed here, the heat conduction calculation within the particle can also be performed by inputting the specific heat of the particle, the heat conductivity, the heat transfer coefficient between the resin material and the particle, etc. The temperature at an arbitrary position of the particle obtained by heat transfer calculation can also be used as the temperature shown in FIG.

Thereafter, the analysis ends at the set analysis end time. At this time, the deformation amount of the particle 1 can be obtained from the interval between the electrodes. In addition, the deformation amount ΔD of the particles can be obtained by (Expression 6).

  Here, D: the diameter of the particle 1 and Dl: the distance between the substrates 4 after the analysis is completed. In addition, although the case where the movement of the electrode 4 is controlled by the pressure has been described above, the present invention is not limited to this, and the movement of the electrode is changed from speed to pressure as shown in the flowchart of FIG. It is also possible to control.

[Analysis example of electrode pressure control (two-layer resin)]
Here, FIG. 16 shows an example of an analysis example (two-dimensional analysis) in which the resin material is divided into two layers.

In an initial state, a resin material having a two-layer structure made of a resin material 11 having different physical property values including particles 1 is formed on the resin material 2 including the conductive particles 1, and the electrode 4 of the semiconductor integrated circuit (IC) 3. And between the electrodes 4 of the substrate 5. Here, the resin material 2 has an initial temperature of 30 ° C., and the exothermic formulas (Formula 7) to (Formula 11) and the viscosity formulas (Formula 12) to (Formula 15) are used. In addition, regarding the constant value, density, thermal conductivity, specific heat value, particle diameter (φD), and density of the exothermic formulas (Formula 7) to (Formula 11) and the viscosity formulas (Formula 12) to (Formula 15), The resin material 2 and particle 1 in the first layer use the values in Table 1, and the values of the embryo material 11 and particles 1 in the second layer are shown in Table 2.

  Here, the temperature of the semiconductor integrated circuit (IC) 3 is set to be constant (185 ° C.), moved by applying a pressure of 5 MPa in the direction of the substrate 5, and the resin materials 2 and 11 are compressed to include the particles 1. Resin materials 2 and 11 are caused to flow. At this time, due to the contact between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the resin materials 2 and 11, the temperature of the tree material 2 and 11 is changed, and the viscosity change due to the temperature change is generated, while the resin material 2 and 11 is changed. It is possible to calculate the process of flowing while being compressed together with the particles 1.

  When the distance between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 becomes smaller than the diameter of the particle 1, the calculation of the contact between the particle 1 and the electrode 4 is not performed in the analysis. That is, in the analysis, when the particles 1 are in contact with each other, and when the particles 1 and the electrode 4 are in contact with each other, the fluidity of only the resin materials 2 and 11 is calculated by setting such that the particles 1 pass through the electrode 4. .

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

  As a result of this calculation, if the load applied from the upper part of the electrode is equal to the compressive load required to deform the particles, the electrode moving speed becomes 0, and the resin temperature calculation without electrode movement is performed. Here, as the resin temperature increases, the compressive load required to deform the particles decreases as shown in FIG. 18, so that the calculation involving the electrode movement is performed again.

  Here, as the temperature shown in FIG. 18, the temperature at an arbitrary place obtained by analysis can be used. For example, an average value of the resin temperature between the electrodes 4 calculated by calculation of the flow process of 1012, a temperature such as the resin temperature in the vicinity of the particles 1 can be used. In addition, although the heat conduction calculation within the particle is not performed here, the heat conduction calculation within the particle can also be performed by inputting the specific heat of the particle, the heat conductivity, the heat transfer coefficient between the resin material and the particle, etc. The temperature at an arbitrary position of the particle obtained by heat transfer calculation can also be used as the temperature shown in FIG.

Thereafter, the analysis ends at the set analysis end time. At this time, the deformation amount of the particle 1 can be obtained from the interval between the electrodes. In addition, the deformation amount ΔD of the particles can be obtained by (Expression 6).

  Here, D: the diameter of the particle 1 and Dl: the distance between the substrates 4 after the analysis is completed. In addition, although the example in which the movement of the electrode 4 is controlled by the pressure has been described above, the present invention is not limited to this, and the movement of the electrode is changed from the speed to the pressure as shown in the flowchart of FIG. It is also possible to control. In addition, although the heat conduction calculation within the particle is not performed here, the heat conduction calculation within the particle can also be performed by inputting the specific heat of the particle, the heat conductivity, the heat transfer coefficient between the resin material and the particle, and the like.

  In addition, although the example of the analysis in which the particle 1 is included in the resin material 11 of the two-phase day has been described above, the present invention is not limited to this, and the resin material 11 of the two-phase day includes the particle 1. It is also possible to perform analysis in a state where

[Prediction of conductivity, main force of particle coordinates (pressure control for 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 according to 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 based on the input of the relationship between the particle deformation amount and the conductivity obtained in the flowchart of FIG. First, in the model shape creation step 3001, the analysis target model specified by the operator through the input device, that is, the electrode to be analyzed, the shape of the resin material including the initial particles, and the space in which the resin material including the particles can flow is obtained. Data is read from the storage device 10.

  Next, in step 3002 for creating a three-dimensional solid element, the shape of the data read in the model shape creating step 1001 is decomposed into a plurality of specific spaces (three-dimensional solid finite elements) to create shape data for each finite element. .

  Next, in the physical property value input step 3003, density, thermal conductivity, specific heat, exothermic equation (Equation 7) to (Equation 11), viscosity equation (Equation 12) to (Equation 15) which are physical property values of the material to be analyzed. ), The arrangement, density and diameter of the particles 1, the deformation amount when a load is applied to each particle 1, the deformation amount per arbitrary number of particles 1, the electrode 4 and the substrate 5 of the semiconductor integrated circuit (IC) 3 The operator prompts the operator to input the conductivity between the electrodes 4 and receives the data from the input device.

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

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

  Next, in step 3006, it is determined whether or not the analysis time is shorter than the set analysis end time tend. If the determination is NO, the analysis is terminated through calculation convergence determination or the like. If the determination is YES, , 3007 is proceeded to.

  In step 3007, it is determined whether the spacing between the electrodes 4 is greater than the particle diameter. If the distance between the electrodes 4 is larger than the diameter of the particles, the process returns to step 3005 to repeat the calculation. If the distance between the electrodes 4 becomes equal to the diameter (φD) of the particles 1, in step 3008, The number of particles 1 in the connection part sandwiched between the electrodes 4 or the coordinates of the particle 1 in the connection part sandwiched between the electrodes 4 is output. Next, calculations in steps 1008 to 1016 shown in FIG. 13 are performed.

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

  The conductivity is a current value I when an arbitrary voltage is applied between the electrodes. Here, FIG. 9 shows an example of the relationship between the inputted “deformation amount per arbitrary number of particles 1 and conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5”. Here, Nl, N2, and N3 are shown as an arbitrary number of representative values of particles 1, and in step 3008, the number of particles 1 in the connection portion sandwiched between the electrodes 4 is other than Nl, N2, and N3. In this case, the value can be obtained by interpolation and extrapolation.

  Here, in step 3012, calculation convergence is determined. The convergence determination method compares the pressure with a predetermined pressure range, and determines that the pressure is within the range as convergence. If it does not converge, the process returns to one of steps 3001 to 3004. At this time, the operator is prompted to input and a step to be returned is determined.

  In step 3013, the appropriateness of particle deformation is determined. Here, it is determined whether or not the deformation amount of the particles is within a specified value range. If the deformation amount is outside the specified range, the process returns to any of steps 3001 to 3004. At this time, the operator is prompted to input and a step to be returned is determined.

  After determining that the calculation has converged in step 3012 and determining that the particle deformation is appropriate in step 3013, the calculation is terminated in step 3014. The “deformation amount per arbitrary number of particles 1 and the conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5” input in step 3003 are “per particle number 1 per arbitrary number of particles 1. “The contact area between the particle 1 and the electrode 4 and the conductivity between the electrode 4 of the semiconductor integrated circuit (IC) 3 and the electrode 4 of the substrate 5 obtained from the relationship between the deformation amount and the contact area between the particle 1 and the electrode 4”. "Can also be entered. In addition, although the electrical conductivity is a current value when an arbitrary voltage is applied between the electrodes, the present invention is not limited to this, and a resistance value between the electrodes can be used.

  Here, the coordinates of the particle 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. It is assumed that the coordinates of the output particle 1 can output an arbitrary position of the particle 1, and here, the coordinates of the center of the particle 1 are output.

  By structural analysis using the input conditions (coordinates of the particle 1 sandwiched between the electrodes 4 and the moving speed of the electrode 4) and the physical properties of the particles (elastic modulus, density, Poisson's ratio, etc.) output in this fluid calculation, As shown in FIG. 20, it is possible to obtain a deformation form when the particle 1 to which coordinates are input is compressed on the substrate 4 having the velocity of the electrode 4 as an input value, and the contact area between the particle 1 and the electrode by analysis. it can.

  Note that the conductivity can also be calculated from the contact area between the particle 1 and the electrode calculated in FIG. 20 using the relationship between the contact area between the particle 1 and the electrode 4 and the conductivity shown in FIG.

Claims (24)

(1) Import data from a storage device into a computing device, with a convex substrate to be analyzed, the shape of the resin material including the initial particles, and the space in which the resin material including the particles can flow,
(2) Based on the data, decompose into 3D solid elements,
(3) At least the density of resin material, thermal conductivity, specific heat, viscosity, particle external dimensions, density, relationship of load and displacement applied to each particle, external load F applied to a convex substrate Input,
(4) By calculating the continuous equation, Navi-Stokes equation, and energy conservation equation based on the three-dimensional solid element, the change in the resin temperature is calculated by the contact between the convex substrate and the resin material. Calculate the process in which the resin material flows while being compressed along with the particles by moving the convex substrate.
(5) In a time when the gap between the compressed convex substrates is equal to the diameter of the particles, the number of particles N sandwiched between the convex substrates is output and calculated.
(6) After the time when the gap between the convex substrate after compression in (5) is equal to the diameter of the particle, the contact between the electrode and the particle is ignored, and the load applied to the convex substrate is From the load F input in the above (3), the relationship between the load and displacement applied per particle input in the above (3) from the gap between the convex substrates and the convex shape obtained in the above (5) Using a value obtained by subtracting the load obtained by the product of the number N of particles sandwiched between the substrates, the resin material containing the particles is compressed with a convex substrate from two directions, thereby causing the resin material and the particles to flow. A method for analyzing a flow of a resin material containing particles, wherein the process is calculated. (1) Import data from a storage device into a computing device, with a convex substrate to be analyzed, the shape of the resin material including the initial particles, and the space in which the resin material including the particles can flow,
(2) Based on the data, decompose into 3D solid elements,
(3) Enter at least the resin material density, thermal conductivity, specific heat, viscosity, particle density, external dimensions, and the load-displacement relationship applied to each particle,
(4) Input the movement speed Vd of the convex substrate, the maximum external load Fmax applied to the convex substrate,
(5) By calculating the continuous equation, Navi-Stokes equation, and energy conservation equation based on the three-dimensional solid element, the change in resin temperature is calculated by the contact between the convex substrate and the seed material. And calculating the process in which the resin material flows while being compressed together with the particles by the moving speed Vd of the convex substrate,
(6) After the time when the gap between the compressed convex substrates is equal to the diameter of the particles, the number N of particles sandwiched between the convex substrates is output and calculated.
(7) After the time when the gap between the convex substrates after compression in (6) is equal to the diameter of the particles, contact between the convex substrate and the particles is ignored, and the convex substrate After calculating the deformation amount ΔH of the particle from the amount of movement, the load Δ applied per particle by the deformation amount ΔH of the particle from the relation of load-displacement applied per particle input in (4) above. F is calculated, the load applied to the particles (FR = NXΔF) is calculated, and the load FJ applied to the resin by the moving convex substrate is defined as the contact area between the moving convex substrate and the resin Calculate as the product of the resin pressure of the part,
(8) If the maximum external load Fmax 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 substrate Is controlled by the moving speed Vd, and the maximum external load Fmax 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). The boundary condition of the certain substrate movement is switched to the external load (maximum load Fmax) applied to the convex substrate, and the resin material containing particles is compressed by the convex substrate from two directions, A flow analysis method for a resin material containing particles, wherein the step of flowing the resin material and particles is calculated. In the flow analysis method of the resin material in which the particles according to claim 1 or 2 are contained,
As a method of inputting the relationship between the load applied to the particle and the displacement, the particle is characterized by inputting the relationship between the load applied to any number of particles and the displacement, or the relationship between the stress applied to any number of particles and the deformation rate. Flow analysis method for internal resin materials. In the flow analysis method of the resin material in which the particles according to claim 1 or 2 are contained,
Particles having conductivity, and calculating the conductivity between the convex substrates by inputting the relationship between the number of particles at the connecting portion, the deformation rate, and the zero conductivity. Flow analysis method for internal resin materials. In the flow analysis method of the resin material in which the particles according to claim 1 or 2 are contained,
The particle has conductivity, and by inputting the relationship between the number of particles in the connecting portion, the contact area between the particle and the convex substrate, and the conductivity, the conductivity between the convex substrates is output and calculated. A flow analysis method of a resin material containing particles characterized by the above. In the flow analysis method of the resin material in which the particles according to claim 1 or 2 are contained,
A flow analysis method for a resin material containing particles, wherein an exothermic reaction equation of the resin material and a viscosity equation which is a function including the resin temperature are input and a flow process of the resin material and particles is output. In the flow analysis method of the resin material in which the particles according to claim 1 or 2 are contained,
The resin material is formed of two or more layers having different physical property values, the particles are arranged in one or more resins, and an exothermic reaction formula of the two or more layers of resin, a viscosity formula that is a function including the resin temperature, is input, A flow analysis method for a resin material containing particles, wherein the flow process of two or more layers of resin and particles is output. In the flow analysis method of the resin material in which the particles according to claim 1 or 2 are contained,
A method for analyzing a flow of a resin material containing particles, wherein the convex substrate is a semiconductor integrated circuit including an electrode and a substrate including an electrode. (1) An input unit for importing 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 that performs decomposition processing on a three-dimensional solid element based on the data,
(3) At least the density of resin material, thermal conductivity, specific heat, viscosity, particle external dimensions, density, relationship of load and displacement applied to each particle, external load F applied to a convex substrate Input part to input,
(4) By calculating the continuous equation, Navi-Stokes equation, and energy conservation equation based on the three-dimensional solid element, the change in the resin temperature is calculated by the contact between the convex substrate and the resin material. , A calculation unit that calculates a process in which the resin material flows while being compressed together with the particles by moving the substrate having a convex shape,
(5) an output unit that outputs and calculates the number N of particles sandwiched between the convex-shaped substrates in a time when the gap between the convex-shaped substrates after compression is equal to the diameter of the particles;
(6) After the time in which the gap between the convex substrates after compression in (5) is equal to the diameter of the particles, contact between the convex substrate and the particles is ignored, and the convex substrate is formed. The applied load was determined from the load F input in (3) above, the load-displacement relationship applied per particle input in (3) above from the gap between the convex substrates, and (5) above. Using a value obtained by subtracting the load obtained by the product of the number N of particles sandwiched between the convex substrates, the resin material containing the particles is compressed with the convex substrate from two directions, and the resin material and A flow analysis system for a resin material containing particles, comprising a calculation unit for calculating a flow of particles. (1) An input unit for importing 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 that performs decomposition processing on a three-dimensional solid element based on the data,
(3) An input unit for inputting a relationship of at least the density of the resin material, the thermal conductivity, the specific heat, the viscosity, the particle density, the external dimensions, and the load-displacement applied to each particle,
(4) An input unit for inputting the movement speed Vd of the convex substrate, the maximum external load Fmax applied to the convex substrate,
(5) By calculating the continuous equation, Navi-Stokes equation, and energy conservation equation based on the three-dimensional solid element, the change in resin temperature is calculated by the contact between the convex substrate and the seed material. And a calculation unit for calculating a process in which the resin material flows while being compressed together 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 is equal to the diameter of the particles, an output calculation unit that outputs and calculates the number N of particles sandwiched between the convex substrates;
(7) After the time when the gap between the convex substrates after compression in (6) is equal to the diameter of the particles, contact between the convex substrate and the particles is ignored, and the convex substrate After calculating the deformation amount ΔH of the particle from the movement amount of the resin material in the moving direction, the particle 1 is calculated by the deformation amount ΔH of the particle from the relational expression of one load applied per particle input in the above (4). The load ΔF applied to each piece is calculated, the load applied to the particles (FR = NXΔF) is calculated, and the load FJ applied to the resin by the moving convex substrate is used to move the convex substrate. And a calculation unit that calculates the product of the resin contact area and the resin pressure of the part,
(8) If the maximum external load Fmax 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 substrate Is controlled by the moving speed Vd, and the maximum external load Fmax 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). The boundary condition of the certain substrate movement is switched to the external load (maximum load Fmax) applied to the convex substrate, and the resin material containing particles is compressed by the convex substrate from two directions, A flow analysis system for resin material containing particles, comprising a calculation unit for calculating a flow of resin material and particles. (1) Import data from a storage device into a computing device, with a convex substrate to be analyzed, the shape of the resin material including the initial particles, and the space in which the resin material including the particles can flow,
(2) Based on the data, decompose into 3D solid elements,
(3) At least the density of resin material, thermal conductivity, specific heat, viscosity, particle external dimensions, density, relationship of load and displacement applied to each particle, external load F applied to a convex substrate Input,
(4) By calculating the continuous equation, Navi-Stokes equation, and energy conservation equation based on the three-dimensional solid element, the change in the resin temperature is calculated by the contact between the convex substrate and the resin material. Calculate the process in which the resin material flows while being compressed along with the particles by moving the convex substrate.
(5) In a time when the gap between the compressed convex substrates is equal to the diameter of the particles, the number of particles N sandwiched between the convex substrates is output and calculated.
(6) After the time when the gap between the convex substrate after compression in (5) is equal to the diameter of the particle, the contact between the electrode and the particle is ignored, and the load applied to the convex substrate is From the load F input in the above (3), the relationship between the load and displacement applied per particle input in the above (3) from the gap between the convex substrates and the convex shape obtained in the above (5) Particles characterized by calculating a process of compressing a resin material containing particles with a substrate having a 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. Of flow analysis of resin material that contains. (1) Import data from a storage device into a computing device, with a convex substrate to be analyzed, the shape of the resin material including the initial particles, and the space in which the resin material including the particles can flow,
(2) Based on the data, decompose into 3D solid elements,
(3) At least density of resin material, thermal conductivity, specific heat, viscosity, particle external dimensions, density, relationship of load-displacement considering temperature change applied per particle, external applied to convex substrate Enter the load F from
(4) By calculating the continuous equation, Navi-Stokes equation, and energy conservation equation based on the three-dimensional solid element, the change in the resin temperature is calculated by the contact between the convex substrate and the resin material. Calculate the process in which the resin material flows while being compressed along with the particles by moving the convex substrate.
(5) In a time when the gap between the compressed convex substrates is equal to the diameter of the particles, the number of particles N sandwiched between the convex substrates is output and calculated.
(6) After the time when the gap between the convex substrate after compression in (5) is equal to the diameter of the particle, the contact between the electrode and the particle is ignored, and the load applied to the convex substrate is From the load F input in the above (3), the load-displacement relationship considering the temperature change applied per particle input in the above (3) from the gap between the convex substrates, and the above (5) Using the value obtained by subtracting the load obtained by the product of the number N of particles sandwiched between the convex substrates, the process of compressing the resin material containing the particles with the convex substrate from two directions is calculated,
(7) The load F input in (3) above is
If it is larger than the load obtained by the product of the relationship between the load-displacement applied per particle input in (3) above and the number N of particles sandwiched between the convex substrates obtained in (5) above, Repeatedly calculate the process of compressing the resin material containing the particles of (6) with a convex substrate from two directions,
The load F input in (3) above is
If the load-displacement relationship applied per particle input in (3) above is equal to the load determined by the product of the number of particles N sandwiched between the convex substrates determined in (5) above,
The movement speed of the electrode is set to 0, the temperature of the resin material is calculated using the energy equation, and the relationship between the load and the displacement applied to each particle input in (3) changes as the temperature rises.
The load F input in (3) above is the load-displacement relationship applied per particle input in (3) above and the number N of particles sandwiched between the convex substrates determined in (5) above. If it becomes larger than the load obtained by the product of
By repeatedly calculating the process of compressing the resin material containing particles of the above (6) with a convex substrate from two directions, the step of causing the resin material and the particles to flow is calculated. Of flow analysis of plastic materials. (1) Import data from a storage device into a computing device, with a convex substrate to be analyzed, the shape of the resin material including the initial particles, and the space in which the resin material including the particles can flow,
(2) Based on the data, decompose into 3D solid elements,
(3) Enter at least the relationship of load-displacement considering the density, thermal conductivity, specific heat, viscosity, particle density, external dimensions, and temperature change per particle,
(4) Enter the movement velocity Vd of the convex substrate and the external load F applied to the convex substrate,
(5) By calculating the continuous equation, Navi-Stokes equation, and energy conservation equation based on the three-dimensional solid element, the change in resin temperature is calculated by the contact between the convex substrate and the seed material. And calculating the process in which the resin material flows while being compressed together with the particles by the moving speed Vd of the convex substrate,
(6) The load FJ applied to the resin by the moving convex substrate is calculated as a product of the contact area between the moving convex substrate and the resin and the resin pressure, and the loads F and FJ input in (4) above. Relationship
If F ≧ FJ, the process of moving the electrode at the moving speed Vd of the convex substrate input in (4) above is calculated,
If F <FJ, the electrode is compressed by the load F input in (4) above, and the process of movement is calculated.
(7) After the time when the gap between the compressed convex substrates is equal to the particle diameter, the number N of particles sandwiched between the convex substrates is output and calculated.
(8) After the time when the gap between the convex substrate after compression in (7) is equal to the diameter of the particle, the contact between the electrode and the particle is ignored, and the load applied to the convex substrate is From the load F input in the above (4), the load-displacement relationship considering the temperature change applied per particle input in the above (3) from the gap between the convex substrates, and the above (7) Using the value obtained by subtracting the load obtained by the product of the number N of particles sandwiched between the convex substrates, the process of compressing the resin material containing the particles with the convex substrate from two directions is calculated,
(9) The load F input in (4) above is
If it is larger than the load obtained by the product of the relationship between the load-displacement applied per particle input in (3) above and the number N of particles sandwiched between the convex substrates obtained in (7) above,
Repeatedly calculate the process of compressing the resin material containing the particles of (8) with a convex substrate from two directions,
The load F input in (4) above is
If the load-displacement relationship applied per particle input in (3) above is equal to the load determined by the product of the number N of particles sandwiched between convex substrates determined in (7) above,
The movement speed of the electrode is set to 0, the temperature of the resin material is calculated using the energy equation, and the relationship between the load and the displacement applied to each particle input in (3) changes as the temperature rises.
The load F input in (4) above is the relationship between the load and displacement applied per particle input in (3) above and the number N of particles sandwiched between the convex substrates determined in (7) above. If it becomes larger than the load obtained by the product of
By repeatedly calculating the process of compressing the resin material containing the particles of the above (8) with a substrate having a convex shape from two directions, the step of causing the resin material and the particles to flow is calculated. Of flow analysis of plastic materials.   The flow analysis method for a resin material containing particles according to claim 11, claim 12, or claim 13, wherein the load and displacement applied to any number of particles as an input method of a relationship between the load applied to the particles and the displacement A flow analysis method for a resin material containing particles, characterized by inputting a relationship that takes into account the temperature change of the particle, or a relationship that takes into account the temperature applied to any number of particles and the stress and deformation rate. In the relationship considering the temperature change of the load applied to the particles according to claim 14 and displacement,
A method for analyzing a flow of a resin material containing particles, wherein the temperature is an average value of resin temperatures between substrates obtained by analysis or a resin temperature at an arbitrary location between substrates. In the flow analysis method of the resin material in which the particles according to claim 11 or claim 12 or claim 13 are contained,
The particle having the relationship of the deformation amount considering the temperature change according to claim 14 has conductivity, and by inputting the relationship between the number of particles of the connecting portion, the deformation rate, and the conductivity, the convex shape A flow analysis method for a resin material containing particles, wherein the conductivity between a certain substrate is output. In the flow analysis method of the resin material in which the particles according to claim 11 or claim 12 or claim 13 are contained,
The particle having the relationship of the deformation amount considering the temperature change according to claim 14 has conductivity, and the relationship between the number of particles in the connecting portion, the contact area between the particle and the convex substrate, and the conductivity is input. A method for analyzing the flow of a resin material containing particles, characterized in that the conductivity between convex substrates is output. In the flow analysis method of the resin material in which the particles according to claim 11 or claim 12 or claim 13 are contained,
The resin material is formed of two or more layers having different physical property values, and the particles having the relationship of the deformation amount considering the temperature change according to claim 4 are arranged in one or more resins, A flow analysis method for a resin material containing particles, wherein an exothermic reaction equation and a viscosity equation that is a function including a resin temperature are input and a flow process of two or more layers of resin and particles is output. In the flow analysis method of the resin material in which the particles according to claim 11 or claim 12 or claim 13 are contained,
A flow analysis method for a resin material containing particles, wherein the calculated positions of the particles sandwiched between the electrodes are output.   The moving speed of the electrode calculated by the flow analysis method of the resin material containing the particles according to claim 11, claim 12, or claim 13, the particles sandwiched between the substrates output by the calculation method according to claim 18. A calculation method characterized by performing structural analysis using a position as an input condition and calculating a deformation amount of a particle, a deformation form of the particle, or a contact area between the particle and the electrode. The deformation amount of the particle calculated by the calculation method according to claim 20, or the contact area between the particle and the electrode,
Conductivity between convex-shaped substrates using the relationship between the number of particles in the connecting portion, deformation rate, and conductivity, or the relationship between the number of particles in the connecting portion and the contact area between the particles and the convex substrate. The calculation method of the resin material which included the particle | grains characterized by carrying out output calculation of this. (1) An input unit for importing 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 that performs decomposition processing on a three-dimensional solid element based on the data,
(3) At least the density of resin material, thermal conductivity, specific heat, viscosity, particle external dimensions, density, relationship of load and displacement applied to each particle, external load F applied to a convex substrate Input part to input,
(4) By calculating the continuous equation, Navi-Stokes equation, and energy conservation equation based on the three-dimensional solid element, the change in the resin temperature is calculated by the contact between the convex substrate and the resin material. , A calculation unit that calculates a process in which the resin material flows while being compressed together with the particles by moving the substrate having a convex shape,
(5) an output unit that outputs and calculates the number N of particles sandwiched between the convex-shaped substrates in a time when the gap between the convex-shaped substrates after compression is equal to the diameter of the particles;
(6) After the time when the gap between the convex substrate after compression in (5) is equal to the diameter of the particle, the contact between the electrode and the particle is ignored, and the load applied to the convex substrate is From the load F input in the above (3), the relationship between the load and displacement applied per 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 is provided that calculates a process of compressing a resin material containing particles from two directions with a convex substrate using a value obtained by subtracting the load obtained by the product of the number N of particles sandwiched between the substrates. A flow analysis system for resin materials containing particles. (1) An input unit for importing 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 that performs decomposition processing on a three-dimensional solid element based on the data,
(3) At least density of resin material, thermal conductivity, specific heat, viscosity, particle external dimensions, density, relationship of load-displacement considering temperature change applied per particle, external applied to convex substrate An input unit for inputting the load F from
(4) By calculating the continuous equation, Navi-Stokes equation, and energy conservation equation based on the three-dimensional solid element, the change in the resin temperature is calculated by the contact between the convex substrate and the resin material. , A calculation unit that calculates a process in which the resin material flows while being compressed together with the particles by moving the substrate having a convex shape,
(5) an output unit that outputs and calculates the number N of particles sandwiched between the convex-shaped substrates in a time when the gap between the convex-shaped substrates after compression is equal to the diameter of the particles;
(6) After the time when the gap between the convex substrate after compression in (5) is equal to the diameter of the particle, the contact between the electrode and the particle is ignored, and the load applied to the convex substrate is From the load F input in the above (3), the load-displacement relationship considering the temperature change applied per particle input in the above (3) from the gap between the convex substrates, and the above (5) Of calculating the process of compressing a resin material containing particles from two directions with a convex substrate using a value obtained by subtracting the load obtained by the product of the number N of particles sandwiched between the convex substrates. Part,
(7) The load F input in (3) above is
If it is larger than the load obtained by the product of the relationship between the load-displacement applied per particle input in (3) above and the number N of particles sandwiched between the convex substrates obtained in (5) above,
Repeatedly calculate the process of compressing the resin material containing the particles of (6) with a convex substrate from two directions,
The load F input in (3) above is
If the load-displacement relationship applied per particle input in (3) above is equal to the load determined by the product of the number of particles N sandwiched between the convex substrates determined in (5) above,
The movement speed of the electrode is set to 0, the temperature of the resin material is calculated using the energy equation, and the relationship between the load and the displacement applied to each particle input in (3) changes as the temperature rises.
The load F input in (3) above is the load-displacement relationship applied per particle input in (3) above and the number N of particles sandwiched between the convex substrates determined in (5) above. If it becomes larger than the load obtained by the product of
It is characterized by comprising an arithmetic unit for calculating the step of flowing the resin material and the particles by repeatedly calculating the process of compressing the resin material containing the particles of (6) from two directions with a convex substrate. Flow analysis method of resin material with particles to be contained. (1) An input unit for importing 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) Based on the data, decompose into 3D solid elements,
(3) An input unit for inputting a relationship of load and displacement in consideration of at least density of resin material, thermal conductivity, specific heat, viscosity, particle density, external dimensions, temperature change applied per particle,
(4) An input unit for inputting the movement speed Vd of the convex substrate, the maximum external load Fmax applied to the convex substrate,
(5) By calculating the continuous equation, Navi-Stokes equation, and energy conservation equation based on the three-dimensional solid element, the change in resin temperature is calculated by the contact between the convex substrate and the seed material. And a calculation unit for calculating a process in which the resin material flows while being compressed together with the particles by the moving speed Vd of the convex substrate,
(6) The load FJ applied to the resin by the moving convex substrate is calculated as the product of the contact area between the moving convex substrate and the resin and the resin pressure, and the maximum load Fmax input in (4) above is calculated. FJ relationship
If Fmax ≧ FJ, calculate the process of the electrode 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 (4) above, and a calculation unit that calculates the process of moving,
(7) After the time when the gap between the convex substrates after compression becomes equal to the diameter of the particles, an output unit that outputs and calculates the number N of particles sandwiched between the convex substrates;
(8) After the time when the gap between the convex substrate after compression in (7) is equal to the diameter of the particle, the contact between the electrode and the particle is ignored, and the load applied to the convex substrate is From the load Fmax input in the above (4), the load-displacement relationship considering the temperature change applied per particle input in the above (3) from the gap between the convex substrates, and the above (7) Of calculating the process of compressing a resin material containing particles from two directions with a convex substrate using a value obtained by subtracting the load obtained by the product of the number N of particles sandwiched between the convex substrates. Part,
(9) The load Fmax input in (4) above is
If it is larger than the load obtained by the product of the relationship between the load-displacement applied per particle input in (3) above and the number N of particles sandwiched between the convex substrates obtained in (7) above,
Repeatedly calculate the process of compressing the resin material containing the particles of (8) with a convex substrate from two directions,
The load Fmax input in (4) above is
If the load-displacement relationship applied per particle input in (3) above is equal to the load determined by the product of the number N of particles sandwiched between convex substrates determined in (7) above,
The movement speed of the electrode is set to 0, the temperature of the resin material is calculated using the energy equation, and the relationship between the load and the displacement applied to each particle input in (3) changes as the temperature rises.
The load Fmax input in the above (4) is the load-displacement relationship applied per particle input in the above (3) and the number N of particles sandwiched between the convex substrates determined in the above (7). If it becomes larger than the load obtained by the product of
It is characterized by comprising an arithmetic unit for calculating a step of causing the resin material and the particles to flow by repeatedly calculating the process of compressing the resin material containing the particles of (8) with a convex substrate from two directions. Flow analysis system of resin material with particles to be contained.

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