Simulation method and simulation program for resin curing reactions

Abstract

This document provides a simulation method and a simulation program for resin curing reactions. [Solution] The resin curing reaction simulation method comprises the steps of: estimating the degree of curing of resin contained in a plurality of workpieces placed in a furnace by coupled analysis of a master curve representing the relationship between temperature history and the degree of resin curing and thermal fluid analysis; and extracting the portion of the plurality of workpieces in which the resin curing is slowest based on the results of the estimation.

Description

Technical Field

[0001] The embodiments relate to a method for simulating a resin curing reaction and a simulation program.

Background Art

[0002] When manufacturing industrial products such as semiconductor products, the resin may be thermally cured. The degree of cure of the resin can be measured by differential scanning calorimetry (DSC) or Fourier transform infrared spectroscopy (FT-IR). However, with these methods, only one workpiece can be measured at a time, and a great deal of time and labor are required to explore the heat treatment conditions. Therefore, a method for simulating a resin curing reaction is desired.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] An object of the embodiments is to provide a method for simulating a resin curing reaction and a simulation program.

Means for Solving the Problems

[0005] The method for simulating a resin curing reaction according to the embodiments includes a step of estimating the degree of cure of the resin contained in a plurality of workpieces arranged in a furnace by a coupled analysis of a master curve representing the relationship between the temperature history and the degree of cure of the resin and a thermal fluid analysis, and a step of extracting, based on the result of the estimation, the portion where the curing of the resin is the slowest among the plurality of workpieces.

[0006] The resin curing reaction simulation program according to the embodiment causes a computer to perform the following steps: estimate the degree of curing of the resin contained in a plurality of workpieces placed in a furnace by coupled analysis of a master curve representing the relationship between temperature history and the degree of resin curing and thermal fluid analysis; and based on the results of the estimation, extract the portion of the plurality of workpieces in which the resin curing is slowest. [Brief explanation of the drawing]

[0007] [Figure 1] Figure 1 is a flowchart showing the method for creating a master curve in an embodiment. [Figure 2] Figure 2(a) is a graph showing the DSC measurement results with temperature on the horizontal axis and heat generation on the vertical axis, and (b) is a graph showing the relationship between the degree of resin hardening and heat generation, with the degree of resin hardening on the horizontal axis and the heat generation of the peak portion on the vertical axis. [Figure 3] Figure 3(a) is a graph showing the FT-IR measurement results, with wavenumber on the horizontal axis and absorbance on the vertical axis, and (b) is a graph showing the relationship between the degree of resin curing and peak intensity, with the degree of resin curing on the horizontal axis and the peak intensity corresponding to the absorption of epoxy groups on the vertical axis. [Figure 4] Figure 4(a) is a graph showing the measurement results of DSC or FT-IR with temperature or time on the horizontal axis and resin curing degree on the vertical axis, and (b) is a graph showing the master curve with the logarithm of the temperature history Θ on the horizontal axis and resin curing degree on the vertical axis. [Figure 5] Figure 5 shows the target of the simulation according to the embodiment. [Figure 6] Figure 6 is a flowchart showing the simulation method according to the embodiment. [Figure 7] Figures 7(a) and 7(b) show the simulation results according to this embodiment, where (a) shows the temperature distribution of multiple workpieces placed in the furnace, and (b) shows the degree of hardening of the resin portion contained in the multiple workpieces. [Figure 8]Figures 8(a) and (b) are graphs showing the curing reaction of the resin, with time on the horizontal axis and reaction rate on the vertical axis. (a) shows the fastest curing portion, and (b) shows the slowest curing portion. [Figure 9] Figures 9(a) and (b) are graphs showing the curing behavior at the slowest point, with time on the horizontal axis and temperature and resin curing degree on the vertical axis. (a) shows the case where heat treatment is excessive, and (b) shows the case where heat treatment is insufficient. [Modes for carrying out the invention]

[0008] The following describes the simulation method for the resin curing reaction according to this embodiment. In this embodiment, the workpiece to be simulated is a component containing a thermosetting resin (hereinafter also simply referred to as "resin"), for example, a semiconductor device in which a semiconductor chip is encapsulated in resin. In addition to the semiconductor chip and resin, the workpiece may also include metal parts such as leads, wires, and bumps, and ceramic parts such as a wiring board.

[0009] First, as preparation for the simulation, a master curve is created. A master curve is created each time the type of resin included in the workpiece is changed. Figure 1 is a flowchart showing the method for creating a master curve in this embodiment. Figure 2(a) is a graph showing the DSC measurement results with temperature on the horizontal axis and heat generation on the vertical axis, and (b) is a graph showing the relationship between the degree of resin hardening and heat generation, with the degree of resin hardening on the horizontal axis and the heat generation of the peak portion on the vertical axis. Figure 3(a) is a graph showing the FT-IR measurement results, with wavenumber on the horizontal axis and absorbance on the vertical axis, and (b) is a graph showing the relationship between the degree of resin curing and peak intensity, with the degree of resin curing on the horizontal axis and the peak intensity corresponding to the absorption of epoxy groups on the vertical axis. Figure 4(a) is a graph showing the measurement results of DSC or FT-IR with temperature or time on the horizontal axis and resin curing degree on the vertical axis, and (b) is a graph showing the master curve with the logarithm of the temperature history Θ on the horizontal axis and resin curing degree on the vertical axis.

[0010] As shown in step S11 of Figure 1, the degree of hardening of the resin contained in the workpiece is measured. The degree of hardening of the resin is an index that represents the degree of hardening of the resin within the range of 0% to 100%, with the unhardened state being 0% and the fully hardened state being 100%.

[0011] The degree of resin curing is measured, for example, by the DSC method. As shown in Figure 2(a), the peak area of ​​the difference between the heat generation profile of the uncured resin and the heat generation profile of the cured resin corresponds to the total amount of heat generated S during the curing reaction. As shown in Figure 2(b), the total amount of heat generated S increases as the resin curing progresses. The degree of curing of the resin when the amount of heat generated S is zero is defined as 0%, and the degree of curing of the resin when the amount of heat generated S reaches a predetermined value is defined as 100%, and the range in between is interpolated using a linear function.

[0012] Alternatively, the degree of resin curing may be measured by the FT-IR method. As shown in Figure 3(a), we focus on the peak P representing the epoxy group CO stretching vibration in the measurement results obtained by the FT-IR method. Peak P shows a constant intensity in uncured resin and disappears in cured resin. Therefore, as shown in Figure 3(b), the degree of curing of the resin is set to 0% when the intensity of peak P is at its initial value I0, and to 100% when the intensity of peak P becomes zero, and the interval between these is interpolated by a linear function. Note that the degree of curing of the resin may also be measured by methods other than the DSC method and the FT-IR method.

[0013] Next, a master curve is created as shown in step S12 of Figure 1. Fig. 4(a) shows the measurement results of the degree of curing by the DSC method or the FT-IR method. As shown in Fig. 4(a), the relationship between the temperature or time of the heat treatment applied to the resin and the degree of curing of the resin varies depending on the heat treatment conditions such as the heating rate. The change in the degree of curing from the uncured state to the fully cured state of the resin is measured at least two or more times, preferably three or more times. Fig. 4(a) shows an example in which the change in the degree of curing was measured three times with different heating rates.

[0014] As shown in Fig. 4(b), from the plurality of measurement results shown in Fig. 4(a), one master curve MSC is created. The master curve MSC is a function showing the relationship between the temperature history and the degree of curing. For example, the master curve MSC is represented by the following Equation 1. In Equation 1 below, t is time, T is temperature, Q is the activation energy, R is the gas constant, and the temperature history Θ(t,T) is the sum of the temperature histories from the start point of the heat treatment to an arbitrary time t and temperature T. The master curve MSC varies depending on the type of resin.

[0015] [Equation]

[0016] Next, a method for simulating the resin curing reaction according to the present embodiment will be described. Fig. 5 is a diagram showing the object of simulation according to the present embodiment. Fig. 6 is a flowchart showing the simulation method according to the present embodiment. Figs. 7(a) and (b) are diagrams showing the simulation results according to the present embodiment. (a) shows the temperature distribution of a plurality of workpieces arranged in the furnace, and (b) shows the degree of curing of the resin portions included in the plurality of workpieces. Figs. 8(a) and (b) are graphs showing the curing reaction of the resin with time on the horizontal axis and the reaction rate on the vertical axis. (a) shows the portion where curing is the fastest, and (b) shows the portion where curing is the slowest. Figures 9(a) and (b) are graphs showing the curing behavior at the slowest point, with time on the horizontal axis and temperature and resin curing degree on the vertical axis. (a) shows the case where heat treatment is excessive, and (b) shows the case where heat treatment is insufficient.

[0017] As shown in Figure 5, this embodiment involves a plurality of workpieces 100 placed inside a furnace 200. The furnace 200 is a heating furnace, and the atmosphere inside the furnace 200 is, for example, air or nitrogen. The workpieces 100 are products containing thermosetting resin, for example, semiconductor devices in which semiconductor chips are encapsulated by the resin. In the initial state, the resin is uncured.

[0018] As shown in step S21 of Figure 6, a coupled analysis of the master curve MSC shown in Figure 4(b) and thermal fluid analysis is performed inside the furnace 200. There are three types of heat transfer: conduction, convection, and radiation. These are taken into consideration to simulate the temperature changes in each part of the furnace 200. In addition, the temperature changes in each part of each workpiece 100 are simulated, mainly considering heat conduction.

[0019] As shown in Figure 7(a), there are temperature differences within the furnace 200 depending on the location. For example, areas closer to the heating device (not shown) heat up faster than areas further away, and the upper part of the furnace 200 is hotter than the lower part. However, this temperature distribution depends on the configuration of the furnace 200. Also, within each workpiece 100, the metal parts have a relatively high heat transfer rate, while the resin parts have a relatively low heat transfer rate. The temperature distribution shown in Figure 7(a) changes over time.

[0020] The degree of resin curing is estimated based on the temperature distribution shown in Figure 7(a). At this time, the temperature history Θ(t,T) is calculated using Equation 1 based on the temperature history from the start of heating to any given point in time. The degree of curing is then estimated based on the calculated temperature history Θ(t,T) and the master curve MSC shown in Figure 4(b). As a result, the distribution of the degree of resin curing at any given point in time is estimated, as shown in Figure 7(b). This distribution of curing changes over time. The part where the resin hardens fastest is designated as part A, and the part where the resin hardens slowest is designated as part B. Parts A and B are, for example, parts of mutually different workpieces 100.

[0021] Figure 8(a) shows part A where the resin hardens fastest, and Figure 8(b) shows part B where the resin hardens slowest. In Figures 8(a) and (b), hardening is estimated to be complete at time ta and tb, when the reaction rate initially increases to a maximum value, then decreases back to the baseline.

[0022] Next, as shown in step S22 of Figure 6, the portion B where the resin hardens the slowest is extracted from the hardening degree distribution shown in Figure 7(b). As shown in Figure 8(b), at time tb when the hardening of portion B, where the resin hardens the slowest, is completed, it is determined that the resin has hardened in all workpieces 100 placed inside the furnace 200.

[0023] Next, as shown in step S23 of Figure 6, the time tb at which the curing of the slowest part B of the resin is completed is output.

[0024] Next, as shown in step S24 of Figure 6, the excess or deficiency of the heat treatment is estimated. In Figures 9(a) and (b), the solid lines show the assumed temperature profile, and the dashed lines show the degree of resin curing.

[0025] As shown in Figure 9(a), if the degree of hardening reaches 100% during the heat treatment, it can be determined that the subsequent heat treatment is excessive. In this case, it may be possible to shorten the heat treatment time by the excess amount L. This can improve throughput and reduce the cost of the resin curing process.

[0026] Furthermore, as shown in Figure 9(b), if the degree of hardening of section B does not reach 100% until the end of the heat treatment, it can be determined that the heat treatment is insufficient. In this case, the set temperature for the heat treatment is increased, or a new condition is set by increasing the set time, and the above simulation is repeated. In this way, the conditions under which the degree of hardening of section B reaches 100% are found. As a result, the resin in section B, which is the slowest to harden, is reliably cured, and the quality of workpiece 100 is stabilized. In this way, the simulation of the resin curing reaction is completed.

[0027] The above-described simulation can be performed on a computer using a simulation program for resin curing reactions. The computer may be a general-purpose machine equipped with an arithmetic unit, memory unit, input / output unit, etc., or it may be a dedicated machine.

[0028] The resin curing reaction simulation program according to this embodiment causes the computer to perform the following steps: estimate the degree of curing of the resin contained in a plurality of workpieces 100 placed in the furnace 200 by performing a coupled analysis of a master curve MSC representing the relationship between temperature history and the degree of resin curing and thermal fluid analysis; and based on the results of this estimation, extract the portion B of the plurality of workpieces 100 in which the resin curing is slowest.

[0029] Next, the effects of this embodiment will be described. According to this embodiment, the degree of resin curing can be simulated. This makes it possible to estimate the degree of resin curing at any point in the heat treatment for any part of each workpiece 100 in the furnace 200. As a result, the resin curing reaction can be visualized and excessive or insufficient heat treatment can be detected. Consequently, the resin curing treatment conditions can be optimized.

[0030] According to the embodiments described above, a simulation method and simulation program for resin curing reactions can be realized.

[0031] Although embodiments of the present invention have been described above, these embodiments are presented as examples and are not intended to limit the scope of the invention. These novel embodiments can be implemented in various other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their variations are included in the scope and spirit of the invention, as well as in the claims of the invention and its equivalents.

[0032] The present invention includes the following embodiments.

[0033] (Note 1) A process to estimate the degree of curing of resin contained in multiple workpieces placed in a furnace by coupled analysis of a master curve representing the relationship between temperature history and the degree of resin curing and thermal fluid analysis, Based on the results of the estimation, a step is made to extract the part of the plurality of workpieces in which the resin hardens most slowly, A method for simulating resin curing reactions, equipped with [a specific feature / feature].

[0034] (Note 2) The simulation method described in Appendix 1, in which time is t, temperature is T, gas constant is R, activation energy is Q, and the temperature history is Θ(t,T), the temperature history is given by the following formula. TIFF2026056841000003.tif20170

[0035] (Note 3) The aforementioned formula is derived from the simulation method described in Appendix 2, which is based on the results of differential scanning calorimetry.

[0036] (Note 4) The aforementioned formula is derived from the simulation method described in Appendix 2, which is based on the measurement results of Fourier transform infrared spectroscopy.

[0037] (Note 5) The simulation method according to any one of the appendices 1 to 4, further comprising the step of outputting the time at which the curing of the slowest part of the resin is completed.

[0038] (Note 6) On the computer, The process involves a coupled analysis of a master curve representing the relationship between temperature history and resin curing degree, and thermal fluid analysis, to estimate the curing degree of resin contained in multiple workpieces placed inside the furnace. Based on the results of the estimation, the step of extracting the part of the workpiece from which the resin hardens most slowly, A simulation program that executes the resin curing reaction.

[0039] (Note 7) The simulation program described in Appendix 6 gives the temperature history by the following formula, where θ(t,T), time is t, temperature is T, gas constant is R, and activation energy is Q. TIFF2026056841000004.tif20170

[0040] (Note 8) The simulation method according to Appendix 6 or 7, further comprising the step of outputting the time at which the curing of the slowest part of the resin is completed. [Explanation of Symbols]

[0041] 100 Work 200 furnace A: The part where the resin hardens the fastest. B. The part where the resin hardens the slowest. L excess MSC Master Curve P Peak S Heat output T temperature t, ta, tb time

Claims

1. A process to estimate the degree of curing of resin contained in multiple workpieces placed in a furnace by coupled analysis of a master curve representing the relationship between temperature history and the degree of resin curing and thermal fluid analysis, Based on the results of the estimation, a step is made to extract the part of the plurality of workpieces in which the resin hardens most slowly, A method for simulating resin curing reactions, equipped with [a specific feature / feature].

2. The simulation method according to claim 1, wherein when time is t, temperature is T, gas constant is R, activation energy is Q, and the temperature history is Θ(t, T), the temperature history is given by the following formula.

3. The simulation method according to claim 2, wherein the aforementioned formula is created based on the results of differential scanning calorimetry.

4. The simulation method according to claim 2, wherein the aforementioned mathematical formula is created based on the measurement results of Fourier transform infrared spectroscopy.

5. The simulation method according to any one of claims 1 to 4, further comprising the step of outputting the time at which the curing of the slowest part of the resin is completed.

6. On the computer, The process involves a coupled analysis of a master curve representing the relationship between temperature history and resin curing degree, and thermal fluid analysis, to estimate the curing degree of resin contained in multiple workpieces placed inside the furnace. Based on the results of the estimation, the step of extracting the portion of the workpieces in which the resin hardens most slowly, A simulation program for executing resin curing reactions.

7. The simulation program according to claim 6, wherein the temperature history is given by the following formula, where θ(t, T), time is t, temperature is T, gas constant is R, and activation energy is Q.

8. The simulation program according to claim 6 or 7, further comprising the step of outputting the time at which the curing of the slowest part of the resin is completed.

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