Simulation system, simulation method and simulation program

Abstract

To predict a change in shape of a resin film of an element having changed in heat.SOLUTION: A simulation system is configured to: acquire object information related to a structure of an object comprising a substrate and a resin film formed on the substrate, boundary conditions for dividing the object into a finite number of elements, and heat information related to heat as to the object; generate an analytic model representing the object with the finite number of elements on the basis of the object information and the boundary conditions; execute simulation based on the analytic model and the heat information; analyze changes of the finite number of respective elements when the object changes in heat; and specify a shape profile of a top surface of the resin film of the object having changed in heat on the basis of results of the analysis.SELECTED DRAWING: Figure 3

Description

Technical Field

[0001] One aspect of the present disclosure relates to a simulation system, a simulation method, and a simulation program.

Background Art

[0002] A structure including a substrate and a resin film formed on the substrate is known. For example, Patent Document 1 describes a structure including a semiconductor substrate, a protective film covering the semiconductor substrate, a first conductor layer formed on an exposed circuit element, and an interlayer insulating film made of a polyimide resin or the like formed on the protective film and the first conductor layer.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] A method for predicting a change in the shape of a resin film in an element whose temperature has changed is desired.

Means for Solving the Problems

[0005] A simulation system according to an aspect of the present disclosure includes at least one processor. The at least one processor acquires object information regarding the structure of an object including a substrate and a resin film formed on the substrate, boundary conditions for dividing the object into a finite number of elements, and thermal information regarding heat of the object, generates an analysis model representing the object by a finite number of elements based on the object information and the boundary conditions, executes a simulation based on the analysis model and the thermal information to analyze changes of each of the finite number of elements when heat changes in the object, and specifies a shape profile of the upper surface of the resin film in the object where heat has changed based on the result of the analysis.

[0006] A simulation method according to an aspect of the present disclosure is executed by a simulation system including at least one processor. The simulation method includes acquiring object information regarding the structure of an object including a substrate and a resin film formed on the substrate, boundary conditions for dividing the object into a finite number of elements, and thermal information regarding heat of the object; generating an analysis model representing the object by a finite number of elements based on the object information and the boundary conditions; executing a simulation based on the analysis model and the thermal information to analyze changes of each of the finite number of elements when heat changes in the object; and specifying a shape profile of the upper surface of the resin film in the object where heat has changed based on the result of the analysis.

[0007] A simulation program according to an aspect of the present disclosure causes a computer to execute steps of: obtaining object information regarding the structure of an object including a substrate and a resin film formed on the substrate, boundary conditions for dividing the object into a finite number of elements, and heat information regarding heat of the object; generating an analysis model representing the object by a finite number of elements based on the object information and the boundary conditions; executing a simulation based on the analysis model and the heat information to analyze changes in each of the finite number of elements when heat changes in the object; and specifying a shape profile of the upper surface of the resin film in the object in which heat has changed based on the result of the analysis.

[0008] In such an aspect, a situation of the object including the resin film on the substrate is simulated using an analysis model representing the object by a finite number of elements, and changes in each element are analyzed. Then, based on the result of the analysis, a shape profile of the upper surface of the resin film is specified. In this way, by obtaining the shape profile through simulation, a change in the shape of the resin film in an element in which heat has changed can be predicted.

Advantages of the Invention

[0009] According to an aspect of the present disclosure, a change in the shape of the resin film in an element in which heat has changed can be predicted.

Brief Description of the Drawings

[0010]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Embodiments for Carrying Out the Invention

[0011] Hereinafter, embodiments in the present disclosure will be described in detail with reference to the accompanying drawings. In the description of the drawings, the same or equivalent elements are denoted by the same reference numerals, and redundant descriptions are omitted.

[0012] [Overview of the System] A simulation system 10 according to an example is a system that analyzes changes in an object by simulation. The object is, for example, an element including a substrate and a resin film formed on the substrate. The resin film is formed, for example, by applying a photosensitive resin material on the substrate and drying the photosensitive resin material.

[0013] In one example, a process of curing the resin film by changing the heat in the element to form an insulating film can be performed. In the present disclosure, "changing the heat" is a concept including adding heat and removing heat. In the formed insulating film, it is desirable that the upper surface thereof is flat, but due to the change in heat in the element, the shape of the element (for example, the shape of the upper surface of the resin film) may change during the curing process. For example, distortion may occur on the upper surface of the resin film. In one example, the simulation system 10 is used to analyze such changes in the element where heat has changed. That is, it can be said that the simulation system 10 is a system that analyzes changes in an object where heat has changed.

[0014] In the present disclosure, the "object with changed heat" is a concept including an object to which heat is applied and an object from which heat is removed. In the present disclosure, the "object to which heat is applied" is a concept including an object to which heat is applied by being intentionally heated and an object to which heat is passively applied as a result of the surrounding environment rather than depending on intentional heating. In the present disclosure, the "object from which heat is removed" is a concept including an object from which heat is removed by being intentionally cooled and an object from which heat is passively removed as a result of the surrounding environment rather than depending on intentional cooling.

[0015] When curing the resin film, the resin film may be cured by removing the heat from the element to which heat is applied, or the resin film may be cured only by applying heat to the element, or the resin film may be cured by both applying heat to the element and removing the heat from the element. That is, the simulation system 10 may analyze the change of the object after the heat is removed after the heat is applied, or may analyze the change of the object to which heat is applied.

[0016] The photosensitive resin material for forming the resin film described above may be a photosensitive resin material for forming a rewiring layer. The photosensitive resin material contains, for example, a maleimide compound having a specific structure, a crosslinking agent, and a photopolymerization initiator as its components. The maleimide compound is a reaction product of a tetracarboxylic dianhydride, an amine, and maleic anhydride. The amine includes a dimer diamine.

[0017] In one example, the simulation system 10 analyzes the changes in the object with the changed heat by executing a simulation using an analysis model that represents the object by a finite number of elements, and specifies the shape profile of the upper surface of the resin film on the object. The analysis model refers to a mathematical model that represents the relationship between a finite number of elements representing the object by a function or parameters. The shape profile of the upper surface of the resin film refers to information indicating each position of the upper surface in the normal direction of the upper surface. That is, the shape profile indicates the shape of the upper surface when viewed along the extending direction of the upper surface of the resin film. For example, the shape profile indicates whether phenomena such as distortion and undulation occur on the upper surface of the resin film, or whether the upper surface is flat. The simulation system 10 converts the object into a finite number of elements and sets the relationship between the elements. Then, the simulation system 10 analyzes the changes in the object with the changed heat by simulation and specifies the shape profile. Such a method is also called a discretization method. Examples of the discretization method include the finite element method (FEM), the finite difference method (FDM), and the finite volume method (FVM). In one example, the simulation system 10 executes the simulation using the finite element method.

[0018] [Configuration of the System] FIG. 1 is a diagram showing an example of the functional configuration of the simulation system 10. In one example, the simulation system 10 includes, as functional modules, an acquisition unit 11, a generation unit 12, an analysis unit 13, a specification unit 14, and an output unit 15.

[0019] The acquisition unit 11 is a functional module that acquires object information regarding the structure of an object, boundary conditions for dividing the object into a finite number of elements, and heat information regarding the heat of the object. In the present disclosure, "the heat of the object" is a concept that includes the heat applied to the object and the heat removed from the object. The generation unit 12 is a functional module that generates an analysis model based on the acquired object information and boundary information. The analysis unit 13 is a functional module that executes a simulation based on the generated analysis model and the acquired heat information, and analyzes the changes of each of the finite number of elements when the heat changes in the object. The specifying unit 14 is a functional module that specifies the shape profile of the upper surface of the resin film in the object in which the heat has changed based on the results of the analysis. The output unit 15 is a functional module that outputs the processing result.

[0020] In one example, the generation unit 12, the analysis unit 13, and the specifying unit 14 are implemented by the modeling software "COMSOL Multiphysics" of COMSOL. Alternatively, the generation unit 12, the analysis unit 13, and the specifying unit 14 may be implemented by the structural analysis software "ANSYS" of ANSYS, or may be implemented by the analysis software "SIMULIA / Abaqus" of Intermesh Japan. Alternatively, the generation unit 12, the analysis unit 13, and the specifying unit 14 may be implemented by the numerical analysis software "MATLAB" of MathWorks, or may be implemented by the analysis software "CATIA V5 Analysis" of IDAJ.

[0021] FIG. 2 is a diagram showing an example of a general hardware configuration of a computer 100 that constitutes the simulation system 10. For example, the computer 100 includes a processor (e.g., CPU) 101 that executes an operating system, application programs, etc., a main memory unit 102 composed of a ROM and a RAM, an auxiliary storage unit 103 composed of a storage device such as a hard disk and a flash memory, a communication control unit 104 composed of a network card or a wireless communication module, an input device 105 such as a keyboard and a mouse, and an output device 106 such as a monitor.

[0022] Each functional module of the simulation system 10 is realized by causing the processor 101 to load a predetermined program on the processor 101 or the main memory unit 102 and execute the program. The processor 101 operates the communication control unit 104, the input device 105, or the output device 106 according to the program, and reads and writes data in the main memory unit 102 or the auxiliary storage unit 103. Data or databases required for processing are stored in the main memory unit 102 or the auxiliary storage unit 103.

[0023] The simulation system 10 is constituted by at least one computer. When a plurality of computers are used, these computers are connected via a communication network such as the Internet or an intranet, thereby logically constructing one simulation system 10.

[0024] A simulation program for causing a computer or a computer system to function as a simulation system 10 includes program codes for causing the computer or the computer system to function as an acquisition unit 11, a generation unit 12, an analysis unit 13, an identification unit 14, and an output unit 15. This simulation program may be provided after being non-temporarily recorded on a tangible recording medium such as a CD-ROM, a DVD-ROM, or a semiconductor memory. Alternatively, the simulation program may be provided via a communication network as a data signal superimposed on a carrier wave. The provided simulation program is stored in, for example, an auxiliary storage unit 103. By the processor 101 reading out and executing the simulation program from the auxiliary storage unit 103, each of the above functional modules is realized.

[0025] [Operation of the System] With reference to FIG. 3, an example of the processing by the simulation system 10 and the simulation method according to the present embodiment will be described. Hereinafter, an example of the processing by the simulation system 10 will be described by taking as an example the case where the simulation system 10 analyzes the change of an object after heat is applied and then the heat is removed. FIG. 3 is a flowchart showing an example of the processing by the simulation system 10.

[0026] In step S1, the acquisition unit 11 acquires object information regarding the structure of the object, boundary conditions for dividing the object into a finite number of elements, and heat information regarding the heat of the object. The acquisition unit 11 acquires these pieces of information for an object represented in two dimensions or three dimensions.

[0027] In one example, the acquisition unit 11 acquires, as object information, shape information regarding the shape of the object and physical property value information regarding the physical property values of the object. That is, the object information may include shape information regarding the shape of the object and physical property value information regarding the physical property values of the object. The acquisition unit 11 acquires, for example, as the shape information, the respective widths, depths, and heights of the components of the object including at least the substrate and the resin film, and as the physical property value information, the respective storage elastic moduli, coefficients of thermal expansion, Poisson's ratios, thermal conductivities, and heat capacities of the components of the object.

[0028] In one example, the acquisition unit 11 acquires, as boundary conditions, the positions and sizes of the respective elements representing the object. That is, the boundary conditions may include the positions and sizes of the respective elements representing the object. In one example, the position of each element regarding a two-dimensional object is defined by an X coordinate indicating the position in the width direction of the object and a Y coordinate indicating the position in the height direction of the object. The position of each element regarding a three-dimensional object is defined using, in addition to the X and Y coordinates, a Z coordinate which is the position in the depth direction of the object. The size of each element may be set based on, for example, the height of the substrate or the resin film. In this case, the maximum value of the size may be set to 1 / 5 of the height of the substrate or the resin film. The sizes of the elements may be unified, or may be set individually based on the positions of the elements.

[0029] In one example, the acquisition unit 11 acquires, as thermal information, the initial temperature, the final temperature, the curing temperature, the cooling conditions of the object, and the amount of heat insulation at the interface between the components of the object including at least the substrate and the resin film. The initial temperature is the temperature of the object before the heat of the object changes. The final temperature is the temperature of the object after the heat of the object has changed. The curing temperature is the temperature at which the resin film cures. The cooling conditions of the object are the conditions indicating how to remove heat from the object.

[0030] When the simulation system 10 analyzes the change of an object after heat is removed after heat is applied, for example, the initial temperature is the temperature of the object after heat is applied to the object, and the final temperature is the temperature of the object after the heat is removed from the object. In this case, in one example, the initial temperature is set to be 150°C or higher and 250°C or lower, and the final temperature is set to be 1°C or higher and 30°C or lower. When the simulation system 10 analyzes the above change, for example, the cooling condition of the object is set to cooling from the lower surface of the substrate.

[0031] The acquisition unit 11 may receive object information, boundary conditions, and heat information input by a user operation, may access a given database or file system to read out the object information, boundary conditions, and heat information, or may receive the object information, boundary conditions, and heat information from another computer.

[0032] In step S2, the generation unit 12 generates an analysis model. The generation unit 12 generates an analysis model representing the object by a finite number of elements based on the acquired object information and boundary conditions. When a two-dimensional object is specified, the generation unit 12 may represent the object by a two-dimensional analysis model, and when a three-dimensional object is specified, the generation unit 12 may represent the object by a two-dimensional or three-dimensional analysis model. For example, the generation unit 12 represents a two-dimensional analysis model on a plane defined by the width direction and the height direction of the object. In another example, the generation unit 12 represents a three-dimensional analysis model in a space defined by the width direction, the depth direction, and the height direction.

[0033] When generating the analysis model, the generation unit 12 determines the structure of the analysis model based on the acquired object information. In one example, the generation unit 12 sets the shape of the analysis model based on the shape information and sets the physical property value of the analysis model based on the physical property value information.

[0034] With reference to FIG. 4, the configuration of the object and the configuration of the analysis model will be described. FIG. 4 is a side view showing an example of those configurations. The object 200 shown in FIG. 4 includes a substrate 201, a conductive portion 202, and a resin film 203. In the object 200, the conductive portion 202 is formed on the substrate 201, and the resin film 203 is formed on the substrate 201 so as to cover the substrate 201 and the conductive portion 202. In one example, the substrate 201 is a silicon substrate, the conductive portion 202 is made of copper, and the resin film 203 is a film formed of the photosensitive resin material described above. For the object 200, the shape profile of the upper surface 203a of the resin film 203 is specified by the simulation system 10. Here, it should be noted that the object 200 shown in FIG. 4 is an object in a state where heat has not been applied and heat has not been removed. In the following description, the above state may be referred to as the "reference state".

[0035] The analysis model 210 shown in FIG. 4 is a two-dimensional analysis model representing the object 200 by a finite number of elements 220. The analysis model 210 is represented on a plane defined by the width direction (X-axis) and the height direction (Y-axis) of the object 200.

[0036] The analysis model 210 has a first portion 211 corresponding to the substrate 201, a second portion 212 corresponding to the conductive portion 202, and a third portion 213 corresponding to the resin film 203. The upper surface 213a of the third portion 213 corresponds to the upper surface 203a of the resin film 203. The finite number of elements 220 are divided into a plurality of first elements 221 constituting the first portion 211, a plurality of second elements 222 constituting the second portion 212, and a plurality of third elements 223 constituting the third portion 213. That is, in the analysis model 210, the substrate 201 is represented by a plurality of first elements 221, the conductive portion 202 is represented by a plurality of second elements 222, and the resin film 203 is represented by a plurality of third elements 223.

[0037] In the analysis model 210, the shapes of the first part 211, the second part 212, and the third part 213 are set based on the shape information of the substrate 201, the conductive part 202, and the resin film 203, respectively. The physical property values of the first part 211, the second part 212, and the third part 213 are set based on the physical property value information of the substrate 201, the conductive part 202, and the resin film 203, respectively.

[0038] The plurality of first elements 221, the plurality of second elements 222, and the plurality of third elements 223 are set based on the boundary conditions of the substrate 201, the conductive part 202, and the resin film 203, respectively. In the example shown in FIG. 4, the sizes and shapes of all the elements 220 are not unified, and the sizes or shapes of some of the elements 220 are different from those of the other elements 220. In the region 230 including the boundary between the vicinity of the corner of the second part 212 and the third part 213, the sizes of the second element 222 and the third element 223 are set to be smaller than the sizes of the first element 221, the second element 222, and the third element 223 located in other regions.

[0039] Returning to FIG. 3. In step S3, the analysis unit 13 performs a simulation based on the analysis model and the thermal information to analyze the changes of each of the finite number of elements when the heat changes in the object. The analysis unit 13 may perform a simulation on the analysis model based on a discretization method such as the finite element method, for example. In one example, the analysis unit 13 simulates an object on which a process of cooling the object to the final temperature has been performed for an object in which the resin film is cured at the curing temperature and heated to the initial temperature, and analyzes the changes of each of the finite number of elements constituting the analysis model. The analysis unit 13 may also simulate an object on which a series of processes of curing the resin film at the curing temperature and cooling the object to the final temperature have been performed for an object heated to the initial temperature.

[0040] In one example, the analysis unit 13 may analyze the change in the position (coordinates) of each element or the change in the shape of each element as the change of a finite number of elements. Alternatively, in addition to the change of a finite number of elements, the analysis unit 13 may analyze the distribution of stress generated when heat changes in the object. When the analysis unit 13 analyzes the distribution of the stress, the cooling condition of the object may be set to cooling from the lower surface of the substrate. In this case, since heat is removed from the object only by cooling from the substrate side among the substrate and the resin film having different heat characteristics, the stress generated by the temperature difference between the substrate and the resin film can be analyzed.

[0041] When executing the simulation based on the analysis model 210 shown in FIG. 4, the analysis unit 13 analyzes each change of a finite number of elements 220 when heat changes in the object 200 and the distribution of stress generated when heat changes in the object 200. In the simulation, the analysis unit 13 analyzes the change in the position (coordinates) of each third element 223 as each change of a finite number of elements 220.

[0042] Referring to FIG. 5, the analysis result obtained by executing the simulation based on the analysis model 210 shown in FIG. 4 will be described. FIG. 5 is a diagram showing an example of the analysis result. This example represents the two-dimensional shape of the third portion 213 composed of a plurality of third elements 223 and the two-dimensional distribution of stress generated by removing heat from the object 200. The darker the color of the analysis result, the greater the stress. It should be noted that in this analysis result, the boundary lines of each third element 223 are omitted to clarify the stress distribution. The vertical axis and the horizontal axis of the analysis result indicate the height position [μm] and the width position [μm] of each third element 223, respectively. The width position is the position along the X-axis direction, and the height position is the position along the Y-axis direction. The analysis result shows that the outer shape of the third portion 213 has changed from the shape 2131 to the shape 2132 due to the removal of heat from the object 200. The analysis result also shows that stress is concentrated in the region 230 including the boundary between the vicinity of the corner of the second portion 212 and the third portion 213.

[0043] Return to FIG. 3. In step S4, the specifying unit 14 specifies the shape profile of the upper surface of the resin film. In one example, the specifying unit 14 first extracts the coordinates of each element corresponding to the upper surface of the resin film from among a finite number of elements based on the result of the analysis by simulation. Next, the specifying unit 14 specifies the relationship between the width position and the height position indicated by the coordinates of those elements as the shape profile of the upper surface of the resin film.

[0044] In one example, the specifying unit 14 may calculate an evaluation value for evaluating the shape of the upper surface of the resin film based on the specified shape profile. For example, the specifying unit 14 calculates a statistical value of the height position (Y coordinate) of the upper surface of the resin film indicated by the shape profile as the evaluation value. The statistical value is, for example, the standard deviation or the variance.

[0045] FIG. 6 is a diagram showing an example of the shape profile of the upper surface of the resin film in an object in which heat has changed, and corresponds to the analysis result shown in FIG. 5. This example shows the shape profile 291 of the upper surface 203a of the resin film 203 in the object 200 in the reference state and the shape profile 292 of the upper surface 203a of the resin film 203 in the object 200 from which heat has been removed. The shape profiles 291 and 292 respectively correspond to the shapes 2131 and 2132 in FIG. 5. The vertical axis and the horizontal axis of the graph respectively indicate the height position (Y coordinate) and the width position (X coordinate) of each third element 223 constituting the upper surface 203a, and the units of these positions are μm. It can also be said that the vertical axis is an axis along the normal direction of the upper surface 203a, and the horizontal axis is an axis along the extending direction of the upper surface. From this graph, it can be seen that the height position of the upper surface 203a has changed due to the change in heat in the object 200, and that undulations or distortions have occurred on the upper surface 203a because the degree of the change is different when viewed along the width direction.

[0046] Return to FIG. 3. In step S5, the output unit 15 outputs the processing result. In one example, the output unit 15 outputs the shape profile of the upper surface of the resin film as the processing result. The output unit 15 may output a processing result representing the shape profile by a graph as shown in FIG. 6. In addition to the shape profile, the output unit 15 may output at least one of an evaluation value for evaluating the shape of the upper surface of the resin film and the result of the simulation analysis as the processing result. The output unit 15 may store the processing result in a predetermined storage device such as a memory or a database, may display the processing result on a display device, or may transmit the processing result to another computer system.

[0047] As described above, the simulation system 10 can process a three-dimensional model showing the three-dimensional shape of an object to identify the shape profile of the upper surface of the resin film of the object. With reference to FIGS. 7 and 8, an example of the processing of the three-dimensional analysis model will be described. FIG. 7 is a perspective view showing another example of the configuration of the object and the configuration of the analysis model. FIG. 8 is a diagram showing an example of the analysis result obtained by executing a simulation based on the analysis model.

[0048] The object 300 shown in FIG. 7 includes a substrate 301 and a resin film 303. The resin film 303 is formed on the substrate 301 so as to cover the substrate 301. In one example, the substrate 301 is a silicon substrate, and the resin film 303 is a film formed of the photosensitive resin material described above. For the object 300, the shape profile of the upper surface 303a of the resin film 303 is identified by the simulation system 10. Here, it should be noted that the object 300 shown in FIG. 7 is the object 300 in the reference state.

[0049] The analysis model 310 shown in FIG. 7 is a three-dimensional analysis model representing the object 300 by a finite number of elements 320. The analysis model 310 is represented in a space defined by the width direction (X-axis), the depth direction (Z-axis), and the height direction (Y-axis) of the object 300.

[0050] The analysis model 310 has a first part 311 corresponding to the substrate 301 and a second part 313 corresponding to the resin film 303. The upper surface 313a of the second part 313 corresponds to the upper surface 303a of the resin film 303. The finite number of elements 320 are divided into a plurality of first elements 321 that make up the first part 311 and a plurality of second elements 323 that make up the second part 313. That is, in the analysis model 310, the substrate 301 is represented by the plurality of first elements 321, and the resin film 303 is represented by the plurality of second elements 323.

[0051] In the analysis model 310, the shapes of the first part 311 and the second part 313 are set based on the shape information of the substrate 301 and the resin film 303, respectively. The physical property values of the first part 311 and the second part 313 are set based on the physical property value information of the substrate 301 and the resin film 303, respectively.

[0052] The simulation system 10 can execute a simulation based on the analysis model 310 and output the analysis result shown in FIG. 8. The example in FIG. 8 shows the three-dimensional outer shape of the analysis model 310 composed of a finite number of elements 320 and the three-dimensional distribution of the stress generated by removing heat from the object 300. The vertical axis and the horizontal axis in FIG. 8 indicate the height position [μm] and the width position [μm] of each element 320, respectively. The width position is the position along the X-axis direction, and the height position is the position along the Y-axis direction. The analysis result indicates that the darker the color, the greater the stress. It should be noted that in this analysis result, the illustration of the boundary line of each element 320 is omitted in order to clarify the stress distribution. The analysis result shows that when heat is removed from the object 300, the outer shape of the object 300 changes, and the shape of the upper surface 313a, which was flat, changes to rise. The analysis result also shows that stress particularly concentrates near the boundary between the first part 311 and the second part 313 and in the second part 313.

[0053] The simulation system 10 executes the above steps S1 to S5 for the object 300 to identify the shape profile of the upper surface 303a of the resin film 303. Corresponding to the analytical model 310 being a three-dimensional model, the simulation system 10 may identify the three-dimensional shape profile for the upper surface 313a. Alternatively, the simulation system 10 may identify the two-dimensional shape profile in the end face or cross section defined by one of the X-axis and Z-axis and the Y-axis for the upper surface 313a.

[0054] Next, with reference to FIG. 9, yet another example of the configuration of the object will be described. FIG. 9 is a cross-sectional view showing yet another example of the configuration of the object.

[0055] The object 400 shown in FIG. 9 includes a substrate 401, a resin film 403, a chip 404, a pillar 405, solder balls 406, and resin 407. The resin film 403 is formed on the substrate 401 so as to cover the substrate 401. The chip 404 is electrically connected to the substrate 401. In one example, the solder balls 406 are formed on the upper surface 403a of the resin film 403, and the pillar 405 is formed on the solder balls 406. In this example, the resin 407 is formed so as to cover the side surface of the pillar 405, the solder balls 406, and the upper surface 403a. Therefore, it can be said that the resin film 403 supports the solder balls 406 and the resin 407. Further, in this example, the chip 404 is formed so as to cover the upper surface of the pillar 405. Here, note that the object 400 shown in FIG. 9 is the object 400 in the reference state.

[0056] In one example, the substrate 401 is a silicon substrate, and the resin film 403 is a resin film for forming a redistribution layer. In this example, the object 400 further includes copper wirings disposed within the resin film 403. Thus, in this example, the resin film 403 and the copper wirings constitute a redistribution layer. This copper wiring may have a single-layer structure or a multilayer structure within the resin film 403. That is, in this example, the chip 404 is electrically connected to the substrate 401 via the redistribution layer, the pillar 405, and the solder ball 406. In one example, the chip 404 is a silicon chip, the pillar 405 is a copper pillar, and the solder ball 406 is a Sn-Ag-Cu-based solder ball.

[0057] The simulation system 10 executes the above steps S1 to S5 for this object 400 to specify the shape profile of the upper surface 403a of the resin film 403 that supports the solder ball 406 and the resin 407. At this time, corresponding to the object 400, the simulation system 10 may generate a two-dimensional analysis model and specify the two-dimensional shape profile in the cross-section defined by the X-axis and the Y-axis for the upper surface 403a.

[0058] [Modification Example] As described above, various examples in the present disclosure have been described in detail. However, the present disclosure is not limited to the above examples. With respect to the present disclosure, various modifications are possible without departing from the gist thereof.

[0059] When the simulation system 10 analyzes the change of an object after heat is applied and then removed, the initial temperature may be the temperature of the object in the reference state, and the final temperature may be the temperature of the object after heat is removed from the object. In this case, the acquisition unit 11 may further acquire the maximum temperature as heat information. The maximum temperature is the temperature set as the level that the object to which heat is applied can reach. The analysis unit 13 may simulate the object on which a series of processes of heating the object at the initial temperature to the maximum temperature, curing the resin at the curing temperature, and then cooling the object to the final temperature, and analyze the changes of each of the finite number of elements constituting the analysis model.

[0060] As described above, the simulation system 10 may analyze the change of the object to which heat is applied. In this case, the initial temperature may be the temperature of the object in the reference state, and the final temperature may be the temperature of the object after heat is applied to the object. The analysis unit 13 may simulate the object on which a series of processes of heating the object at the initial temperature to the final temperature and curing the resin film at the curing temperature are performed, and analyze the changes of each of the finite number of elements constituting the analysis model.

[0061] The simulation method executed by at least one processor is not limited to the above example. For example, some of the above steps or processes may be omitted, or each step may be executed in a different order. Also, any two or more of the above steps may be combined, or a part of the steps may be modified or deleted. Alternatively, other steps may be executed in addition to the above steps.

[0062] In the present disclosure, the expression "at least one processor executes a first process, executes a second process, ..., executes an nth process." or a corresponding expression indicates a concept including the case where the processor that executes the n processes from the first process to the nth process changes midway. That is, this expression indicates a concept including both the case where all of the n processes are executed by the same processor and the case where the processor changes in an arbitrary manner among the n processes.

[0063] [Appendix] As can be understood from the various examples above, the present disclosure includes the following aspects. <Item 1> Comprising at least one processor, wherein the at least one processor acquires object information regarding the structure of an object including a substrate and a resin film formed on the substrate, boundary conditions for dividing the object into a finite number of elements, and thermal information regarding heat of the object, generates an analysis model representing the object by the finite number of elements based on the object information and the boundary conditions, executes a simulation based on the analysis model and the thermal information to analyze the respective changes of the finite number of elements when the heat changes in the object, identifies a shape profile of the upper surface of the resin film in the object in which the heat has changed based on the result of the analysis, A simulation system. <Item 2> The at least one processor calculates an evaluation value for evaluating the shape of the upper surface of the resin film based on the shape profile. The simulation system according to Item 1. <Item 3> The at least one processor outputs a processing result representing the shape profile by a graph defined by an axis along the extending direction of the upper surface and an axis along the normal direction of the upper surface. The simulation system according to Item 1 or 2. <Item 4> At least one of the processors analyzes a stress distribution generated when the heat changes in the object. The simulation system according to any one of Items 1 to 3. <Item 5> At least one of the processors executes a simulation based on the finite element method for the analysis model. The simulation system according to any one of Items 1 to 4. <Item 6> The object further includes a conductive portion formed on the substrate. The resin film is formed on the substrate so as to cover the substrate and the conductive portion. The simulation system according to any one of Items 1 to 5. <Item 7> The object further includes a chip electrically connected to the substrate and the resin film. The simulation system according to any one of Items 1 to 5. <Item 8> A simulation method executed by a simulation system including at least one processor, acquiring object information regarding the structure of an object including a substrate and a resin film formed on the substrate, boundary conditions for dividing the object into a finite number of elements, and heat information regarding heat of the object; generating an analysis model representing the object by the finite number of elements based on the object information and the boundary conditions; executing a simulation based on the analysis model and the heat information to analyze changes in each of the finite number of elements when the heat changes in the object; identifying a shape profile of the upper surface of the resin film in the object in which the heat has changed based on the result of the analysis; and a simulation method including the above. <Item 9> Step of acquiring object information regarding the structure of an object including a substrate and a resin film formed on the substrate, boundary conditions for dividing the object into a finite number of elements, and heat information regarding heat of the object. Step of generating an analysis model representing the object by the finite number of elements based on the object information and the boundary conditions. Step of performing a simulation based on the analysis model and the heat information to analyze the change of each of the finite number of elements when the heat changes in the object. Step of specifying the shape profile of the upper surface of the resin film in the object in which the heat has changed based on the result of the analysis. A simulation program for causing a computer to execute the above.

[0064] According to items 1, 8, and 9, the situation of the object with a resin film on the substrate is simulated using an analysis model representing the object by a finite number of elements, and the change of each element is analyzed. Then, based on the result of the analysis, the shape profile of the upper surface of the resin film is specified. In this way, by obtaining the shape profile by simulation, the change in the shape of the resin film in the element when the heat changes can be predicted. This prediction can contribute to the efficient design or manufacture of the element.

[0065] According to item 2, an evaluation value for evaluating the shape of the upper surface of the resin film is calculated based on the specified shape profile. By calculating such an evaluation value, the change in the shape of the upper surface when the heat changes in the element can be quantitatively evaluated.

[0066] According to item 3, a processing result representing the specified shape profile by a graph is output. By using the graph in this way, the specified shape profile can be clearly displayed.

[0067] According to Item 4, by executing the above-described simulation, in addition to the changes for each element, the distribution of stress that can occur in the element is analyzed. As a result, the stress that occurs when the heat changes in the element can also be predicted.

[0068] By using the finite element method, even when the object has a complex shape, the change in its shape can be analyzed. Therefore, according to Item 5, regardless of the shape of the object, the change in the shape of the resin film when the heat changes in the element can be predicted.

[0069] According to Item 6, the change in the shape of the resin film when the heat changes in the element including the conductive part in addition to the substrate and the resin film can be predicted. Further, since the shape profile can represent the correlation between the positional relationship of the conductive part and the resin film and the change in the shape of the resin film, by considering the correlation, the element including the conductive part and the resin film can be efficiently designed or manufactured.

[0070] According to Item 7, the change in the shape of the resin film when the heat changes in the element including the chip electrically connected to the substrate and the resin film in addition to the substrate and the resin film can be predicted. Further, since the shape profile can represent the correlation between the positional relationship of the chip and the resin film and the change in the shape of the resin film, by considering the correlation, the element including the chip and the resin film can be efficiently designed or manufactured.

Explanation of Signs

[0071] 10…Simulation system, 200, 300, 400…Objects, 201, 301, 401…Substrates, 202…Conductive part, 203, 303, 403…Resin films, 203a, 303a…Upper surfaces, 210, 310…Analysis models, 220, 320…Elements, 404…Chip.

Claims

1. comprising at least one processor, wherein the at least one processor obtains object information regarding the structure of an object including a substrate and a resin film formed on the substrate, boundary conditions for dividing the object into a finite number of elements, and thermal information regarding heat of the object, generates an analysis model representing the object by the finite number of elements based on the object information and the boundary conditions, performs a simulation based on the analysis model and the thermal information to analyze changes of each of the finite number of elements when the heat changes in the object, identifies a shape profile of an upper surface of the resin film in the object when the heat changes based on a result of the analysis, a simulation system.

2. wherein the at least one processor calculates an evaluation value for evaluating a shape of the upper surface of the resin film based on the shape profile, the simulation system according to Claim 1.

3. wherein the at least one processor outputs a processing result representing the shape profile by a graph defined by an axis along an extending direction of the upper surface and an axis along a normal direction of the upper surface, the simulation system according to Claim 1.

4. wherein the at least one processor analyzes a distribution of stress generated when the heat changes in the object, the simulation system according to Claim 1.

5. wherein the at least one processor performs a simulation based on the finite element method on the analysis model, the simulation system according to Claim 1.

6. wherein the object further includes a conductive portion formed on the substrate, and the resin film is formed on the substrate so as to cover the substrate and the conductive portion, the simulation system according to any one of Claims 1 to 5.

7. wherein the object further includes a chip electrically connected to the substrate and the resin film, the simulation system according to any one of Claims 1 to 5.

8. a simulation method executed by a simulation system comprising at least one processor, A step of obtaining object information regarding the structure of an object including a substrate and a resin film formed on the substrate, boundary conditions for dividing the object into a finite number of elements, and thermal information regarding heat for the object; A step of generating an analysis model representing the object by the finite number of elements based on the object information and the boundary conditions; A step of performing a simulation based on the analysis model and the thermal information to analyze changes in each of the finite number of elements when the heat changes in the object; A step of specifying a shape profile of the upper surface of the resin film in the object in which the heat has changed based on the result of the analysis; A simulation method including the above steps.

9. A step of obtaining object information regarding the structure of an object including a substrate and a resin film formed on the substrate, boundary conditions for dividing the object into a finite number of elements, and thermal information regarding heat for the object; A step of generating an analysis model representing the object by the finite number of elements based on the object information and the boundary conditions; A step of performing a simulation based on the analysis model and the thermal information to analyze changes in each of the finite number of elements when the heat changes in the object; A step of specifying a shape profile of the upper surface of the resin film in the object in which the heat has changed based on the result of the analysis; A simulation program that causes a computer to execute the above steps.

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