JP2023082383A - Creation method and creation device of simple heat simulation model of multilayer substrate, and simple model creation program - Google Patents

Abstract

To provide a simple model which can highly accurately simulate the influence of substrate heat release in comparison to a conventional simple model using the average equivalent thermal conductivity.SOLUTION: There is provided a simple heat simulation model corresponding to a virtual two-layer substrate having two wiring layers P11, P12 at positions satisfying a prescribed condition with respect to a thermal gravity center position HG by calculating the thermal gravity center position HG of a multilayer substrate. Here, the prescribed condition comprises: the first condition in which the thermal inertial moment of the multilayer substrate is equal to the thermal inertial moment of the virtual two-layer substrate replacing the multilayer substrate; and the second condition in which the thermal conductance of the multilayer substrate is equal to the thermal conductance of the virtual two-layer substrate. Consequently, the substrate heat release characteristics in a case where a heat generating component is placed on a substrate surface of a simple model can be simulated in consideration of a distance to the first wiring layer P11 from the substrate surface.SELECTED DRAWING: Figure 5

Description

The present invention relates to a simple thermal simulation model creation method, creation apparatus, and simple model creation program for a multilayer substrate, and more particularly to a simple thermal simulation model for a multilayer substrate including a plurality of wiring layers of three or more layers and a plurality of insulating layers. It relates to a method and apparatus for making.

2. Description of the Related Art Conventionally, in designing a product, it has been common practice to model the product so that it can be handled as data on a computer, and perform thermal evaluation by simulation using the finite element method or the like. For example, in small chip parts, as electronic devices become smaller and generate more heat, excessive temperature rise due to insufficient heat dissipation has become a problem. The importance of predicting

Here, the temperature rise of small chip components mounted on a printed board (multilayer board) in which a plurality of materials are layered is greatly affected by the heat dissipation state of the multilayer board. In order to reflect this heat dissipation state in the thermal fluid simulation as accurately as possible, detailed modeling is performed including the wiring patterns of each layer of the multilayer substrate. In the case of substrates in which multiple materials with different thermal conductivities are laminated in layers, thermal conductivity is anisotropic between the in-plane direction and the perpendicular direction. A detailed model is designed from

However, the simulation using the detailed model as described above has the problem that more analysis time is required. In recent years, substrates in particular have become multi-layered, so there are cases where the number of wiring layers including wiring patterns made of copper foil reaches 10 or more. When the detailed temperature rise of components mounted on such a multilayer substrate is obtained by simulation using a detailed model, the analysis time increases due to the increase in model scale.

Further, a detailed model including detailed wiring patterns cannot be created unless the wiring patterns included in the board and the layout of all the components mounted on the board are determined. Therefore, there is a problem that a detailed model cannot be used when it is desired to grasp a rough trend in the initial stage of designing.

In view of the problems of detailed models as described above, techniques for performing simulations using simple models have also been provided. In the general simple model currently provided, the thermal resistance in the in-plane direction and the thermal resistance in the thickness direction (perpendicular to the plane) of the board containing the copper foil are calculated in order to consider the effect of the copper foil inside the board. An average equivalent thermal conductivity that is equivalent to each other is obtained and used as a simple simulation model. For example, there is known a method of calculating thermal conductivity using a simple model that takes into consideration wiring patterns on an electronic substrate (see, for example, Patent Document 1).

In the method described in Patent Document 1, the equivalent thermal conductivity of the electronic substrate is calculated using the wiring partial area area ratio information of the electrode pattern layer, taking into account that the ratio of the insulator mixed in the electrode pattern layer differs from place to place. to calculate That is, after dividing the electronic substrate into smaller regions and calculating the wiring partial area ratio in each electrode pattern layer for each divided small region, the in-plane equivalent thermal conductivity of the electronic substrate for each small region Calculate

Japanese Patent Application Laid-Open No. 2000-180395

By using a simple model (equivalent thermal conductivity) as disclosed in Patent Document 1, it is possible to express the multilayer substrate as a simple model. However, at present, there is no simple model that can take into account the influence of substrate heat radiation with relatively high accuracy. In other words, the heat dissipation performance of heat-generating components mounted on the board surface varies greatly depending on the distance from the heat-generating component to the copper foil on the inner layer of the board. Therefore, there is a problem in reproducibility of substrate heat dissipation characteristics.

The present invention was made to solve such problems, and is a simple model that can simulate the effects of substrate heat radiation with higher accuracy than conventional simple models that use average equivalent thermal conductivity. The purpose is to be able to provide

In order to solve the above-described problems, in the present invention, the thermal barycentric position of a multi-layer substrate including three or more wiring layers and a plurality of insulating layers is calculated, and a predetermined condition is applied to the thermal barycentric position. A simple thermal simulation model corresponding to a virtual two-layer board having two wiring layers at positions satisfying the following is generated. Here, the predetermined conditions are the first condition that the thermal moment of inertia of the multilayer substrate and the thermal moment of inertia of the virtual two-layer substrate replacing the multilayer substrate are equal, and the thermal conductance of the multilayer substrate and the virtual two-layer substrate. is equal to the thermal conductance of .

According to the present invention configured as described above, the thermal conductivity of each wiring layer and the thermal conductivity of each insulating layer of the multilayer substrate are not simply replaced by the average equivalent thermal conductivity, but the thermal conductivity is A simplified model of a hypothetical two-layer board having two wiring layers satisfying the first condition on the physical moment of inertia and the second condition on the thermal conductance is substituted. Therefore, it is possible to simulate the substrate heat dissipation characteristics when heat-generating components are arranged on the substrate surface of the simplified model, taking into consideration the distance from the substrate surface to the wiring layer. Since the simple model is generated so as to satisfy the first condition regarding the thermal moment of inertia, the distance from the board surface to the wiring layer in the simple model is close to the actual distance from the surface of the multilayer board to the wiring layer. . As a result, by using the simple model generated by applying the present invention, it is possible to simulate the effects of substrate heat dissipation with higher accuracy than with the conventional simple model using the average equivalent thermal conductivity. .

1 is a block diagram showing a functional configuration example of a simple thermal simulation model creation device (simple model creation device) for a multilayer substrate according to the present embodiment; FIG. FIG. 4 is a diagram schematically showing replacement of a detailed model of a multilayer board with a simplified model; FIG. 4 is a diagram for explaining a general moment of inertia; FIG. 3 is a diagram for explaining a detailed model of a multilayer board and various information related thereto; It is a figure for demonstrating the simple model of this embodiment, and various information about this. 4 is a flow chart showing an operation example of the simple model creating apparatus according to the present embodiment (processing procedure of a method for creating a simple thermal simulation model of a multilayer substrate according to the present embodiment). FIG. 10 is a diagram showing the results of a simulation using a simple model created on the premise that the thermal moment of inertia is proportional to the square of the distance from the reference position; FIG. 4 is a diagram showing the results of a simulation using a simple model created on the premise that the thermal moment of inertia is proportional to the fourth power of the distance from the reference position; FIG. 5 is a block diagram showing another functional configuration example of the simple model creation device according to the present embodiment; It is a figure for demonstrating the processing content of the model simplification part by this embodiment.

An embodiment of the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram showing an example of the functional configuration of an apparatus for creating a simple thermal simulation model of a multilayer substrate (hereinafter referred to as a simple model creating apparatus 10) according to this embodiment. As shown in FIG. 1, the simple model generating device 10 of the present embodiment includes a board information input unit 11, a gravity center calculator 12, and a simple model generator 13 as functional configurations. The simple model generation unit 13 includes a thickness calculation unit 13A, a thermal conductivity calculation unit 13B, and a distance calculation unit 13C as more specific functional configurations.

The functional blocks 11 to 13 can be configured by hardware, DSP (Digital Signal Processor), or software. For example, when configured by software, the functional blocks 11 to 13 are actually configured with a computer CPU, RAM, ROM, etc., and a program stored in a storage medium such as RAM, ROM, hard disk, or semiconductor memory. It is realized by working.

A simple model creating apparatus 10 of the present embodiment is an apparatus for creating a simple thermal simulation model (hereinafter simply referred to as a simple model) of a multilayer board including a plurality of wiring layers of three or more and a plurality of insulating layers. FIG. 2 is a diagram schematically showing the replacement of a detailed model of a multilayer board with a simple model executed by the simple model creating apparatus 10 of the present embodiment. The simple model creating apparatus 10 of this embodiment creates a simple model by replacing a detailed model with a simple model so as to satisfy a predetermined condition. In this specification, a substrate having n wiring layers is expressed as an n-layer substrate, and a substrate with n≧3 is expressed as a multilayer substrate.

FIG. 2(a) is a diagram schematically showing a detailed model of a multilayer substrate. Here, a multilayer board (five-layer board) in which five wiring layers (copper foil pattern layers) P1 to P5 and five insulating layers (resin layers) S1 to S5 are alternately arranged is illustrated. The upper side of the drawing is the substrate surface, and the lower side is the substrate back surface. Heat-generating components such as chip components are arranged on the substrate surface. The detailed model is a model that reproduces the thickness and thermal conductivity of each layer P1 to P5 and S1 to S5 of the multilayer substrate as computer data. Note that the detailed model handled in this embodiment does not necessarily include information on the detailed wiring patterns of the wiring layers P1 to P5, and can be set even at the initial stage of design.

FIG. 2B is a diagram schematically showing a simple model of a virtual two-layer board created by the simple model creating apparatus 10 of this embodiment. In this embodiment, the five wiring layers P1 to P5 of the detailed model are combined into two wiring layers P11 and P12, and the two wiring layers P11 and P12 are sandwiched between three insulating layers S11 to S13. Create a model. In this simplified model, the total thermal conductance in the in-plane direction and the thickness direction of the entire substrate is equal to that of the detailed model, and the first wiring layer (hereinafter referred to as the first wiring layer) counted from the substrate surface. It is created so that the distance from the substrate surface is approximately equal to that of the detailed model.

In the present embodiment, in order to create a simple model such that the distance from the substrate surface of the first wiring layer P11 in the simple model is approximately equal to the distance from the substrate surface of the first wiring layer P1 in the detailed model, a thermal Introduce the concept of the physical moment of inertia. FIG. 3 is a diagram for explaining a general moment of inertia that occurs when an object is rotated around a certain rotation axis. In FIG. 3, a plate-like object having a mass of M and a thickness of t is placed at a position separated by a distance d from the rotation axis AX so that the in-plane axis of the object and the rotation axis AX are parallel. state. When this object is rotated around the rotation axis AX, the object generates a moment of inertia Ig as shown in (Equation 1) below. In this embodiment, by replacing the mass M of the object with the in-plane thermal conductance λt (λ is the thermal conductivity, t is the thickness) of one layer, the thermal inertia shown by the following (Equation 2) A moment HIg is introduced. How to use this thermal moment of inertia HIg will be described later.

The processing contents of the functional blocks 11 to 13 shown in FIG. 1 will be described below. The board information input unit 11 inputs board information regarding a detailed model of a multilayer board. The information input by the board information input unit 11 is information relating to the structural properties and thermal properties of the multilayer board, and is information of known values for the multilayer board. For example, the board information input unit 11 acquires board information input by a user to a computer using an input device such as a keyboard or touch panel. Alternatively, the board information input unit 11 may acquire board information stored in advance in a storage medium.

FIG. 4 is a diagram for explaining a detailed model of a multilayer board and various information related thereto. FIG. 4 shows information input by the board information input unit 11. As shown in FIG. The detailed model of the multilayer substrate shown in FIG. 4 is the detailed model shown in FIG. The substrate information input unit 11 inputs the thicknesses t ₁ to t ₁₀ of the five wiring layers P1 to P5 and the five insulating layers S1 to S5 as information indicating the structural properties of the multilayer substrate, and also inputs the thermal properties. As information on the thermal conductivities λ ₁ to λ ₁₀ of the five wiring layers P1 to P5 and the five insulating layers S1 to S5, respectively, are input.

The center-of-gravity calculation unit 12 calculates the thermal center-of-gravity position of the multilayer board based on the board information input by the board information input unit 11 . The thermal center-of-gravity position is a concept corresponding to the center-of-gravity positions of a plurality of objects having masses M ₁ to M _n , and the thermal conductances λ ₁ t ₁ to λ _n t _n obtained by replacing the masses M ₁ to M _n . The position of the thermal center of gravity. FIG. 4 shows this thermal center of gravity position HG. As shown in FIG. 4, when the distances from the substrate surface to the center of each layer in the thickness direction are x ₁ to x ₁₀ and the distance from the substrate surface to the thermal center of gravity HG is x _g , the thermal center of gravity HG is It is represented by the following (Equation 3). The distances x ₁ to x ₁₀ from the substrate surface to the center of each layer in the thickness direction can be calculated from the thicknesses t ₁ to t ₁₀ of each layer input by the substrate information input section 11 .

The simple model generating unit 13 generates a simple model corresponding to a virtual two-layer board having two wiring layers P11 and P12 at positions satisfying a predetermined condition with respect to the thermal center of gravity position HG calculated by the center of gravity calculating unit 12. . FIG. 5 is a diagram for explaining the simple model (corresponding to the first model in the scope of claims) of the present embodiment generated by the simple model generation unit 13 and various information related thereto. b) corresponds to that shown.

In the simplified model shown in FIG. 5, two wiring layers P11 and P12 are arranged at a predetermined distance _dp from the thermal center of gravity position HG, and the two wiring layers P11 and P12 are arranged in a symmetrical relationship with respect to the thermal center of gravity position HG. Three insulating layers S11 to S13 are arranged so as to sandwich P11 and P12. Both of the two wiring layers P11 and P12 have a thermal conductivity of λ _p and a thickness of t _p /2. Each of the three insulating layers S11 to S13 has a thermal conductivity of λ _s and a thickness of t _s1 , t _s2 and t _s3 respectively. The total thickness of the three insulating layers S11 to S13 is t _s (=t _s1 +t _s2 +t _s3 ).

In the simplified model shown in FIG. 5, the sum of the thicknesses of the wiring layers P11 and P12 (=t _p ) and the sum of the thicknesses of the insulating layers S11 to S13 (=t _s ) of the virtual two-layer board are shown in FIG. The sum of the thicknesses of the wiring layers P1 to P5 (=Σt _2k : k=1 to 5) and the sum of the thicknesses of the insulating layers S1 to S5 (=Σt _2k−1 : k=1 to 5) of the multilayer substrate shown, and each equal. That is, it is assumed that (Equation 4) and (Equation 5) shown below hold.

Here, the predetermined conditions to be satisfied for the simple model shown in FIG. 5 include the following first and second conditions. The first condition is that the thermal moment of inertia of the multilayer substrate shown in FIG. 4 is equal to the thermal moment of inertia of the virtual two-layer substrate shown in FIG. 5 in which the multilayer substrate is replaced. The second condition is that the total thermal conductance of the multilayer substrate shown in FIG. 4 and the total thermal conductance of the virtual two-layer substrate shown in FIG. 5 are equal.

Specifically, the first condition is the sum of the thermal moments of inertia with respect to the thermal center of gravity position HG of the plurality of wiring layers P1 to P5 of the multilayer board, and the sum of the two wiring layers P11 and P12 of the virtual two-layer board. The condition is that the sum of the thermal moments of inertia with respect to the thermal center of gravity position HG is equal. Here, the sum of the thermal moments of inertia with respect to the thermal center-of-gravity position HG of the multiple wiring layers P1 to P5 of the multilayer substrate is represented by the following (Equation 6). Further, the sum of the thermal moments of inertia with respect to the thermal center of gravity position HG of the two wiring layers P11 and P12 of the virtual two-layer board is represented by the following (Equation 7). The first condition is that the value represented by (Equation 6) and the value represented by (Equation 7) are equal, and is represented by (Equation 8).

Specifically, the second condition is the thermal conductivity λ _2k (k=1 to 5) of the wiring layers P1 to P5 and the thermal conductivity λ _2k−1 (k=1 to 5) of the insulating layers S1 to S5 of the multilayer substrate. 5), the thermal conductance in the in-plane direction and the thermal conductance in the thickness direction, the thermal conductivity λ _p of the wiring layers P11 and P12 of the virtual two-layer substrate, and the thermal conductivity λ _s of the insulating layers S11 to S13 The condition is that the thermal conductance in the in-plane direction and the thermal conductance in the thickness direction calculated from are equal to each other.

Here, the condition that the total thermal conductance in the in-plane direction of the multilayer substrate and the total thermal conductance in the in-plane direction of the virtual two-layer substrate are equal is represented by the following (Equation 9). The condition that the total thermal conductance in the thickness direction of the multilayer substrate and the total thermal conductance in the thickness direction of the virtual two-layer substrate are equal is expressed by the following (Equation 10).

The simple model generating unit 13 uses (Equation 3) representing the thermal center of gravity position HG calculated by the center of gravity computing unit 12 and (Equation 4) to (Equation 10) representing various conditions to be satisfied by the simple model. , the thickness t _p /2 of the wiring layers P11 and P12 of the virtual two-layer board, the thermal conductivities λ _p and λ _s of the wiring layers P11 and P12 and the insulating layers S11 to S13, and the thermal barycentric position HG to the wiring layer P11 , P12, the simplified model shown in _FIG . 5 is generated. If the distance d _p is determined from the thickness t _p /2 of the wiring layers P11 and P12 and the thermal center of gravity position HG, the thicknesses t _s1 , t _s2 and t _s3 of the insulating layers S11 to S13 are also determined. Specifically, each of the above information can be calculated as follows.

The thickness calculation unit 13A calculates the total thickness t _p of the wiring layers P11 and P12 of the virtual two-layer board from (Equation 4), and calculates the total thickness t _s of the insulating layers S11 to S13 of the virtual two-layer board. is calculated from (Equation 5).

The thermal conductivity calculator 13B uses the substrate information (the thicknesses t ₁ to t ₁₀ of each layer and the thermal conductivity λ ₁ to λ ₁₀ of each layer) input by the substrate information input unit 11 and the thickness calculated by the thickness calculator 13A. By substituting the total thickness t _p of the wiring layers P11 and P12 and the total thickness t _s of the insulating layers S11 to S13 into (Equation 9) and (Equation 10) and solving the simultaneous equations, the virtual two-layer board has The thermal conductivity λ _p of the wiring layers P11 and P12 and the thermal conductivity λ _s of the insulating layers S11 to S13 are calculated.

The distance calculation unit 13C calculates the total thickness t _p and the thermal conductivity λ _p of the wiring layers P11 and P12 calculated as described above, and the substrate information input by the substrate information input unit 11 (wiring layers P1 to P5 (thickness t _2k and thermal conductivity λ _2k ), the distance x _2k from the substrate surface to the wiring layers P1 to P5, and the distance x _g from the substrate surface to the thermal center of gravity position HG are substituted into (Equation 8). The distance d _p from the thermal center of gravity position HG to the wiring layers P11 and P12 is calculated by solving the equation.

FIG. 6 is a flow chart showing an operation example of the simple model creating apparatus 10 according to this embodiment configured as described above (processing procedure of a method for creating a simple thermal simulation model of a multilayer substrate according to this embodiment).

First, the substrate information input unit 11 inputs substrate information (thicknesses t ₁ to t ₁₀ and thermal conductivities λ ₁ to λ ₁₀ of each layer) regarding a detailed model of a multilayer substrate (step SP1). Next, the center-of-gravity calculation unit 12 calculates the thermal center-of-gravity position HG of the multilayer board based on the board information input by the board information input unit 11 (step SP2). Then, the simple model generator 13 creates a virtual two-layer board having two wiring layers P11 and P12 at positions that satisfy the first condition and the second condition with respect to the thermal center of gravity position HG calculated by the center of gravity calculator 12 . A corresponding simple model is generated (steps SP3 to SP5).

That is, the thickness calculation unit 13A of the simple model generation unit 13 calculates the total thickness t _p of the wiring layers P11 and P12 of the virtual two-layer board based on the above-described (Equation 4) and (Equation 5). , the total thickness t _s of the insulating layers S11 to S13 of the virtual two-layer board is calculated (step SP3). Next, the thermal conductivity calculator 13B calculates the thermal conductivity λ _p of the wiring layers P11 and P12 and the thermal conductivity λ _s of the insulating layers S11 to S13 based on the above-described (equation 9) and (equation 10). (step SP4). Then, the distance calculator 13C calculates the distance d _p from the thermal center of gravity position HG to the wiring layers P11 and P12 based on the above-described (Equation 8) (step SP5). As described above, the process of creating the simple model shown in FIG. 6 is completed.

As described in detail above, in the present embodiment, the thermal barycentric position HG of a multilayer substrate including a plurality of wiring layers of three or more and a plurality of insulating layers is calculated, and a predetermined A simple model corresponding to a virtual two-layer board having two wiring layers P11 and P12 at positions satisfying the conditions is generated. Here, the predetermined conditions are the first condition that the thermal moment of inertia of the multilayer substrate and the thermal moment of inertia of the virtual two-layer substrate replacing the multilayer substrate are equal, and the thermal conductance of the multilayer substrate and the virtual two-layer substrate. is equal to the thermal conductance of .

According to this embodiment configured as described above, the thermal conductivity λ 2k of each of the wiring layers P1 to P5 of the multilayer substrate and the thermal conductivity λ _2k of each of the insulating layers S1 to _S5 are equal to the average equivalent thermal conductivity. Instead of being simply replaced by the coefficient, it is replaced by a simplified model of a virtual two-layer board having two wiring layers P11 and P12 that satisfy the first condition regarding the thermal moment of inertia and the second condition regarding the thermal conductance. Therefore, it is possible to simulate the substrate heat dissipation characteristics when heat-generating components are arranged on the substrate surface of the simplified model, taking into consideration the distance from the substrate surface to the wiring layer P11.

When a heat-generating component is arranged on the substrate surface, the temperature distribution in the substrate greatly differs depending on the distance from the substrate surface to the first wiring layer. For example, the closer the first wiring layer is to the substrate surface, the better the heat dissipation and the lower the thermal resistance. According to this embodiment, since the simple model is generated so as to satisfy the first condition regarding the moment of inertia, the distance from the substrate surface of the simple model to the wiring layer P11 is the distance from the surface of the multilayer substrate to the wiring layer P1. becomes close to the actual distance of As a result, by using the simple model generated by applying this embodiment, it is possible to perform a simulation that takes into account the difference in arrangement of the wiring layers in the substrate, so that the average equivalent thermal conductivity is used. It is possible to simulate the influence of substrate heat radiation with higher accuracy than the conventional simple model used.

FIG. 7 is a diagram showing the result of calculating the thermal resistance of the substrate by simulating using the detailed model of the multilayer substrate and the simplified model of the virtual two-layer substrate. The horizontal axis indicates the thermal resistance calculated using the detailed model, and the vertical axis indicates the thermal resistance calculated using the simple model. The simulation was performed for each of multiple types of multilayer substrates in which multiple wiring layers were arranged differently. Here, the thickness and thermal conductivity of the plurality of wiring layers are assumed to be the same value, and the thermal conductivity of the plurality of insulating layers are assumed to be the same value. In addition to setting the detailed model, multiple types of simple models corresponding to each detailed model were created. The total thickness of each layer was set to be the same for all types of multilayer substrates. As a result, a plurality of types of detailed models and a plurality of types of corresponding simplified models are made to have different distances from the substrate surface to the first wiring layer.

A plurality of plotted points shown in FIG. 7 indicate coordinate positions corresponding to combinations of the thermal resistance calculated from the detailed model and the thermal resistance calculated from the simple model for the plurality of types of multilayer substrates. A solid oblique line L1 shown in FIG. 7 indicates a coordinate position where the thermal resistance calculated from the detailed model and the thermal resistance calculated from the simple model completely match. As shown in FIG. 7, all plotted points are located near the solid line L1. This means that the error between the thermal resistance calculated from the simple model and the thermal resistance calculated from the detailed model is within a predetermined range.

On the other hand, the dotted line L2 shown in FIG. 7 indicates the coordinate position of the thermal resistance calculated from the simple model created using the average equivalent thermal conductivity. Conventional simple models are not created considering the position of the wiring layers in the board, so even if you prepare multiple types of multilayer boards with different wiring layer arrangements, the simple models created from them are the same, and the thermal resistance calculated from the simple model is a constant value. The solid line L1 and the dotted line L2 intersect only at one point, and the further away from the intersection, the greater the error between the thermal resistance calculated from the simple model and the thermal resistance calculated from the detailed model. As is clear from FIG. 7, according to the present embodiment, the effect of substrate heat radiation can be simulated with higher accuracy than the conventional simplified model using the average equivalent thermal conductivity.

Note that the first condition regarding the thermal moment of inertia used in the above embodiment is based on the premise that the thermal moment of inertia is proportional to the square of the distance from the reference position as shown in (Equation 2). set. Alternatively, the first condition may be set on the premise that the thermal moment of inertia is proportional to the fourth power of the distance from the reference position. Assuming that the thermal moment of inertia is proportional to the fourth power of the distance from the reference position, the above (Equation 2) is replaced by the following (Equation 11). Also, the above (Equation 8) is replaced by the following (Equation 12).

Thus, when the weight of the distance is set to the fourth power, the dependency of the distance d _p from the thermal center of gravity position HG appears more clearly in the simple model to be created. This makes it possible to improve the calculation accuracy of the distance d _p and simulate the influence of substrate heat dissipation with higher accuracy. FIG. 8 is a diagram showing simulation results when a simple model is created using (Equation 12) instead of (Equation 8) for the multiple types of multilayer substrates described in FIG. The detailed model is as explained in FIG. As can be seen by comparing FIG. 7 and FIG. 8, the error between the thermal resistance calculated from the simple model and the thermal resistance calculated from the detailed model is greater than that of the simple model created with the weight of the distance squared. is smaller in the simplified model created by raising to the 4th power.

Further, in the above-described embodiment, an example was described in which the first model in which the two wiring layers P11 and P12 were arranged at symmetrical positions a distance d _p from the thermal center of gravity HG was created as a simple model. is not limited to For example, the first model may be further simplified to a second model having only one wiring layer.

FIG. 9 is a block diagram showing a functional configuration example of the simple model creating device 10' when creating the second model. In FIG. 9, the components denoted by the same reference numerals as those shown in FIG. 1 have the same functions, and redundant description will be omitted here. The simple model creation device 10 ′ shown in FIG. 9 further includes a model simplification unit 14 . 10A and 10B are diagrams for explaining the processing contents of the model simplification unit 14. FIG. 10A shows the first model, and FIG. 10B shows the second model.

The model simplification unit 14 generates a second model in which the two wiring layers P11 and P12 and the insulating layer S13 therebetween of the first model generated by the simple model generation unit 13 are replaced with one wiring layer P21. do. Here, the model simplification unit 14 replaces the first model with the second model so as to satisfy the condition that the thermal conductance of the first model and the thermal conductance of the second model are equal. That is, by setting the thickness of the wiring layer P21 to t _ps and the thermal conductivity to λ _ps , the following simultaneous equations (Equation 13) and (Equation 14) are solved to obtain the thermal conductivity λ of the wiring layer P21 of the second model. Calculate _ps .

In this way, the calculation load of the simulation using the second model can be reduced by creating the second model that further simplifies the first model by consolidating into one wiring layer P21. Further, by performing the simplification by the above method, the distance from the surface of the substrate to the surface of the wiring layer P21 in the second model (=thickness of the first insulating layer S11) is changed from the surface of the substrate in the first model to Since the first model can be simplified to the second model without changing the distance to the surface of the first wiring layer P11 (=thickness of the first insulating layer S11), the effect of the distance to the inner layer is equally affected. Considering the simulation can be performed.

Although FIG. 10 illustrates an example in which the two wiring layers P11 and P12 of the first model and the insulating layer S13 therebetween are collectively replaced with one wiring layer P21, the present invention is not limited to this. For example, at a position where _the distance from the surface of the substrate to the surface of the wiring layer in the second model is the same as the thickness of the first insulating layer S11, The first model may be replaced with the second model in such a manner that one wiring layer having a thickness is arranged.

In the above embodiment, the thermal conductivity λ _k (k = 1 to n) is used as information on the thermal properties _of each layer. ε _k λ _k may be used. The value of the copper foil residual ratio ε _k is 0 to 1 for the wiring layer and 1 for the insulating layer. The value of the copper foil residual ratio ε _p in the wiring layers P11 and P12 of the simple model can be, for example, the average value of the copper foil residual ratios ε _2k (k=1 to 5) of the wiring layers P1 to P5 in the detailed model. It is possible.

Further, in the above embodiment, an example of creating a simple model from a detailed model composed of five wiring layers P1 to P5 and five insulating layers S1 to S5 has been described, but this detailed model is only an example and is limited to this. not to be For example, the number of layers may be other than five layers. Also, the number of wiring layers and the number of insulating layers may not be the same. For example, the insulating layer may be arranged on the backmost side.

In addition, the above-described embodiments are merely examples of specific implementations of the present invention, and the technical scope of the present invention should not be construed in a limited manner. Thus, the invention may be embodied in various forms without departing from its spirit or essential characteristics.

10, 10' Simple model creation device 11 Board information input unit 12 Gravity center calculation unit 13 Simple model generation unit 13A Thickness calculation unit 13B Thermal conductivity calculation unit 13C Distance calculation unit 14 Model simplification unit

Claims (10)

A method for creating a simple thermal simulation model of a multilayer substrate including a plurality of wiring layers of three or more and a plurality of insulating layers, comprising:
a center-of-gravity calculation step in which a center-of-gravity calculator of a computer calculates a thermal center-of-gravity position of the multilayer substrate;
a simple model generating step of generating a simple thermal simulation model in which the simple model generating unit of the computer generates a simple thermal simulation model corresponding to a virtual two-layer board having two wiring layers at positions satisfying a predetermined condition with respect to the thermal center of gravity position; death,
The above predetermined conditions are
A first condition that the thermal moment of inertia of the multilayer substrate and the thermal moment of inertia of the virtual two-layer substrate replacing the multilayer substrate are equal, and the thermal conductance of the multilayer substrate and the heat of the virtual two-layer substrate. A method for creating a simple thermal simulation model for a multi-layer substrate, characterized by including a second condition that conductance and conductance are equal to each other. In the simple model, the sum of the thicknesses of the wiring layers and the sum of the thicknesses of the insulating layers of the virtual two-layer board are equal to the sum of the thicknesses of the wiring layers and the sum of the thicknesses of the insulating layers of the multilayer board, and 2. The multi-layer board according to claim 1, wherein said first model is a first model in which said two wiring layers are arranged at positions at a predetermined distance from said thermal center of gravity and are symmetrical with respect to said thermal center of gravity. How to create a simple thermal simulation model. A model simplification step of generating a second model in which the model simplification unit of the computer replaces the two wiring layers of the first model generated by the simple model generation unit with one wiring layer. death,
In the second model, the distance from the surface of the substrate to the surface of the one wiring layer in the second model is the same as the distance from the surface of the substrate to the surface of the first wiring layer in the first model, and 3. The method of creating a simple thermal simulation model for a multilayer substrate according to claim 2, wherein the model satisfies the condition that the thermal conductance of the first model and the thermal conductance of the second model are equal. 4. The multilayer substrate according to claim 3, wherein the second model is a model in which the two wiring layers and the insulating layer therebetween of the first model are collectively replaced with the one wiring layer. How to create a simple thermal simulation model. The first condition is the sum of the thermal moments of inertia of the plurality of wiring layers of the multilayer board with respect to the thermal center of gravity, and the two wiring layers of the virtual two-layer board with respect to the thermal center of gravity. 5. The method for creating a simple thermal simulation model of a multilayer substrate according to claim 2, wherein the condition is that the sum of the thermal moments of inertia is equal. 6. A simplified multilayer substrate according to claim 5, wherein said first condition is set on the premise that said thermal moment of inertia is proportional to the square of the distance from the reference position. How to create a thermal simulation model. 6. A simplified multilayer substrate according to claim 5, wherein said first condition is set on the premise that said thermal moment of inertia is proportional to the fourth power of the distance from the reference position. How to create a thermal simulation model. The second condition includes the thermal conductance in the in-plane direction and the thermal conductance in the thickness direction calculated from the thermal conductivity of the wiring layer and the thermal conductivity of the insulating layer of the multilayer substrate, and the wiring of the virtual two-layer substrate. 8. The condition is that the thermal conductance in the in-plane direction and the thermal conductance in the thickness direction calculated from the thermal conductivity of the layer and the thermal conductivity of the insulating layer are equal to each other. A method for creating a simple thermal simulation model for a multilayer substrate according to item 1. An apparatus for creating a simple thermal simulation model of a multi-layer substrate including a plurality of wiring layers of three or more and a plurality of insulating layers,
a center-of-gravity calculation unit for calculating a thermal center-of-gravity position of the multilayer substrate;
a simple model generating unit for generating a simple thermal simulation model corresponding to a virtual two-layer board having two wiring layers at positions satisfying a predetermined condition with respect to the thermal center of gravity position;
The above predetermined conditions are
A first condition that the thermal moment of inertia of the multilayer substrate and the thermal moment of inertia of the virtual two-layer substrate replacing the multilayer substrate are equal, and the thermal conductance of the multilayer substrate and the heat of the virtual two-layer substrate. 1. An apparatus for creating a simple thermal simulation model for a multi-layer substrate, characterized by including a second condition that the conductance and the conductance are equal to each other. A simple model creation program for causing a computer to execute a process of creating a simple thermal simulation model of a multi-layer board including a plurality of wiring layers of three or more and a plurality of insulating layers,
a center-of-gravity calculation means for calculating a thermal center-of-gravity position of the multilayer board; and a simple thermal simulation model corresponding to a virtual two-layer board having two wiring layers at positions satisfying a predetermined condition with respect to the thermal center-of-gravity position. functioning the computer as a simple model generating means,
The above predetermined conditions are
A first condition that the thermal moment of inertia of the multilayer substrate and the thermal moment of inertia of the virtual two-layer substrate replacing the multilayer substrate are equal, and the thermal conductance of the multilayer substrate and the heat of the virtual two-layer substrate. A simple model creation program characterized by including a second condition that conductance and conductance are equal.

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