JP2011039741A - Board warp analysis method, board warp analysis system, and board warp analysis program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To solve the problem that it is difficult to quickly and highly precisely calculate a warp when manufacturing a component built-in board in which an electronic component is embedded in a layer of a printed circuit board. <P>SOLUTION: A component built-in board is divided into a region where a built-in component exists and a region where any built-in component does not exist, and division model numbers are added, and a local coordinate system and boundary conditions are set, and then, the warp of each of those division models is calculated by a multi-layer beam theory. Furthermore, the post-deformation divisions are combined, and reconverted into the warp of the model as a whole. Thus, it is possible to instantly calculate the warp of the component built-in board without creating an FEM model, and to achieve the optical design by suppressing the warp in design. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a substrate warpage analysis method, a substrate warpage analysis system, and a substrate warpage analysis program for analyzing, for example, warpage generated on a substrate in a reflow process.

In recent years, electronic devices have been rapidly reduced in weight, thickness, and size, and electronic components and printed boards to be incorporated in a housing are also required to be reduced in size and thickness. Further, with the downsizing and thinning of mounting parts of electronic devices, higher density and higher reliability are required for mounting technology.
Therefore, when the substrate is heated in a reflow process in which the electronic component is mounted on the printed wiring board with a solder material, the electronic component or the printed circuit board is warped due to a difference in thermal expansion coefficient between various materials used. It has also been pointed out that when electronic components and printed circuit boards are connected in a state of being deformed due to warpage, solder materials are likely to be unfused and connection reliability may be reduced. Further, since the bending rigidity is further lowered when the substrate is thinned, the substrate is likely to be warped. For this reason, it is important to predict in advance the warping behavior during reflow.

However, it is very difficult to actually monitor the warping at high temperatures, so related companies, universities, research institutes, etc. are currently studying prediction technology by simulation using the Finite Element Method (FEM). Has been.
For example, a system that analyzes the warpage of a board in a simulation using model data representing the shape of a printed wiring board that is a multilayer board has been proposed (see Patent Document 1).
As a prediction method other than FEM, there is a multilayer beam theory that can handle warpage of a multilayer substrate (see Non-Patent Document).

JP 2004-013437 A

J. Oda, “Evaluation of stress and deformation of printed circuit board by multilayer beam theory”, Transactions of the Japan Society of Mechanical Engineers, Vol.59, No.563, pp. 203-208, 1993.

  However, when analyzing the warpage of the component-embedded substrate in which the electronic component is embedded in the layer of the printed wiring board, the layers constituting the multilayer structure are not in a state continuous in the plane direction by the electronic component. For this reason, there is a problem that it is difficult to predict the warpage generated in the substrate using the multilayer beam theory, and it is difficult to calculate the warp in a short time with high definition.

More specifically, when FEM is used, modeling is performed from elements composed of nodes using a discretization method. However, when the analysis target (substrate) becomes thinner, the aspect ratio (element aspect ratio) There is a first problem that analysis accuracy deteriorates and analysis accuracy decreases.
Here, the decrease in the analysis accuracy due to the deterioration in the aspect ratio will be explained. Ideally, the aspect ratio is preferably 1, and the default is generally 0.5 in general-purpose FEM software. The impact is small. However, when the default is 0.5 or less, the aspect ratio is generally improved by reducing the elements to prevent the analysis accuracy from being lowered.

However, if an element with a poor aspect ratio is made fine, the nodes that make up the element need to be continuous, so the entire area must also be made fine, and the total number of elements increases significantly. Therefore, a second problem that analysis time increases as the number of elements increases occurs.
For example, if an LSI with a length of 10 mm and a thickness of 50 μm has the same length and is built in a multi-layer board with 8 layers, the model is created in two dimensions. The ratio is 0.005. Therefore, in order to set the aspect ratio to 0.5, it is necessary to divide it into 100 in the length direction, which requires 800 times as many elements.
Furthermore, if warpage analysis is performed with a model in which a component-embedded board is mounted on a motherboard, the fineness of the elements affects the creation of the motherboard model, and the number of elements further increases.

On the other hand, for such an increase in the number of elements, there is a method using the multilayer beam theory described in Non-Patent Document 1. Multi-layer beam theory is a method of calculating warpage from the balance equation of bending moment, axial force, and deformation of multi-layer beam generated by this, and it is not necessary to model from elements. The prediction accuracy can be increased. For this reason,
When manufacturing a component-embedded substrate in which an electronic component is embedded in a printed wiring board layer, the first problem described above can be improved by using the multilayer beam theory.
In addition, since the multilayer beam theory is used, only the theoretical formula is calculated, so that the second problem described above can also be improved.

However, in this multilayer beam theory, each layer needs to be continuous, and other materials cannot be interposed in the middle. In other words, when electronic parts made of different materials and deposited layers are stacked in layers with the same level in the thickness direction of the multilayer structure, the warpage that occurs in the substrate is predicted using multilayer beam theory. The third problem that cannot be done arises.
Therefore, as long as the third problem cannot be solved, there is a problem that the first and second problems cannot be solved.

  The present invention has been made in view of such circumstances and has been made to solve the above-described problems. The object of the present invention is to increase the warpage that occurs in a component-embedded substrate in which electronic components are embedded in the inner layer of a printed wiring board. An object of the present invention is to provide a substrate warpage prediction system, a substrate warpage prediction method, and a substrate warpage prediction program capable of improving connection reliability in the design stage by predicting with accuracy.

  In order to solve the above problem, the present invention is a substrate warpage analysis system for analyzing warpage occurring in a substrate of a multilayer structure stacked in a first direction, and extends in a second direction intersecting the first direction. When the first material layer and the second material layer having different physical properties are included in the layer, the model data representing the shape of the substrate is obtained at the boundary between the first material layer and the second material layer. According to the warp obtained by the calculation unit, a division unit that virtually cuts in a first direction and divides into a plurality of divided parts, a calculation unit that calculates the warp of each divided part according to the multilayer beam theory A combined conversion unit that virtually deforms each divided part, virtually combines the deformed divided parts to form a substrate, and calculates a warp of the entire substrate based on each warp of the divided parts; To have And butterflies.

  By predicting the warpage occurring in the component-embedded substrate in which the electronic component is embedded in the inner layer of the printed wiring board in a short time and with high accuracy, the connection reliability at the design stage can be improved.

1 is a block diagram illustrating an example of a substrate warpage analysis system according to a first embodiment of the present invention. It is the schematic which shows an example of the analysis object of the board | substrate curvature analysis system which concerns on 1st Embodiment. It is the schematic which shows the example of a division | segmentation of the analysis object of the board | substrate curvature analysis system which concerns on 1st Embodiment. It is the schematic which shows an example of the division | segmentation part of the analysis object of the board | substrate curvature analysis system which concerns on 1st Embodiment. It is the schematic for demonstrating an example of the coupling | bonding method of the board | substrate curvature analysis system which concerns on 1st Embodiment. It is a flowchart which shows an example of the analysis method in the board | substrate curvature analysis system which concerns on 1st Embodiment. It is the schematic which shows the example of a division | segmentation of the analysis object of the board | substrate curvature analysis system which concerns on the 2nd Embodiment of this invention. It is the schematic which shows an example of the division | segmentation part of the analysis object of the board | substrate curvature analysis system which concerns on 2nd Embodiment. It is the schematic which shows the example of a division | segmentation of the analysis object of the board | substrate curvature analysis system which concerns on the 3rd Embodiment of this invention. It is the schematic which shows the example of a division | segmentation of the analysis object of the board | substrate curvature analysis system which concerns on 3rd Embodiment. It is a block diagram which shows the other structural example of the board | substrate curvature analysis system which concerns on this invention. It is a cross-sectional schematic diagram of the multilayer structure before deform | transforming by curvature. It is a cross-sectional schematic diagram of the multilayer structure after deform | transforming by curvature.

[First Embodiment]
Next, a first embodiment according to the present invention will be described in detail with reference to the drawings.
FIG. 1 is a schematic diagram illustrating an example of a substrate warpage analysis system according to the present embodiment.

As shown in FIG. 1, the substrate warpage analysis system according to the present embodiment includes an input device 1, a data processing device 2, a storage device 3, and an output device 4. Further, the data processing device 2 includes a data capturing unit 21, a model creation unit 22, a model division unit 23, a calculation unit 24, a model combination unit 25, and a data conversion unit 26.
The input device 1 is a device equipped with, for example, CAD (Computer Aided Design). A user (for example, an analyst who analyzes substrate model data using the substrate warpage analysis system according to the present embodiment) uses the input device 1 to input the shape data of the substrate or electronic component and input the model data. Generate and store in a model data storage unit (not shown). The shape data includes the length and thickness of the electronic component, the mounting position on the substrate, the length of the substrate on which the electronic component is stacked, the thickness of the insulating layer and the wiring layer, and the like. The input device 1 includes a keyboard and a mouse that receive user input.
Further, the input device 1 reads model data to be analyzed from a model data storage unit (not shown) and outputs the model data to the data processing device 2.

For example, a personal computer or the like can be used as the data processing device 2, and substrate warpage analysis is performed on the model data from the input data 1 to obtain an analysis result representing warpage generated on the substrate.
As the storage device 3, for example, a magnetic disk storage device or the like can be used, and stores information that is referred to when the data processing device 2 performs substrate warpage analysis. In this storage device 3, information representing the physical properties of the analysis target is stored in the material library, and physical property values such as the dielectric constant and relative dielectric constant of the analysis target are stored as the material characteristic values of the analysis target. .
For example, a display or the like can be used as the output device 4, and the analysis result obtained by the data processing device 2 is converted into image data, and an image represented by the image data is displayed on the screen.

Next, an example of a substrate used as an analysis target will be described with reference to FIG. FIG. 2 shows an example of a substrate in which an electronic component used as an analysis target in this embodiment is embedded.
As shown in FIG. 2, the substrate 100 includes a first layer 101, a second layer 102, and a third layer 103, and is a substrate having a three-layer structure that is laminated in this order. That is, the second layer 102 is sandwiched between the first layer 101 and the third layer 103.
For convenience of explanation, the direction toward the left side of the page is defined as the positive direction of the X axis, the direction toward the upper side of the page is defined as the positive direction of the Y axis, and the direction from the back side to the surface of the sheet is defined as the positive direction of the Z axis. explain. The positive direction of the Y axis is the upward direction, and the negative direction of the Y axis is the downward direction. These coordinates have the same relationship as local coordinates described later. That is, the surface direction of each layer of the substrate 100 is the XY axis direction, and the height direction (thickness direction) of each layer is the Y axis direction.
Further, the substrate 100 includes an electronic component 101 embedded so as to be sandwiched between the second layer 102 and the third layer 103. Model data representing the shape of the substrate 100 is stored in the input device 1.

Next, returning to FIG. 1, each configuration of the data processing device 2 will be described in detail.
The data capturing unit 21 reads model data of the analysis target board from the input device 1.
The model creation unit 22 is based on the model data read by the data capture unit 21 and material properties such as the Young's modulus E and the thermal expansion coefficient α of the electronic component 104 and the first layer 101 to the third layer 103 included in the model data. The value is read from the material library of the storage device 3 and output to the model dividing unit 23 in association with the model data.

When the model data associated with the material property value is input by the model creating unit 22, the model dividing unit 23 determines whether or not there is an electronic component embedded in the substrate based on the model data. When the component is embedded, the thickness direction in which the electronic component and each layer are in contact is virtually cut and divided into a plurality of divided parts.
For example, referring to the example shown in FIG. 2, the model data represents the substrate 100 in which the electronic component 104 is embedded in the third layer 103 and the second layer 102. Therefore, the model dividing unit 23 determines to divide the substrate 100 based on the model data. On the other hand, when there is no electronic component embedded inside, the model dividing unit 23 determines that it is not necessary to divide.

Further, the model dividing unit 23 detects whether or not there is a portion where the cross-sectional shape of the substrate changes, and determines that the division is performed when there is a portion where the cross-sectional shape is different, and there is no portion where the cross-sectional shape is changed. It may be determined that it is not divided.
Specifically, with reference to FIG. 2, the model dividing unit 23 determines whether or not there are at least two material layers having different physical properties in each layer spreading in the X-axis direction. Here, the second layer 102 is a mixture of a physical layer constituting the second layer 102 and a physical layer composed of the electronic component 104. Therefore, the model dividing unit 23 detects that the cross-sectional shape including the electronic component 104 is different from the cross-sectional shape not including the electronic component 104 in the cross-sectional shape when cut in the thickness (Y-axis) direction. Further, the model dividing unit 23 virtually divides the portion where the cross-sectional shape changes, that is, the boundary portion between the second layer 102 and the electronic component 104 in the thickness direction, and divides the plurality of divided parts. .

Here, the model dividing unit 23 divides the substrate 100 into the surface (X-axis) direction and the thickness (Y-axis) direction as shown in FIG. FIG. 3 is a schematic diagram illustrating an example of division of the substrate 100.
As shown in FIG. 3, the first layer 101 and the third layer 103 have a constant height (substantially uniform) and the same thickness in the X-axis direction. On the other hand, the thickness of the second layer 102 is different when comparing the portion where the electronic component 104 is embedded and the portion where the electronic component 104 is not embedded.
Therefore, the model dividing unit 23 cuts and divides the model data in the YZ direction at the virtual plane Y11 and the virtual plane Y12 corresponding to the boundary plane between the second layer 102 and the electronic component 104 in the YZ direction. .
Further, the model dividing unit 23 cuts and divides the model data in the XZ direction on the virtual plane X11 corresponding to the boundary surface in the XZ direction between the second layer 102 and the electronic component 104.
For example, the model dividing unit 23 virtually cuts the model data at the virtual planes X11, Y11, and Y12 according to the cutting method of material mechanics to obtain six divided parts 151 to 156. The second layer 102 divided by the virtual plane X11 is divided into a divided layer 102A on the first layer 101 side and a divided layer 102B on the third layer 103 side.

Next, the six divided parts 151 to 156 of the divided substrate 100 will be described in detail as shown in FIG. FIG. 4 is a schematic diagram for explaining the divided parts of the substrate 100, wherein (a) to (f) represent the divided parts 151 to 156, respectively.
As shown in FIG. 4, the substrate 100 includes a divided part 151 including a first layer 101 and a divided layer 102 </ b> A of the second layer 102 in the positive direction of the X axis with respect to the virtual surface Y <b> 11, a virtual surface Y <b> 11, and a virtual surface Y <b> 12. Between the first layer 101 and the second layer 102 divided part 152A, and the first layer 101 and the second layer 102 divided layer 102A in the negative direction of the X axis from the virtual plane Y12. Into divided parts 152.
In addition, the substrate 100 includes a divided part 154 composed of the divided layer 102B and the third layer 103 of the second layer 102 in the positive direction of the X axis with respect to the virtual plane Y11, and between the virtual plane Y11 and the virtual plane Y12. A split part 155 composed of the electronic component 104 and the third layer 103, and a split part 156 composed of the split layer 102B of the second layer 102 and the third layer 103 which are in the negative direction of the X axis from the virtual plane Y12. Divided.

Further, the model dividing unit 23 assigns model numbers to the divided parts 151 to 156 constituting the divided model data, assigns local coordinates, and adds constraint conditions.
For example, the model dividing unit 23 assigns model numbers P1 to P6 to the divided parts 151 to 156.
The model dividing unit 23 sets a local coordinate system composed of a two-dimensional X axis and a Y axis for each of the divided parts 151 to 156. As a setting method, the calculation unit 24 calculates a warp as described later according to this local coordinate system, and it is preferable to set one of the coordinate axes along the dividing line. Alternatively, the model data before the division is the center of the substrate 100, the intersection of the surface (half section) perpendicular to the substrate and the bottom surface of the substrate is the origin, the bottom surface of the substrate is the x coordinate, and the determination surface is y You may assign a local coordinate so that it may become a coordinate.
Specifically, the divided part 151 shown in FIG. 4A will be described as an example. The model dividing unit 23 uses the y coordinate of the virtual surface Y11 and the x coordinate of the virtual surface X11 divided by the model dividing unit 23 as local coordinates. Are obtained as information representing local coordinates.

In addition, the model dividing unit 23 obtains information indicating that the virtual planes X11 and Y11 are fixed as a constraint condition of the divided part 151. For example, as a constraint condition, the division part may be constrained as a fixed end, and a desired temperature may be applied to the entire division model data.
Then, the model dividing unit 23 associates the information representing the local coordinates obtained in this way with the information related to the constraint condition, and outputs the information to the calculation unit 24 as the divided model data of the divided part 151.
Similarly, the division model data of the divided parts 152 to 156 is calculated and output to the calculation unit 24.

The calculation unit 24 calculates the warp (deflection) of the divided parts 151 to 156 of the divided model data divided by the model dividing unit 23 using the multilayer beam theory. Here, the calculation unit 24 calculates warpage according to the programmed multilayer beam theory, and associates the calculation result with each local coordinate.
More specifically, in the calculation using the multi-layered beam theory, the tensile force and bending moment that are the same in size and reverse in the direction of action are considered for each part in consideration of the mutual influence of the divided parts 151 to 156. Create multiple balance equations in addition to each cut surface, and determine the undetermined coefficient of the newly added virtual tensile force and bending moment by combining the multiple balance equations to determine the overall displacement (warp). Ask. Then, the warping data is stored in the storage device 3 together with the division information. The warpage may be calculated for each division, or may be divided together and temporarily stored as division information, and sequentially read for each divided block to calculate the warpage.

Here, the calculation of the warp by the multilayer beam theory will be described in detail.
Consider a case where an n-layer beam (n is a natural number) as shown in FIG. 12 is deformed as shown in FIG. The thickness of each layer is considered to be smaller than the radius of curvature, and the representative radius of curvature is set to R assuming that the radius of curvature R1, R2,. The warp of the substrate can be calculated by obtaining the unknown radius R.sub.2. The calculation method is shown below.

R1, R2,... Rn are the radius of curvature of each layer, and R is the representative radius of curvature.
Further, the continuous condition of the strain on the bonding surface of the multilayer beam and the balance formula of the axial force Pi and bending moment Mi generated in each layer are expressed by the following equations.

  However, {ε} is a strain vector and {P} is an axial force vector, which is expressed by the following equation.

  [K] is a stiffness matrix, and the following relationship is established.

  Further, when the elongation of the multi-layer beam is ignored (L ′ = L) and the warp (deflection) generated in the n-layer beam is δ, the following equation is obtained.

  Therefore, the curvature (deflection) δ can be calculated by obtaining the curvature R from the equation (2) and substituting it into the equation (7). By programming this matrix type equation, the warpage of the multilayer substrate can be instantaneously calculated without performing the FEM simulation.

  Note that this calculation method is based on the premise that each layer is a continuous layer (or beam), and if there is a built-in component embedded in the resin layer, each layer will be divided, so it can be used. could not. However, as described above, the model dividing unit 26 can divide the unit into units in which the thicknesses of the respective layers are uniform, so that it is possible to use the multilayer beam theory that can only calculate the warp of the continuous beam. Further, the warpage of the entire component built-in board can be calculated by recombining the deformed divided parts by the model combining unit 25 described later.

The model combining unit 25 virtually deforms each of the divided parts 151 to 156 based on the warp calculated by the arithmetic unit 24 and virtually combines the deformed divided parts 151 to 156 to form the substrate 100. To do. In addition, when the deformed divided parts are combined, the model combining unit 25 rotates the other divided parts in accordance with the deflection angle of the one divided part among the plurality of divided parts 151 to 156, so that one divided part is obtained. The angle-divided parts are joined so that the cut surfaces of the other parts and the cut surfaces of the other divided parts coincide.
This will be specifically described below with reference to FIG. When it is determined that warpage (deflection) of the divided parts 151 and 152 occurs, the model combining unit 25 determines the divided parts according to the deflection obtained by the arithmetic unit 24 as described above, as shown in FIG. 151 and 152 are deformed. Here, the case where the deflection angle of the divided part 151 is β and the deflection angle of the divided part 152 is θ will be described.
Then, a cutting surface 151R (axis corresponding to the virtual surface Y11) positioned in the negative direction of the X axis of the divided part 151 and a cutting surface 152R (corresponding to the virtual surface Y12) of the divided part 152 positioned in the negative direction of the X axis. Align the axis with the Y-axis direction.

Next, as illustrated in FIG. 5B, the model coupling unit 25 rotates the divided part 151 counterclockwise by, for example, the deflection angle θ of the divided part 152, and the cutting surface 151 </ b> R of the divided part 151 and the divided part 152. The direction with the cut surface 152L (axis corresponding to the virtual surface Y11) located in the positive direction of the X axis is matched.
Further, as shown in FIG. 5C, the model combining unit 25 matches the cut surfaces 151 </ b> R of the divided parts 151 and the cut surfaces 152 </ b> L of the divided parts 152 to connect the divided parts 151 and 152. As a result, the deflection angle after the divided parts 151 and 152 are coupled is (θ + β).
In the same manner as described above, the divided parts 152 and 153 are also coupled. In this case, since the divided parts 153 are further combined with the divided parts 151 and 152 being combined, the divided parts 153 are rotated by the deflection angle (θ + β) of the divided parts 151 and 152, and the divided parts 152 and 153 are moved to each other. The cut cut surfaces can be matched and bonded.
Further, the divided part 151 and the divided part 154 can be coupled by being rotated according to the deflection angle so that the cut surfaces at X11 coincide with each other.

The data conversion unit 26 calculates the warp of the entire substrate based on the model data composed of the combined divided parts and outputs the calculated warp to the output device 4.
Note that data relating to the warpage state including the amount of warpage synthesized from the model data processed in the data processing 2 is stored in the storage device 3, and the result is output from the output device 4.

Next, FIG. 6 shows a flowchart from model division to synthesis, which is particularly important in the present invention.
The model dividing unit 23 determines whether or not the model data generated by the model creating unit 22 is to be divided. If the model dividing unit 23 determines to divide the model data, the model dividing unit 23 greatly changes the cross-sectional shape of the model data (for example, virtual planes X11, Y11, Y12) virtually disconnects (step ST1). As a result, the model data of the substrate 100 is divided into a plurality of m (here, m = 6) divided parts 151 to 156 on the virtual planes X11, Y11, and Y12.
If it is determined in step ST1 that there is no need for division, the process ends.
Next, the model dividing unit 23 assigns model numbers P1 to P6 to the divided parts 151 to 156 (step ST2), assigns local coordinates (step ST3), and adds constraint conditions (step ST4). Here, the model dividing unit 23 reads out analysis conditions (for example, a temperature given to the substrate at the time of manufacturing predetermined in the simulation for the purpose of analysis) from the storage device 3 with respect to the entire model data, and stores the model. The data is output to the calculation unit 24 in association with the data.

Then, based on the local coordinates and boundary conditions input from the model dividing unit 23, the calculation unit 24 calculates a warp for each of the divided parts 151 to 156 using multilayer beam theory (step ST5).
Based on this warp, the model combining unit 25 deforms each of the divided parts 151 to 156. For this reason, the warp in each of the divided parts 151 to 156 obtained by the multilayer beam theory is a warp from a separate fixed end in each local coordinate as shown in FIG. Therefore, as described with reference to FIG. 5B, it is necessary to match the warp generated in one divided part with the fixed end of the other divided part between adjacent divided parts. For this reason, the model coupling | bond part 25 rotates the other fixed end by the deflection angle (theta) of a front-end | tip (step ST6).
Further, the model coupling unit 25 moves one of the divided parts while the other divided part 151 is rotated by the rotation θ at the deflection angle θ of the one divided part 152, as shown in FIG. In addition, the divided parts are joined at the cut surfaces that were connected before being divided (step ST7).

  And the model coupling | bond part 25 repeats the process of this step ST6, 7 until all the division | segmentation parts 151-156 are couple | bonded (step ST8-NO). When the combination of all the divided parts 151 to 156 is completed (step ST8—YES), the data changing unit 26 calculates the warpage value of the entire substrate 100 based on the local coordinates of the connected divided parts 151 to 156. . Here, since the local coordinates of the connected divided parts 151 to 156 represent the overall warpage value of the substrate 100, the local coordinates are converted into the overall warpage value of the substrate 100.

  As described above, the substrate warpage analysis system according to the present embodiment has the thickness of the multilayer structure when a plurality of substances having different physical properties exist in a layer due to the embedded electronic component 104. The shape of the cross section in the direction changes. For this reason, the model data is divided at the portion where the cross-sectional shape changes, that is, at the boundary between the electronic component and each layer. Thereby, each layer which comprises the divided | segmented parts 151-156 became uniform thickness. Therefore, it is possible to calculate the warpage of each of the divided parts 151 to 156 using the multilayer beam theory, to calculate the warpage of the substrate 100 in a short time and with high definition, to improve the connection reliability in the design stage, and to improve reliability High optimum conditions can be obtained.

This can also prevent warpage that occurs when manufacturing a component-embedded board in which an electronic component is embedded in the inner layer of the printed circuit board, or warpage that occurs when soldering to a motherboard in a reflow process or the like.
Furthermore, since it is possible to analyze warpage using multilayer beam theory without using FEM, there is no need for specialized knowledge and experience necessary for creating an FEM model, and a processing apparatus capable of executing multilayer beam theory is prepared. Therefore, even if it is not an FEM experienced person, a warp value can be obtained with high accuracy.
In addition, as described above, by cutting not only in the thickness direction of the substrate but also in the surface direction and creating a plurality of divided parts, the influence of warpage in the internal cut surface along the surface direction is locally calculated. can do. Thereby, the curvature which has an influence with respect to the electronic component incorporated can be obtained locally.

In addition, about the experimental result which calculated | required curvature using the board | substrate curvature analysis system based on this embodiment using the 3 layer component-embedded board model of FIGS. 2-4, the curvature was calculated | required using FEM. The following explanation will be given while comparing with the experimental results.
First, when FEM is used, FEM experts can create model data such as cutting elements from model data representing shapes, adding boundary conditions, inputting material constants, setting element types, setting analysis types, etc. Analysis conditions are set. At this time, the time required for these operations was about 8 minutes. In addition, when model data was analyzed with a general desktop personal computer under these conditions, it took about 20 seconds to obtain the analysis result.

On the other hand, when the method according to the present embodiment is used, it is not necessary for the user to perform element cutting that requires the most work time. As for the boundary condition, since the position of the divided part on the substrate 100 is recognized in advance on the processing apparatus 2 side, it is not necessary for the user to directly input or change the setting condition. For this reason, the time required for these operations by the same person who conducted the FEM experiment was about 1 minute. Moreover, when model data was analyzed with the same personal computer as FEM under these conditions, it was only necessary to solve the simultaneous equations of the multilayer beam theory, and it took only 1 to 2 seconds to obtain the analysis result.
As described above, it was confirmed that the present embodiment shortens the analysis time and improves the work efficiency.

  Here, the above-described experimental results were obtained using the substrate 100 in which the built-in electronic component is one three-layer multilayer structure. Therefore, when warpage analysis is performed on a substrate in which the number of layers of the substrate is close to 20 and a plurality of built-in components having different shapes are embedded therein, the method using FEM and the present embodiment With such a method, it is easily imagined that the difference in time reduction effect is further increased.

[Second Embodiment]
The present invention can also use an analysis target having a configuration different from that of the substrate 100 described above, and the substrate 200 that is an analysis target that can be used will be described with reference to FIGS. FIG. 7 is a schematic diagram illustrating an example of division of the substrate 200.
As shown in FIG. 7, the substrate 200 includes a first layer 201, a second layer 202, and a third layer 203, and is embedded in the plurality of layers across the first layer 201 and the second layer 202. The electronic component 204 is provided.
The third layer 203 has a substantially uniform thickness and the same thickness in the X-axis direction. On the other hand, the first layer 201 and the second layer 202 have different thicknesses when comparing a portion where the electronic component 204 is embedded and a portion where the electronic component 204 is not embedded.
Therefore, the model dividing unit 23 converts the model data to the first and second layers 201 and 22 on the virtual plane Y21 and the virtual plane Y22 that are in the YZ direction where the electronic component 204 is in contact with the first and second layers 201 and 202. -Cut in the Z direction and divide.
In addition, the model dividing unit 23 transfers the model data in the XZ direction on the virtual plane X21 that is a boundary surface in the XZ direction where the electronic component 204 is in contact with the first layer 201 and the second layer 202. Cut and split.
As a result, the substrate 200 is divided into six divided parts 251 to 256. Further, the first layer 202 divided by the virtual plane X21 is divided into a divided layer 201A located on the outer side and a divided layer 201B on the second layer 202 side.

Next, the six divided parts 251 to 256 of the divided substrate 200 will be described in detail as shown in FIG. FIG. 8 is a schematic diagram for explaining the divided parts of the substrate 200, where (a) to (f) represent the divided parts 251 to 256, respectively.
As shown in FIG. 8, the substrate 200 is divided into divided parts 251 to 253 including the divided layer 201 </ b> A of the first layer 201. The substrate 100 is divided into divided parts 254 and 256 composed of the divided layer 201B of the first layer 201, the second layer 202, and the third layer 203, and divided parts 255 composed of the electronic component 204 and the third layer 203. Is done.
As described above, the present invention can be provided even when the electronic component incorporated in the substrate is incorporated across a plurality of layers.

[Third Embodiment]
The present invention can also use an analysis target having a configuration different from that of the substrate 100 described above, and the substrate 300 that is an available analysis target will be described with reference to FIGS. FIG. 7 is a schematic diagram illustrating an example of division of the substrate 200.
As shown in FIG. 9, the substrate 300 includes an electronic component 301, a printed wiring board 302, a solder bump 303 that electrically joins the electronic component 301 and the printed wiring board 302, and a resin used to reinforce the solder bump 303. This underfill including 304 (hereinafter referred to as underfill) is filled around the solder bump 303.
The solder bumps 303 are generally formed with a predetermined thickness and pitch.
Even in a substrate having such a configuration, by using the above-described method, model data is obtained in the YZ direction on the virtual planes Y31 to Y38 at the pitch interval of the solder bump 303 as shown in FIG. Can be cut and divided. Thereby, the influence which the material of the underfill 304 has on the curvature of the board | substrate 300 is analyzable, without using FEM.

In addition, this invention is not restricted to the above-mentioned embodiment, For example, a structure as shown in FIG. 11 may be sufficient. That is, as shown in FIG. 11, the warp analysis program 5 may be provided in addition to the input device 1, the data processing device 2, the storage device 3, and the output device 4. The warpage analysis bath gram 5 stores a program that causes the data processing device 2 to function as described above, and the data processing device 2 reads the program to perform data processing and operations on the data processing device 2. To be executed.
Thus, if the data processing device 2 is a computer such as a general personal computer, the same processing as the processing by the data processing device 2 according to the above-described embodiment is executed by reading the program of the warp analysis program 5. can do.
The present invention is also effective for an electronic component mounted on the surface of the substrate. A printed wiring board in which an electronic component mounted on the surface and an electronic component built in the substrate are mixedly mounted. It is also possible to calculate warpage.

By predicting the warpage occurring in the component-embedded substrate in which the electronic component is embedded in the inner layer of the printed wiring board in a short time and with high accuracy, the connection reliability at the design stage can be improved.
Specifically, in the present invention, for example, when an electronic component or the like is embedded in a substrate, and a different material layer is included in a layer having the same level in the thickness direction of the multilayer structure, The substrate model data was cut in the thickness direction into regions where electronic components existed and regions where electronic components did not exist, and divided into a plurality of divided parts. As a result, the thickness of each divided part becomes uniform (that is, each layer constituting each divided part becomes a continuous layer). Therefore, the warp of each divided part is calculated using multilayer beam theory. Can do. Thus, since the multilayer beam theory can be used, there is an effect that the third problem can be solved (first effect). In addition, since the multilayer beam theory can be used, the problem of the aspect ratio of elements in the FEM can be solved, and the first problem that the analysis accuracy is reduced can be solved (second effect) ).
In the present invention, the multilayer beam theory can be used as described above. For this reason, the problem of the increase in the number of elements in the FEM can be solved, and the second problem that the analysis time increases can be solved (third effect).

Furthermore, the operation process of the sampling providing device 1 or the storefront display device 2 can be used as a program to be executed by a computer or a computer-readable recording medium as the program, and read and executed by the computer system. Thus, the above processing is performed. The “computer system” here includes a CPU, various memories, an OS, and hardware such as peripheral devices.
Further, the “computer system” includes a homepage providing environment (or display environment) if a WWW system is used.
The “computer-readable recording medium” means a flexible disk, a magneto-optical disk, a ROM, a writable nonvolatile memory such as a flash memory, a portable medium such as a CD-ROM, a hard disk built in a computer system, etc. This is a storage device.

Further, the “computer-readable recording medium” means a volatile memory (for example, DRAM (for example, DRAM) inside a computer system that becomes a server or a client when a program is transmitted via a network such as the Internet or a communication line such as a telephone line. Dynamic Random Access Memory)), etc., which hold programs for a certain period of time.
The program may be transmitted from a computer system storing the program in a storage device or the like to another computer system via a transmission medium or by a transmission wave in the transmission medium. Here, the “transmission medium” for transmitting the program refers to a medium having a function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication line) such as a telephone line.
The program may be for realizing a part of the functions described above. Furthermore, what can implement | achieve the function mentioned above in combination with the program already recorded on the computer system, and what is called a difference file (difference program) may be sufficient.

  According to the present invention, in a design department that needs to develop an electronic component or an electronic device in a short period of time, a warp that occurs when the electronic component is manufactured and mounted on a motherboard by reflow is predicted at the design stage, It can be applied to applications such as support tools for taking reduction measures.

DESCRIPTION OF SYMBOLS 1 Input device 2 Data processing device 3 Storage device 4 Output device 5 Warp analysis program 21 Data acquisition part 22 Model preparation part 23 Model division part 24 Calculation part 25 Model coupling part 26 Data conversion part

Claims (8)

A substrate warpage analysis system for analyzing warpage generated in a substrate of a multilayer structure stacked in a first direction,
In the case where the first material layer and the second material layer having different physical properties are included in the layer extending in the second direction intersecting the first direction, model data representing the shape of the substrate is obtained as the first model data. A dividing portion that virtually cuts in the first direction at a boundary portion between the material layer and the second material layer and divides into a plurality of divided parts;
An arithmetic unit that calculates the warpage of each divided part according to the multilayer beam theory,
Each divided part is virtually deformed according to the warp obtained by the arithmetic unit, and the deformed divided parts are virtually combined to form a substrate, and based on each warp of the divided parts, A board warpage analysis system comprising: a coupling conversion unit that calculates warpage of the entire board.   When the height of the first material layer, which is the length in the first direction, is different, the dividing unit changes the shape of the substrate at a boundary portion between the first material layer and the second material layer. The substrate warpage analysis system according to claim 1, wherein model data to be represented is virtually cut in the second direction and divided into a plurality of the divided parts. The calculation unit calculates a deflection angle representing each warp of the divided parts,
The coupling conversion unit, when coupling the deformed divided parts, rotates the other divided parts according to the deflection angle of the one divided part among the plurality of divided parts, and cuts the one divided part 3. The substrate warpage analysis system according to claim 1, wherein the surface and the cut surface of the other divided part are matched and coupled.   The substrate warpage analysis system according to any one of claims 1 to 3, wherein the substrate to be analyzed has an electronic component embedded in a multilayer structure as the second material layer.   The substrate warpage analysis system according to claim 4, wherein the electronic component is embedded in a plurality of layers over the plurality of layers.   The substrate to be analyzed is characterized in that the first material layer and the second material layer are arranged at predetermined intervals in the same layer. The board | substrate curvature analysis system as described in any one of these. A substrate warpage analysis method in a substrate warpage analysis system for analyzing warpage of a substrate of a multilayer structure stacked in a first direction,
The division is
In the case where the first material layer and the second material layer having different physical properties are included in the layer extending in the second direction intersecting the first direction, model data representing the shape of the substrate is obtained as the first model data. Virtually cutting in the first direction at the boundary between the material layer and the second material layer, and dividing into a plurality of divided parts;
The computing unit is
Calculating the warp of each divided part according to the multilayer beam theory, and virtually deforming each divided part according to this warp;
Join conversion part
A substrate warpage analysis method comprising: forming a substrate by virtually combining the deformed divided parts, and calculating warpage of the entire substrate based on respective warpages of the divided parts. In a computer that analyzes the warpage of the substrate of the multilayer structure stacked in the first direction,
When the first material layer and the second material layer having different physical properties are included in the layer extending in the second direction crossing the first direction, model data representing the shape of the substrate is obtained as the first model data. Dividing means for virtually cutting along the first direction at the boundary between the material layer and the second material layer and dividing the material layer into a plurality of divided parts;
Calculation means for calculating the warp of each divided part according to the multilayer beam theory, and virtually deforming each divided part according to this warp,
A combined conversion unit that virtually combines the deformed divided parts to form a substrate, and calculates a warp of the entire substrate based on each warp of the divided parts;
Program to function as.

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