Equivalent thermal modeling method and device for solder joint structure

Abstract

The present invention provides an equivalent thermal modeling method and device for a solder joint structure, the method comprising: S1: constructing an original model of a single solder joint basic unit with a buffer block based on geometric parameters of the solder joint and material thermal conductivity; S2: applying boundary conditions and a heat source to the original model, and obtaining the average temperature of the plane where the heat source is located through numerical simulation; S3: replacing the original solder joint with a square column having the same volume as the solder joint structure in the original model to construct an equivalent model; S4: applying the same boundary conditions and heat source as the original model to the equivalent model, performing parameter scanning on the thermal conductivity of the square column, and determining the equivalent thermal conductivity of the square column; S5: repeating steps S1 to S4 for different ratios of solder joint height to solder joint diameter, and different ratios of basic unit side length to solder joint diameter, to extract the equivalent thermal conductivity of the corresponding square column; S6: obtaining an equivalent thermal conductivity model of the square column using a parameter fitting method based on the data obtained in step S5.

Description

Technical Field

[0001] The present invention relates to the technical field of microelectronic packaging, and in particular to an equivalent thermal modeling method and device for solder joint structures. Background Art

[0002] With the advancement of electronic packaging technology, the power density of electronic systems continues to increase, and heat dissipation issues are becoming increasingly serious. Excessively high temperatures can affect the reliability of electronic components and even cause failure of the entire electronic system. Therefore, thermal management is a critical issue facing electronic systems. Solder joints are widely used in electronic packaging structures, providing vertical electrical interconnection and heat transfer and diffusion. Therefore, as a critical component of electronic systems, it is necessary to accurately evaluate their heat transfer characteristics.

[0003] The existing methods for evaluating the heat transfer performance of solder joints mainly include the equivalent thermal resistance network method and the numerical method based on finite elements. When extracting the thermal resistance of the solder joint structure, the equivalent thermal resistance network method derives an approximate formula based on the electrical-thermal dual relationship to calculate the thermal resistance of the solder joint, thereby constructing a thermal resistance network. Since the details in the structure are ignored, the accuracy of this method is not high. The numerical method based on finite elements models the structure of the real solder joint in detail, which has high accuracy, but requires the division of a large number of grids, consumes high computing resources, and has low overall computing efficiency. Therefore, it is necessary to develop an equivalent thermal modeling method for solder joint structures that has a simple modeling process, is accurate and efficient, and is used to quickly evaluate the heat transfer characteristics of solder joint structures. Summary of the Invention

[0004] In view of the defects in the prior art, the purpose of the present invention is to provide an equivalent thermal modeling method and equipment for solder joint structures with a simple modeling process, high model accuracy and wide applicability, which is used to quickly evaluate the heat transfer characteristics of solder joint structures.

[0005] In order to solve the above problems, the technical solution of the present invention is:

[0006] An equivalent thermal modeling method for a solder joint structure comprises the following steps:

[0007] S1: Based on the geometric parameters of the solder joint and the thermal conductivity of the material, an original model of a single solder joint basic unit with a buffer block is constructed;

[0008] S2: Apply boundary conditions and heat sources to the original model, and obtain the average temperature of the plane where the heat source is located through numerical simulation;

[0009] S3: Use square columns with the same volume as the solder joints in the original model to replace the original solder joints and construct an equivalent model;

[0010] S4: Apply the same boundary conditions and heat sources as the original model to the equivalent model, perform parameter sweep on the thermal conductivity of the square column, and determine the equivalent thermal conductivity of the square column;

[0011] S5: Repeat steps S1 to S4 for different ratios of solder point height to solder point diameter, and different ratios of basic unit side length to solder point diameter, to extract the corresponding equivalent thermal conductivity of the square pillar;

[0012] S6: Based on the data obtained in step S5, an equivalent thermal conductivity model of the square cylinder is obtained using a parameter fitting method.

[0013] Preferably, in step S1, the original model includes a dielectric area, the interior of the dielectric area includes a solder joint structure, the outer side of the dielectric area is provided with a buffer block structure, the solder joint structure material is alloy solder, and the material of the dielectric area is epoxy resin.

[0014] Preferably, the buffer block structure is a rectangular block with high thermal conductivity. When extracting the thermal conductivity of the solder joint in the horizontal direction, the buffer block structure is located on the side of the dielectric area in the horizontal direction. When extracting the thermal conductivity of the solder joint in the vertical direction, the buffer block structure is located on the side of the dielectric area in the vertical direction.

[0015] Preferably, in step S2, the process of applying boundary conditions and heat sources to the original model includes: applying a uniform heat source on one side of the buffer block structure, applying a constant temperature boundary condition on the other side of the medium area parallel to the plane, and setting other surfaces to adiabatic boundary conditions.

[0016] Preferably, in step S2, the average temperature of the plane where the heat source is located is calculated by a finite element numerical simulation method.

[0017] Preferably, in step S3, a square column with the same volume as the solder joint area is used to replace the original area. The height of the square column is the same as the height of the solder joint area. The solder joint structure in the original model is a spherical table with a diameter of d and a height of h. The side length of the square column with the same volume as the solder joint structure is The height is h.

[0018] Preferably, in step S3, when extracting the equivalent thermal conductivity of the square column in the horizontal direction, the buffer block structure is provided on the side of the dielectric area in the horizontal direction; when extracting the equivalent thermal conductivity of the square column in the vertical direction, the buffer block structure is provided on the side of the dielectric area in the vertical direction.

[0019] Preferably, in step S4, parameter scanning is performed on the thermal conductivity of the square pillar until the relative error of the average temperature of the equivalent model and the original model on the heat source plane is less than a tolerance value, thereby determining the equivalent thermal conductivity of the square pillar.

[0020] Preferably, in step S6, the equivalent thermal conductivity model of the square column includes:

[0021] The compact expression for the thermal conductivity of a square column in the horizontal direction is:

[0022] k ex =a(p)×m b(p) +c(p)

[0023] a(p)=a1p 2 +a2p+a3

[0024] b(p)=b1p 2 +b2p+b3

[0025] c(p)=c1p 2 +c2p+c3

[0026] Among them, k ex is the equivalent thermal conductivity of the square column in the horizontal direction, a1, a2, a3, b1, b2, b3, c1, c2, c3 are fitting parameters, m is the ratio of the solder joint height to the solder joint diameter, and p is the ratio of the basic unit side length to the solder joint diameter;

[0027] The compact expression for the thermal conductivity of a square column in the vertical direction is:

[0028] k ez =e1m e2 +e3

[0029] Among them, k ez is the equivalent thermal conductivity in the vertical direction of the square cylinder, and e1, e2, and e3 are fitting parameters.

[0030] Furthermore, the present invention also provides a computer device, comprising a processor and a memory for storing executable instructions of the processor, wherein the processor is configured to perform the above-mentioned equivalent thermal modeling method for solder joint structures by executing the executable instructions.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] 1. According to the characteristics of the solder joint structure, the present invention uses a square column with the same volume as the solder joint to replace the original area, extracts the equivalent thermal conductivity of the square column in the horizontal and vertical directions, and simplifies the solder joint model.

[0033] 2. The solder joint equivalent model of the present invention has high accuracy and wide engineering applicability and can be used to process complex solder joint structures of various sizes.

[0034] 3. The present invention obtains a compact expression for the equivalent thermal conductivity of the solder joint based on the parameter fitting method. The expression is very concise. According to the expression, the anisotropic thermal conductivity of the square column in the equivalent model can be directly obtained, which is very convenient to implement. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0036] Figure 1 This is a flowchart of the equivalent thermal modeling method for solder joint structure of the present invention;

[0037] Figure 2 Schematic diagram for extracting horizontal thermal conductivity of the original model;

[0038] Figure 3 Schematic diagram for extracting the thermal conductivity in the vertical direction of the original model;

[0039] Figure 4 Schematic diagram for extracting the horizontal thermal conductivity of the equivalent model;

[0040] Figure 5 Schematic diagram for extracting the vertical thermal conductivity of the equivalent model;

[0041] Figure 6 is the relationship diagram between the equivalent thermal conductivity in the horizontal direction and the independent variables m and p;

[0042] Figure 7 This is the relationship diagram between the equivalent thermal conductivity in the vertical direction and the independent variables m and p. DETAILED DESCRIPTION

[0043] The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those skilled in the art, several changes and improvements can be made without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0044] Specifically, the present invention provides an equivalent thermal modeling method for solder joint structures, such as Figure 1 As shown, the method includes the following steps:

[0045] S1: Based on the geometric parameters of the solder joint and the thermal conductivity of the material, an original model of a single solder joint basic unit with a buffer block is constructed;

[0046] Specifically, if Figure 2 and Figure 3As shown, the original model of the single solder joint structure includes a dielectric region 1, a solder joint structure 2, and a buffer block structure 3. The dielectric region 1 is made of epoxy resin. The solder joint structure 2 is made of alloy solder and is located in the center of the dielectric region 1. The buffer block structure 3 is a rectangular block material and is located outside the dielectric region 1. When extracting the horizontal thermal conductivity of the solder joint, the buffer block structure 3 is located on the horizontal side of the dielectric region 1, for example Figure 2 The left side is shown, and its function is to make the heat flow smoothly enter the dielectric area 1. In order to reduce its influence on the model accuracy, the thermal conductivity of the buffer block is usually set to a larger value. Correspondingly, when extracting the thermal conductivity in the vertical direction of the solder joint, the buffer block structure 3 is located on the side of the dielectric area 1 in the vertical direction, for example Figure 3 Underside shown.

[0047] S2: Apply boundary conditions and heat sources to the original model, and obtain the average temperature of the plane where the heat source is located through numerical simulation;

[0048] Specifically, if Figure 2 As shown, when extracting the equivalent thermal conductivity in the horizontal direction, a uniform heat source is applied to the left side of the buffer block structure 3, a constant temperature boundary condition is applied to the right side of the medium area 1 parallel to the plane, and other surfaces are set to adiabatic boundary conditions. The average temperature of the plane where the heat source is located is calculated using the finite element method numerical simulation method.

[0049] like Figure 3 As shown, when extracting the equivalent thermal conductivity in the vertical direction, a uniform heat source is applied to the lower surface of the buffer block structure 3, a constant temperature boundary condition is applied to the upper surface of the medium area 1 parallel to the plane, and other surfaces are set to adiabatic boundary conditions. The average temperature of the plane where the heat source is located is calculated using the finite element method numerical simulation method.

[0050] S3: Use square columns with the same volume as the solder joints in the original model to replace the original solder joints and construct an equivalent model;

[0051] Specifically, if Figure 4 and Figure 5 As shown, a square column 4 with the same volume as the solder joint area is used to replace the original area. The height of the square column 4 is the same as that of the solder joint area and the square column 4 is located in the center of the dielectric area 1. In the original model, the solder joint area is a spherical table with a radius of r and a height of h. The side length of the square column 4 with the same volume as the solder joint structure is The height is h.

[0052] The buffer block structure 3 is a rectangular block material with high thermal conductivity. When extracting the equivalent thermal conductivity of the square column 4 in the horizontal direction, the buffer block structure 3 is arranged on the horizontal side of the medium area 1. When extracting the equivalent thermal conductivity of the square column 4 in the vertical direction, the buffer block structure 3 is arranged on the vertical side of the medium area 1.

[0053] S4: Apply the same boundary conditions and heat sources as the original model to the equivalent model, perform parameter sweep on the thermal conductivity of the square column, and determine the equivalent thermal conductivity of the square column;

[0054] Specifically, when extracting the equivalent thermal conductivity in the horizontal direction, the same boundary conditions and heat sources as those in the original model in step S2 are applied, and a parameter sweep is performed on the thermal conductivity of the square pillar 4 until the relative error between the average temperature of the heat source plane of the equivalent model and the original model is less than the tolerance value, thereby determining the equivalent thermal conductivity in the horizontal direction of the square pillar 4;

[0055] When extracting the equivalent thermal conductivity in the vertical direction, the same boundary conditions and heat sources as those in the original model corresponding to step S2 are applied, and a parameter scan is performed on the thermal conductivity of the square pillar 4 until the relative error in the average temperature of the heat source plane between the equivalent model and the original model is less than the tolerance value, thereby determining the equivalent thermal conductivity in the vertical direction of the square pillar 4.

[0056] S5: Repeat steps S1 to S4 for different ratios of solder point height to solder point diameter, and different ratios of basic unit side length to solder point diameter, to extract the corresponding equivalent thermal conductivity of the square pillar;

[0057] Specifically, since the materials of each structure in the original model have been determined, the equivalent thermal conductivity of the square column 4 is only related to the ratio m of the solder joint height to the solder joint diameter and the ratio p of the basic unit side length to the solder joint diameter. Different values ​​of m and p are selected, and the equivalent thermal conductivity of the square column 4 in the horizontal and vertical directions is extracted respectively using the scheme of step S4, thereby obtaining multiple sets of discrete data of the corresponding equivalent thermal conductivity changing with the values ​​of m and p.

[0058] S6: Based on the data obtained in step S5, an equivalent thermal conductivity model of the square cylinder is obtained using a parameter fitting method.

[0059] Specifically, fitting is performed based on the discrete data obtained in step S5 to obtain an equivalent thermal conductivity model of the square cylinder.

[0060] The equivalent thermal conductivity model of the square column 4 includes:

[0061] The compact expression for the thermal conductivity of a square column in the horizontal direction is:

[0062] k ex =a(p)×m b(p) +c(p)

[0063] a(p)=a1p 2 +a2p+a3

[0064] b(p)=b1p 2 +b2p+b3

[0065] c(p)=c1p 2 +c2p+c3

[0066] Among them, k ex is the equivalent thermal conductivity of the square column in the horizontal direction, a1, a2, a3, b1, b2, b3, c1, c2, c3 are fitting parameters, m is the ratio of the solder joint height to the solder joint diameter, and p is the ratio of the basic unit side length to the solder joint diameter;

[0067] The compact expression for the thermal conductivity of a square column in the vertical direction is:

[0068] k ez =e1m e2 +e3

[0069] Among them, k ez is the equivalent thermal conductivity in the vertical direction of the square cylinder, and e1, e2, and e3 are fitting parameters.

[0070] According to the above-mentioned equivalent thermal modeling method for solder joint structure, calculation is performed using a specific embodiment:

[0071] In this embodiment, the dielectric region 1 is made of epoxy resin with a thermal conductivity of 0.5 W / (m·K); the solder joint structure 2 has a thermal conductivity of 50 W / (m·K); and the buffer block structure 3 has a thermal conductivity of 20,000 W / (m·K).

[0072] In this embodiment, the length and width of the dielectric region 1 are both 200 μm, the height is 60 μm, the diameter of the solder joint structure is 100 μm, the ratio of the solder joint height to the solder joint diameter is 0.6, and the ratio of the basic unit side length to the solder joint diameter is 2.

[0073] According to step S1, when extracting the equivalent thermal conductivity of the solder joint in the horizontal direction, the buffer block structure 3 is located to the left of the dielectric region 1, with a length of 200 μm, a width of 50 μm, and a height of 60 μm. When extracting the equivalent thermal conductivity of the solder joint in the vertical direction, the buffer block structure 3 is located below the dielectric region 1, with a length and width of 200 μm and a height of 50 μm.

[0074] According to step S2, when extracting the equivalent thermal conductivity of the solder joint in the horizontal direction, a uniform heat source of 0.01 W was applied to the left side of the buffer block structure 3, and a constant temperature boundary condition of 293.15 K was applied to the right side of the dielectric region 1 parallel to the plane. Adiabatic boundary conditions were set for the remaining surfaces. The finite element method was used to solve for the average temperature of the heat source plane to be 527.40 K. When extracting the equivalent thermal conductivity of the solder joint in the vertical direction, a uniform heat source of 0.5 W was applied to the lower surface of the buffer block structure 3, and a constant temperature boundary condition of 293.15 K was applied to the upper surface of the dielectric region 1 parallel to the plane. Adiabatic boundary conditions were set for the remaining surfaces. The finite element method was used to solve for the average temperature of the heat source plane to be 380.14 K.

[0075] According to step S3 , a square column 4 having the same volume as the solder joint area is used to replace the original area. The equivalent square column 4 has a side length of 78.6 μm and a height of 60 μm. The dimensions of the dielectric area 1 and the buffer block structure 3 remain unchanged.

[0076] According to step S4, when extracting the equivalent thermal conductivity in the horizontal direction, the same boundary conditions and heat source as those in the original model corresponding to step S2 are applied, and a parameter sweep is performed on the thermal conductivity of square pillar 4. When the thermal conductivity of square pillar 4 is 15.65 W / (m·K), the heat source plane temperature of the equivalent model is 527.41 K, and the relative error from the original model is less than the tolerance value of 0.1%. The equivalent thermal conductivity in the horizontal direction of square pillar 4 is thus determined. When extracting the equivalent thermal conductivity in the vertical direction, the same boundary conditions and heat source as those in the original model corresponding to step S2 are applied, and a parameter sweep is performed on the thermal conductivity of square pillar 4. When the thermal conductivity of square pillar 4 is 47.54 W / (m·K), the heat source plane temperature of the equivalent solder joint model is 380.15 K, and the relative error from the original model is less than the tolerance value of 0.1%. The equivalent thermal conductivity in the vertical direction of square pillar 4 is thus determined.

[0077] According to step S5, for different ratios m of solder point height to solder point diameter and different ratios p of basic unit side length to solder point diameter, steps S1 to S4 are repeated to extract the equivalent thermal conductivity of the square column 4 in the horizontal and vertical directions, respectively.

[0078] According to step S6, the discrete data obtained in step S5 are fitted to obtain a compact expression for the thermal conductivity of the square column 4 in the horizontal direction:

[0079] k ex =a(p)×m b(p) +c(p)

[0080] a(p)=-0.36p 2 -15.47p+136.40

[0081] b(p)=-0.47p2 +3.24p+2.62

[0082] c(p)=-0.18p 2 +0.57p+12.03

[0083] Figure 6 The fitted curve shown indicates that the above expression is in good agreement with the original data.

[0084] On the other hand, the compact expression of the thermal conductivity of the square pillar 4 in the vertical direction is:

[0085] k ez =-24.17m 4.84 +49.53

[0086] Figure 7 The fitted curve shown indicates that the above expression is in good agreement with the original data.

[0087] According to another aspect of an embodiment of the present application, a computer device is provided, which includes a processor and a memory for storing executable instructions of the processor, and the processor is configured to execute the equivalent thermal modeling method for the solder joint structure described in the embodiment of the present application by executing the executable instructions.

[0088] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. An equivalent thermal modeling method for solder joint structure, characterized in that: The method comprises the following steps: S1: Based on the geometric parameters of the solder joint and the thermal conductivity of the material, an original model of a single solder joint basic unit with a buffer block is constructed; S2: Apply boundary conditions and heat sources to the original model, and obtain the average temperature of the plane where the heat source is located through numerical simulation; S3: Use square columns with the same volume as the solder joints in the original model to replace the original solder joints and construct an equivalent model; S4: Apply the same boundary conditions and heat sources as the original model to the equivalent model, perform parameter sweep on the thermal conductivity of the square column, and determine the equivalent thermal conductivity of the square column; S5: Repeat steps S1 to S4 for different ratios of solder point height to solder point diameter, and different ratios of basic unit side length to solder point diameter, to extract the corresponding equivalent thermal conductivity of the square pillar; S6: Based on the data obtained in step S5, an equivalent thermal conductivity model of the square pillar is obtained using a parameter fitting method. The equivalent thermal conductivity model of the square pillar includes: The compact expression for the thermal conductivity of a square column in the horizontal direction is: k ex =a(p)×m b(p) +c(p) <h2 style=";text-align:left;direction:ltr">a(p) = a1p<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +a2p+a3 b(p)=b1p 2 +b2p+b3 c(p)=c1p 2 +c2p+c3 Among them, k ex is the equivalent thermal conductivity of the square column in the horizontal direction, a1, a2, a3, b1, b2, b3, c1, c2, c3 are fitting parameters, m is the ratio of the solder joint height to the solder joint diameter, and p is the ratio of the basic unit side length to the solder joint diameter; The compact expression for the thermal conductivity of a square column in the vertical direction is: Among them, k ez is the equivalent thermal conductivity in the vertical direction of the square cylinder, and e1, e2, and e3 are fitting parameters.

2. The equivalent thermal modeling method for solder joint structure according to claim 1, characterized in that: In step S1, the original model includes a dielectric area, the interior of the dielectric area includes a solder joint structure, the outer side of the dielectric area is provided with a buffer block structure, the solder joint structure material is alloy solder, and the material of the dielectric area is epoxy resin.

3. The equivalent thermal modeling method for solder joint structure according to claim 2, characterized in that: The buffer block structure is a rectangular block with high thermal conductivity. When extracting the thermal conductivity of the solder joint in the horizontal direction, the buffer block structure is located on the side of the dielectric area in the horizontal direction. When extracting the thermal conductivity of the solder joint in the vertical direction, the buffer block structure is located on the side of the dielectric area in the vertical direction.

4. The equivalent thermal modeling method for solder joint structure according to claim 2, characterized in that: In step S2, the process of applying boundary conditions and heat sources to the original model includes: applying a uniform heat source to one side of the buffer block structure, applying a constant temperature boundary condition to the other side of the medium area parallel to the plane, and setting other surfaces to adiabatic boundary conditions.

5. The equivalent thermal modeling method for solder joint structure according to claim 1, characterized in that: In step S2, the average temperature of the plane where the heat source is located is calculated by a finite element method numerical simulation method.

6. The equivalent thermal modeling method for solder joint structure according to claim 1, characterized in that: In step S3, a square column with the same volume as the solder joint area is used to replace the original area. The height of the square column is the same as the height of the solder joint area. The solder joint structure in the original model is a spherical table with a diameter of d and a height of h. The side length of the square column with the same volume as the solder joint structure is The height is h.

7. The equivalent thermal modeling method for solder joint structure according to claim 6, characterized in that: In step S3, when extracting the equivalent thermal conductivity of the square column in the horizontal direction, the buffer block structure is set on the side of the dielectric area in the horizontal direction; when extracting the equivalent thermal conductivity of the square column in the vertical direction, the buffer block structure is set on the side of the dielectric area in the vertical direction.

8. The equivalent thermal modeling method for solder joint structure according to claim 1, characterized in that: In step S4, a parameter scan is performed on the thermal conductivity of the square pillar until the relative error of the average temperature of the equivalent model and the original model on the heat source plane is less than the tolerance value, thereby determining the equivalent thermal conductivity of the square pillar.

9. A computer device, characterized in that: The computer device includes a processor and a memory for storing executable instructions of the processor, wherein the processor is configured to perform the equivalent thermal modeling method for solder joint structures according to any one of claims 1 to 8 by executing the executable instructions.

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