A method for calculating the equivalent thermal parameters of a micro solder joint layer

Abstract

The present invention relates to the field of thermal analysis of micro solder joint layers in microsystem packaging structures, and particularly to a method for calculating equivalent thermal parameters of a micro solder joint layer, comprising the following steps: S1, selecting a basic unit; S2, extracting a micro layer structure from the basic unit as an analysis and calculation object, and calculating the overall thermal resistance of the micro layer structure respectively; S3, combining the overall thermal resistance of the micro layer structure with Fourier's law and geometric dimension relationships, calculating and deriving the equivalent thermal conductivity of the micro layer structure; S4, using the differential method to organize and derive the result of S3 to obtain the equivalent thermal conductivity of the basic unit of the micro solder joint layer. The present invention adopts the "differential" idea to conduct theoretical analytical calculations on the equivalent thermal conductivity of the micro solder joint layer, effectively simplifying the complexity of the microsystem, greatly reducing the simulation calculation amount, having great engineering application value, and at the same time, the method based on the actual solder ball structure also improves the accuracy of equivalent modeling during microsystem thermal analysis.

Description

Technical Field

[0001] The present invention relates to the field of thermal analysis of micro solder joint layers in microsystem packaging structures, and specifically to a method for calculating equivalent thermal parameters of micro solder joint layers. Background Art

[0002] As microelectronics develops along the direction beyond Moore's Law, the development of microsystems based on three-dimensional integration technology has entered a new stage. The three-dimensional integration technology centered on TSV (Through-Silicon Via) has been widely regarded as the leading technology in the field of future high-density packaging and an effective way to break through Moore's Law.

[0003] The increase in the internal power density of highly integrated microsystem packaging and the increase in the number of stacked chips have brought a series of thermal management problems. These heat dissipation problems will directly affect the life reliability of products and have received great attention. Numerical simulation technology can greatly shorten the product development cycle, reduce the design cost, and improve the thermal reliability of products. It has become an indispensable means in product thermal management design and packaging thermal characteristic evaluation.

[0004] For microsystems with complex TSV packaging structures, due to the very large number of internal TSVs and micro solder joints, and the large difference in structural dimensions resulting in cross-scale problems, detailed modeling will cause difficulties in mesh generation and low computational efficiency. Especially when the module is used for system-level thermal simulation analysis, the above problems will be exacerbated. Therefore, equivalent modeling of complex packaging devices can greatly simplify the computational workload and has great engineering application value. A large number of studies have carried out thermal equivalent modeling research on TSV structures, micro solder joints, and underfill layers through methods such as numerical calculation or simulation. Currently, most of these equivalent modeling methods are equivalent volume methods, which simplify the solder joints into cubes. Some studies even do not perform volume equivalence and directly use the maximum outer dimension equivalence to take the diameter as the side length of the cube. However, the actual solder ball morphology of the micro solder joint layer is a truncated spherical crown, which is quite different from the above. The above simplification methods will lead to large computational errors. Summary of the Invention

[0005] In view of the problems existing in the prior art, the present invention provides a method for calculating the equivalent thermal parameters of a micro-solder joint layer. Aiming at the modeling problem of the micro-solder joint layer composed of solder joints and underfill, a method for equivalent calculation of thermal characteristic parameters based on the differential idea is proposed to calculate the anisotropic thermal conductivity of the micro-solder joint layer. Compared with the conventional equivalent modeling method, the present invention takes into account the actual truncated spherical solder ball structure of the micro-solder joint layer, and adopts the "differential" idea to conduct theoretical analytical calculation of the equivalent thermal conductivity of the micro-solder joint layer, solving the problems of difficult numerical simulation modeling and low calculation efficiency caused by the complex internal structure of the micro-system, the huge number of micro-solder joints and the cross-scale difference, effectively simplifying the complexity of the micro-system, greatly reducing the simulation calculation amount, having great engineering application value, and at the same time, the method based on the actual solder ball structure also improves the accuracy of equivalent modeling in micro-system thermal analysis.

[0006] The present invention is realized through the following technical solutions:

[0007] 1. A method for calculating the equivalent thermal parameters of a micro-solder joint layer, characterized by comprising the following steps:

[0008] S1, based on the micro-solder joints of the micro-system arranged in a regular array form, select a basic unit;

[0009] S2, extract a small layer structure from the basic unit as the analysis and calculation object, and calculate the overall thermal resistance of the small layer structure respectively; the overall thermal resistance includes the overall thermal resistance in the X direction, the overall thermal resistance in the Y direction and the overall thermal resistance in the Z direction, and the overall thermal resistance in the X direction is the same as the overall thermal resistance in the Y direction;

[0010] S3, combine the overall thermal resistance of the small layer structure with Fourier's law and geometric dimension relationship, and calculate and deduce the equivalent thermal conductivity of the small layer structure;

[0011] S4, use the differential method to organize and deduce the equivalent thermal conductivity of the small layer structure to obtain the equivalent thermal conductivity of the basic unit of the micro-solder joint layer.

[0012] 2. The method for calculating the equivalent thermal parameters of a micro-solder joint layer according to claim 1, characterized in that the small layer structure is regarded as a regular cylinder.

[0013] Preferably, the basic unit includes a solder ball and underfill, the solder ball is located above the underfill, and the solder balls are arranged in an array; the height of the basic unit is h, the length is p, p is the distance between the centers of two adjacent solder balls, and the radius of the solder ball is R.

[0014] Preferably, the equivalent thermal conductivity of the small layer structure includes the equivalent thermal conductivity k x in the X direction, the equivalent thermal conductivity k y in the Y direction and the equivalent thermal conductivity k z; The equivalent thermal conductivity of the basic unit includes the equivalent thermal conductivity k in the X direction X , the equivalent thermal conductivity k in the Y direction Y and the equivalent thermal conductivity k in the Z direction Z .

[0015] Preferably, the expression of the thermal conductivity k in the Z direction of the micro-layer structure z is:

[0016]

[0017] Where k z is the equivalent thermal conductivity in the Z direction of the micro-layer structure, k u and k b are the thermal conductivities of the underfill and the solder ball respectively, and α is the volume ratio of the solder ball to the underfill.

[0018] Preferably, the expression of the equivalent thermal conductivity k in the Z direction of the basic unit Z is:

[0019]

[0020] Preferably, the specific steps for the thermal conductivity k in the Y direction of the micro-layer structure y are as follows: Divide the XY plane of the micro-layer structure into part A and part B. Among them, part A is the underfill, and part B is composed of the solder ball and the underfill; then, combine the equivalent thermal conductivity in the Y direction of part A and the equivalent thermal conductivity in the Y direction of part B to obtain the thermal conductivity k in the Y direction of the micro-layer structure y , and the calculation expression of k y is:

[0021] Where k By is the equivalent thermal conductivity in the Y direction of part B in the micro-layer structure.

[0022] Preferably, the calculation steps for the equivalent thermal conductivity k in the Y direction of part B in the micro-layer structure are as follows: First, use the differential idea to intercept a small cube in the micro-layer structure as the analysis object. Among them, the height of the small cube is dy, the length is p, and the depth is dz; then, calculate the equivalent thermal conductivity in the Y direction of the small cube according to the thermal resistance parallel theory, and then use the differential method to combine Fourier's law and the set and size relationship to derive the equivalent thermal conductivity k in the Y direction of part B By .

[0023] Preferably, the expression of the equivalent thermal conductivity k in the Y direction of part B in the micro-layer structure By is as follows:

[0024]

[0025] Preferably, the equivalent thermal conductivity k in the Y direction of the basic unit Y has the following expression:

[0026]

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] The equivalent thermal parameter calculation method for a solder joint layer of the present invention, which is a thermal characteristic parameter equivalent calculation method based on the differential idea, effectively simplifies the complexity of the microsystem and greatly reduces the simulation calculation amount. The traditional equivalent modeling method is the equivalent volume method based on simplifying the solder joint into a cube, without considering the truncated crown spherical structure of the actual solder ball, and there is a certain deviation in the calculated equivalent thermal conductivity.

[0029] The present invention proposes a thermal characteristic parameter equivalent calculation method based on the differential idea, and this invention specifically conducts theoretical calculations for the truncated crown spherical structure of the actual solder ball, having higher accuracy in equivalent modeling of the microsystem structure. Based on this equivalent calculation method, only by substituting the solder ball radius, solder ball pitch, and the height of the microsolder joint layer of the microsystem can the equivalent thermal conductivities in the Z direction, X direction, and Y direction of the microsolder joint layer be solved. The method is efficient and concise, greatly simplifies the complexity of microsystem modeling, and also greatly reduces the simulation calculation amount. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a schematic diagram of the basic unit of the microsolder joint layer in the present invention.

[0031] Figure 2 It is a schematic structural diagram for calculating the Z-direction thermal conductivity of the basic unit of the microsolder joint layer in the present invention.

[0032] Figure 3 It is a schematic structural diagram for calculating the Y-direction thermal conductivity of the basic unit of the microsolder joint layer in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0033] The following further elaborates on the present invention in detail with specific embodiments, which is an explanation rather than a limitation of the present invention.

[0034] The present invention discloses an equivalent thermal parameter calculation method for a microsolder joint layer, including the following steps:

[0035] S1, for the microsolder joints of the microsystem arranged in a regular array form, referring to Figure 1, select a single solder ball and a part of the underfill in the micro-solder joint layer as the basic unit for theoretical calculation. The basic unit includes a solder ball and an underfill. The solder ball is located above the underfill, and a solder ball array is set. The height of the basic unit is h, and the length is p. p is the distance between the centers of two adjacent solder balls, and the radius of the solder ball is R.

[0036] S2, Extract a micro-layer structure from the basic unit as the object of analysis and calculation, and calculate the overall thermal resistance of the micro-layer structure.

[0037] Extract a micro-layer structure from the middle of the basic unit as the object of analysis and calculation. Due to its very small thickness, the micro-layer structure can be regarded as a cylinder with an extremely small height and regular shape.

[0038] The overall thermal resistance includes the overall thermal resistance in the X direction, the overall thermal resistance in the Y direction, and the overall thermal resistance in the Z direction. The overall thermal resistance in the X direction is the same as that in the Y direction.

[0039] S3, Combine the overall thermal resistance of the micro-layer structure with Fourier's law and geometric dimension relationships to calculate and deduce the equivalent thermal conductivity of the micro-layer structure.

[0040] S4, Use differential methods to organize and deduce the equivalent thermal conductivity of the micro-layer structure to obtain the equivalent thermal conductivity of the basic unit of the micro-solder joint layer.

[0041] The calculation process of the equivalent thermal conductivity in the Z direction of the basic unit is as follows:

[0042] Refer to Figure 2 , the overall thermal resistance in the Z direction of the micro-layer structure is a parallel thermal conduction path formed by the parallel connection of the solder ball thermal resistance and the underfill thermal resistance. The overall thermal resistance in the Z direction of the micro-layer structure can be calculated. Then, combined with Fourier's law and geometric dimension relationships, the equivalent thermal conductivity k in the Z direction of the micro-layer structure is calculated and deduced. z , the expression is:

[0043]

[0044] Among them, k z is the equivalent thermal conductivity in the Z direction of the micro-layer structure, k u and k b are the thermal conductivities of the underfill and the solder ball respectively, and α is the volume ratio of the solder ball to the underfill.

[0045] The overall thermal resistance in the Z direction of the basic unit of the micro-solder joint layer can be considered as a series thermal conduction path formed by the series connection of countless micro-layer structures;

[0046] Use differentiation to replace summation, and the summation of the thermal resistances of countless series-connected micro-layer structures becomes a differential form. After organizing and deducing, the equivalent thermal conductivity in the Z direction of the basic unit of the micro-solder joint layer is obtained;

[0047]

[0048] The equivalent thermal conductivity k of the basic unit in the Y direction Y The calculation process is as follows:

[0049] (1) Intercept the XY plane of the micro-layer structure to calculate the thermal conductivity in the Y direction (due to the structural symmetry, the X direction is the same as the Y direction); the XY plane of the micro-layer structure can be divided into two parts, A and B. Part A is composed of the lower filling adhesive, and part B is composed of solder balls and the lower filling adhesive.

[0050] (2) Since the solder balls in part B are circular, the thermal resistance is not simply composed of two materials in parallel. First, use the differential idea to intercept a small square body in the micro-layer structure as the analysis object, referring to Figure 3 , where y is the Y-direction coordinate position of the small square body, r z is the radius of the solder ball of the micro-layer structure, and a y is the length of the solder ball material in the small square body; since the thickness of the small square body is very small, it can be regarded as a small square body with a height of dy, a length of p, and a depth of dz.

[0051] Calculate the equivalent thermal conductivity in the Y direction of the small square body according to the thermal resistance parallel theory;

[0052]

[0053] Among them, k′ y is the equivalent thermal conductivity in the Y direction of the small square body.

[0054] (3) Use differentiation to replace summation, and the summation of thermal resistance in series becomes a differential form. Combine the equivalent thermal conductivity in the Y direction of the small square body with Fourier's law and geometric dimension relationships, and organize and deduce the equivalent thermal conductivity k By in the Y direction of part B of the micro-layer structure:

[0055]

[0056] Among them, k By is the equivalent thermal conductivity in the Y direction of part B of the micro-layer structure.

[0057] (4) The overall thermal resistance of the micro-layer structure in the Y direction can be considered as a series thermal conduction path formed by the series connection of the thermal resistance of part A and the thermal resistance of part B. Therefore, combine the series theory of the thermal resistance of part A and part B to calculate the thermal conductivity k y in the Y direction of the micro-layer structure:

[0058]

[0059] (5) The overall thermal resistance of the basic unit of the micro-solder joint layer in the Y direction can be considered as a parallel thermal conduction path formed by the parallel connection of countless tiny layer structures. By using differential to replace summation, the summation of the thermal resistances of countless tiny layer structures in parallel becomes a differential form. After sorting and derivation, the equivalent thermal conductivity k of the basic unit of the micro-solder joint layer in the Y direction is obtained. Y :

[0060]

[0061] The structure of the micro-solder joint layer in a certain micro-system is as follows: the radius R of the solder ball is 0.045 mm, the distance p between the centers of two solder balls is 0.2 mm, and the height h of the micro-solder joint layer after welding is 0.07 mm. Substituting the above structure parameters into the calculation equation in the technical solution respectively, the following equivalent thermal parameters can be calculated: the equivalent thermal conductivity in the Z direction is 6.25 W / m·k, and the equivalent thermal conductivities in the X direction and the Y direction are both 0.33 W / m·k.

Claims

1. A method for calculating the equivalent thermal parameters of a micro-solder joint layer, characterized in that, It includes the following steps: S1. Select a basic unit based on the micro solder joints arranged in the form of a regular array; the basic unit includes solder balls and underfill glue, the solder balls are located above the underfill glue, and the solder ball array is arranged; S2. Extract a micro-layer structure from the basic unit as the object of analysis and calculation, and calculate the overall thermal resistance of the micro-layer structure respectively; the overall thermal resistance includes the overall thermal resistance in the X direction, the overall thermal resistance in the Y direction, and the overall thermal resistance in the Z direction, and the overall thermal resistance in the X direction is the same as the overall thermal resistance in the Y direction; S3. Combine the overall thermal resistance of the micro-layer structure with Fourier's law and geometric dimension relationships to calculate and deduce the equivalent thermal conductivity of the micro-layer structure; S4. Use the differential method to organize and deduce the equivalent thermal conductivity of the micro-layer structure to obtain the equivalent thermal conductivity of the basic unit of the micro solder joint layer.

2. The equivalent thermal parameter calculation method of the micro solder joint layer according to claim 1, characterized in that The micro-layer structure is regarded as a regular cylinder.

3. The equivalent thermal parameter calculation method of the micro solder joint layer according to claim 1, characterized in that, The height of the basic unit is h , and the length is p , p which is the distance between the centers of two adjacent solder balls, and the radius of the solder ball is R .

4. The method for calculating the equivalent thermal parameters of the micro-solder joint layer according to claim 3, wherein The equivalent thermal conductivity of the micro-layer structure includes the equivalent thermal conductivity in the X direction k x , the equivalent thermal conductivity in the Y direction k y and the equivalent thermal conductivity in the Z direction k z ; the equivalent thermal conductivity of the basic unit includes the equivalent thermal conductivity in the X direction k X , the equivalent thermal conductivity in the Y direction k Y and the equivalent thermal conductivity in the Z direction k Z .

5. The method for calculating the equivalent thermal parameters of the micro solder joint layer according to claim 4, characterized in that The Z-direction thermal conductivity of the micro-layer structure k z is expressed as: Among them, k z is the equivalent thermal conductivity in the Z direction of the micro-layer structure, k u and k b are the thermal conductivities of the underfill and the solder ball respectively, α is the volume ratio of the solder ball to the underfill.

6. The method for calculating the equivalent thermal parameters of the micro-solder joint layer according to claim 5, characterized in that The equivalent thermal conductivity of the basic unit in the Z direction k Z is expressed as: 。 7. The equivalent thermal parameter calculation method of the micro solder joint layer according to claim 5, characterized in that The Y-direction thermal conductivity of the micro-layer structure k y The specific steps are as follows: Divide the XY plane of the micro-layer structure into part A and part B. Among them, part A is the underfill, and part B consists of solder balls and underfill. Then, combine the equivalent thermal conductivity in the Y direction of part A and the equivalent thermal conductivity in the Y direction of part B to obtain the Y-direction thermal conductivity of the micro-layer structure k y , k y The calculation expression is: , where k By is the equivalent thermal conductivity in the Y direction of part B in the micro-layer structure; r z is the solder ball radius of the micro-layer structure.

8. The method for calculating the equivalent thermal parameters of the micro solder joint layer according to claim 7, wherein, The equivalent thermal conductivity k of part B in the Y direction in the described micro-layer structure By The calculation steps are as follows: First, use the differential idea to intercept a small cube in the micro-layer structure as the analysis object. Among them, the height of the small cube is dy, the length is p, and the depth is dz; then calculate the equivalent thermal conductivity in the Y direction of the small cube according to the thermal resistance parallel theory, and then use the differential method to combine Fourier's law and the set size relationship to derive the equivalent thermal conductivity of part B in the Y direction k By .

9. The method for calculating the equivalent thermal parameters of the micro solder joint layer according to claim 8, characterized in that The equivalent thermal conductivity of part B of the micro-layer structure in the Y direction k By is expressed as follows: In the formula, y is the Y coordinate position in the x direction of the tiny cube.

10. The method for calculating the equivalent thermal parameters of the micro solder joint layer according to claim 7, wherein The equivalent thermal conductivity of the basic unit in the Y direction k Y is expressed as: 。

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