A method for analyzing the thermal fatigue life of POP stack solder joints

Abstract

This invention discloses a method for analyzing the thermal fatigue life of POP stacked solder joints, comprising the following steps: 1) obtaining the coordinate values ​​of the three-dimensional morphological geometric feature parameters of the POP solder joints; 2) establishing an overall finite element analysis model of the POP stacked solder joint package; 3) creating a single spherical solder joint model at key locations and a single parametric equivalent solder joint model; 4) obtaining the thermal stress values ​​of the spherical solder joints and the parametric equivalent solder joints; 5) determining the optimal morphological parameter values ​​of the equivalent solder joints; 6) constructing an overall parametric equivalent model of the POP stacked solder joint package to complete the thermal cycling load analysis; 7) calculating the thermal fatigue life of the solder joints. This method can quickly and accurately predict the thermal fatigue life of POP stacked solder joints, save simulation calculation time, and improve efficiency.

Description

Technical Field

[0001] This invention relates to the field of simulation and prediction technology for electronic packaging devices, specifically a method for analyzing the thermal fatigue life of POP stacked solder joints. Background Technology

[0002] With the increasing demands for portability and comprehensive functionality in electronic products, electronic packaging is rapidly developing towards higher density and miniaturization. To meet the special requirements of portable mobile devices, such as multifunctional flexibility, high electrical performance, small size, and low cost, packaging on packaging (POP) has become one of the preferred packaging technologies for integrated circuit chips in mobile devices. Research on the reliability of interconnect solder joints mainly employs two methods: finite element simulation analysis and experimental analysis. However, due to the complexity of the device's service environment, experimental analysis requires significant manpower and financial resources to complete solder joint reliability experiments. The finite element method, as a numerical simulation calculation method, has been widely used in the field of electronic packaging device reliability analysis. Leveraging the powerful computing capabilities of computers, it greatly improves work efficiency and quality.

[0003] When performing solder joint reliability analysis by establishing a finite element simulation model of component package solder joints, in order to meet the model mesh generation accuracy, the number of simulation model elements and model nodes will be large, resulting in a large amount of computer storage space being occupied and a long calculation time. Summary of the Invention

[0004] The purpose of this invention is to provide a method for analyzing the thermal fatigue life of solder joints in a POP (Polymer Optical Component) stack. This method can quickly and accurately predict the thermal fatigue life of solder joints in a POP stack, save simulation calculation time, and improve efficiency.

[0005] The technical solution to achieve the objective of this invention is:

[0006] A method for analyzing the thermal fatigue life of POP stacked solder joints includes the following steps:

[0007] 1) Obtain the coordinate values ​​of the three-dimensional geometric feature parameters of POP solder joints: Based on the principle of minimum energy, the coordinate values ​​of the three-dimensional geometric feature parameters of POP solder joints are extracted and obtained using Surface Evolver software. The resulting solder joint morphology diagram is used to establish an overall simulation analysis model for POP stacked solder joint packaging.

[0008] 2) Establish an overall finite element analysis model for POP stacked solder joint packaging: A coarse mesh is generated for the overall finite element analysis model of the POP stacked solder joint packaging. The stress distribution of the POP solder joints under thermal cycling load is simulated to determine the location of key POP solder joints and the displacement field ΔD of the surrounding cut surfaces. x (V,t ), ΔD y ( V ,t), ΔD z ( V,t Specifically, referring to Amkor's packaged devices and based on the ANAND constitutive model, a POP stacked solder joint overall simulation model was established. A coarse mesh was generated to meet the displacement accuracy. A thermal cycling load was applied to simulate the thermal stress distribution of solder joints at different positions in the array. The positions of critical solder joints in the array and the displacement fields of the surrounding cut surfaces were determined. The positions of critical solder joints in the array and the displacement fields of the surrounding cut surfaces are shown in formulas (1), (2), and (3).

[0009] (1),

[0010] (2),

[0011] (3),

[0012] ΔD in the formula x ΔD y ΔD z denoted as , where is the average relative xyz direction displacement of the critical weld joint cutting surface; and , where dix, diy, and diz are the xyz direction displacements of the critical weld joint cutting surface nodes as a function of the load step. V This refers to the volume of the solder joint.

[0013] 3) Create a single spherical solder joint model at a critical location and a single parametric equivalent solder joint model: Using sub-modeling technology, cut the solder joints at critical locations in the overall model to construct a single spherical solder joint model. Based on the nonlinear load deformation response and maintaining a constant solder joint height, introduce parameters r1 and r2 based on the principle of equal volume to establish a single parametric equivalent solder joint model. The boundary condition for both models is the displacement field ΔD of the cut surface around the critical solder joint in the overall model. x ( V,t ), ΔD y ( V,t ), ΔD z ( V,t The simulation analysis was completed by applying a temperature load T(t). The objective functions of parameter values ​​r1 and r2 were set. Combined with the optimal evolution algorithm, the optimal parameter values ​​r1 and r2 of the equivalent solder joint were determined by iterative calculation. The single parameterized equivalent solder joint model is shown in formula (4):

[0014] (4),

[0015] In the formula, V is the volume of the solder joint, h is the height of the solder joint, and r1 and r2 are equivalent solder joint parameters. The temperature load T(t) is as follows: the heating and cooling rate is 36℃ / min, the high and low temperature holding time is 10min, and the temperature cyclic loading starts from 125℃ for a total of 4 temperature cycles.

[0016] 4) Obtaining the thermal stress values ​​of the spherical weld joint and the parameterized equivalent weld joint: The displacement field of the cut surface around the key weld joint in the overall model is used as the boundary condition for the two individual weld joint models. Displacement interpolation is performed using the displacement shape function, and a temperature load T(t) is applied to obtain the thermal stress values ​​of the spherical weld joint and the parameterized equivalent weld joint. Specifically:

[0017] Displacement interpolation was performed using an eight-point displacement shape function to obtain the thermal stress value R of the spherical weld joint. a ( V ,t j The thermal stress value R of the parameterized equivalent weld joint e ( V ,t j As shown in formulas (5), (6) and (7):

[0018] (5),

[0019] (6),

[0020] (7),

[0021] μ in the formula L ,ν L and ω L μ represents the interpolation value of a single solder joint model node in X, Y, Z. i G ,ν i G and ω i G The displacement values ​​of the cutting surface in the X, Y, and Z directions are analyzed for the overall model, where G represents the nodes of the overall model, L represents the nodes of the individual weld point model, and N represents the displacement values ​​of the individual weld point model. i (ξ,η,ζ) is the shape function in spatial coordinates;

[0022] 5) Determine the optimal morphological parameter value of the equivalent solder joint: Calculate the error ε between the Von mises values ​​of the solder joints in the two models, and use iterative calculation to determine the optimal morphological parameter value of the equivalent solder joint. The process of determining the optimal morphological parameter value of the equivalent solder joint is as follows: Determine the range of values ​​of parameterized equivalent solder joints r1 and r2 according to the diameter of the spherical solder joint and set the parameter value r1 < r2. Calculate the error ε between the Von mises values ​​of the spherical solder joint and the parameterized equivalent solder joint. Iterate the parameter values ​​r1 and r2 more than 10 times to obtain the optimal morphological parameter value of the equivalent solder joint, as shown in formula (8) and formula (9).

[0023] (8),

[0024] (9),

[0025]

[0026] In the formula, Std[ ] is the standard deviation function. r For parameterized solder joint parameter vectors, l i For the constraints of equivalent solder joints r1 and r2, n c The total number of limiting conditions;

[0027] 6) Construct an overall parameterized equivalent model of POP stacked solder joint package to complete thermal cycling load analysis: The overall parameterized equivalent model of POP stacked solder joint package is to replace the spherical solder joint in the overall model with the best equivalent solder joint and then use displacement field and thermal load to complete thermal cycling load analysis.

[0028] 7) Calculate the thermal fatigue life of the weld joint: The thermal fatigue life of the weld joint is calculated using the weld joint plastic strain energy density increment and Darveaux formula, as shown in formulas (10), (11), (12) and (13):

[0029] (10)

[0030] (11),

[0031] (12)

[0032] (13)

[0033] ΔW in the formula i It has a volume of V i The plastic strain energy density accumulated by the i-th element in each cycle, where n is the number of elements; ΔW aveThe density of plastic strain energy accumulated during each thermal cycle; N0 is the weld crack initiation lifetime; dD / dN is the weld crack propagation lifetime; N f is the thermal fatigue life of the weld joint; D is the characteristic length of the weld joint fracture; K1, K2, K3 and K4 are the crack propagation constants of the weld joint.

[0034] This technical solution first extracts the three-dimensional morphological parameters of the POP stacked solder joints using Surface Evolver software, establishes an overall model of the POP stacked solder joint package, completes thermal cycling analysis, and determines the location of key solder joints and the displacement field ΔD of the surrounding cut surfaces. x ( V,t ), ΔD y ( V ,t), ΔD z ( V,t Secondly, a single spherical weld joint model is created, and two parameters r1 and r2 are introduced based on the nonlinear load deformation response to create a single parameterized equivalent weld joint model. The boundary condition for both models is the displacement field ΔD of the cutting surface around the key weld joint of the overall model. x ( V,t ), ΔD y ( V,t ), ΔD z ( V,t Simultaneously, the thermal load T(t) is introduced to complete the simulation analysis. The objective functions of parameter values ​​r1 and r2 are set. Combined with the optimal evolution algorithm, the optimal parameter values ​​r1 and r2 of the equivalent solder joint are determined through iterative calculation. Finally, the optimal equivalent solder joint is used to replace the spherical solder joint in the overall model. The thermal fatigue life of the solder joint is calculated based on the plastic strain energy density and Darveaux formula. The parameterized sub-model can well characterize the stress distribution state of the POP stack solder joint under thermal cycling load and accurately predict the thermal fatigue life of the solder joint.

[0035] This technical solution can save a lot of computation time and improve the efficiency of simulation analysis. The parameterized equivalent model can well characterize the stress distribution of POP stack solder joints under thermal cycling load and accurately predict the thermal fatigue life of POP stack solder joints, which greatly facilitates the calculation of solder joint thermal fatigue life.

[0036] This method can quickly and accurately predict the thermal fatigue life of POP stack solder joints, save simulation calculation time, and improve efficiency. Attached Figure Description

[0037] Figure 1 This is a flowchart illustrating the method used in this embodiment.

[0038] Figure 2 This is a schematic diagram of the predicted three-dimensional morphology of the POP stack solder joints in the embodiment.

[0039] Figure 3 This is a schematic diagram of the overall finite element analysis model of the POP stacked solder joint packaged device in the embodiment;

[0040] Figure 4 This is a schematic diagram of thermal cycling loading in the embodiment;

[0041] Figure 5 This is a schematic diagram of the stress distribution of solder joints at different locations in the overall model solder joint array in the embodiment;

[0042] Figure 6 This is a schematic diagram of a single spherical weld point with different mesh precision models in the embodiment;

[0043] Figure 7 This is a schematic diagram showing the relative displacement of the center point of the solder ball corresponding to different grid accuracies for a single spherical solder joint in the embodiment.

[0044] Figure 8 This is a schematic diagram of the boundary displacement constraints between the single spherical solder joint model and the single parametric equivalent solder joint model in the embodiment.

[0045] Figure 9 This is a schematic diagram comparing the maximum thermal stress of a single spherical solder joint with that of a single optimally parameterized equivalent solder joint in the embodiment.

[0046] Figure 10 This is a schematic diagram of the stress distribution at different locations of the weld joints in the parametric equivalent model of the embodiment. Detailed Implementation

[0047] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this is not intended to limit the scope of the invention.

[0048] Example:

[0049] Reference Figure 1 A method for analyzing the thermal fatigue life of POP stack solder joints includes the following steps:

[0050] 1) Obtain the coordinate values ​​of the three-dimensional geometric feature parameters of the POP solder joint: Based on the principle of minimum energy, the Surface Evolver software is used to extract and obtain the coordinate values ​​of the three-dimensional geometric feature parameters of the POP solder joint, as shown in the figure. Figure 2 The solder joint morphology diagram shown is used to establish an overall simulation analysis model for POP stacked solder joint packaging;

[0051] 2) Establish an overall finite element analysis model for POP stacked solder joint packaging: Establish, for example... Figure 3 The overall finite element analysis model of the POP stacked solder joint package shown is roughly meshed based on... Figure 4The temperature loading curve T(t) shown simulates the stress distribution of POP solder joints under thermal cycling load, determining the location of key POP solder joints and the displacement field ΔD of the surrounding cut surface. x ( V, t ), ΔD y ( V ,t), ΔD z ( V,t Specifically, referencing Amkor's packaged devices and based on the ANAND constitutive model, a coarse mesh was created to meet displacement accuracy requirements for the overall simulation model of POP stacked solder joints. Thermal cycling loads were applied to simulate the thermal stress distribution at different locations within the array, such as... Figure 5 As shown, the location of the critical solder joints in the array and the displacement field of the surrounding cutting surfaces are determined. The location of the critical solder joints in the array and the displacement field of the surrounding cutting surfaces are shown in formulas (1), (2), and (3):

[0052] (1),

[0053] (2),

[0054] (3),

[0055] ΔD in the formula x ΔD y ΔD z denoted as , where is the average relative xyz direction displacement of the critical weld joint cutting surface; and , where dix, diy, and diz are the xyz direction displacements of the critical weld joint cutting surface nodes as a function of the load step. V This refers to the volume of the solder joint.

[0056] In this example, the finite element analysis model diagram includes five parts: PCB board, copper pads, BGA solder joints, substrate, and chip. The structural parameters of each part are shown in Table 1, the material parameters are shown in Table 2, and the ANAND constitutive model parameters are shown in Table 3.

[0057] Table 1. Structural parameters of each part of the overall model of POP stacked solder joint packaging

[0058] ,

[0059] Table 2 Structural material parameters of each part of the packaged device

[0060] ,

[0061] Table 3 Parameters of the ANAND constitutive model

[0062] ;

[0063] 3) Create single spherical solder joint models at key locations, and create single parametric equivalent solder joint models: Use sub-modeling techniques to cut solder joints at key locations in the overall model to construct single spherical solder joint models, such as... Figure 6 and Figure 7 As shown, the meshing accuracy of a single spherical weld point is determined based on the relative displacement of the weld ball's center point. Based on the principle of equal volume and maintaining a constant weld point height under nonlinear load deformation response, parameters r1 and r2 are introduced to establish a parameterized equivalent weld point model. The boundary condition for both models is the displacement field ΔD of the cutting surface around the critical weld point in the overall model. x ( V,t ), ΔD y ( V,t ), ΔD z ( V,t The simulation analysis was completed by applying a temperature load T(t). The objective functions of parameter values ​​r1 and r2 were set. Combined with the optimal evolution algorithm, the optimal parameter values ​​r1 and r2 of the equivalent solder joint were determined by iterative calculation. The single parameterized equivalent solder joint model is shown in formula (4):

[0064] (4),

[0065] In the formula, V is the solder joint volume, h is the solder joint height, and r1 and r2 are equivalent solder joint parameters. The temperature load T(t) is expressed as follows: Figure 4 The following is a description of the temperature increase and decrease rate: 36℃ / min, high and low temperature holding time: 10min, temperature cyclic loading starting from 125℃, for a total of 4 temperature cycles.

[0066] 4) Obtain the thermal stress values ​​of the spherical weld joint and the parameterized equivalent weld joint: For example... Figure 8 The displacement field of the cut surface around the key weld point in the overall model is used as the boundary condition for two individual weld point models. Displacement interpolation is performed using the displacement shape function, and the thermal stress values ​​of the spherical weld point and the parameterized equivalent weld point are obtained by applying a temperature load T(t). Specifically:

[0067] Displacement interpolation was performed using an eight-point displacement shape function to obtain the thermal stress value R of the spherical weld joint. a ( V ,t j The thermal stress value R of the parameterized equivalent weld joint e ( V ,t j As shown in formulas (5), (6) and (7):

[0068] (5),

[0069] (6),

[0070] (7),

[0071] μ in the formula L ,ν L and ω L μ represents the interpolation value of a single solder joint model node in X, Y, Z. i G ,ν i G and ω i G The displacement values ​​of the cutting surface in the X, Y, and Z directions are analyzed for the overall model, where G represents the nodes of the overall model, L represents the nodes of the individual weld point model, and N represents the displacement values ​​of the individual weld point model. i (ξ,η,ζ) is the shape function in spatial coordinates;

[0072] 5) Determine the optimal morphological parameter values ​​for the equivalent solder joint: Calculate the error ε between the Von mises values ​​of the solder joints in the two models, such as... Figure 9 As shown, the optimal morphological parameter values ​​of the equivalent solder joint are determined by iterative calculation. The process of determining the optimal morphological parameters of the equivalent solder joint is as follows: the range of values ​​of parameterized equivalent solder joints r1 and r2 is determined according to the diameter of the spherical solder joint and the parameter value r1 < r2 is set. The error ε between the spherical solder joint and the Von mises value of the parameterized equivalent solder joint is calculated. The parameter values ​​r1 and r2 are continuously changed and iteratively calculated more than 10 times to obtain the optimal morphological parameter values ​​of the equivalent solder joint, as shown in formula (8) and formula (9).

[0073] (8),

[0074] (9),

[0075]

[0076] In the formula, Std[ ] is the standard deviation function. r For parameterized solder joint parameter vectors, l i For the constraints of equivalent solder joints r1 and r2, n c To limit the total number of conditions, in this example, the parameter value r1 < r2. Therefore, the value of r1 is in the range of 70%-90% of the diameter of the spherical weld joint. The values ​​of r1 and r2 are shown in Table 4.

[0077] Table 4. Range of Equivalent Weld Joint Parameters

[0078] ;

[0079] 6) Constructing an overall parametric equivalent model of the POP stacked solder joint package to complete thermal cycling analysis: The overall parametric equivalent model of the POP stacked solder joint package replaces the spherical solder joints in the overall model with the optimal equivalent solder joints, and then uses displacement field and thermal load to complete the thermal cycling analysis. The results are as follows: Figure 10 As shown;

[0080] 7) Calculate the thermal fatigue life of the weld joint: The thermal fatigue life of the weld joint is calculated using the weld joint plastic strain energy density increment and the Darveaux formula, as shown in formulas (10), (11), (12) and (13):

[0081] (10)

[0082] (11),

[0083] (12)

[0084] (13)

[0085] ΔW in the formula i It has a volume of V i The plastic strain energy density accumulated by the i-th element in each cycle, where n is the number of elements; ΔW ave The density of plastic strain energy accumulated during each thermal cycle; N0 is the weld crack initiation lifetime; dD / dN is the weld crack propagation lifetime; N f is the thermal fatigue life of the weld joint; D is the characteristic length of the weld joint fracture; K1, K2, K3, and K4 are the crack propagation constants of the weld joint. The thermal fatigue life of the weld joint calculated in this column is 1023 cycles. The increase in plastic strain energy density of the weld joint in each thermal cycle is shown in Table 5.

[0086] Table 5. Increment of viscoplastic strain energy density during the equivalent weld joint temperature cycle.

[0087] .

Claims

1. A method for analyzing the thermal fatigue life of POP stack solder joints, characterized in that, Includes the following steps: 1) Obtain the coordinate values ​​of the three-dimensional geometric feature parameters of the POP solder joint: Based on the principle of minimum energy, the coordinate values ​​of the three-dimensional geometric feature parameters of the POP solder joint are extracted and obtained using SurfaceEvolver software to obtain the solder joint morphology diagram; 2) Establish an overall finite element analysis model for POP stacked solder joint packaging: A coarse mesh is generated for the overall finite element analysis model of the POP stacked solder joint packaging. The stress distribution of the POP solder joints under thermal cycling load is simulated to determine the location of key POP solder joints and the displacement field ΔD of the surrounding cut surfaces. x ( V,t ), ΔD y ( V ,t), ΔD z ( V,t Specifically, referring to Amkor's packaged devices and based on the ANAND constitutive model, a POP stacked solder joint overall simulation model was established. A coarse mesh was generated to meet the displacement accuracy. A thermal cycling load was applied to simulate the thermal stress distribution of solder joints at different positions in the array. The positions of critical solder joints in the array and the displacement fields of the surrounding cut surfaces were determined. The positions of critical solder joints in the array and the displacement fields of the surrounding cut surfaces are shown in formulas (1), (2), and (3). （1）， （2）， （3）， ΔD in the formula x ΔD y ΔD z denoted as , where is the average relative xyz direction displacement of the critical weld joint cutting surface; and , where dix, diy, and diz are the xyz direction displacements of the critical weld joint cutting surface nodes as a function of the load step. V This refers to the volume of the solder joint. 3) Create a single spherical solder joint model at a critical location and a single parametric equivalent solder joint model: Using sub-modeling technology, cut the solder joints at critical locations in the overall model to construct a single spherical solder joint model. Based on the nonlinear load deformation response and maintaining a constant solder joint height, introduce parameters r1 and r2 based on the principle of equal volume to establish a single parametric equivalent solder joint model. The boundary condition for both models is the displacement field ΔD of the cut surface around the critical solder joint in the overall model. x ( V,t ), ΔD y ( V,t ), ΔD z ( V,t The simulation analysis was completed by applying a temperature load T(t). The objective functions of parameter values ​​r1 and r2 were set. Combined with the optimal evolution algorithm, the optimal parameter values ​​r1 and r2 of the equivalent solder joint were determined by iterative calculation. The single parameterized equivalent solder joint model is shown in formula (4): （4）， In the formula, V is the volume of the solder joint, h is the height of the solder joint, and r1 and r2 are equivalent solder joint parameters. The temperature load T(t) is as follows: the heating and cooling rate is 36℃ / min, the high and low temperature holding time is 10min, and the temperature cyclic loading starts from 125℃ for a total of 4 temperature cycles. 4) Obtaining the thermal stress values ​​of the spherical weld joint and the parameterized equivalent weld joint: The displacement field of the cut surface around the key weld joint in the overall model is used as the boundary condition for the two individual weld joint models. Displacement interpolation is performed using the displacement shape function, and the thermal stress values ​​of the spherical weld joint and the parameterized equivalent weld joint are obtained using the temperature thermal load T(t). Specifically: Displacement interpolation was performed using an eight-point displacement shape function to obtain the thermal stress value R of the spherical weld joint. a ( V ,t j The thermal stress value R of the parameterized equivalent weld joint e ( V ,t j As shown in formulas (5), (6) and (7): （5）， （6）， （7）， μ in the formula L ,ν L and ω L μ represents the interpolation value of a single solder joint model node in X, Y, Z. i G ,ν i G and ω i G The displacement values ​​of the cutting surface in the X, Y, and Z directions are analyzed for the overall model, where G represents the nodes of the overall model, L represents the nodes of the individual weld point model, and N represents the displacement values ​​of the individual weld point model. i (ξ,η,ζ) is the shape function in spatial coordinates; 5) Determine the optimal morphological parameter value of the equivalent solder joint: Calculate the error ε between the Von mises values ​​of the solder joints in the two models, and use iterative calculation to determine the optimal morphological parameter value of the equivalent solder joint. The process of determining the optimal morphological parameter value of the equivalent solder joint is as follows: Determine the range of values ​​of parameterized equivalent solder joints r1 and r2 according to the diameter of the spherical solder joint and set the parameter value r1 < r2. Calculate the error ε between the Von mises values ​​of the spherical solder joint and the parameterized equivalent solder joint. Iterate the parameter values ​​r1 and r2 more than 10 times to obtain the optimal morphological parameter value of the equivalent solder joint, as shown in formula (8) and formula (9). （8）， （9）， In the formula, Std[ ] is the standard deviation function. r For parameterized solder joint parameter vectors, l i For the constraints of equivalent solder joints r1 and r2, n c The total number of limiting conditions; 6) Construct an overall parameterized equivalent model of POP stacked solder joint package to complete thermal cycling load analysis: The overall parameterized equivalent model of POP stacked solder joint package is to replace the spherical solder joint in the overall model with the best equivalent solder joint and then use displacement field and thermal load to complete thermal cycling load analysis. 7) Calculate the thermal fatigue life of the weld joint: The thermal fatigue life of the weld joint is calculated using the weld joint plastic strain energy density increment and Darveaux formula, as shown in formulas (10), (11), (12) and (13): （10）， （11）， （12）， （13）， ΔW in the formula i It has a volume of V i The plastic strain energy density accumulated by the i-th element in each cycle, where n is the number of elements; ΔW ave The density of plastic strain energy accumulated during each thermal cycle; N0 is the weld crack initiation lifetime; dD / dN is the weld crack propagation lifetime; N f is the thermal fatigue life of the weld joint; D is the characteristic length of the weld joint fracture; K1, K2, K3 and K4 are the crack propagation constants of the weld joint.

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