A simulation method, apparatus, medium, and device for underfilling of flip chips

Abstract

This invention discloses a simulation method, apparatus, medium, and device for flip chip underfill, relating to the field of flip chip underfill simulation technology. The invention simulates the flip chip underfill process within a computational domain divided into two meshes in a flow plane perpendicular to the depth direction using a color gradient lattice Boltzmann model. A color function clearly distinguishes between the wetting phase (filler adhesive) and the non-wetting phase (air) to dynamically track the two-phase interface. When simulating the flow field changes during the self-absorption process of flip chip underfill, the average curvature of the interface in the depth direction and the average frictional force of the upper and lower solid walls of the flip chip are introduced to determine the force applied at the two-phase fluid interface, thus reflecting three-dimensional physical effects. While maintaining near-two-dimensional computational costs, this invention significantly improves the accuracy of flip chip underfill simulation and can quickly predict the entire flip chip underfill process at a lower cost.

Description

Technical Field

[0001] This invention relates to the field of flip chip underfill simulation technology, and particularly to a simulation method, apparatus, medium and device for flip chip underfill. Background Technology

[0002] Currently, underfill technology in flip-chip packaging is a key step in improving the reliability of electronic products. It effectively protects solder joints by filling the micro-gap between the chip and the substrate with epoxy resin. This process is essentially a multiphase flow process dominated by capillary forces, where the resin displaces air. Numerical simulation is an important tool for gaining a deeper understanding and optimizing this process.

[0003] In existing technologies, while complete 3D models can capture the true physical effects of flip chip packaging, they are computationally expensive and difficult to apply to rapid process optimization. Simplified 2D models, while computationally efficient, cannot reflect the key physical effects in the depth direction (Z-direction) of the filled region. Ignoring these 3D effects can lead to deviations in the prediction of capillary driving forces, which in turn seriously affects the accuracy of filling process, filling time, and defect (such as void) prediction.

[0004] Therefore, there is an urgent need for a new numerical simulation method that can effectively reflect three-dimensional physical effects at near-two-dimensional computational costs, so as to quickly predict the entire process of flip chip bottom filling at a lower cost. Summary of the Invention

[0005] Therefore, it is necessary to provide a simulation method, apparatus, medium, and device for bottom filling of flip chips to address the above-mentioned technical problems.

[0006] The present invention adopts the following technical solution:

[0007] This invention provides a method for simulating underfilling of a flip chip, comprising:

[0008] A two-dimensional mesh is created in the flow plane perpendicular to the depth direction of the flip chip to construct the computational domain of the bottom filling region of the flip chip;

[0009] A color gradient lattice Boltzmann model was established, and the wetting phase representing the filler and the non-wetting phase representing air were distinguished in the computational domain by a color function in order to track the dynamic interface of the two-phase fluid.

[0010] Based on the filling method of the bottom fill, the corresponding boundary conditions are implemented at the boundary of the computational domain to initialize the initial distribution and velocity field of the fluid field, the filler gel and the air two-phase fluid within the computational domain.

[0011] Based on the color gradient lattice Boltzmann model, the force applied to the interface between the two phases of the flip chip is determined by the average curvature of the interface in the depth direction and the average friction force of the upper and lower solid walls of the flip chip, so as to drive the interfacial tension effect. The flow field change during the bottom filling self-absorption process of the flip chip is simulated by numerical iterative calculation. The numerical iterative calculation includes fluid collision, recoloring based on color function, and fluid migration.

[0012] Optionally, the color gradient lattice Boltzmann model is an incompressible color gradient lattice Boltzmann model.

[0013] Optionally, the step of implementing corresponding boundary conditions at the boundary of the computational domain based on the bottom fill method specifically includes:

[0014] When the bottom filling method is Type I filling, before the fluid migration in the numerical iterative calculation, the color distribution functions of all two-phase fluids pointing out of the computational domain under the periodic inlet and outlet boundary conditions are exchanged to obtain the corrected periodic inlet and outlet boundary conditions as the boundary conditions corresponding to Type I filling.

[0015] When the bottom fill is an L-shaped fill, the non-equilibrium part of the color distribution function is extrapolated through the non-equilibrium extrapolation boundary conditions to form the boundary conditions corresponding to the L-shaped fill.

[0016] When the bottom filling method is U-shaped filling, the boundary conditions corresponding to the U-shaped filling are formed according to the unbalanced extrapolation boundary conditions and the Zou-He pressure boundary conditions.

[0017] Optionally, the solid boundary conditions of the upper and lower solid walls of the flip chip in the boundary conditions adopt a half-step bounce boundary method to achieve no-slip boundary conditions; and / or,

[0018] By adjusting the gradient direction of the color function around the contact line between the fluid and the solid to control the contact angle, a wetting boundary is formed around the multiphase interface.

[0019] Optionally, the step of simulating the flow field changes during the self-priming process at the bottom of the flip chip through numerical iterative calculation specifically includes:

[0020] The sum of the color distribution functions of the two-phase fluids is used as the total distribution function of the two-phase fluids. The collision process is processed according to the multi-relaxation time scheme, and the total distribution function of the collision process is evolved through the collision operator corresponding to the multi-relaxation time scheme to realize the fluid collision process.

[0021] The average viscosity at the interface in the relaxation parameters of the collision operator corresponding to the multi-relaxation time scheme is obtained by weighting the local viscosity of the two pure phases using the harmonic averaging method.

[0022] Optionally, the step of simulating the flow field changes during the self-priming process at the bottom of the flip chip through numerical iterative calculation specifically includes:

[0023] The color function drives the color distribution function of the two-phase fluid to converge towards the same color region, and allows partial mixing in the interface normal direction of the two-phase fluid, thus realizing the recoloring process based on the color function.

[0024] Optionally, the step of simulating the flow field changes during the self-priming process at the bottom of the flip chip through numerical iterative calculation specifically includes:

[0025] The color distribution function of the recolored two-phase fluid is migrated to the nearest grid point according to the discrete velocity vector direction to realize the fluid migration process.

[0026] This invention provides a simulation device for underfilling of flip chips, comprising:

[0027] The meshing module is used to perform two-dimensional meshing in the flow plane perpendicular to the depth direction of the flip chip, and to construct the computational domain of the bottom filling region of the flip chip;

[0028] The module is used to build a color gradient lattice Boltzmann model and distinguish the wetting phase representing the filler and the non-wetting phase representing air in the computational domain through a color function, so as to track the dynamic interface of the two-phase fluid.

[0029] The initialization module is used to implement corresponding boundary conditions at the boundary of the computational domain according to the filling method of the bottom filler, and to initialize the initial distribution and velocity field of the fluid field, filler glue and air two-phase fluid in the computational domain.

[0030] The simulation module is used to determine the force applied at the interface of the two-phase fluid based on the color gradient lattice Boltzmann model, the average curvature of the interface in the depth direction, and the average friction force of the upper and lower solid walls of the flip chip, so as to drive the interfacial tension effect. The simulation module simulates the flow field changes during the bottom filling self-absorption process of the flip chip through numerical iterative calculation. The numerical iterative calculation includes fluid collision, recoloring based on color function, and fluid migration.

[0031] The present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described simulation method for bottom filling of a flip chip.

[0032] The present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described simulation method for bottom filling of a flip chip.

[0033] The above-mentioned at least one technical solution adopted in this invention can achieve the following beneficial effects:

[0034] This invention simulates the bottom filling process of flip chips by employing a color gradient lattice Boltzmann model within a two-grid computational domain on a flow plane perpendicular to the depth direction. It uses a color function to clearly distinguish between the wetting phase (filler adhesive) and the non-wetting phase (air) to dynamically track the interface between the two phases. When simulating the flow field changes during the self-absorption process of flip chip bottom filling, it introduces the average curvature of the interface in the depth direction and the average frictional force of the upper and lower solid walls of the flip chip to determine the force applied at the interface between the two fluid phases, thus reflecting three-dimensional physical effects. While maintaining near-two-dimensional computational costs, it significantly improves the accuracy of flip chip bottom filling simulation and can quickly predict the entire flip chip bottom filling process at a lower cost. Attached Figure Description

[0035] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0036] Figure 1 A schematic flowchart of a simulation method for bottom filling of a flip chip provided by the present invention;

[0037] Figure 2 A schematic diagram of a flip-chip bottom filling adhesive encapsulation process provided by the present invention;

[0038] Figure 3 A schematic diagram of a type I filling method provided by the present invention;

[0039] Figure 4 A schematic diagram of an L-shaped filling method provided by the present invention;

[0040] Figure 5 This is a schematic diagram of a U-shaped filling method provided by the present invention;

[0041] Figure 6 A schematic diagram of a half-step bounce boundary method provided by the present invention;

[0042] Figure 7 A schematic diagram of the discrete velocity direction in a D2Q9 model provided by the present invention;

[0043] Figure 8 This is a schematic diagram comparing the simulation results of a type I filling method provided by the present invention with experimental results and other numerical simulation methods;

[0044] Figure 9 A schematic diagram showing the comparison between simulation results and experimental results of a U-shaped filling method provided by the present invention;

[0045] Figure 10 This is a schematic diagram of LBM simulation results corresponding to different bottom fill volume fractions under different filling methods (I-type, L-type, and U-type) provided by the present invention.

[0046] Figure 11 A schematic diagram of a simulation device for bottom filling of a flip chip provided by the present invention;

[0047] Figure 12 A schematic diagram of a computer device for implementing a simulation method of bottom filling of a flip chip, provided by the present invention. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0049] Currently, existing numerical simulation methods face a series of prominent challenges in accurately and efficiently simulating this process, specifically:

[0050] First, there is a dilemma regarding model dimensions. While a fully three-dimensional model can capture realistic physical effects, its computational cost is high, making it unsuitable for rapid process optimization. Conversely, while a simplified two-dimensional model is computationally efficient, it fails to reflect key physical effects along the depth direction (Z-direction) of the filled region, particularly the average interface curvature changes caused by the upper and lower solid wall boundaries and the frictional resistance of the upper and lower walls. Ignoring these three-dimensional effects can lead to biased predictions of capillary driving forces, severely impacting the accuracy of filling process, filling time, and defect (such as void) predictions.

[0051] Second, there is a lack of a flexible boundary condition framework that can uniformly handle various practical dispensing paths. Underfill processes involve multiple filling methods, such as I-shaped, L-shaped, and U-shaped, depending on the dispensing location. Existing simulation methods, such as those using modified I-shaped periodic boundary conditions, require flow symmetry across the edges of the computational domain, which cannot capture the complex flow behavior caused by L-shaped and U-shaped polygonal dispensing. Furthermore, conventional single-pressure boundary conditions or non-equilibrium extrapolation boundary conditions, such as those using U-shaped filling, are prone to numerical instability and computational divergence when dealing with multiphase interface evolution.

[0052] Third, at the mesoscale, there is a lack of a multiphase flow model that can simultaneously guarantee interface tracking accuracy, numerical stability, and computational efficiency. Traditional interface tracking methods based on the Navier-Stokes equations (such as VOF and Level Set) face problems such as interface diffusion and mass non-conservation when dealing with strong capillary forces at the microscale and complex wetting boundaries. Although the Lattice Boltzmann (LBM) method is applicable to complex boundaries and multiphase flows, existing LBM multiphase flow models are prone to generating non-physical "spurious velocities" under high viscosity ratio conditions, leading to interface morphology deviations or local non-physical flows, which affect simulation accuracy. How to reduce the impact of spurious velocities and improve the stability of the model under high viscosity ratio conditions while ensuring interface clarity and wettability control accuracy remains one of the key challenges in current LBM multiphase flow research.

[0053] Therefore, there is an urgent need in this field for an innovative numerical simulation method that can effectively reflect three-dimensional physical effects at near-two-dimensional computational costs; can flexibly adapt to different dispensing paths; and possesses excellent numerical stability and interface tracking accuracy to reliably predict the entire process of flip chip bottom filling.

[0054] The technical solutions provided by the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0055] Figure 1 This is a schematic diagram of a simulation method for bottom filling of a flip chip according to the present invention, which specifically includes the following steps:

[0056] S101: Two-dimensional meshing is performed in the flow plane perpendicular to the depth direction of the flip chip to construct the computational domain of the bottom filling region of the flip chip.

[0057] S102: Establish a color gradient lattice Boltzmann model and use a color function to distinguish between the wetting phase representing the filler and the non-wetting phase representing air within the computational domain in order to track the dynamic interface of the two-phase fluid.

[0058] S103: Implement corresponding boundary conditions at the boundary of the computational domain according to the filling method of the bottom filler, and initialize the initial distribution and velocity field of the fluid field, filler glue and air two-phase fluid in the computational domain.

[0059] S104: Based on the color gradient lattice Boltzmann model, the force applied to the interface between the two phases is determined based on the average curvature of the interface in the depth direction and the average friction force of the upper and lower solid walls of the flip chip, so as to drive the interface tension effect. The flow field change during the bottom filling self-absorption process of the flip chip is simulated by numerical iterative calculation; the numerical iterative calculation includes fluid collision, recoloring based on color function and fluid migration.

[0060] For ease of explanation, the following description focuses solely on the server as the executing entity. The server mentioned in this invention can be a server set up on a business platform, or a device such as a desktop computer or laptop computer capable of executing the solution of this invention.

[0061] Figure 2 This is a schematic diagram of a flip chip bottom filling adhesive encapsulation process according to the present invention, wherein, Figure 2 (a) Part shows the distribution of solder joints on the chip and the process of placing the chip on the substrate; Figure 2 (b) describes the application process of the filler adhesive. Figure 2 (c) is the curing process of the filler adhesive.

[0062] To address the technical challenges of existing technologies in effectively reflecting three-dimensional physical effects at near-two-dimensional computational costs, adapting flexibly to different dispensing paths, and achieving excellent numerical stability and interface tracking accuracy, thus making it difficult to reliably predict the entire process of flip chip underfill, one or more embodiments of this invention can use a color gradient lattice Boltzmann model to simulate underfill behavior in flip chip packaging. Simultaneously, based on the two-dimensional solver, the average interface curvature in the depth direction and the average frictional force of the upper and lower solid walls of the flip chip are introduced. This allows for the representation of key three-dimensional effects, such as changes in depth curvature and wall viscous resistance, while maintaining two-dimensional computational costs. It also offers advantages such as handling complex geometry, mass conservation, and surface wettability modeling.

[0063] Preferably, the color gradient lattice Boltzmann model can be an incompressible color gradient lattice Boltzmann model, that is, the fluid dynamics equations used in the simulation are incompressible Navier-Stokes equations, and allow the fluid density to fluctuate only minimally within the target range.

[0064] The model exhibits good stability and accuracy under low Mach number conditions, and is particularly suitable for numerical simulation of typical low-speed, incompressible flow processes such as bottom filling of flip chips.

[0065] Based on this, the server can establish a computational domain for simulating the bottom filling region of a flip chip through two-dimensional mesh partitioning, build a color gradient lattice Boltzmann model, and use a color function to distinguish the wetting phase representing the filler adhesive and the non-wetting phase representing air within the computational domain, and track the dynamic interface of the two-phase fluids, using distribution functions in the model respectively. and In the D2Q9 model, the two immiscible fluids, filler (represented in red) and air (represented in blue), are labeled. The value range is 9 integers within [0, 8], which represents the th There are nine discrete velocity directions, which correspond to nine discrete velocity directions within the lattice space. For the D2Q9 model, please refer to the subsequent description. Therefore, the total distribution function of the two-phase fluid... It can be defined as the sum of the distribution functions of the two-phase fluid, i.e. .

[0066] Then, in one or more embodiments of the present invention, the server can set boundary conditions at the boundary of the computing domain. The boundary conditions include at least inlet / outlet boundary conditions and solid boundary conditions, wherein the inlet / outlet boundary conditions can be set according to the filling method.

[0067] Specifically, when the bottom filling method is Type I filling, before fluid migration in the numerical iterative calculation, the color distribution functions of all two-phase fluids pointing out of the computational domain under the periodic inlet and outlet boundary conditions can be exchanged to obtain the corrected periodic inlet and outlet boundary conditions as the boundary conditions corresponding to Type I filling. When the bottom filling method is Type L filling, the non-equilibrium part of the color distribution function can be extrapolated using non-equilibrium extrapolation boundary conditions to form the boundary conditions corresponding to Type L filling. When the bottom filling method is Type U filling, the boundary conditions corresponding to Type U filling can be formed based on the non-equilibrium extrapolation boundary conditions and the Zou-He pressure boundary conditions.

[0068] For example, for type I fill, such as Figure 3 As shown, Figure 3 This is a schematic diagram of a type I filling method in this invention. Before the migration step, the red and blue distribution functions in all distribution functions pointing outside the computational domain are swapped to maintain the continuity of the phase interface. The entry point is on the left side. The exit is on the right side. At this point, the corrected periodic boundary condition can be expressed as:

[0069] when The time is as follows:

[0070]

[0071]

[0072] when The time is as follows:

[0073]

[0074]

[0075] In the above formula, and Representing coordinates In time The distribution function of the red and blue two-phase fluid at that time. and Representing coordinates In time The distribution function of the red and blue two-phase fluid at that time. and Representing coordinates In time The distribution functions of the fluids recolored to blue and red after recoloring are compared. and Representing coordinates In time The distribution functions of the fluids that were recolored and marked in red and blue after recoloring.

[0076] Because periodic boundary conditions require strict consistency of physical variables on opposite sides, it is difficult to satisfy the asymmetric flow and interface evolution caused by multi-sided dispensing in chip packaging. Therefore, it is not suitable for situations with multiple inlets during bottom filling.

[0077] For L-shaped filling, such as Figure 4 As shown, Figure 4 This is a schematic diagram of an L-shaped filling method in this invention. A non-equilibrium extrapolation boundary condition is introduced. By extrapolating the non-equilibrium part of the distribution function, numerical stability is maintained while adapting to the dispensing requirements in different directions. Its mathematical expression is as follows:

[0078]

[0079] In the formula, Indicates the position at the boundary of the two-phase fluid. The node at the location The time is at the Distribution function in each discrete velocity direction, Indicates the position at the boundary of the two-phase fluid. The node at the location The time is at the The equilibrium distribution function in each discrete velocity direction. Represents a node Distribution function of adjacent nodes, Represents a node The equilibrium distribution function of a neighboring node, where the spatial location vector and time step of the neighboring node are: and .

[0080] For U-shaped filling, such as Figure 5 As shown, Figure 5This is a schematic diagram of a U-shaped filling method in this invention, which combines non-equilibrium extrapolation boundary conditions and Zou-He pressure boundary conditions.

[0081] Furthermore, in one or more embodiments of the present invention, in order to achieve a no-slip condition at the solid boundary, the solid boundary conditions of the upper and lower solid walls of the flip chip adopt a half-step bounce boundary method to achieve a no-slip boundary condition. For example... Figure 6 As shown, Figure 6 This is a schematic diagram of a half-step bounce boundary method in this invention. Figure 6 It can be observed that the solid boundary point is obtained by extending half a grid cell outward from the fluid grid point. Furthermore, in one or more embodiments of the present invention, to further accurately simulate the wetting behavior of the solid surface, the contact angle can be effectively controlled by adjusting the gradient direction of the color function around the contact line between the fluid and the solid, thereby forming a physically consistent wetting state near the multiphase interface, i.e., forming a wetting boundary around the multiphase interface.

[0082] Then, the fluid field within the computational domain can be initialized, and the initial distribution and velocity field of the two-phase fluid of filler and air can be given.

[0083] Finally, numerical iterative calculations can be performed based on the color gradient lattice Boltzmann model to simulate the evolution of the fluid field. The iterative calculation process includes collisions, recoloring using color functions, and migration, which can obtain the fluid interface morphology, filling time, and flow characteristics, providing a theoretical basis for the selection of packaging materials and the formulation of process parameters for bottom filling of flip chips.

[0084] In one or more embodiments of the present invention, for the fluid collision process, the server can use the sum of the color distribution functions of the two-phase fluids as the total distribution function of the two-phase fluids, process the collision process according to a multi-relaxation time scheme, and evolve the total distribution function of the collision process through the collision operator corresponding to the multi-relaxation time scheme to realize the fluid collision process. The average viscosity at the interface in the relaxation parameters of the collision operator corresponding to the multi-relaxation time scheme is obtained by weighting the local viscosity of the two pure phases using a harmonic averaging method.

[0085] For a color function-based recoloring process, the server can drive the color distribution function of the two-phase fluids to converge towards the same color region according to the color function, and allow partial mixing in the interface normal direction of the two-phase fluids, thereby realizing a color function-based recoloring process.

[0086] For the fluid migration process, the server can migrate the color distribution function of the recolored two-phase fluid to the nearest grid point according to the discrete velocity vector direction to realize the fluid migration process.

[0087] For example, after pre-defining the total distribution function of the two-phase fluid as the sum of the two-phase distribution functions during the collision process, a multi-relaxation time scheme is introduced to process the collision process, and the total distribution function of the collision process is evolved through the corresponding collision operator. The collision process can be represented as:

[0088]

[0089] In the formula, and Let these represent the spatial position vector and time step of the fluid particle in the distribution function, respectively. and These represent the positions before and after the collision, respectively. and The total distribution function over time, This represents the force applied at the interface between two fluid phases, used to drive the interfacial tension effect. Indicates the location and To improve the numerical stability of simulating bottom flow filling of flip chips under high viscosity ratio conditions and suppress the occurrence of non-physical spurious velocities, a multiple-relaxation-time (MRT) format is used to process the collision process. The corresponding collision operator form is shown below:

[0090]

[0091] In the above formula, This is the transformation matrix mapping from velocity space to moment space, which can be obtained using the Gram-Schmidt orthogonalization method. The relaxation matrix is ​​diagonally oriented in velocity space. In the D2Q9 model, both can be taken as follows:

[0092]

[0093]

[0094] In the above formula, and They represent the first Relaxation parameters for discrete velocity directions.

[0095] D2Q9 is one of the most commonly used methods in the color gradient lattice Boltzmann method. For two-dimensional problems, the velocity discretization strategy adopts a two-dimensional nine-velocity (2D 9-velocity, D2Q9) model, such as... Figure 7 As shown, Figure 7 This is a schematic diagram of the discrete velocity direction in a D2Q9 model of the present invention. The discrete velocity values ​​can be:

[0096]

[0097] in, The grid velocity is defined as the ratio of the grid length to the time step, which is 1.0. In this invention, unless otherwise specified, the grid length can be taken as [value missing]. Therefore, under normal circumstances, the lattice speed is .

[0098] For the equilibrium distribution function in the above equation Since the entire process is essentially a spontaneous capillary aspiration process with a slow local fluid filling rate, a second-order Taylor expansion of the Boltzmann-Maxwell distribution function can be performed, which can be expressed as:

[0099]

[0100] in, This represents the total density of the two-phase mixture. To improve the stability of numerical calculations and simplify model parameter settings, the density can be set to 1. Indicates the grid number in the first position. Discrete velocities in discrete velocity directions Indicates the first In the D2Q9 model, the weight coefficients for each discrete velocity direction take the following values:

[0101]

[0102] The relaxation parameter is defined as follows:

[0103]

[0104] In the above formula, It is the viscosity of a two-phase mixture, which can be expressed by the formula... calculate, The relaxation time is dimensionless. This is the speed of sound within a lattice in the medium. To simplify the calculation, the lattice length is used here. Grid Time and grid speed All values ​​are set to 1; considering the potential difference in dynamic viscosity between the two-phase fluids, a harmonic averaging method is further used to determine the local viscosity of the two-phase fluids (i.e., the local viscosity of the filler gel marked in red). and the local viscosity of air marked in blue. Weighting is performed to obtain the average viscosity at the interface:

[0105]

[0106] Among them, color function The expression used to distinguish between two-phase fluids is:

[0107]

[0108] In the formula, Represents spatial position vector and time step Related color functions, and These represent the positions of the fluids (i.e., filler gel and air) corresponding to the red and blue phases, respectively. Place Local density value over time.

[0109] Forces applied at the interface of two-phase fluids The calculation formula is:

[0110]

[0111] In the above formula, Since it is the identity matrix, the forces acting on the two-phase fluid interface in nine discrete velocity directions can be obtained, and can be expressed as: , The expression is:

[0112]

[0113] In the above formula, Indicates the first Force acting in the direction of discrete velocity The average frictional force from the upper and lower solid walls is given by Calculations show that, , which is the equivalent frictional force parameter; in addition, interfacial tension. The expression is:

[0114]

[0115] In the above formula, It is the height of the filled area. It is the gradient operator. The interfacial tension coefficient, It is the local interface curvature, assuming the contact angle is... The average curvature effect of the interface along the depth direction can be defined as:

[0116]

[0117] in, Let the unit normal vector of the interface be... These are the gradient parameters.

[0118] To enhance the phase separation effect of the two-phase fluid in the simulation and maintain its immiscibility, it was recolored. By pushing the two-phase fluid to accumulate in the same color region and allowing limited mixing in the interface normal direction at the interface between the two phases, the spurious velocity problem was effectively alleviated, and the lattice locking phenomenon caused by insufficient color mixing was avoided. The distribution function of the fluid marked in red after recoloring is shown. Distribution function of the fluid labeled in blue The expression is:

[0119]

[0120]

[0121] In the above formula, This is a parameter that controls the thickness of the two-phase interface; in this invention, it can be set to 0.7. Indicates the location In After recoloring, the fluid distribution function over time migrates to neighboring grid points along the discrete velocity vector direction, performing the migration step:

[0122]

[0123] Indicates according to vector direction After relocation, at the location Place Time Distribution function of the phase fluid.

[0124] Figure 8 This is a schematic diagram comparing the simulation results of a type I filling method in this invention with experimental results and other numerical simulation methods. Figure 8 As can be seen, when the bottom filling ratio of the microcontroller chip reaches 42% under the Type I filling method, the flow front is compared. Figure 8 In the figures, (a) represents the experimental results; (b) represents the simulation results of this invention; (c) represents the simulation results of Wanghui et al.; and (d) represents the simulation results of Fluent.

[0125] Figure 9 This is a schematic diagram comparing the simulation results and experimental results of a U-shaped filling method in this invention. Figure 9 As can be seen, when the bottom filling ratio of a certain experimental chip under the U-shaped filling method reaches 25%, 55%, 75%, 90% and 98% respectively, the experimental results and the simulation results of the method of this invention show that the location of the void phenomenon is consistent.

[0126] Figure 10This invention relates to different bottom fill volume fractions under different filling methods (I-type, L-type, and U-type). A schematic diagram of the corresponding LBM simulation results.

[0127] based on Figure 1 The simulation method for flip chip bottom filling shown in this invention uses a color gradient lattice Boltzmann model to simulate the flip chip bottom filling process in a computational domain divided into two meshes in a flow plane perpendicular to the depth direction. The color function is used to clearly distinguish between the wetting phase (filler glue) and the non-wetting phase (air) to dynamically track the interface between the two phases. When simulating the flow field changes during the self-absorption process of flip chip bottom filling, the average curvature of the interface in the depth direction and the average friction force of the upper and lower solid walls of the flip chip are introduced to determine the force applied at the interface between the two phases of fluid, thereby reflecting three-dimensional physical effects (such as changes in depth curvature and wall viscous resistance). While maintaining near-two-dimensional computational costs, it can significantly improve the accuracy of flip chip bottom filling simulation and can quickly predict the entire flip chip bottom filling process at a lower cost.

[0128] This invention addresses the common I-type, L-type, and U-type dispensing paths in flip chip bottom filling by designing a flexible and unified boundary condition framework. By customizing inlet and outlet boundary conditions for different filling methods (e.g., using distribution function exchange to maintain interface continuity for I-type, introducing non-equilibrium extrapolation for L-type, and combining non-equilibrium extrapolation with Zou-He pressure conditions for U-type) and incorporating solid boundary treatment (using a half-step bounce method to achieve slip-free conditions and wetting boundary control of the contact angle), it effectively overcomes the limitations of traditional periodic boundaries or single pressure / velocity boundaries in simulating asymmetric dispensing flows. This ensures numerical stability, reduces the risk of computational divergence, and allows the simulation process to more realistically reflect the complex flow behavior and interface evolution in actual processes, greatly improving the applicability and reliability of the simulation.

[0129] This invention introduces a multi-relaxation time scheme to process the evolution of the total distribution function of the two-phase fluid during the collision process, and uses a harmonic averaging method to weight the local viscosity of the two phases to obtain the average viscosity at the interface. This design significantly enhances the numerical stability of the model under high viscosity ratio conditions, effectively suppresses the generation of non-physical "spurious velocities," and avoids interface distortion and computational instability. At the same time, the accurate modeling of interfacial tension effects and average friction ensures the smoothness and consistency of physical quantity changes at the interface, thereby achieving high-precision interface tracking at the mesoscale. This provides a solid numerical foundation for accurately simulating the capillary-driven bottom-filling process and improves the robustness of the entire simulation.

[0130] This invention employs an optimized recoloring method to drive two-phase fluids to converge toward their respective color regions during numerical iteration, while allowing limited mixing in the interface normal. This enhances phase separation and strictly maintains fluid immiscibility. This mechanism effectively mitigates spurious velocity phenomena, avoids lattice locking caused by insufficient color mixing, and ensures clear and stable evolution of the dynamic interface. Combined with the migration step, it achieves efficient transfer of the distribution function, further improving the interface tracking accuracy and numerical computation efficiency of multiphase flow simulation. This enables the model to more reliably predict interface morphology evolution and flow characteristics during the filling process, providing key technical support for process optimization and defect analysis.

[0131] This invention, through adaptive boundary condition setting, fluid field initialization, and numerical iterative calculation (including collision, recoloring, and migration steps), reflects three-dimensional physical effects while maintaining near-two-dimensional computational costs. It significantly improves the accuracy of predictions for filling processes, filling times, and defects (such as voids). At the same time, this method has the advantages of handling complex geometries, strict mass conservation, and accurate surface wettability modeling, providing an efficient and reliable theoretical basis and numerical tool for the selection of flip chip packaging materials and optimization of process parameters.

[0132] When applying the simulation method for bottom filling of flip chips provided by this invention, it is not necessary to... Figure 1 The steps shown are executed in sequence. The specific execution order of each step can be determined as needed, and this invention does not impose any restrictions on it.

[0133] The above describes a simulation method for underfilling of flip chips according to one or more embodiments of the present invention. Based on the same idea, the present invention also provides a corresponding simulation device for underfilling of flip chips, such as... Figure 11 As shown.

[0134] Figure 11 A schematic diagram of a simulation device for bottom filling of a flip chip provided by the present invention includes:

[0135] The partitioning module 201 is used to perform two-dimensional mesh partitioning in a flow plane perpendicular to the depth direction of the flip chip, and to construct the computational domain of the bottom filling region of the flip chip;

[0136] Module 202 is used to build a color gradient lattice Boltzmann model and distinguish the wetting phase representing the filler and the non-wetting phase representing air in the computational domain through a color function in order to track the dynamic interface of the two-phase fluid.

[0137] Initialization module 203 is used to implement corresponding boundary conditions at the boundary of the computational domain according to the filling method of the bottom filler, and to initialize the initial distribution and velocity field of the fluid field, filler glue and air two-phase fluid in the computational domain.

[0138] The simulation module 204 is used to determine the force applied at the interface of the two-phase fluid based on the color gradient lattice Boltzmann model, the average curvature of the interface in the depth direction and the average friction force of the upper and lower solid walls of the flip chip, so as to drive the interface tension effect. The simulation module simulates the flow field change during the bottom filling self-absorption process of the flip chip through numerical iterative calculation. The numerical iterative calculation includes fluid collision, recoloring based on color function and fluid migration.

[0139] Specific limitations regarding the simulation device for flip-chip underfilling can be found in the limitations of the simulation method for flip-chip underfilling described above, and will not be repeated here. Each module in the aforementioned simulation device for flip-chip underfilling can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independently of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the operations corresponding to each module.

[0140] The present invention also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 A simulation method for bottom filling of flip-chip is provided.

[0141] The present invention also provides Figure 12 The schematic diagram of the computer device shown is as follows: Figure 12 As shown, at the hardware level, this computer device includes a processor, internal bus, network interface, memory, and non-volatile memory, and may also include other hardware required for business operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then executes it to achieve the above. Figure 1 A simulation method for bottom filling of flip-chip is provided.

[0142] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0143] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this invention.

Claims

1. A simulation method for bottom filling of a flip chip, characterized in that, include: A two-dimensional mesh is created in the flow plane perpendicular to the depth direction of the flip chip to construct the computational domain of the bottom filling region of the flip chip; A color gradient lattice Boltzmann model was established, and the wetting phase representing the filler and the non-wetting phase representing air were distinguished in the computational domain by a color function in order to track the dynamic interface of the two-phase fluid. Depending on the bottom filling method, corresponding boundary conditions are applied at the boundary of the computational domain. Specifically, when the bottom filling method is Type I filling, before fluid migration in the numerical iterative calculation, the color distribution functions of all two-phase fluids pointing out of the computational domain under the periodic inlet and outlet boundary conditions are exchanged to obtain the corrected periodic inlet and outlet boundary conditions as the boundary conditions corresponding to Type I filling; when the bottom filling method is Type L filling, the non-equilibrium part of the color distribution function is extrapolated through non-equilibrium extrapolation boundary conditions to form the boundary conditions corresponding to Type L filling; when the bottom filling method is Type U filling, the boundary conditions corresponding to Type U filling are formed based on the non-equilibrium extrapolation boundary conditions and the Zou-He pressure boundary conditions. The initial distribution and velocity fields of the fluid field, filler adhesive, and air two-phase fluid within the computational domain are initialized. Based on the color gradient lattice Boltzmann model, the force applied at the interface of the two-phase fluid is determined based on the average curvature of the interface in the depth direction and the average friction force of the upper and lower solid walls of the flip chip to drive the interfacial tension effect. The flow field changes during the self-absorption process of bottom filling of the flip chip are simulated through numerical iterative calculation. The numerical iterative calculation includes fluid collision, recoloring based on color functions, and fluid migration.

2. The simulation method for bottom filling of a flip chip as described in claim 1, characterized in that, The color gradient lattice Boltzmann model is an incompressible color gradient lattice Boltzmann model.

3. The simulation method for bottom filling of a flip chip as described in claim 1, characterized in that, The solid boundary conditions of the flip chip's upper and lower solid walls adopt a half-step bounce boundary method to achieve slip-free boundary conditions; and / or, by adjusting the gradient direction of the color function around the contact line between the fluid and the solid to control the contact angle, a wetting boundary is formed around the multiphase interface.

4. The simulation method for bottom filling of a flip chip as described in claim 1, characterized in that, The simulation of the flow field changes during the self-priming process at the bottom of the flip chip through numerical iterative calculation specifically includes: using the sum of the color distribution functions of the two-phase fluids as the total distribution function of the two-phase fluids, processing the collision process according to a multi-relaxation time scheme, and evolving the total distribution function of the collision process through the collision operator corresponding to the multi-relaxation time scheme to realize the fluid collision process; wherein, the average viscosity at the interface in the relaxation parameters of the collision operator corresponding to the multi-relaxation time scheme is obtained by weighting the local viscosity of the two pure phases using a harmonic averaging method.

5. The simulation method for bottom filling of a flip chip as described in claim 1, characterized in that, The simulation of flow field changes during the bottom filling self-absorption process of the flip chip through numerical iterative calculation specifically includes: driving the color distribution function of the two-phase fluid to gather towards the same color region according to the color function, and allowing partial mixing in the interface normal direction of the two-phase fluid, thereby realizing a recoloring process based on the color function.

6. The simulation method for bottom filling of a flip chip as described in claim 1, characterized in that, The simulation of the flow field changes during the bottom filling self-absorption process of the flip chip through numerical iterative calculation specifically includes: migrating the color distribution function of the recolored two-phase fluid to the adjacent grid points according to the discrete velocity vector direction to realize the fluid migration process.

7. A simulation device for bottom filling of a flip chip, characterized in that, include: The meshing module is used to perform two-dimensional meshing in the flow plane perpendicular to the depth direction of the flip chip, and to construct the computational domain of the bottom filling region of the flip chip; The system comprises the following modules: a construction module for establishing a color gradient lattice Boltzmann model and distinguishing the wetting phase (representing the filler adhesive) and the non-wetting phase (representing the air) within the computational domain using color functions to track the dynamic interface of the two-phase fluids; an initialization module for implementing corresponding boundary conditions at the boundary of the computational domain based on the bottom filling method, and initializing the fluid field, initial distribution, and velocity field of the filler adhesive and air two-phase fluids within the computational domain; and a simulation module for determining the force applied at the interface of the two-phase fluids based on the color gradient lattice Boltzmann model, the average curvature of the interface in the depth direction, and the average frictional force of the upper and lower solid walls of the flip chip, to drive the interfacial tension effect, and simulating the flow field changes during the self-absorption process of the flip chip bottom filling through numerical iterative calculations. The numerical iterative calculations include fluid collision, color function-based recoloring, and fluid migration.

8. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the method as described in any one of claims 1 to 6.

9. A computer device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the method as described in any one of claims 1 to 6.

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