A method and system for nonlinear modeling and iterative equalization of HBM variable-temperature bonding

Abstract

This invention belongs to the field of semiconductor material preparation technology, and relates to a method and system for HBM variable-temperature bonding nonlinear coupling modeling and multi-scale iterative equilibrium. It achieves original breakthroughs in three core dimensions: dynamic reconstruction of finite element modeling, collaborative solution of multi-scale equations, and temporal nonlinear deviation compensation algorithm. This is achieved by reconstructing the temporal dynamic evolution characterization logic of the entire variable-temperature bonding process, establishing multi-scale structural simultaneous equilibrium iterative solution rules, and building a quantitative correction calculation system for temporal coupling lag deviation. The invention effectively improves the simulation distortion of the entire HBM variable-temperature bonding field evolution, the decoupling of macro- and micro-structures, and the coupling misalignment defects of temporal operating conditions, thereby enhancing the mechanical equilibrium, metallurgical bonding synchronization, and long-term structural stability of the multilayer chip stacking bonding interface.

Description

Technical Field

[0001] This invention belongs to the field of semiconductor materials technology, and in particular to a method and system for nonlinear modeling and iterative equalization of HBM temperature bonding. Background Technology

[0002] HBM high-bandwidth memory achieves high-density interconnection through multi-layer DRAM vertical stacking and low-temperature eutectic bonding with micro-bumps. Variable-temperature bonding utilizes a time-sequential temperature control logic involving preheating, isothermal bonding, and gradient cooling, combined with constant holding voltage, to achieve metallurgical bonding at the metal bump interface. As the number of HBM stacking layers continues to increase, the temporal nonlinear evolution characteristics, multi-scale structural coupling characteristics, and temperature-pressure temporal linkage characteristics of the entire bonding process become increasingly significant. Currently, the industry's bonding equipment structure, material formulation, basic temperature control logic, and conventional stress simulation are covered by numerous patents and literature. Previous innovations have been completed in areas such as weak coupling perturbation, non-equilibrium boundaries, and local bump mismatch. This time, we focus on specific technical pain points:

[0003] 1. The variable-temperature bonding field exhibits strong temporal nonlinear evolution characteristics, and traditional static time-invariant homogeneous modeling suffers severe distortion. HBM variable-temperature bonding is a typical temporal continuous evolution process, where the coefficient of thermal expansion, interfacial viscoelastic properties, metal plastic deformation, and interfacial bonding stiffness exhibit continuous nonlinear dynamic changes with temperature rise and fall. Existing bonding simulation modeling all adopt the static time-invariant homogeneous assumption, fixing material parameters and field constraints at different time stages to constant values, failing to characterize the nonlinear dynamic changes of thermodynamic parameters with temperature evolution. Traditional fixed-parameter finite element models lack the ability to iterate and update temporally, and the field properties are completely decoupled from the temporal conditions, resulting in systematic distortion of the simulation results of stress evolution and deformation response at different stages of heating, isothermal, and slow cooling, making it impossible to accurately predict time-induced progressive bonding defects.

[0004] 2. HBM exhibits a dual-scale structure of macroscopic stacking and microscopic bumps, leading to fragmented multi-scale solutions and a lack of iterative equilibrium. HBM as a whole is a centimeter-scale macroscopic stacked encapsulation structure, with bonding interconnect units being micrometer-scale micro-bump arrays, naturally forming a macroscopic-microscopic cross-scale composite structure. Existing numerical solutions employ a scale-segmented, step-by-step calculation mode, first solving for the overall macroscopic deformation, then separately calculating the microscopic bump stress, lacking bidirectional parameter transfer and coordinated computation across scales. The macroscopic and microscopic solution equations are independent of each other, with inconsistent iteration rhythms, lacking a multi-scale iterative equilibrium control mechanism. Macroscopic deformation cannot be synchronously transmitted to the microscopic bump computational domain, and microscopic local stress concentrations cannot provide back-feedback to correct macroscopic boundaries, resulting in severe cross-scale solution discontinuities, and scale biases continuously amplified after multi-layer stacking.

[0005] 3. The temperature-dependent bonding conditions and the pressure-holding load exhibit a time-series coupling lag effect. Without quantitative modeling and algorithmic compensation mechanisms, the temperature field heating / cooling response rate and interface metallurgical reaction progress in temperature-dependent bonding cannot be fully synchronized with the application, maintenance, and unloading of the mechanical pressure-holding load, resulting in an objective temperature-pressure time-series coupling lag deviation. Existing process control and numerical calculations assume instantaneous synchronous response of temperature and pressure time sequences, completely ignoring multiple time-series deviations such as thermal field evolution lag, interface metallurgical lag, and mechanical load transfer lag. Without a quantitative accounting model and dynamic resolution algorithm for time-series lag deviations, relying solely on manual fixed delays for coarse compensation, the lag deviations cannot be finely calculated or directionally corrected. This leads to inconsistent metallurgical bonding progress across different chip layers and significant differences in interlayer bonding strength, directly impacting the overall reliability and batch consistency of HBM stacks. Summary of the Invention

[0006] 1. Purpose of the invention

[0007] To address the specific technical issues mentioned above, we have adopted a novel approach, focusing on time-series nonlinear dynamic modeling, multi-scale cross-level equilibrium iterative solutions, and temperature-pressure time-series coupled lag algorithm correction.

[0008] 1: Finite element reconstruction modeling of dynamic evolution of nonlinear field in temperature-dependent bonding sequence

[0009] To address the distortions and temporal mismatches in static homogeneous modeling, this invention abandons the traditional time-invariant fixed-parameter modeling approach and constructs a temporal nonlinear dynamic evolution modeling architecture. Following a full-time time-series node progression of preheating, bonding, and slow cooling, core modeling parameters such as material thermal properties, mechanical constitutive models, and interface bonding stiffness are dynamically updated in real time. A temporal nonlinear evolution gradient interval is defined, and a dynamic temperature-parameter correlation equation is established to accurately characterize the continuous nonlinear changes in the field throughout the bonding process. Through temporal dynamic reconstruction of the finite element model, real-time synchronization between the modeling system and the variable-temperature time-series operating conditions is achieved, fundamentally resolving the core deficiency of static fixed models in adapting to nonlinear evolution conditions from the simulation level.

[0010] 2: Macro-micro multi-scale cross-level coupled simultaneous equilibrium iterative solution

[0011] To address the shortcomings of fragmented solutions and iterative imbalances in dual-scale structural solutions, this invention pioneers a cross-scale integrated coupled modeling system for macroscopic stacked structures and microscopic convex point arrays using HBM, establishing a bidirectional parameter mapping and transfer matrix between macro and micro scales. A multi-scale collaborative iterative equilibrium solution algorithm is developed, unifying the iteration rhythm of the macroscopic overall and microscopic local equations and setting multi-scale equilibrium convergence constraints. It achieves synchronous assignment of macroscopic deformation fields to the microscopic computational domain, and uses back-feedback from microscopic stress concentration characteristics to correct macroscopic boundary constraints, breaking the step-by-step fragmented solution mode, completing a self-consistent solution across dual-scale fields, and eliminating cross-scale computational discontinuities.

[0012] 3: Quantitative Modeling and Dynamic Resolution of Temperature-Pressure Time-Series Coupling Lag Deviation

[0013] Addressing the pain points of timing lag and lack of quantification correction in temperature-pressure holding time series, this invention analyzes the characteristics of three types of timing deviations: heat conduction lag, metallurgical reaction lag, and load transfer lag, and establishes a multi-dimensional timing coupling lag error quantification calculation model. It innovatively designs a dynamic timing lag resolution operator, abandoning the fixed-delay coarse compensation method, and dynamically calculates the deviation compensation coefficient based on the real-time timing evolution progress. Through timing backtracking calculation and adaptive adjustment of the lead amount, it directionally compensates for temperature-pressure coupling misalignment deviations, achieving time-series coordinated matching of temperature evolution, pressure loading, and interface metallurgical reaction, and eliminating the accumulation of long-cycle timing deviations.

[0014] 4: Adaptive Allocation and Operation Architecture for Multi-Factor Gradient Weights in Temporal Evolution Fields

[0015] To address the issues of frequent shifts in the dominant roles of different time-series fields and the solidification of solution weights, this invention constructs a time-series evolution multi-factor gradient weight allocation model. Based on the dominant strengths of the thermal field, force field, deformation field, and metallurgical reaction field at different process stages, the model adaptively adjusts the solution weight coefficients of each physical field. A smooth transition operation rule for gradient weights is established to avoid solution oscillations caused by abrupt weight changes during time-series transitions. Through differentiated weight linkage allocation, the model enhances the solution accuracy of core fields, balances the computational efficiency of secondary fields, and improves the stability and adaptability of multi-physics coupling solutions across the entire time series.

[0016] 5: Multi-layer stacked temporal evolution boundary condition hierarchical iterative dynamic update mechanism

[0017] To address the issues of poor adaptability of static temporal boundary constraints and failure of multi-layer boundary linkages, this invention establishes a layered temporal boundary dynamic update system based on the differentiated characteristics of thermal conditions, deformation constraints, and heat dissipation environments of each HBM stack layer. As the bonding timeline evolves, the finite element operation matrices of the heat exchange boundary, mechanical constraint boundary, and interlayer displacement coordination boundary are iteratively updated layer by layer. This achieves a combination of independent adaptive adjustment of single-layer boundaries and coordinated constraint linkage of multi-layer boundaries, taking into account both individual differences and overall linkage in multi-layer stacked structures, and adapting to the dynamic boundary changes required under temporal nonlinear evolution.

[0018] 6: Bonding full-process multi-scale evolution steady-state self-consistent closed-loop calibration algorithm

[0019] To address the issues of benchmark drift and decreased steady-state performance in multi-scale solutions during long-cycle mass production, this invention collects characteristics of slow variables such as aging deviations in the cavity thermal environment, deformation of multi-layered tooling, and material aging during the mass production process, and establishes a benchmark deviation identification model for time-series evolution. It periodically calibrates the coefficients of the time-series nonlinear evolution equation, the parameters of the multi-scale mapping matrix, and the benchmark threshold of the time-series lag resolution operator, forming a closed-loop iterative system encompassing time-series modeling, multi-scale solution, lag correction, boundary update, and benchmark calibration. This system effectively ensures the consistency and robustness of solving large-scale HBM bonding time-series evolution problems.

[0020] Beneficial effects

[0021] 1. This invention pioneers a time-series nonlinear dynamic evolution finite element reconstruction modeling system, completely breaking through the technical constraints of traditional HBM bonding static time-invariant homogeneous modeling. With time-series dynamic parameter iterative updates and gradient interval refined modeling as its core, it fully recreates the continuous nonlinear evolution of material properties and field characteristics throughout the entire temperature-dependent bonding process. It addresses the defects of field response distortion and parameter mismatch at different process stages from the bottom layer of simulation modeling. The level of refinement in time-series modeling far exceeds that of existing static simulation schemes, providing accurate model support for the progressive defect prediction of temperature-dependent bonding.

[0022] 2. This invention presents an original macro-micro multi-scale, cross-level coupled equilibrium iterative solution algorithm that breaks down the solution barriers between macroscopic HBM stacking and microscopic convex point arrays. It constructs a dual-scale, bidirectional parameter linkage feedback mechanism and unifies multi-scale iterative convergence rules. This effectively solves the problems of fragmented step-by-step solutions, amplified scale bias, and the inability to simultaneously consider local and global aspects. It achieves integrated, self-consistent solution of global deformation in multi-layer stacking and local stress in micro-convex points, significantly improving the completeness and accuracy of numerical simulations of high-density interconnected structures.

[0023] 3. This invention establishes a novel temperature-pressure time-series coupling lag quantification correction computational system, for the first time incorporating multiple types of time-series lag deviations into the algorithm's quantification correction scope, abandoning the industry-standard fixed-delay coarse-grained compensation mode. Through a combination of time-series deviation modeling, dynamic resolution operators, and time-series backtracking compensation algorithm logic, it precisely coordinates the temporal synchronization of temperature, pressure, and metallurgical reactions, eliminating the defects of interlayer bonding progress differences in multilayer stacking, and improving the consistency of HBM batch preparation and the reliability of interface bonding from the time-series algorithm level.

[0024] This invention combines multi-layer temporal boundary hierarchical update, multi-factor gradient weight allocation and global closed-loop self-consistent calibration mechanism, and is suitable for high-order multi-layer HBM stacked structures and long-cycle mass production conditions. Attached Figure Description

[0025] Figure 1 Flowchart. Detailed Implementation

[0026] Example 1

[0027] A method for nonlinear coupling modeling and multi-scale iterative equilibrium of HBM variable-temperature bonding includes the following steps: S1, collecting full-time thermal, mechanical, and multi-layer structural deformation characteristic data of HBM variable-temperature bonding, constructing a time-series nonlinear field dynamic evolution finite element reconstruction model, and dynamically updating physical property parameters and constraints in time-series gradient intervals; S2, building a macroscopic- A microscopic multi-scale cross-level bidirectional mapping matrix is ​​used to establish a dual-scale coupled simultaneous equation system. A formula for calculating the self-consistent coefficient of time-series nonlinear evolution is introduced, and multi-scale collaborative equilibrium iterative simultaneous solution is performed. S3: The differences in time-series operation under variable temperature conditions and pressure holding loads are monitored. Multiple types of time-series coupling lag deviations are quantified and calculated. A dynamic time-series lag resolution operator is invoked to achieve directional compensation and collaborative correction of temperature and pressure time-series coupling deviations. S4: A multi-factor gradient weight adaptive allocation architecture is configured for the time-series evolution field. The multi-physics field solution weights are dynamically adjusted according to the process stage to ensure a smooth transition during time-series switching. S5: For HBM multi-layer stacked structures, a layered iterative dynamic update mechanism for time-series boundaries is established to adapt to the differentiated requirements of time-series evolution boundaries for each stacked layer. S6: The drift characteristics of long-cycle, slow-variable conditions in mass production are identified. Multi-scale evolution steady-state self-consistent closed-loop calibration is performed, and modeling parameters and algorithm operation coefficients are globally refreshed to achieve steady-state solution control throughout the entire HBM multi-layer variable-temperature bonding process. The formula for calculating the self-consistent coefficient of time-series nonlinear evolution is as follows: Specific steps

[0028] Step 1: Continuously collect furnace temperature time-series curves, interlayer deformation time-series response, and interface mechanical parameter evolution data throughout the entire time cycle of HBM variable-temperature bonding from low-temperature preheating to gradient slow cooling. Identify and classify the nonlinear variation patterns of material viscoelasticity, plastic deformation, and thermal expansion characteristics across different temperature ranges, and classify and aggregate the time-series features. Step 2: Divide the bonding time-series nonlinear evolution gradient intervals, dynamically reconstruct the finite element model interval by interval, and update the material constitutive parameters and field constraints at each time-series node in real time. Introduce a time-series nonlinear evolution self-consistency coefficient as the core quantitative criterion for determining the matching degree of dynamic modeling and solution. In the formula: These are the self-consistent coefficients for time-series nonlinear evolution; These are the time-series evolution matching coefficients for individual thermal field, force field, deformation field, and reaction field; For each field, a time-series dynamic weighting factor; This represents the quantized value of the temporal nonlinear evolution deviation. This is the nonlinear deviation correction coefficient. Step 3: Construct a dynamic correlation iterative equation for temperature and time-series physical property parameters, abandoning the traditional fixed parameter assignment method, and continuously iteratively refreshing the core parameters of the finite element calculation domain as the time axis progresses, realizing the synchronous evolution of the model structure and time-series operating conditions. Step 4: Real-time calculation of the time-series nonlinear evolution self-consistency coefficient, iterative optimization of parameter update frequency and interval division accuracy, continuously reducing the time-series evolution modeling deviation, completing the steady-state solution of the dynamic evolution of the entire variable-temperature bonding process, and providing an accurate time-series model basis for multi-scale coupled operations.

[0030] The core innovation of this embodiment lies in its temporal nonlinear dynamic reconstruction modeling architecture and evolutionary self-consistent coefficient quantification iterative algorithm, which is completely different from the existing static time-invariant fixed modeling mode. At the modeling level, it breaks through the limitations of idealized modeling with fixed parameters and constraints, and for the first time uses nonlinear evolution in the time dimension as the core modeling dimension. This enables the finite element model to dynamically and adaptively update with temperature, time sequence, and reaction progress, fully restoring the real physical evolution process of HBM's continuous and gradual bonding at varying temperatures. At the algorithm level, relying on the temporal evolution self-consistent calculation formula, it quantitatively controls the degree of temporal matching across multiple fields. Through dynamic weight iteration and nonlinear deviation directional correction, it continuously weakens the modeling misalignment problem caused by temporal evolution. It solves the defects of traditional static models in simulation distortion and parameter disconnection at multiple time stages from the root of numerical simulation, significantly improving the continuity and accuracy of the representation of the entire temperature-varying field evolution. The algorithm's temporal adaptability and the degree of modeling dynamism are completely upgraded.

[0031] Example 2

[0032] Specific steps

[0033] Step 1: Complete the global scale partitioning of HBM, distinguishing between the macroscopic computational domain of multi-layer chip stacks and the microscopic computational domain of micro-bump arrays, defining the boundary region between the two scales, and establishing the interface for the geometric relationship and physical parameter interaction between macroscopic and microscopic structures. Step 2: Construct a multi-scale bidirectional parameter mapping and transfer matrix, establishing the coupled relationship between the macroscopic overall equilibrium equation and the microscopic local stress equation, unifying the iterative calculation step size and convergence criteria of the two-scale equation system, and eliminating the rhythm differences in step-by-step solutions. Step 3: Activate the multi-scale collaborative equilibrium iterative solution algorithm, first completing the macroscopic stack overall deformation and stress basis solution, and synchronously transferring the macroscopic boundary loads and displacement constraints to the microscopic bump computational domain through the mapping matrix; then collecting microscopic local stress concentration and plastic deformation characteristics, and using backfeed to correct the macroscopic inter-layer constraint conditions. Step 4: Execute the multi-scale equilibrium convergence judgment mechanism throughout the process, dynamically adjusting the macroscopic and microscopic solution weight ratio, avoiding excessive deviation in single-scale solutions, continuously maintaining the balance and self-consistency of the dual-scale joint operation, and achieving accurate cross-scale integrated solution of the entire HBM domain.

[0034] Algorithm efficiency enhancement and modeling innovation principles

[0035] This embodiment focuses on multi-scale, cross-level coupled modeling and balanced collaborative iterative solution algorithms as its core innovations, addressing the industry shortcomings of traditional methods that separate macro- and micro-scale processes and decouple step-by-step solutions. At the modeling level, it constructs a dual-scale integrated coupled computational system, breaking down the parameter transfer barriers between macroscopic structures and microscopic interconnected units, and overcoming the limitation of single-scale modeling in failing to consider both overall and local features. At the algorithm level, it innovatively unifies multi-scale iterative logic, relying on a bidirectional mapping matrix to achieve closed-loop parameter feedback, coupled with a balanced convergence control mechanism, eliminating problems of imbalance and data disconnect between scales. It thoroughly improves the technical blind spots of traditional step-by-step computation, where macroscopic deformation cannot be accurately represented and microscopic defects cannot be fully characterized, allowing HBM bond simulation to simultaneously cover overall stacking stability and microscopic convex interconnect reliability, significantly enhancing the synergy and completeness of multi-scale solutions.

[0036] Example 3

[0037] Specific steps

[0038] Step 1: Independently monitor three core processes: temperature rise and fall response time, mechanical pressure holding and loading maintenance time, and interface metallurgical bonding reaction time. Compare the differences in time response, classify and identify three types of coupling deviation characteristics: heat transfer lag, load conduction lag, and physicochemical reaction lag, and establish a time lag characteristic database. Step 2: Build a quantitative model of time coupling lag deviation, abandoning the idealized assumption of time synchronization, calculate the degree of lag offset at different bonding stages, distinguish between fixed inherent lag and time-varying dynamic lag, and achieve refined identification and quantitative characterization of deviation types. Step 3: Call the time lag dynamic resolution operator, combine the real-time time evolution progress, adaptively calculate the time compensation amount and the coordinated adjustment amount, and adopt a composite operation logic combining time backtracking operation and advanced adjustment to replace the traditional fixed-delay coarse compensation method. Step 4: Link the multi-factor gradient weight allocation mechanism to synchronously coordinate the solution time sequence weights of the thermal field and the force field, gradually eliminate the temperature and pressure coupling misalignment deviation, ensure the time sequence synchronization of the metallurgical reaction progress and pressure bonding state at each interface of the multilayer chip, and suppress the gradual accumulation and amplification of time sequence deviation.

[0039] Algorithm efficiency enhancement and modeling innovation principles

[0040] This embodiment innovatively constructs a timing-coupled lag quantization modeling and dynamic resolution operator correction algorithm, filling the technical gap in refined calculation of timing dimension deviations in HBM temperature-bonding. At the modeling level, it breaks through the idealized constraints of instantaneous synchronization, incorporating multi-process timing misalignment and time lag effects into the numerical calculation system, aligning with the objective timing laws of actual equipment response, material conduction, and interface reaction. At the algorithm level, it abandons passive fixed delay compensation and adopts an active dynamic quantization calculation architecture. Through a composite algorithm logic of classification correction, timing backtracking, and adaptive compensation, it achieves precise resolution of lag deviations. It solves the core problems of temperature-pressure timing coupling imbalance and interlayer bonding asynchrony from the operational mechanism level, strengthens the multi-process collaborative matching capability, and ensures the consistency of multi-layer HBM stacking bonding processes.

[0041] Example 4

[0042] Specific steps

[0043] Step 1: Based on the differences in heat dissipation environment, tooling contact position, and thermal radiation intensity of each HBM stack layer, the multilayer structure is divided into boundary layers, distinguishing the differentiated temporal boundary characteristics of the top, middle, and bottom layers. Step 2: Following the evolution of temperature-dependent bonding, boundary operation parameters such as heat exchange coefficients, contact friction constraints, and interlayer displacement coordination conditions are iteratively updated layer by layer, employing a progressive boundary smoothing update logic to avoid solution oscillations caused by abrupt changes in boundary parameters. Step 3: Under long-term mass production conditions, the evolution characteristics of slow variables such as cavity thermal drift, tooling micro-deformation, and temporal aging of packaging materials are continuously identified, and the interference effects of slow variables on the temporal evolution model and multi-scale mapping relationships are analyzed. Step 4: Periodically closed-loop calibration of the coefficients of the temporal nonlinear evolution equation, multi-scale linkage mapping parameters, and hysteresis resolution operator baseline thresholds is performed, refreshing the global operation parameters of the modeling and algorithm, forming a self-consistent calibration closed loop for the entire temporal evolution process, ensuring a unified and stable solution standard for mass production.

[0044] Algorithm efficiency enhancement and modeling innovation principles

[0045] The core of this embodiment is a multi-layered temporal boundary hierarchical iterative modeling and a full-process steady-state self-consistent closed-loop calibration algorithm, adapted to high-order multi-layer HBM and industrial continuous mass production scenarios. At the modeling level, for the differentiated chemical conditions of multi-layer stacks, it achieves hierarchical and refined characterization of boundary conditions, upgrading from a uniform homogeneous boundary to a hierarchical dynamic temporal boundary, accurately matching the asynchronous evolution characteristics of multi-layer structures. At the algorithm level, it builds a long-term closed-loop calibration computation system to actively offset the modeling benchmark shift caused by slow variable drift during mass production, enabling the entire temporal evolution, multi-scale solution, and deviation correction algorithm to have self-adaptive and self-optimizing steady-state control capabilities. It maintains the accuracy and stability of multi-batch, multi-level HBM bond numerical solutions for a long time, significantly enhancing the algorithm's robustness and engineering adaptability.

[0046] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for HBM variable-temperature bonding nonlinear modeling and iterative equalization, characterized in that, Includes the following steps: S1. Collect full-time thermal and mechanical conditions and multi-layer structure deformation characteristic data of HBM temperature bonding, construct a time-series nonlinear field dynamic evolution finite element reconstruction model, and dynamically refresh physical property parameters and constraint conditions in time-series gradient intervals. S2. Construct a macro-micro multi-scale cross-level bidirectional mapping matrix, establish a dual-scale coupled simultaneous equation system, introduce a time-series nonlinear evolution self-consistent coefficient calculation formula, and perform multi-scale collaborative equilibrium iterative simultaneous solution. S3. Monitor the time-series differences between temperature-changing conditions and pressure-holding loads, quantify and calculate various types of time-series coupling lag deviations, and call the time-series lag dynamic resolution operator to achieve directional compensation and collaborative correction of temperature-pressure time-series coupling deviations; S4. Configure a multi-factor gradient weight adaptive allocation architecture for the time-series evolution field, dynamically adjust the multi-physics field solution weights according to the process stage, and ensure a smooth transition of the solution during the time-series switching stage; S5. For the HBM multi-layer stacked structure, establish a time-series boundary layer-by-layer iterative dynamic update mechanism to adapt to the differentiated requirements of the time-series evolution boundaries of each stacked layer; S6. Identify the drift characteristics of long-cycle slow-variable conditions in mass production, perform multi-scale evolution steady-state self-consistent closed-loop calibration, and globally refresh the modeling parameters and algorithm operation coefficients to achieve steady-state solution control of the entire HBM multi-layer temperature-changing bonding process; In step S1, the dynamic evolution finite element reconstruction model abandons static fixed parameter assignment and continuously iterates and updates the material mechanical and thermophysical nonlinear parameters with the temperature-changing time series.

2. The method according to claim 1, characterized in that: In step S2, the multi-scale equilibrium iterative solution unifies the iteration step size of the macroscopic and microscopic equations, and realizes bidirectional linkage feedback and joint convergence determination of dual-scale parameters.

3. The method according to claim 1, characterized in that: In step S3, the time lag dynamic resolution operator, combined with time backtracking operation and adaptive adjustment of lead amount, replaces the fixed delay coarse compensation mode.

4. The method according to claim 1, characterized in that: In step S4, the gradient weight allocation architecture sets weight smooth transition operation rules to suppress numerical oscillations during time sequence switching.

5. The method according to claim 1, characterized in that: In step S5, the layered timing boundary update independently adjusts the thermal boundary, mechanical boundary, and displacement constraint of each chip layer, taking into account both multi-layer differentiation and overall linkage.

6. The method according to claim 1, characterized in that: In step S6, the closed-loop calibration periodically corrects the reference operation parameters of the multi-scale mapping matrix, the time-series evolution equation, and the hysteresis correction operator.

7. A system for modeling and solving the HBM variable-temperature bonding temporal nonlinear coupled evolution and multi-scale iterative equilibrium, used to implement the method described in any one of claims 1 to 7, characterized in that, include: The system comprises four modules: a time-series global parameter acquisition module, a time-series nonlinear dynamic modeling module, a multi-scale cross-level equilibrium solution module, a time-series lag deviation correction module, a gradient weight allocation and boundary update module, and a global steady-state closed-loop calibration module. The time-series global parameter acquisition module is used to acquire characteristic data of multiple operating conditions and multi-layer structures under varying temperatures throughout the entire time series. The time-series nonlinear dynamic modeling module incorporates a self-consistent coefficient formula for time-series nonlinear evolution, enabling dynamic reconstruction of the finite element model over time. The multi-scale cross-level equilibrium solution module is used for bidirectional mapping between macro and micro scales, coupled simultaneous solution, and iterative equilibrium control. The time-series lag deviation correction module is equipped with a time-series deviation quantization model and a dynamic resolution operator. The gradient weight allocation and boundary update module is used for adaptive allocation of weights across multiple fields and iterative updating of multi-layer time-series boundaries. The global steady-state closed-loop calibration module is used for mass production condition drift identification and global self-consistent calibration of algorithm parameters.

8. The system according to claim 8, characterized in that: The time-series nonlinear dynamic modeling module has the functions of interval parameter iterative refresh and dynamic assignment of nonlinear correlation equations.

9. The system according to claim 8, characterized in that: The multi-scale cross-level equilibrium solution module stores a library of macro-micro coupled simultaneous equations and supports dual-scale linkage feedback and equilibrium convergence control.

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