Thermal management and signal integrity co-optimization method in three-dimensional package

Abstract

This invention provides a method for co-optimizing thermal management and signal integrity in 3D stacked packaging, relating to the field of 3D stacked packaging. The method involves acquiring heat source and signal path data, calculating the temperature field and heat flux density, identifying the intersections of thermal and electrical paths, and calculating time delay offsets. It then quantifies the thermal-electric coupling strength, filters out strong coupling locations, iteratively offsets the signal path along the vertical direction of the heat flux density gradient to weaken the coupling, and finally re-lays out the signal path and adjusts the vertical interconnects. This achieves the effect of simultaneously optimizing heat dissipation and signal integrity in 3D stacked packaging.

Description

Technical Field

[0001] This invention relates to three-dimensional stacked packaging technology, and more particularly to a method for co-optimizing thermal management and signal integrity in three-dimensional stacked packaging. Background Technology

[0002] 3D stacked packaging technology integrates multiple chips or functional layers into a single package through vertical interconnects, significantly improving system integration and performance. In this technological field, ensuring the reliable operation of high-density integrated systems requires addressing both the thermal management challenges arising from the dramatic increase in power density and the signal integrity issues encountered when transmitting high-speed signals through complex interconnect structures. Current conventional practices typically treat thermal management and signal integrity design as two relatively independent processes.

[0003] In terms of thermal management, conventional practices focus on reducing the overall temperature or hotspot temperature of the package by optimizing the heat dissipation structure, such as using thermal interface materials, integrated microchannels, or heat sinks. The core objective is to control the junction temperature to meet reliability requirements, and the analysis data relied upon is primarily steady-state or transient temperature field distribution. Regarding signal integrity, the design focus is on planning the topology of the signal transmission path, adjusting line width and spacing, optimizing termination matching, and shielding against interference. The analysis is based on electrical parameter models and electromagnetic simulations, aiming to control impedance continuity and reduce crosstalk and reflections. These two design flows are often performed sequentially or with only limited data exchange, such as evaluating the minor impact of heat distribution on conductor resistance after initial routing, or attempting to route around high-temperature areas in a fixed heat source layout.

[0004] This conventional separate design approach has inherent flaws. Because the design goals and constraints of the thermal and electrical domains differ, and the analysis models and optimization variables are independent, the design results are prone to getting trapped in local optima. Specifically, the heat dissipation paths and high heat flux density regions determined during the thermal design phase may spatially overlap or be closely adjacent to critical high-speed signal paths in the subsequent wiring phase. This physical proximity can trigger severe inter-domain coupling effects: on the one hand, the non-uniform temperature field generated by the nearby heat flow in the signal path's metal conductors changes its resistance and the dielectric constant of the surrounding medium, causing dynamic shifts in signal propagation delay and threatening timing convergence; on the other hand, current changes in the signal path may also generate additional Joule heating, slightly perturbing the local thermal field, but this feedback is often ignored in separate designs. Existing methods lack a systematic mechanism for quantitatively identifying and co-optimizing the "thermal-electrical" coupling strength. Relying solely on empirical spacing constraints or post-hoc corrections cannot fundamentally solve the performance and reliability risks caused by coupling effects such as thermally induced delay drift. Summary of the Invention

[0005] This invention provides a method for co-optimizing thermal management and signal integrity in three-dimensional stacked packaging, which can solve the problems in the prior art.

[0006] A first aspect of this invention provides a method for co-optimizing thermal management and signal integrity in a three-dimensional stacked package, comprising:

[0007] Acquire heat source distribution data and signal transmission path data of a three-dimensional stacked packaging structure;

[0008] Temperature field data is calculated based on heat source distribution data, and heat conduction paths are traced along the gradient direction of the temperature field data to calculate heat flux density values.

[0009] The locations where the distance between the heat conduction path and the signal transmission path is less than a preset distance threshold are selected as intersection locations. The heat flux density value of the intersection location is converted into the medium temperature rise rate, and the time delay offset is calculated based on the medium temperature rise rate.

[0010] Calculate the coupling strength between the time delay offset and the heat flux density value at the intersection, and select intersections with coupling strength exceeding a preset strength threshold as coupling positions;

[0011] Calculate the spatial gradient of the heat flux density at the coupling position, determine the vertical direction of the spatial gradient as the offset direction, adjust the position of the signal transmission path along the offset direction, recalculate the coupling strength, increase the adjustment amplitude until the coupling strength drops below the preset strength threshold, and record the adjustment amplitude as the target offset distance.

[0012] The signal transmission paths at the coupling positions are re-laid according to the target offset distance, and the positions of the vertical interconnect structures are adjusted to match the re-laid signal transmission paths.

[0013] The temperature field data is calculated based on the heat source distribution data. The heat conduction path is traced along the gradient direction of the temperature field data, and the heat flux density value is calculated, including:

[0014] The heat source distribution data is spatially discretized according to the interlayer interface of the packaging structure and the chip layout boundary. The heat source intensity distribution is marked on the discretized spatial nodes, and the temperature field data of the spatial grid nodes is calculated based on the heat source intensity distribution.

[0015] Spatial difference calculation is performed on the temperature field data to obtain the temperature gradient vector of each spatial node. Spatial nodes whose temperature gradient vector magnitude exceeds the preset gradient threshold are selected as candidate starting nodes. From the candidate starting nodes, the spatial node with the largest temperature field data value is selected as the heat conduction starting node.

[0016] Starting from the heat conduction initiation node, trace each node along the spatial direction pointed by the corresponding temperature gradient vector, record the sequence of spatial node coordinates traversed, and connect the spatial node coordinate sequences to form a heat conduction path.

[0017] Extract the temperature gradient vector corresponding to the coordinates of each spatial node on the heat conduction path and the thermal conductivity data of each layer of the encapsulation structure. Perform a dot product operation on the temperature gradient vector and the thermal conductivity data to obtain the heat flux density value of each spatial node on the heat conduction path.

[0018] Locations where the distance between the heat conduction path and the signal transmission path is less than a preset distance threshold are selected as intersection points. The heat flux density value at the intersection point is converted into the medium temperature rise rate. The time delay offset is calculated based on the medium temperature rise rate, including:

[0019] The heat conduction path and the signal transmission path are projected onto the same plane coordinate system of the package structure. The spatial distance between each spatial node on the heat conduction path and each wiring node on the signal transmission path is calculated. Spatial nodes and wiring node pairs with a spatial distance less than a preset distance threshold are selected as intersection positions.

[0020] Extract the heat flux density value corresponding to the intersection position, obtain the thermal response characteristic curve of the medium layer where the signal transmission path is located, map the heat flux density value to the thermal response characteristic curve to obtain the corresponding temperature rise response value, and perform time differentiation operation on the temperature rise response value to obtain the medium temperature rise rate at the intersection position.

[0021] The dielectric constant temperature dependence of the dielectric layer where the signal transmission path is located is obtained. The temperature rise rate of the dielectric at the intersection is substituted into the dielectric constant temperature dependence to calculate the change in dielectric constant. The change in signal propagation speed is calculated based on the change in dielectric constant. The change in signal propagation speed is combined with the length of the signal transmission path to calculate the time delay offset.

[0022] The coupling strength between the time delay offset and the heat flux density value at the intersection is calculated, and intersections with coupling strength exceeding a preset strength threshold are selected as coupling locations, including:

[0023] Extract the time delay offset and heat flux density value at the intersection to obtain the global distribution data of the time delay offset and heat flux density value in the packaging structure;

[0024] Based on the global distribution data, the normalized intervals of the time delay offset and the heat flux density value are determined. The time delay offset is mapped to the normalized interval to obtain the normalized time delay offset, and the heat flux density value is mapped to the normalized interval to obtain the normalized heat flux density value.

[0025] Obtain the timing constraints and heat dissipation performance constraints of the signal transmission path, determine the delay influence weighting coefficient based on the timing constraints, and determine the heat flow influence weighting coefficient based on the heat dissipation performance constraints;

[0026] The time delay contribution component is obtained by weighting the normalized time delay offset with the time delay influence weighting coefficient. The heat flux contribution component is obtained by weighting the normalized heat flux density value with the heat flux influence weighting coefficient. The coupling strength at the intersection position is obtained by fusing the time delay contribution component and the heat flux contribution component.

[0027] Calculate the spatial gradient of heat flux density at the coupling location, determine the vertical direction of the spatial gradient as the offset direction, adjust the signal transmission path position along the offset direction, recalculate the coupling strength, and increase the adjustment amplitude until the coupling strength drops below a preset strength threshold. Record the adjustment amplitude as the target offset distance.

[0028] Extract the heat flux density value at the coupling location, calculate the spatial gradient of the heat flux density value, perform orthogonal decomposition on the spatial gradient to obtain the vertical direction of the spatial gradient, and determine the vertical direction of the spatial gradient as the offset direction.

[0029] Based on the movable space boundary of the signal transmission path detected by the offset direction, the upper limit of the adjustment range is determined according to the movable space boundary;

[0030] Set an initial value for the adjustment amplitude, adjust the signal transmission path of the coupling position along the offset direction based on the initial value for the adjustment amplitude, extract the heat flux density value of the coupling position after adjustment, calculate the time delay offset based on the heat flux density value of the coupling position after adjustment, and calculate the adjusted coupling strength based on the time delay offset and the heat flux density value of the coupling position after adjustment.

[0031] Determine whether the adjusted coupling strength drops below the preset strength threshold. When the adjusted coupling strength drops below the preset strength threshold, record the initial value of the adjustment range as the target offset distance.

[0032] If the adjusted coupling strength does not drop below the preset strength threshold, determine whether the initial value of the adjustment amplitude is less than the upper limit of the adjustment amplitude. If the initial value of the adjustment amplitude is less than the upper limit of the adjustment amplitude, increase the initial value of the adjustment amplitude and return the signal transmission path that adjusts the coupling position along the offset direction based on the initial value of the adjustment amplitude. Stop the adjustment when the initial value of the adjustment amplitude reaches the upper limit of the adjustment amplitude.

[0033] Based on the movable space boundary of the offset direction detection signal transmission path, the upper limit of the adjustment range is determined according to the movable space boundary, including:

[0034] A ray is projected from the coupling position along the offset direction. The intersection of the ray with the interlayer interface of the package structure and the intersection of the ray with the chip layout boundary are detected. The spatial distance from the coupling position to the intersection of the interlayer interface and the spatial distance from the coupling position to the intersection of the chip layout boundary are calculated.

[0035] Compare the spatial distance from the coupling location to the intersection of the interlayer interface with the spatial distance from the coupling location to the intersection of the chip layout boundary, and select the minimum value of the spatial distance as the movable spatial boundary.

[0036] Extract the minimum wiring spacing of the encapsulation layer where the signal transmission path is located, subtract the minimum wiring spacing from the movable space boundary to obtain the allowable adjustment distance, and determine the allowable adjustment distance as the upper limit of the adjustment range.

[0037] The signal transmission paths at the coupling locations are redeployed according to the target offset distance, and the positions of the vertical interconnect structures are adjusted to match the redeployed signal transmission paths, including:

[0038] Obtain the original starting point coordinates and original ending point coordinates of the signal transmission path at the coupling position. Calculate the offset of the original starting point coordinates and the offset of the original ending point coordinates based on the target offset distance and offset direction. Add the offset to the original starting point coordinates to obtain the new starting point coordinates. Add the offset to the original ending point coordinates to obtain the new ending point coordinates.

[0039] Based on the new starting point coordinates and the new ending point coordinates, the signal transmission path of the coupling position is re-arranged, and the connection node position between the re-arranged signal transmission path and the vertical interconnection structure is extracted.

[0040] Calculate the coordinate deviation between the location of the connection node and the current location of the vertical interconnect structure, and adjust the spatial position of the vertical interconnect structure in the package structure based on the coordinate deviation, so that the adjusted vertical interconnect structure and the re-laid signal transmission path form an electrical connection at the connection node location.

[0041] A second aspect of the present invention provides an electronic device, comprising:

[0042] processor;

[0043] Memory used to store processor-executable instructions;

[0044] The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0045] A third aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0046] In this embodiment, by acquiring heat source distribution and signal path data, and calculating the temperature field and heat conduction path, accurate modeling of the internal thermal environment of the package is achieved. Based on the heat flux density, the medium temperature rise rate and time delay offset are calculated, enabling quantitative assessment of the strength of the thermal-electric coupling effect at specific locations and automatically identifying critical coupling locations where thermal and signal interference is severe. This method avoids the blindness of relying on experience or global uniform adjustments, allowing optimization resources to be precisely focused on the most problematic areas, significantly improving optimization efficiency. The offset direction of the signal path is determined based on the spatial gradient of the heat flux density at the coupling location, ensuring the physical rationality of the adjustment direction, i.e., keeping the signal path as far away as possible from areas of drastic heat flux changes. The signal transmission path is dynamically adjusted along the determined offset direction, and iterative calculations ensure that the coupling strength is reduced to below an acceptable threshold, achieving active suppression of thermal-electric coupling interference. This process directly correlates and synchronously optimizes the thermal management target and the signal integrity target. The signal path is redeployed according to the finally determined target offset distance, and the vertical interconnect structure is adjusted synchronously, ensuring the feasibility of design changes. The final thermal-electric co-design scheme is physically self-consistent and manufacturable. Attached Figure Description

[0047] Figure 1 This is a flowchart illustrating the method for coordinated optimization of thermal management and signal integrity in a three-dimensional stacked package according to an embodiment of the present invention.

[0048] Figure 2 This is a flowchart illustrating the signal transmission path adjustment logic of an embodiment of the present invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] The technical solution of the present invention will be described in detail below with reference to specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0051] Figure 1 This is a flowchart illustrating the method for coordinated optimization of thermal management and signal integrity in a three-dimensional stacked package according to an embodiment of the present invention. Figure 1 As shown, the method includes:

[0052] Acquire heat source distribution data and signal transmission path data of a three-dimensional stacked packaging structure;

[0053] Temperature field data is calculated based on heat source distribution data, and heat conduction paths are traced along the gradient direction of the temperature field data to calculate heat flux density values.

[0054] The locations where the distance between the heat conduction path and the signal transmission path is less than a preset distance threshold are selected as intersection locations. The heat flux density value of the intersection location is converted into the medium temperature rise rate, and the time delay offset is calculated based on the medium temperature rise rate.

[0055] Calculate the coupling strength between the time delay offset and the heat flux density value at the intersection, and select intersections with coupling strength exceeding a preset strength threshold as coupling positions;

[0056] Calculate the spatial gradient of the heat flux density at the coupling position, determine the vertical direction of the spatial gradient as the offset direction, adjust the position of the signal transmission path along the offset direction, recalculate the coupling strength, increase the adjustment amplitude until the coupling strength drops below the preset strength threshold, and record the adjustment amplitude as the target offset distance.

[0057] The signal transmission paths at the coupling positions are re-laid according to the target offset distance, and the positions of the vertical interconnect structures are adjusted to match the re-laid signal transmission paths.

[0058] The temperature field data is calculated based on the heat source distribution data. The heat conduction path is traced along the gradient direction of the temperature field data, and the heat flux density value is calculated, including:

[0059] The heat source distribution data is spatially discretized according to the interlayer interface of the packaging structure and the chip layout boundary. The heat source intensity distribution is marked on the discretized spatial nodes, and the temperature field data of the spatial grid nodes is calculated based on the heat source intensity distribution.

[0060] Spatial difference calculation is performed on the temperature field data to obtain the temperature gradient vector of each spatial node. Spatial nodes whose temperature gradient vector magnitude exceeds the preset gradient threshold are selected as candidate starting nodes. From the candidate starting nodes, the spatial node with the largest temperature field data value is selected as the heat conduction starting node.

[0061] Starting from the heat conduction initiation node, trace each node along the spatial direction pointed by the corresponding temperature gradient vector, record the sequence of spatial node coordinates traversed, and connect the spatial node coordinate sequences to form a heat conduction path.

[0062] Extract the temperature gradient vector corresponding to the coordinates of each spatial node on the heat conduction path and the thermal conductivity data of each layer of the encapsulation structure. Perform a dot product operation on the temperature gradient vector and the thermal conductivity data to obtain the heat flux density value of each spatial node on the heat conduction path.

[0063] After acquiring the heat source distribution data of the three-dimensional stacked package structure, it needs to be spatially discretized. The package structure typically contains multiple functional layers, such as heat dissipation layers, chip layers, and interconnect layers, with clearly defined interface boundaries between each layer. These interface boundaries are then meshed to generate three-dimensional spatial mesh nodes. Meshing can use hexahedral or tetrahedral elements; the size of the mesh elements depends on the required accuracy and computational resources, typically ranging from μm to mm. On the discretized spatial mesh nodes, the heat source intensity distribution value corresponding to each node is labeled. The heat source intensity is usually expressed as the heat power density per unit volume, with units of W / m³. 3 .

[0064] Based on the labeled heat source intensity distribution, the temperature field data within the entire encapsulation structure is calculated using the heat conduction equation. The heat conduction equation can be expressed as the divergence of the product of thermal conductivity and temperature gradient equal to the sum of the products of heat source density and specific heat capacity, density, temperature, and time derivatives. For steady-state analysis, the temperature field calculation can be simplified to solving the Laplace equation. During the solution process, appropriate boundary conditions need to be set at the encapsulation boundary, such as isothermal, adiabatic, or convective boundary conditions. The heat conduction equation is discretized using numerical methods such as the finite difference method, finite element method, or finite volume method, ultimately obtaining the temperature value of each spatial grid node in the encapsulation structure, forming complete three-dimensional temperature field data.

[0065] After obtaining the temperature field data, spatial difference calculations are performed to obtain the temperature gradient vectors of each spatial node. For a temperature field T(x, y, z) in three-dimensional space, its temperature gradient vector is ∇T = (∂T / ∂x, ∂T / ∂y, ∂T / ∂z). In practical calculations, the central difference scheme can be used to calculate the temperature partial derivatives in each direction. After the calculation is completed, spatial nodes whose temperature gradient vector magnitude exceeds a preset gradient threshold are selected as candidate starting nodes. The preset gradient threshold can be selected based on thermal management design requirements, usually taking a certain proportion of the maximum temperature gradient value, such as 20% to 30%. From the candidate starting nodes that meet the gradient threshold condition, the spatial node with the largest temperature field data value is selected as the heat conduction starting node. This node is usually located in the main heat source region.

[0066] Starting from a determined heat conduction initiation node, the system traces node by node along the spatial direction pointed to by the corresponding temperature gradient vector. The temperature gradient vector points in the direction of the fastest temperature decrease, opposite to the direction of heat flow. The tracing process is implemented iteratively: the temperature gradient vector of the current node determines the next search direction, and the nearest grid node in that direction is selected as the next tracing point. If there are multiple candidate nodes for the next step, the node with the lowest temperature value is selected to continue tracing. During the tracing process, the coordinates of all spatial nodes traversed are recorded, forming a node coordinate sequence. The tracing process terminates when the encapsulation boundary is reached or the temperature gradient value is less than the termination threshold. The recorded node coordinate sequence is connected by line segments to form a complete heat conduction path.

[0067] To calculate the heat flux density along the heat conduction path, it is necessary to extract the temperature gradient vector data corresponding to the coordinates of each spatial node along the path, and simultaneously obtain the thermal conductivity data of each layer of the encapsulation structure. Different material layers in the encapsulation structure have different thermal conductivities; the thermal conductivity of silicon is approximately 149 W / (m·K), while that of polymer materials is only 0.1-0.3 W / (m·K). According to Fourier's law of heat conduction, heat flux density equals the product of thermal conductivity and the negative temperature gradient, i.e., q = -k∇T, where k is the thermal conductivity and ∇T is the temperature gradient. For each node along the heat conduction path, based on the thermal conductivity value of its material layer, the temperature gradient vector of that node is multiplied by the corresponding thermal conductivity, i.e., k·|∇T|·cos(0°) = k·|∇T|, to obtain the heat flux density value of that node, in W / m². 2 In this way, a series of heat flux density values ​​can be obtained along the entire heat conduction path, reflecting the intensity distribution of heat transfer.

[0068] The heat conduction path and heat flux density data obtained through the above methods can intuitively present the main channels of heat conduction and the distribution of heat flux intensity in the packaging structure. This enables precise tracking and quantification of the heat conduction process in a three-dimensional stacked packaging structure, providing a basis for subsequent packaging design optimization. The visualization of the heat conduction path shows the actual path of heat flow from the high-temperature region to the low-temperature region, helping to identify heat conduction bottleneck areas, while the heat flux density values ​​quantify the heat conduction efficiency of each path node.

[0069] Locations where the distance between the heat conduction path and the signal transmission path is less than a preset distance threshold are selected as intersection points. The heat flux density value at the intersection point is converted into the medium temperature rise rate. The time delay offset is calculated based on the medium temperature rise rate, including:

[0070] The heat conduction path and the signal transmission path are projected onto the same plane coordinate system of the package structure. The spatial distance between each spatial node on the heat conduction path and each wiring node on the signal transmission path is calculated. Spatial nodes and wiring node pairs with a spatial distance less than a preset distance threshold are selected as intersection positions.

[0071] Extract the heat flux density value corresponding to the intersection position, obtain the thermal response characteristic curve of the medium layer where the signal transmission path is located, map the heat flux density value to the thermal response characteristic curve to obtain the corresponding temperature rise response value, and perform time differentiation operation on the temperature rise response value to obtain the medium temperature rise rate at the intersection position.

[0072] The dielectric constant temperature dependence of the dielectric layer where the signal transmission path is located is obtained. The temperature rise rate of the dielectric at the intersection is substituted into the dielectric constant temperature dependence to calculate the change in dielectric constant. The change in signal propagation speed is calculated based on the change in dielectric constant. The change in signal propagation speed is combined with the length of the signal transmission path to calculate the time delay offset.

[0073] When detecting intersections, the obtained heat conduction paths and signal transmission paths need to be projected onto the same plane coordinate system of the package structure. The heat conduction path typically consists of a series of three-dimensional spatial node coordinates, while the signal transmission path is represented by a sequence of wiring node coordinates in the wiring layer. The projection process can use orthogonal projection to map the three-dimensional coordinates (x, y, z) to a two-dimensional plane (x, y). For multi-layer wiring structures, a specific reference plane can be selected, or projection analysis can be performed separately for each layer of wiring. After projection, the spatial distance between each spatial node on the heat conduction path and each wiring node on the signal transmission path is calculated. The spatial distance is calculated using the Euclidean distance formula. For two points P1(x1, y1, z1) and P2(x2, y2, z2) in three-dimensional space, the spatial distance is [(x1-x2) / ... 2 +(y1-y2) 2 +(z1-z2) 2 ] 1 / 2 .

[0074] Based on the calculated spatial distance, a preset distance threshold is set to determine whether the heat conduction path and the signal transmission path intersect. The selection of the preset distance threshold depends on the size of the package structure and the thermally affected area; a typical value can be set to 1-3 times the signal line width, and in three-dimensional stacked packages, it is usually tens to hundreds of μm. The spatial distances of all node pairs are compared, and spatial nodes and wiring node pairs with spatial distances less than the preset distance threshold are selected. The locations of these node pairs are the intersections of the heat conduction path and the signal transmission path. The intersection location is a critical area where heat conduction affects signal transmission, and its thermoelectric coupling effect needs to be analyzed in detail.

[0075] For each selected intersection, its corresponding heat flux density value is extracted. The heat flux density value reflects the heat conduction intensity at that location, with units of W / m². Simultaneously, the thermal response characteristic curve of the dielectric layer containing the signal transmission path is obtained. The thermal response characteristic curve describes the temperature response change of the dielectric material under different heat flux density inputs and can be obtained through experimental measurements or theoretical models. Typical dielectric materials such as FR-4 and polyimide have different thermal response characteristics. The heat flux density values ​​at the intersections are mapped to the thermal response characteristic curves to obtain the corresponding temperature rise response values. The temperature rise response value represents the temperature increase of the dielectric material after a specific time at a given heat flux density, with units of K.

[0076] After obtaining the temperature rise response value, a time differential operation is performed to calculate the temperature rise rate of the medium at the intersection. The time differential can be implemented using the finite difference method, i.e., ΔT / Δt, where ΔT is the change in temperature rise value and Δt is the corresponding time interval. The temperature rise rate reflects how quickly the medium temperature changes at the intersection, and its unit is K / s. The temperature rise rate is a key parameter for analyzing thermoelectric coupling effects and directly affects the dynamic changes in signal transmission characteristics. In high-speed signal transmission, even a small temperature rise rate can lead to significant fluctuations in signal delay.

[0077] Next, the temperature dependence of the dielectric constant of the dielectric layer in the signal transmission path is obtained. The dielectric constant of the dielectric material changes with temperature, and this dependence can usually be expressed as ε. r (T)=ε r0 [1+α e [(T-T0)], where ε r (T) is the dielectric constant at temperature T, ε r0 Let α be the dielectric constant at the reference temperature T0. e The temperature coefficient of dielectric constant is given. Different dielectric materials have different temperature coefficients; for example, the temperature coefficient of FR-4 is approximately several hundred ppm / K. Substituting the temperature rise rate of the dielectric at the intersection into the temperature dependence of the dielectric constant, the change in dielectric constant Δε per unit time is calculated. r / Δt.

[0078] Changes in dielectric constant directly affect the signal propagation speed in a transmission line. The relationship between signal propagation speed v and dielectric constant εᵣ is v = c / (εᵣ). r ) 1 / 2 Where c is the speed of light in a vacuum. Based on the change in dielectric constant, the change in signal propagation speed Δv is calculated. For small changes in dielectric constant, it can be approximated as Δv / v = -0.5·Δε r / ε r After obtaining the change in signal propagation speed, it is combined with the signal transmission path length L to calculate the time delay offset ΔtD = L·Δv / v2 Delay offset represents the change in signal transmission delay due to thermal effects, measured in seconds. In high-speed signal transmission, delay offset can lead to timing violations or signal integrity issues.

[0079] For signal transmission paths with multiple intersections, the time delay offset caused by each intersection needs to be calculated cumulatively to obtain the total time delay offset effect. Simultaneously, the intersections can be prioritized based on the magnitude of the time delay offset to identify the critical regions where thermoelectric coupling effects are most significant, providing a basis for subsequent optimization design.

[0080] This invention achieves precise quantification of the synergistic relationship between thermal management and signal integrity by screening the intersections of heat conduction paths and signal transmission paths and calculating the time delay offset caused by heat flux density. This technical solution establishes a direct mapping relationship between heat flux density and signal delay variation, revealing the thermoelectric coupling mechanism and providing a theoretical basis for the coordinated optimization of thermal and signal transmission in 3D stacked packaging. By identifying key intersection locations and predicting time delay offsets, designers can specifically optimize wiring layouts, adjust heat dissipation structures, or select appropriate dielectric materials to reduce the adverse effects of thermal effects on signal transmission. This method not only improves the accuracy of signal integrity analysis but also provides a quantitative basis for the trade-off design between thermal management and signal integrity, enabling optimal thermal performance while ensuring signal quality, effectively improving the overall reliability and performance stability of 3D stacked packaging.

[0081] The coupling strength between the time delay offset and the heat flux density value at the intersection is calculated, and intersections with coupling strength exceeding a preset strength threshold are selected as coupling locations, including:

[0082] Extract the time delay offset and heat flux density value at the intersection to obtain the global distribution data of the time delay offset and heat flux density value in the packaging structure;

[0083] Based on the global distribution data, the normalized intervals of the time delay offset and the heat flux density value are determined. The time delay offset is mapped to the normalized interval to obtain the normalized time delay offset, and the heat flux density value is mapped to the normalized interval to obtain the normalized heat flux density value.

[0084] Obtain the timing constraints and heat dissipation performance constraints of the signal transmission path, determine the delay influence weighting coefficient based on the timing constraints, and determine the heat flow influence weighting coefficient based on the heat dissipation performance constraints;

[0085] The time delay contribution component is obtained by weighting the normalized time delay offset with the time delay influence weighting coefficient. The heat flux contribution component is obtained by weighting the normalized heat flux density value with the heat flux influence weighting coefficient. The coupling strength at the intersection position is obtained by fusing the time delay contribution component and the heat flux contribution component.

[0086] In a three-dimensional stacked packaging structure, the spatial proximity of the heat conduction path and the signal transmission path can cause the temperature field to interfere with the signal timing characteristics. To accurately quantify the intensity of this interference, a computational model of the coupling strength needs to be established.

[0087] For the intersections of known heat conduction paths and signal transmission paths, the corresponding time delay offsets and heat flux density values ​​are extracted. The time delay offset represents the change in signal transmission delay caused by thermal effects, and the heat flux density reflects the intensity of heat conduction at the intersection. During the extraction process, the spatial coordinates and corresponding parameter values ​​of each intersection are recorded, forming a spatial distribution dataset of time delay offsets and heat flux density values. For three-dimensional stacked packages integrating multiple chips, the intersections are usually located in areas where signal transmission vertically traverses multiple layers of the structure, where strong heat conduction often occurs simultaneously. After collecting parameter data for all intersections in the package structure, a global distribution database containing location information, time delay offsets, and heat flux density values ​​is established to provide a data foundation for subsequent analysis.

[0088] Based on the acquired global distribution data, the normalization intervals for time delay offset and heat flux density values ​​are determined. Normalization eliminates dimensional differences between different physical quantities, making the parameters comparable. The normalization interval is set to [0, 1], mapping all parameters to a uniform scale. Normalization is performed on the time delay offset using the formula: Normalized Time Delay Offset = (Original Time Delay Offset - Minimum Time Delay Offset) / (Maximum Time Delay Offset - Minimum Time Delay Offset). The heat flux density values ​​are normalized using the same method: Normalized Heat Flux Density = (Original Heat Flux Density - Minimum Heat Flux Density) / (Maximum Heat Flux Density - Minimum Heat Flux Density). Through normalization, parameters of different magnitudes and units are converted into dimensionless relative values, facilitating a comprehensive assessment of their impact.

[0089] Obtain the timing and thermal performance constraints of the signal transmission path. Timing constraints include parameters such as the maximum allowable delay, clock frequency, and setup time margin, reflecting the design's requirements for timing accuracy. Thermal performance constraints include parameters such as the maximum allowable operating temperature, temperature gradient limits, and upper limits for heat flux density, reflecting the design's requirements for thermal management. Determine the delay impact weighting coefficient based on the timing constraints, using the formula: Delay Impact Weighting Coefficient = Delay Offset / Maximum Allowable Delay Offset. When the delay offset approaches the maximum allowable value, the weighting coefficient approaches 1, indicating that the delay impact is extremely critical.

[0090] The weighting coefficient for the influence of heat flux is determined based on the heat dissipation performance constraints. The calculation formula is: Heat flux influence weighting coefficient = Heat flux density / Maximum allowable heat flux density. When the heat flux density is close to the maximum allowable value, the weighting coefficient approaches 1, indicating that the influence of heat flux is extremely critical. The value range of the weighting coefficient is [0, 1], and the larger the value, the more significant the impact of the corresponding parameter on system performance. The determination of the weighting coefficient needs to consider the specific working environment and application scenario. For high-speed signal processing circuits, the weighting of the delay influence can be appropriately increased, while for high-power circuits, the weighting of the heat flux influence needs to be increased.

[0091] The normalized time delay offset is weighted by a time delay influence weighting coefficient to obtain the time delay contribution component. The weighting is calculated using a product: Time Delay Contribution Component = Normalized Time Delay Offset × Time Delay Influence Weighting Coefficient. The time delay contribution component characterizes the actual impact of the time delay offset considering timing constraints. Similarly, the normalized heat flux density value is weighted by a heat flux influence weighting coefficient: Heat Flux Contribution Component = Normalized Heat Flux Density Value × Heat Flux Influence Weighting Coefficient. The heat flux contribution component characterizes the actual impact of the heat flux density considering heat dissipation constraints.

[0092] The coupling strength at the intersection point is calculated by fusing the time delay contribution component and the heat flow contribution component. The fusing operation can be performed using a linear weighted method: Coupling Strength = Time Delay Contribution Component + Heat Flow Contribution Component. Alternatively, the square root method can be used, which better reflects the combined influence of the two factors. For specific design requirements, the weighting coefficients in the fusing formula can be adjusted to strengthen the influence of time delay or heat flow. The coupling strength ranges from [0, 2], with larger values ​​indicating stronger coupling effects between heat conduction and signal transmission, requiring priority optimization.

[0093] Based on the calculated coupling strength, a heat map of the coupling strength distribution in the package structure can be plotted, visually displaying the critical areas of thermal signal coupling. This coupling strength distribution heat map can be used to identify the locations where thermal management and signal integrity conflicts most severely, providing guidance for subsequent optimization designs. For areas with high coupling strength, measures such as adjusting signal routing paths, optimizing heat conduction paths, adding thermal shielding layers, or selecting materials with low thermal sensitivity can be taken to reduce the thermal signal coupling effect.

[0094] This invention overcomes the limitation of independent thermoelectric analysis in traditional methods by normalizing and fusing key parameters of thermal management and signal integrity. By introducing weighting coefficients for timing and heat dissipation constraints, the coupling strength assessment results better reflect actual engineering needs. Based on coupling strength analysis, designers can accurately identify key areas of thermal-signal coupling, adjust design parameters accordingly, achieve a balanced optimization of thermal management and signal integrity, improve the overall performance and reliability of 3D stacked packaging, and simultaneously shorten the design cycle and reduce design costs.

[0095] like Figure 2 As shown, Figure 2 This is a flowchart illustrating the signal transmission path adjustment logic of an embodiment of the present invention.

[0096] Calculate the spatial gradient of heat flux density at the coupling location, determine the vertical direction of the spatial gradient as the offset direction, adjust the signal transmission path position along the offset direction, recalculate the coupling strength, and increase the adjustment amplitude until the coupling strength drops below a preset strength threshold. Record the adjustment amplitude as the target offset distance.

[0097] Extract the heat flux density value at the coupling location, calculate the spatial gradient of the heat flux density value, perform orthogonal decomposition on the spatial gradient to obtain the vertical direction of the spatial gradient, and determine the vertical direction of the spatial gradient as the offset direction.

[0098] Based on the movable space boundary of the signal transmission path detected by the offset direction, the upper limit of the adjustment range is determined according to the movable space boundary;

[0099] Set an initial value for the adjustment amplitude, adjust the signal transmission path of the coupling position along the offset direction based on the initial value for the adjustment amplitude, extract the heat flux density value of the coupling position after adjustment, calculate the time delay offset based on the heat flux density value of the coupling position after adjustment, and calculate the adjusted coupling strength based on the time delay offset and the heat flux density value of the coupling position after adjustment.

[0100] Determine whether the adjusted coupling strength drops below the preset strength threshold. When the adjusted coupling strength drops below the preset strength threshold, record the initial value of the adjustment range as the target offset distance.

[0101] If the adjusted coupling strength does not drop below the preset strength threshold, determine whether the initial value of the adjustment amplitude is less than the upper limit of the adjustment amplitude. If the initial value of the adjustment amplitude is less than the upper limit of the adjustment amplitude, increase the initial value of the adjustment amplitude and return the signal transmission path that adjusts the coupling position along the offset direction based on the initial value of the adjustment amplitude. Stop the adjustment when the initial value of the adjustment amplitude reaches the upper limit of the adjustment amplitude.

[0102] For a given coupling location, the heat flux density value at that location is extracted. Based on the extracted heat flux density value, its spatial gradient is calculated. The spatial gradient of heat flux density represents the rate of change of heat flux density in three-dimensional space; it is a three-dimensional vector pointing in the direction of the fastest increase in heat flux density. The spatial gradient is calculated using the central difference method. For a heat flux density value q(x, y, z) at a point (x, y, z) in three-dimensional space, its spatial gradient ∇q can be expressed as: ∇q = (∂q / ∂x, ∂q / ∂y, ∂q / ∂z). Here, ∂q / ∂x, ∂q / ∂y, and ∂q / ∂z are the partial derivatives of the heat flux density in the x, y, and z directions, respectively, which can be approximated using the finite difference method.

[0103] The calculated spatial gradient is orthogonally decomposed to obtain its perpendicular direction. Orthogonal decomposition requires first determining the direction vector of the signal transmission path. For two adjacent points P1 and P2 on the signal transmission path, their direction vector m... p =P2-P1. The spatial gradient of heat flux density ∇q is decomposed into a component ∇q1 parallel to the signal transmission path and a component ∇q2 perpendicular to the signal transmission path. The formula for calculating the perpendicular component is: ∇q2=∇q-(∇q·m p )m p / |m p | 2 , where |m p | represents the direction vector m p The modulus length is determined. The vertical direction of the spatial gradient is defined as the offset direction, i.e., the direction of signal transmission path adjustment. The vertical direction ensures minimal change in path length during path adjustment and effectively reduces the impact of heat flux density.

[0104] Based on a defined offset direction, the movable spatial boundary of the signal transmission path is detected. This movable spatial boundary depends on the physical constraints of the package structure, including chip boundaries, wiring forbidden areas, and the positions of other signal lines. The detection method utilizes ray tracing technology, emitting a ray from the coupling position along the offset direction until it encounters a physical constraint boundary. The distance from the coupling position to the boundary is recorded as the movable distance, and an upper limit for the adjustment range is determined based on this movable distance. This upper limit is set to 80%-90% of the movable distance, leaving a certain safety margin.

[0105] Set an initial adjustment range, which can be 10%-20% of the upper limit of the adjustment range. Adjust the signal transmission path at the coupling position along the offset direction based on the initial adjustment range. The adjustment method involves shifting a segment of the signal transmission path near the coupling position along the offset direction by the adjustment range. The shift range can be determined based on the coupling influence area, typically a path segment 3-5 grid cells long before and after the coupling position. After adjustment, extract the heat flux density value at the new position; this value should be lower than the heat flux density value at the original coupling position. Calculate the time delay offset based on the heat flux density value at the adjusted position. The time delay offset calculation needs to consider the temperature rise of the medium caused by the heat flux density, as well as the changes in dielectric constant and signal propagation speed caused by the temperature rise. Based on the calculated time delay offset and the heat flux density value at the adjusted position, calculate the adjusted coupling strength using the aforementioned coupling strength calculation method.

[0106] The system determines whether the adjusted coupling strength has decreased below a preset strength threshold. This threshold is typically set at 50%-70% of the original coupling strength, meaning the coupling strength needs to be reduced to approximately half of its original level to be considered effective optimization. When the adjusted coupling strength falls below the preset threshold, the current adjustment magnitude is recorded as the target offset distance, completing the optimization adjustment for that coupling position. The target offset distance represents the minimum distance the signal transmission path needs to be adjusted to meet the requirement of reducing coupling strength, helping to minimize interference with the original path.

[0107] If the adjusted coupling strength does not drop below the preset strength threshold, determine if the current adjustment range is less than the upper limit. If the adjustment range is less than the upper limit, increase the adjustment range. The adjustment range can be increased linearly or exponentially. Linear increase increases the range by a fixed step size each time, such as increasing it by 50% of the initial adjustment range; exponential increase increases the adjustment range by a certain multiple each time, such as increasing it by 1.5 times. After increasing the adjustment range, return to the previous adjustment steps, readjust the signal transmission path, and calculate the coupling strength. Iterate and increase the adjustment range until the coupling strength drops below the preset threshold or the adjustment range reaches the upper limit. Stop adjusting when the adjustment range reaches the upper limit, indicating that the expected reduction in coupling strength cannot be achieved by adjusting the path under the current constraints, and other optimization schemes need to be considered.

[0108] If the coupling strength is not reduced even after the adjustment reaches its upper limit, alternative solutions can be considered, such as changing the offset direction, adjusting to a longer path segment, using thermal shielding materials, or changing the signal layer design. After optimizing all coupling positions, the integrity of the overall signal network should be verified to ensure that the adjusted signal path meets timing and integrity requirements.

[0109] This invention determines the optimal adjustment direction of the signal path by calculating the spatial gradient of heat flux density and uses an iterative optimization method to determine the minimum adjustment range, achieving precise synergistic optimization of thermal management and signal integrity. Targeted optimization of key signals in 3D stacked packaging significantly improves signal quality and system reliability, and extends package lifespan.

[0110] Based on the movable space boundary of the offset direction detection signal transmission path, the upper limit of the adjustment range is determined according to the movable space boundary, including:

[0111] A ray is projected from the coupling position along the offset direction. The intersection of the ray with the interlayer interface of the package structure and the intersection of the ray with the chip layout boundary are detected. The spatial distance from the coupling position to the intersection of the interlayer interface and the spatial distance from the coupling position to the intersection of the chip layout boundary are calculated.

[0112] Compare the spatial distance from the coupling location to the intersection of the interlayer interface with the spatial distance from the coupling location to the intersection of the chip layout boundary, and select the minimum value of the spatial distance as the movable spatial boundary.

[0113] Extract the minimum wiring spacing of the encapsulation layer where the signal transmission path is located, subtract the minimum wiring spacing from the movable space boundary to obtain the allowable adjustment distance, and determine the allowable adjustment distance as the upper limit of the adjustment range.

[0114] Ray projection along the offset direction from the coupling location is used to detect physical boundaries that may limit signal path adjustment. Ray projection can be represented using parameterized equations, extending along a normalized offset direction vector starting from the coupling location. In three-dimensional stacked package structures, there are two main types of physical boundaries: interlayer interfaces and chip layout boundaries. Interlayer interfaces refer to the interfaces between different functional layers, such as the interfaces between the substrate layer and the chip layer, between adjacent chip layers, and between a chip layer and a heat dissipation layer. These interfaces can typically be described by planar equations, and multiple such interfaces may exist in a real package structure. Chip layout boundaries refer to the edges of individual chips within the package and the boundaries of reserved areas; these boundaries constitute physical barriers that signal routing cannot cross.

[0115] When detecting the intersection of a ray and an interlayer interface, the interlayer interface is represented by a plane equation. For each interlayer interface plane, the equation obtained by simultaneously solving the ray equation and the plane equation is solved to obtain the intersection parameters. If the parameter is positive, the intersection is valid; if it is negative, the intersection is located in the opposite direction of the ray's origin and is invalid. For valid intersection parameters, they are substituted into the ray equation to obtain the spatial coordinates of the intersection. In practical implementation, it is necessary to detect the intersection of the ray with all relevant interlayer interfaces in the encapsulation structure and record the information of all valid intersections.

[0116] A similar method is used to detect the intersection points of rays with chip layout boundaries. Chip layout boundaries are typically composed of multiple planes or polygons, which can be represented as a series of facets. For each facet, the intersection points of the ray with it are detected. 3D packaging design software usually provides ray tracing functionality, which can be directly called to calculate the intersections between rays and chip layout boundaries. The position information of all valid intersection points is recorded; these intersection points represent the chip layout constraints encountered when moving along the offset direction.

[0117] Calculate the spatial distances from the coupling location to each intersection point. For each coupling location and each detected intersection point, calculate the Euclidean distance between the two points. These distance values ​​represent the distances that can be moved from the coupling location along the offset direction to each physical boundary. Obtain the sets of spatial distances from the coupling location to the interlayer interface intersection points and the sets of spatial distances from the coupling location to the chip layout boundary intersection points, respectively.

[0118] Compare all calculated spatial distances and select the minimum value as the movable spatial boundary. The minimum distance represents the maximum distance that can be moved from the coupling position along the offset direction; exceeding this distance will result in a conflict with a physical boundary. If no valid intersection is detected, a default maximum movement distance can be set based on the overall dimensions of the package structure to ensure that the signal path is not adjusted outside the package structure.

[0119] Extract the minimum wiring spacing of the package layer containing the signal transmission path. Minimum wiring spacing is a crucial parameter in package design rules, used to ensure sufficient space between adjacent signal lines to avoid signal interference. Different package layers and different signal types may correspond to different minimum wiring spacing requirements. For critical high-speed signals, the minimum wiring spacing is usually larger to reduce crosstalk; while for general signals, the minimum wiring spacing may be relatively smaller. Based on the package layer containing the signal transmission path and the signal characteristics, query the corresponding minimum wiring spacing value from the design rule base.

[0120] The allowable adjustment distance is obtained by subtracting the minimum wiring spacing from the movable space boundary. Subtracting the minimum wiring spacing ensures that the adjusted signal path maintains necessary safety clearance from surrounding components, avoiding signal integrity issues caused by violating design rules. The allowable adjustment distance equals the minimum distance at the movable space boundary minus the minimum wiring spacing. To increase design margin, the allowable adjustment distance can be further reduced, such as by taking 90% of the value after subtracting the minimum wiring spacing from the movable space boundary, reserving a certain safety margin.

[0121] The calculated allowable adjustment distance is determined as the upper limit of the adjustment range. This upper limit serves as the maximum distance constraint that the signal path can be adjusted during subsequent optimization processes, ensuring that the adjusted path still conforms to physical constraints and design rules. In the signal path optimization algorithm, the adjustment range is limited to within this upper limit to ensure the generated path scheme is practically feasible.

[0122] In practical applications of 3D stacked packaging, coupling points at different locations may face different spatial constraints, requiring separate calculations of their respective adjustment range upper limits. For complex packaging structures, a mesh generation method can be used to pre-calculate the movable boundary information of each point in space, forming a movable boundary map, thereby improving the calculation efficiency of the adjustment range upper limit during path optimization.

[0123] This invention solves the spatial constraint problem of signal path optimization in 3D stacked packaging by accurately detecting the movable spatial boundary of the signal transmission path using ray tracing technology and calculating the upper limit of the adjustment range in combination with design rules. Applicable to complex multi-layer 3D stacked packaging, it provides an effective tool for the coordinated optimization of thermal management and signal integrity, improving the overall performance and design efficiency of 3D stacked packaging, and has broad engineering application value.

[0124] The signal transmission paths at the coupling locations are redeployed according to the target offset distance, and the positions of the vertical interconnect structures are adjusted to match the redeployed signal transmission paths, including:

[0125] Obtain the original starting point coordinates and original ending point coordinates of the signal transmission path at the coupling position. Calculate the offset of the original starting point coordinates and the offset of the original ending point coordinates based on the target offset distance and offset direction. Add the offset to the original starting point coordinates to obtain the new starting point coordinates. Add the offset to the original ending point coordinates to obtain the new ending point coordinates.

[0126] Based on the new starting point coordinates and the new ending point coordinates, the signal transmission path of the coupling position is re-arranged, and the connection node position between the re-arranged signal transmission path and the vertical interconnection structure is extracted.

[0127] Calculate the coordinate deviation between the location of the connection node and the current location of the vertical interconnect structure, and adjust the spatial position of the vertical interconnect structure in the package structure based on the coordinate deviation, so that the adjusted vertical interconnect structure and the re-laid signal transmission path form an electrical connection at the connection node location.

[0128] In implementing the technical solution of repositioning the signal transmission path according to the target offset distance and adjusting the position of the vertical interconnect structure, it is necessary to accurately acquire and process the geometric coordinates of the original signal transmission path. The original starting coordinates of the signal transmission path are obtained by reading the physical position of the signal transmitting end in the packaging structure, which includes the horizontal, vertical, and height coordinates in three-dimensional space. The original ending coordinates correspond to the spatial position of the signal receiving end, which also contains complete three-dimensional coordinate data. This coordinate data is extracted through the geometric modeling module of the packaging design software to ensure that the coordinate accuracy reaches the micrometer level.

[0129] The target offset distance is calculated based on a comprehensive analysis of thermal management and signal integrity requirements. The offset direction is determined through vector analysis, pointing from the center of the heat source to a relatively low-temperature region while avoiding high-frequency signal interference sources. The offset is calculated using a linear superposition method, multiplying the target offset distance by the unit offset direction vector to obtain a three-dimensional offset vector. The offset of the original starting point coordinates is obtained by performing vector operations between the offset vector and the local coordinate system of the starting point, taking into account the encapsulation constraints and electrical connection requirements at the starting point. The calculation process for the offset of the original ending point coordinates is similar, but additional consideration needs to be given to the signal reception characteristics and impedance matching requirements at the ending point.

[0130] The new starting point coordinates are obtained by performing a vector addition operation between the original starting point coordinates and the corresponding offset. Specifically, the x-coordinate, y-coordinate, and height coordinates of the original starting point are added to the corresponding components of the offset to obtain the new three-dimensional coordinate values. The new ending point coordinates are calculated using the same vector superposition method to ensure that the new ending point position meets the offset requirements while maintaining effective connection with the signal receiver. During the coordinate superposition process, the physical feasibility of the new coordinate position needs to be verified to avoid geometric conflicts with other components in the package structure.

[0131] When re-laying the signal transmission path based on new starting and ending coordinates, a piecewise linear interpolation method is used to construct the new transmission path. The path layout process considers the electrical characteristics of signal transmission, ensuring that the characteristic impedance of the new path remains consistent with the original design requirements. The geometry of the transmission path is defined by a sequence of control points, and the coordinates of each control point are calculated through linear or nonlinear interpolation of the starting and ending coordinates. The choice of interpolation method is based on path complexity and signal frequency characteristics; for high-frequency signals, smoother curve interpolation is used to reduce signal reflection.

[0132] The location of the connection nodes between the re-laid signal transmission path and the vertical interconnect structure is extracted through geometric intersection analysis. The vertical interconnect structure is represented in three-dimensional space as a cylinder or rectangular prism, with its axis typically along the vertical direction of the package. The location of the connection node corresponds to the intersection of the transmission path and the surface of the vertical interconnect structure. The coordinates of this intersection point are obtained by solving a system of simultaneous equations for the path equation and the interconnect structure surface equation. The actual geometric dimensions and manufacturing tolerances of the interconnect structure must be considered during the intersection point calculation to ensure the engineering feasibility of the connection node locations.

[0133] The coordinate deviation between the connection node position and the current position of the vertical interconnect structure is calculated using the Euclidean distance metric. The center coordinates of the current vertical interconnect structure are used as a reference position, and a vector difference is calculated between these coordinates and the connection node position to obtain a three-dimensional deviation vector. Each component of the deviation vector represents the required position adjustment in different spatial directions. The symmetry of the vertical interconnect structure is considered during the calculation to ensure that the adjusted position maintains the electrical and mechanical stability of the structure.

[0134] The spatial positioning of the vertical interconnect structure within the package is adjusted via coordinate transformation. The adjustment process uses the calculated coordinate deviation as parameters for translation transformation, spatially shifting the geometric model of the vertical interconnect structure. Position adjustment must simultaneously consider spacing constraints with adjacent components to prevent physical interference between the adjusted interconnect structure and other components within the package. The adjustment process employs an iterative optimization method, gradually converging to the optimal position that satisfies electrical connection requirements.

[0135] The verification of the electrical connection between the adjusted vertical interconnect structure and the re-laid signal transmission path at the connection node locations was completed through impedance continuity analysis. The quality of the electrical connection was evaluated by calculating the contact resistance and signal transmission loss at the connection point. The geometric matching degree at the connection node was determined by measuring the ratio of the actual contact area to the theoretical contact area; this ratio should meet both electrical performance and mechanical reliability requirements.

[0136] In this embodiment, precise coordinate calculations and geometric transformations ensure a reliable connection between the re-laid-out signal path and the vertical interconnect structure. The entire adjustment process is based on rigorous mathematical calculations and geometric analysis, avoiding the inefficiency of traditional trial-and-error methods. This significantly improves the automation and design accuracy of 3D stacked package design, providing an effective technical means for the coordinated optimization of thermal management and signal integrity in complex package structures.

[0137] A second aspect of the present invention provides an electronic device, comprising:

[0138] processor;

[0139] Memory used to store processor-executable instructions;

[0140] The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0141] A third aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0142] This invention can be a method, apparatus, system, and / or computer program product. The computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for performing various aspects of the invention.

[0143] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for co-optimizing thermal management and signal integrity in three-dimensional stacked packaging, characterized in that, include: Acquire heat source distribution data and signal transmission path data of a three-dimensional stacked packaging structure; Temperature field data is calculated based on heat source distribution data, and heat conduction paths are traced along the gradient direction of the temperature field data to calculate heat flux density values. The locations where the distance between the heat conduction path and the signal transmission path is less than a preset distance threshold are selected as intersection locations. The heat flux density value of the intersection location is converted into the medium temperature rise rate, and the time delay offset is calculated based on the medium temperature rise rate. Calculate the coupling strength between the time delay offset and the heat flux density value at the intersection, and select intersections with coupling strength exceeding a preset strength threshold as coupling positions; Calculate the spatial gradient of the heat flux density at the coupling position, determine the vertical direction of the spatial gradient as the offset direction, adjust the position of the signal transmission path along the offset direction, recalculate the coupling strength, increase the adjustment amplitude until the coupling strength drops below the preset strength threshold, and record the adjustment amplitude as the target offset distance. The signal transmission paths at the coupling positions are re-laid according to the target offset distance, and the positions of the vertical interconnect structures are adjusted to match the re-laid signal transmission paths.

2. The method according to claim 1, characterized in that, The temperature field data is calculated based on the heat source distribution data. The heat conduction path is traced along the gradient direction of the temperature field data, and the heat flux density value is calculated, including: The heat source distribution data is spatially discretized according to the interlayer interface of the packaging structure and the chip layout boundary. The heat source intensity distribution is marked on the discretized spatial nodes, and the temperature field data of the spatial grid nodes is calculated based on the heat source intensity distribution. Spatial difference calculation is performed on the temperature field data to obtain the temperature gradient vector of each spatial node. Spatial nodes whose temperature gradient vector magnitude exceeds the preset gradient threshold are selected as candidate starting nodes. From the candidate starting nodes, the spatial node with the largest temperature field data value is selected as the heat conduction starting node. Starting from the heat conduction initiation node, trace each node along the spatial direction pointed to by the corresponding temperature gradient vector, record the sequence of spatial node coordinates traversed, and connect the spatial node coordinate sequences to form a heat conduction path. Extract the temperature gradient vector corresponding to the coordinates of each spatial node on the heat conduction path and the thermal conductivity data of each layer of the encapsulation structure. Perform a dot product operation on the temperature gradient vector and the thermal conductivity data to obtain the heat flux density value of each spatial node on the heat conduction path.

3. The method according to claim 1, characterized in that, Locations where the distance between the heat conduction path and the signal transmission path is less than a preset distance threshold are selected as intersection points. The heat flux density value at the intersection point is converted into the medium temperature rise rate. The time delay offset is calculated based on the medium temperature rise rate, including: The heat conduction path and the signal transmission path are projected onto the same plane coordinate system of the package structure. The spatial distance between each spatial node on the heat conduction path and each wiring node on the signal transmission path is calculated. Spatial nodes and wiring nodes with a spatial distance less than a preset distance threshold are selected as intersection positions. Extract the heat flux density value corresponding to the intersection position, obtain the thermal response characteristic curve of the medium layer where the signal transmission path is located, map the heat flux density value to the thermal response characteristic curve to obtain the corresponding temperature rise response value, and perform time differentiation operation on the temperature rise response value to obtain the medium temperature rise rate at the intersection position. The dielectric constant temperature dependence of the dielectric layer where the signal transmission path is located is obtained. The temperature rise rate of the dielectric at the intersection is substituted into the dielectric constant temperature dependence to calculate the change in dielectric constant. The change in signal propagation speed is calculated based on the change in dielectric constant. The change in signal propagation speed is combined with the length of the signal transmission path to calculate the time delay offset.

4. The method according to claim 1, characterized in that, The coupling strength between the time delay offset and the heat flux density value at the intersection is calculated, and intersections with coupling strength exceeding a preset strength threshold are selected as coupling locations, including: Extract the time delay offset and heat flux density value at the intersection to obtain the global distribution data of the time delay offset and heat flux density value in the packaging structure; Based on the global distribution data, the normalized intervals of the time delay offset and the heat flux density value are determined. The time delay offset is mapped to the normalized interval to obtain the normalized time delay offset, and the heat flux density value is mapped to the normalized interval to obtain the normalized heat flux density value. Obtain the timing constraints and heat dissipation performance constraints of the signal transmission path, determine the delay influence weighting coefficient based on the timing constraints, and determine the heat flow influence weighting coefficient based on the heat dissipation performance constraints; The time delay contribution component is obtained by weighting the normalized time delay offset with the time delay influence weighting coefficient. The heat flux contribution component is obtained by weighting the normalized heat flux density value with the heat flux influence weighting coefficient. The coupling strength at the intersection position is obtained by fusing the time delay contribution component and the heat flux contribution component.

5. The method according to claim 1, characterized in that, Calculate the spatial gradient of heat flux density at the coupling location, determine the vertical direction of the spatial gradient as the offset direction, adjust the signal transmission path position along the offset direction, recalculate the coupling strength, and increase the adjustment amplitude until the coupling strength drops below a preset strength threshold. Record the adjustment amplitude as the target offset distance. Extract the heat flux density value at the coupling location, calculate the spatial gradient of the heat flux density value, perform orthogonal decomposition on the spatial gradient to obtain the vertical direction of the spatial gradient, and determine the vertical direction of the spatial gradient as the offset direction. Based on the movable space boundary of the signal transmission path detected by the offset direction, the upper limit of the adjustment range is determined according to the movable space boundary; Set an initial value for the adjustment amplitude, adjust the signal transmission path of the coupling position along the offset direction based on the initial value for the adjustment amplitude, extract the heat flux density value of the coupling position after adjustment, calculate the time delay offset based on the heat flux density value of the coupling position after adjustment, and calculate the adjusted coupling strength based on the time delay offset and the heat flux density value of the coupling position after adjustment. Determine whether the adjusted coupling strength drops below the preset strength threshold. When the adjusted coupling strength drops below the preset strength threshold, record the initial value of the adjustment range as the target offset distance. If the adjusted coupling strength does not drop below the preset strength threshold, determine whether the initial value of the adjustment amplitude is less than the upper limit of the adjustment amplitude. If the initial value of the adjustment amplitude is less than the upper limit of the adjustment amplitude, increase the initial value of the adjustment amplitude and return the signal transmission path that adjusts the coupling position along the offset direction based on the initial value of the adjustment amplitude. Stop the adjustment when the initial value of the adjustment amplitude reaches the upper limit of the adjustment amplitude.

6. The method according to claim 5, characterized in that, Based on the movable space boundary of the offset direction detection signal transmission path, the upper limit of the adjustment range is determined according to the movable space boundary, including: A ray is projected from the coupling position along the offset direction. The intersection of the ray with the interlayer interface of the package structure and the intersection of the ray with the chip layout boundary are detected. The spatial distance from the coupling position to the intersection of the interlayer interface and the spatial distance from the coupling position to the intersection of the chip layout boundary are calculated. Compare the spatial distance from the coupling location to the intersection of the interlayer interface with the spatial distance from the coupling location to the intersection of the chip layout boundary, and select the minimum value of the spatial distance as the movable spatial boundary. Extract the minimum wiring spacing of the encapsulation layer where the signal transmission path is located, subtract the minimum wiring spacing from the movable space boundary to obtain the allowable adjustment distance, and determine the allowable adjustment distance as the upper limit of the adjustment range.

7. The method according to claim 1, characterized in that, The signal transmission paths at the coupling locations are re-laid according to the target offset distance, and the positions of the vertical interconnect structures are adjusted to match the re-laid signal transmission paths, including: Obtain the original starting point coordinates and original ending point coordinates of the signal transmission path at the coupling position. Calculate the offset of the original starting point coordinates and the offset of the original ending point coordinates based on the target offset distance and offset direction. Add the offset to the original starting point coordinates to obtain the new starting point coordinates. Add the offset to the original ending point coordinates to obtain the new ending point coordinates. Based on the new starting point coordinates and the new ending point coordinates, the signal transmission path of the coupling position is re-arranged, and the connection node position between the re-arranged signal transmission path and the vertical interconnection structure is extracted. Calculate the coordinate deviation between the location of the connection node and the current location of the vertical interconnect structure, and adjust the spatial position of the vertical interconnect structure in the package structure based on the coordinate deviation, so that the adjusted vertical interconnect structure and the re-laid signal transmission path form an electrical connection at the connection node location.

8. An electronic device, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the method described in any one of claims 1 to 7.

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