Multi-objective optimization method and device for electromagnetic transmission characteristics of coaxial through silicon via array

Abstract

The invention discloses a multi-objective optimization method for electromagnetic transmission characteristics of a coaxial through silicon via array, and the method comprises the steps: building a full-wave simulation model of a CTSV array based on the physical structure, material parameters, geometric structure parameter combination and scattering parameters of the to-be-optimized CTSV array; constructing a data set based on the simulation model, wherein the data set comprises multiple groups of geometric structure parameter combinations and corresponding electrical performance indexes; constructing a GRNN network model architecture by using the data set, determining an optimal smoothing factor of the model architecture by using a particle swarm optimization algorithm, and constructing and training a GRNN model based on the smoothing factor and the data set to obtain a trained GRNN model; and based on a genetic algorithm and the trained GRNN network model, carrying out iterative solution on the geometric structure parameter combination of the CTSV array, and when a preset condition is satisfied, outputting the updated geometric structure parameter combination. According to the method, the accuracy of designing the CTSV array parameters can be improved, the calculation cost can be reduced, and the efficiency of optimizing the CTSV array parameters is improved.

Description

Technical Field

[0001] This invention belongs to the field of three-dimensional integrated circuit technology, specifically relating to a multi-objective optimization method and apparatus for the electromagnetic transmission characteristics of a coaxial silicon via array. Background Technology

[0002] With the rapid development of three-dimensional integrated circuit (3D IC) technology, signal transmission in the terahertz band places higher performance demands on through-silicon via (TSV) interconnect structures. Coaxial through-silicon via (CTSV) arrays, due to their excellent shielding properties, exhibit significant advantages in high-frequency, high-speed interconnects. However, the electromagnetic transmission performance of CTSV arrays is strongly influenced by their geometric parameters (such as aperture, spacing, and dielectric layer thickness), and there are complex interrelationships among multiple performance indicators (such as return loss, insertion loss, near-end crosstalk, and far-end crosstalk). This makes the design of CTSV arrays in the terahertz band a typical multi-objective, strongly nonlinear, high-dimensional optimization problem.

[0003] Currently, the design of CTSV arrays mainly relies on full-wave electromagnetic simulation tools based on the finite element method (such as ANSYS HFSS) for performance evaluation and optimization through parameter scanning or trial and error. Although full-wave simulation can provide high accuracy, its computational overhead is huge and the simulation cycle is long. Especially when dealing with multi-parameter combinations and multi-objective optimization, it requires massive simulation iterations, resulting in low design efficiency and high time costs. In addition, traditional equivalent circuit models or analytical methods are often insufficiently accurate in high-frequency complex electromagnetic coupling scenarios, making it difficult to accurately describe the mapping relationship between parameters and performance, thus limiting their applicability in optimization design.

[0004] Therefore, when designing CTSV array parameters, how to improve the accuracy of the mapping relationship between design parameters and performance while reducing computational costs, thereby improving the efficiency of CTSV array parameter optimization, is a technical problem that urgently needs to be solved. Summary of the Invention

[0005] To address the challenge of improving the accuracy of the mapping relationship between design parameters and performance while reducing computational costs, thereby increasing the efficiency of CTSV array parameter optimization, this invention provides a multi-objective optimization method and apparatus for the electromagnetic transmission characteristics of coaxial through-silicon via (CTSV) arrays. The technical problem to be solved by this invention is achieved through the following technical solution: This invention provides a multi-objective optimization method for the electromagnetic transmission characteristics of a coaxial silicon through-hole array, comprising: Based on the physical structure, material parameters, optimizable geometric parameter combinations, and scattering parameters of the coaxial through-silicon via array to be optimized, a full-wave simulation model of the coaxial through-silicon via array is constructed. Based on the full-wave simulation model, the optimizable geometric structure parameter combinations are sampled to obtain multiple sets of geometric structure parameter combinations and the electrical performance indicators corresponding to each set of geometric structure parameter combinations. The multiple sets of geometric structure parameter combinations and the electrical performance indicators corresponding to each set of geometric structure parameter combinations are constructed into a dataset. Using the combination of geometric structural parameters in the dataset as input and the corresponding electrical performance index as output, a generalized regression neural network model architecture is constructed. The particle swarm optimization algorithm is used to determine the optimal smoothing factor of the generalized regression neural network model architecture. Based on the optimal smoothing factor and the dataset, the generalized regression neural network model is constructed and trained to obtain a well-trained generalized regression neural network model. Based on a genetic algorithm and a trained generalized regression neural network model, the geometric structure parameter combination of the coaxial through-silicon via array is iteratively solved. When the preset iteration termination condition is met, the updated geometric structure parameter combination is output and used as the design parameters of the coaxial through-silicon via array.

[0006] In one embodiment of the present invention, a full-wave simulation model of the coaxial through-silicon via (TSV) array is constructed based on the physical structure, material parameters, optimizable geometric parameter combinations, and scattering parameters of the TSV array to be optimized, including: An electromagnetic simulation model of a three-dimensional integrated circuit is established based on the physical structure, material parameters, and optimizable geometric parameters of a coaxial through-silicon via array. The electromagnetic simulation model was calibrated based on the scattering parameters to obtain a full-wave simulation model of the coaxial silicon through-hole array.

[0007] In one embodiment of the present invention, based on a full-wave simulation model, optimizable combinations of geometric parameters are sampled to obtain multiple sets of geometric parameter combinations and electrical performance indicators corresponding to each set of geometric parameter combinations, including: Based on the full-wave simulation model, the combination of geometric structure parameters is sampled to obtain multiple sets of sample parameter combinations; Full-wave simulation was performed on each set of sample parameters to obtain the electrical performance indicators corresponding to each set of geometric structure parameter combinations.

[0008] In one embodiment of the present invention, the dataset is divided into a training set and a validation set according to a preset ratio; The optimal smoothing factor for the generalized regression neural network model architecture is determined using the particle swarm optimization algorithm. Based on the optimal smoothing factor and the training set, the generalized regression neural network model is constructed and trained to obtain a well-trained generalized regression neural network model, including: Initialize the particle swarm, set the search range of the smoothing factor for the initial generalized regression neural network model architecture, and randomly initialize the position and velocity of each particle in the particle swarm. The position of each particle represents a candidate smoothing factor. The particle swarm optimization is performed iteratively, with the following steps executed in each iteration: S3.1 Obtain the smoothing factor represented by the current position of each particle in the particle swarm. Based on the smoothing factor corresponding to each particle and the training set, construct and train the corresponding generalized regression neural network model. Input the geometric structure parameters in the validation set into the generalized regression neural network model corresponding to each particle to obtain the electrical performance index predicted by each generalized regression neural network model. Calculate the error between the electrical performance index predicted by each generalized regression neural network model and the corresponding real electrical performance index in the validation set, and use the error as the current fitness value of the corresponding particle. S3.2, based on the current fitness value, historical best fitness value and historical global best position of each particle, determine the global best position and the individual best position of each particle. The global best position is the position corresponding to the minimum fitness value of the particle determined by the particle swarm during the iteration process. S3.3, based on the individual optimal position of each particle, the global optimal position, the velocity update formula of the particle swarm optimization algorithm, and the position update formula, update the current velocity and current position of each particle; S3.4 Repeat S3.1~S3.3 until the preset maximum number of iterations is reached. Take the smoothing factor corresponding to the current global optimal position as the best smoothing factor, and construct and train the generalized regression neural network model based on the best smoothing factor and the training set to obtain the trained generalized regression neural network model.

[0009] In one embodiment of the present invention, determining the global optimal position and the individual optimal position of each particle based on the current fitness value, the historical best fitness value, and the historical global optimal position includes: For each particle, compare its current fitness value with its historical best fitness value. If the current fitness value is better, then the current position is determined as the particle's individual best position; otherwise, the original individual best position is retained. Based on the individual optimal positions and corresponding fitness values ​​of all particles, determine the target individual optimal position among the individual optimal positions of all particles. Compare the target individual optimal position with the historical global optimal position. If the target individual optimal position is better, then the target individual optimal position is determined as the global optimal position; otherwise, the historical global optimal position is retained. In one embodiment of the present invention, based on a genetic algorithm and a trained generalized regression neural network model, the geometric structure parameter combination of the coaxial through-silicon via (TSV) array is iteratively solved. When a preset iteration termination condition is met, the updated geometric structure parameter combination is output and used as the design parameters of the coaxial TSV array, including: A genetic algorithm is used to encode the combination of geometric structure parameters, and the combination of geometric structure parameters is used as a chromosome representation to construct an initial population. Each individual in the initial population corresponds to a set of geometric structure parameter combinations. The electrical performance index of each individual in the initial population is predicted using a trained generalized regression neural network model. A multi-objective fitness function is constructed based on the predicted electrical performance indicators. The multi-objective fitness function is used to characterize the fitness of each individual. Genetic operations in the genetic algorithm are performed to iteratively update the combination of geometric structure parameters in the initial population. When the preset iteration termination condition is met, the updated combination of geometric structure parameters is output as the design parameters for the coaxial through-silicon via array.

[0010] In one embodiment of the present invention, the genetic operations include selection operations based on roulette wheel strategy, crossover operations based on two-point crossover, and mutation operations based on random bit flipping.

[0011] In one embodiment of the present invention, electrical performance indicators include return loss, insertion loss, near-end crosstalk, and far-end crosstalk. The multi-objective optimization function is a function obtained by weighted summation of the mean values ​​of return loss, insertion loss, near-end crosstalk, and far-end crosstalk.

[0012] In one embodiment of the present invention, the iteration termination condition includes reaching a preset maximum number of iterations or the change in population fitness being less than a preset threshold.

[0013] Another aspect of the present invention provides a multi-objective optimization device for the electromagnetic transmission characteristics of a coaxial through-silicon via array, the device comprising: The building module is used to construct a full-wave simulation model of the coaxial through-silicon via array based on the physical structure, material parameters, optimizable combinations of geometric parameters, and scattering parameters of the coaxial through-silicon via array to be optimized. The building module is also used to sample optimizable combinations of geometric parameters based on the full-wave simulation model, obtain multiple sets of geometric parameter combinations and electrical performance indicators corresponding to each set of geometric parameter combinations, and construct a dataset from the multiple sets of geometric parameter combinations and the electrical performance indicators corresponding to each set of geometric parameter combinations. The model training module is used to construct a generalized regression neural network model architecture by taking the combination of geometric structural parameters in the dataset as input and the corresponding electrical performance index as output. It uses the particle swarm optimization algorithm to determine the optimal smoothing factor of the generalized regression neural network model architecture, and constructs and trains the generalized regression neural network model based on the optimal smoothing factor and the dataset to obtain the trained generalized regression neural network model. The optimization design module is used to iteratively solve the combination of geometric structure parameters of the coaxial through silicon via array based on the genetic algorithm and the trained generalized regression neural network model. When the preset iteration termination condition is met, the updated combination of geometric structure parameters is output and used as the design parameters of the coaxial through silicon via array.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention provides a multi-objective optimization method for the electromagnetic transmission characteristics of a coaxial through-silicon via (CTSV) array. First, based on the physical structure, material parameters, optimizable geometric parameters, and scattering parameters of the CTSV array to be optimized, a full-wave simulation model of the CTSV array is constructed. Then, based on the full-wave simulation model, a dataset including multiple combinations of geometric parameters and corresponding electrical performance indicators is constructed. Next, a generalized regression neural network (GRNN) model architecture is constructed using the dataset, and the optimal smoothing factor of the GRNN model architecture is determined by the particle swarm optimization algorithm. Based on the optimal smoothing factor and the dataset, the GRNN model is constructed and trained to obtain a trained GRNN model. Finally, based on the genetic algorithm and the trained GRNN model, the geometric parameter combination of the CTSV array is iteratively solved, and the updated geometric parameter combination is output as the design parameters of the CTSV array. Therefore, the GRNN model constructed in this invention can quickly predict electrical performance indicators based on the combination of geometric structural parameters. It effectively solves the problem that the relationship between geometric structural parameters and electrical performance indicators of CTSV arrays in the terahertz band is highly nonlinear, strongly coupled, and difficult to describe accurately by analytical methods. It also avoids frequent calls to three-dimensional full-wave electromagnetic simulation during the optimization process, thereby significantly reducing computational complexity and simulation time overhead, and improving the overall efficiency of CTSV array parameter optimization.

[0015] (2) Based on the global search capability of genetic algorithms, this invention performs multi-objective collaborative optimization of the structural parameters of CTSV arrays. Under conditions where multiple performance indicators are mutually constrained, it can automatically optimize and obtain a combination of geometric structural parameters that meets the design requirements of low loss and low crosstalk, avoiding the problem of getting trapped in local optima in traditional empirical design and manual trial-and-error methods. Compared with traditional optimization methods that rely on extensive simulation calculations, this invention significantly shortens the design cycle and reduces design costs while ensuring design accuracy, exhibiting good engineering applicability and scalability. Furthermore, the optimization design method proposed in this invention has good versatility and scalability, and can be flexibly adjusted according to the design requirements of different CTSV array sizes and different application scenarios, making it suitable for various three-dimensional integrated circuit and high-speed interconnect design scenarios.

[0016] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] Figure 1 This is a flowchart of a multi-objective optimization method for the electromagnetic transmission characteristics of a coaxial through-silicon via array provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of a GRNN model framework provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the structure of a multi-objective optimization device for the electromagnetic transmission characteristics of a coaxial silicon through-hole array provided in an embodiment of the present invention. Detailed Implementation

[0018] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following describes in detail a multi-objective optimization method for the electromagnetic transmission characteristics of a coaxial silicon through-hole array proposed according to the present invention, in conjunction with the accompanying drawings and specific embodiments.

[0019] The foregoing and other technical contents, features, and effects of the present invention will be clearly presented in the following detailed description of specific embodiments in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and concrete understanding can be gained of the technical means and effects adopted by the present invention to achieve its intended purpose. However, the accompanying drawings are for reference and illustration only and are not intended to limit the technical solutions of the present invention.

[0020] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or apparatus comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or apparatus that includes said element.

[0021] This invention addresses the challenge of improving the accuracy of the mapping relationship between design parameters and performance while reducing computational costs, thereby increasing the efficiency of CTSV array parameter optimization. It proposes a multi-objective optimization method for the electromagnetic transmission characteristics of coaxial through-silicon via (TSV) arrays. Please refer to [link to relevant documentation]. Figure 1 The method includes the following steps: S1: Based on the physical structure, material parameters, optimizable combinations of geometric parameters, and scattering parameters (S-parameters) of the coaxial through-silicon via (CTSV) array to be optimized, construct a full-wave simulation model of the CTSV array.

[0022] The physical structure can be understood as the fixed and unchanging basic components and layout of the CTSV array in three-dimensional space. This includes the array arrangement (such as rectangular grids, quincunx patterns, etc.), array size (number of rows × number of columns), the definition of signal input / output port locations, and the connection method of the grounding network.

[0023] Material parameters can be understood as the intrinsic electromagnetic properties of the materials that make up each part of the CTSV array. For example, the conductivity of conductor materials such as copper and tungsten, and the resistivity of dielectric materials such as silicon dioxide and silicon substrates.

[0024] An optimizable combination of geometric parameters can be understood as a set of geometric dimensional variables that can be adjusted during the optimization design process to seek optimal performance. For example, an optimizable combination of geometric parameters includes the width of the three conductor layers (CTSV) from the inside out. , The thickness of the three dielectric layers of CTSV from the inside out , And the center-to-center distance p between adjacent through holes and the height h of the through hole.

[0025] S-parameters are a set of standardized network parameters used to describe and characterize the electromagnetic wave behavior in high-frequency, microwave, and millimeter-wave circuits.

[0026] In this embodiment of the invention, a full-wave simulation model of the CTSV array is constructed based on the physical structure, material parameters, optimizable geometric parameter combinations, and S-parameters of the CTSV array to be optimized. This includes: establishing an electromagnetic simulation model of a three-dimensional integrated circuit (3D IC) based on the physical structure, material parameters, and optimizable geometric parameter combinations of the CTSV array; and calibrating the electromagnetic simulation model based on scattering parameters to obtain the full-wave simulation model of the CTSV array.

[0027] Specifically, in full-wave simulation software (such as ANSYS HFSS software), the physical structure, material parameters, and optimizable geometric parameter combinations of the actual CTSV array are input to establish a 3D IC electromagnetic simulation model of the CTSV array. Then, based on the comparison between the measured S-parameters of the CTSV array structure and the simulation results, the electromagnetic simulation model is adjusted until the simulated and measured values ​​of the S-parameters reach the matching threshold, and a full-wave simulation model of the CTSV array with high confidence is output.

[0028] It should be noted that during the construction of the full-wave simulation model of the CTSV array, the electromagnetic simulation model was calibrated based on the measured S-parameters. This made the constructed full-wave simulation model more closely resemble the actual CTSV array structure in terms of electromagnetic characteristics, thereby increasing the confidence of the model and making the simulation data closer to the actual values. This provides more accurate data for subsequent network construction and parameter optimization, thus making the optimization design method more valuable in practical engineering.

[0029] S2: Based on the full-wave simulation model, sample the optimizable geometric structure parameter combinations to obtain multiple sets of geometric structure parameter combinations and the electrical performance indicators corresponding to each set of geometric structure parameter combinations. Construct a dataset from the multiple sets of geometric structure parameter combinations and the electrical performance indicators corresponding to each set of geometric structure parameter combinations.

[0030] Specifically, based on the full-wave simulation model, the geometric structure parameter combinations are sampled to obtain multiple sets of sample parameter combinations. Then, full-wave simulation is performed on each set of sample parameter combinations to obtain the electrical performance index corresponding to each set of geometric structure parameter combinations. Finally, the multiple sets of geometric structure parameter combinations and the electrical performance index corresponding to each set of geometric structure parameter combinations are constructed into a dataset.

[0031] For example, excitation is set at the port of each CTSV unit, and multiple simulation calculations are performed for different combinations of geometric parameters to extract the S-parameter results of the CTSV array in the target frequency band. During the construction of the dataset, multiple geometric parameters of the CTSV array are perturbed in combination to enable the data samples to cover the parameter space under different design conditions, thereby improving the representativeness and diversity of the dataset and providing a reliable data foundation for subsequent neural network modeling and parameter optimization processes.

[0032] It should be noted that during the construction of the above dataset, the combination of geometric parameters was determined within a preset operating frequency band (e.g., 80GHz~220GHz) and simulation boundary conditions. Specifically, the upper and lower limits of the width of the three conductor layers and the thickness of the three dielectric layers in CTSV are jointly determined by TSV / CTSV process design rules, layout manufacturability constraints, and reliability specifications. For example, The range is , The range is , The range is The range of p is The thickness of its dielectric layer , Both the height h of the through hole and the height h are set according to the usage requirements.

[0033] Furthermore, electrical performance indicators can be obtained based on the different excitation ports. These indicators include return loss, insertion loss, near-end crosstalk, and far-end crosstalk. Specifically, the return loss and insertion loss of each CTSV cell in the CTSV array are respectively determined by… and ( The near-end crosstalk generated between CTSV units is characterized by (being odd numbers). ( odd number and To characterize, far-end crosstalk is represented by ) ( Even number, odd number and To characterize it. Among them, Finally, the geometric parameters of the CTSV array are correlated with the corresponding electrical performance indicators to construct a dataset of the CTSV array under various parameter configurations. This dataset serves as the basis for subsequent neural network modeling and optimization calculations.

[0034] It should be noted that the above steps are not limited to a specific size of CTSV array structure. The constructed dataset can be adjusted according to different array sizes and different application requirements, so as to be applicable to the optimization design of CTSV arrays of various sizes and application scenarios.

[0035] S3: Using the combination of geometric structural parameters in the dataset as input and the corresponding electrical performance indicators as output, construct a generalized regression neural network (GRNN) model architecture. Use the particle swarm optimization algorithm to determine the optimal smoothing factor of the GRNN model architecture. Based on the optimal smoothing factor and the dataset, construct and train the GRNN model to obtain a trained GRNN model.

[0036] It should be noted that the GRNN model architecture, constructed using combinations of geometric structural parameters from the dataset as input and corresponding electrical performance indicators as output, includes an input layer, a mode layer, a summation layer, and an output layer. In the mode layer, a Gaussian function is used as the transfer function to process the input data. This GRNN model architecture includes a smoothing factor parameter, the specific value of which is determined by a subsequent particle swarm optimization algorithm. For an illustrative diagram of this GRNN model architecture, please refer to [link to diagram]. Figure 2 The input layer nodes represent optimizable geometric parameters, with the number of nodes corresponding to the number of parameters in the geometric parameter combination. The output layer nodes represent electrical performance prediction results, with the number of nodes corresponding to the number of indicators in the electrical performance index. This enables the final GRNN model to realize the mapping relationship between the geometric parameter combination and the electrical performance index.

[0037] Optionally, before constructing the GRNN model architecture, the dataset can be preprocessed using a min-max normalization method to address model training issues caused by differences in the original data's feature dimensions and scales, thereby improving the stability of the GRNN network training. Subsequently, the dataset is divided into training and validation sets according to a preset ratio for model training and performance evaluation.

[0038] In this embodiment of the invention, the optimal smoothing factor of the GRNN model architecture is determined using the particle swarm optimization algorithm. Based on the optimal smoothing factor and the dataset, a generalized regression neural network model is constructed and trained to obtain a trained GRNN model. Specifically, this includes: Initialize the particle swarm, set the search range of the smoothing factor of the initial GRNN model architecture based on preset rules, and randomly initialize the position and velocity of each particle in the particle swarm. The position of each particle represents a candidate smoothing factor.

[0039] The particle swarm optimization is performed iteratively, with the following steps executed in each iteration: S3.1 Obtain the smoothing factor represented by the current position of each particle in the particle swarm. Construct and train the corresponding GRNN model based on the smoothing factor corresponding to each particle and the training set. Input the geometric structure parameters in the validation set into the GRNN model corresponding to each particle to obtain the electrical performance index predicted by each generalized regression neural network model. Calculate the error between the electrical performance index predicted by each GRNN model and the corresponding real electrical performance index in the validation set, and use the error as the current fitness value of the corresponding particle.

[0040] Optionally, the embodiment uses Symmetric Mean Absolute Percentage Error (SMAPE) to represent the above error, with the specific formula as follows:

[0041] in, It is the first prediction made by the GRNN model. Electrical performance indicators of each sample It is the first in the verification set The actual electrical performance indicators corresponding to each sample This represents the number of samples.

[0042] Understandably, SMAPE effectively avoids the computational problems that may be caused by the denominator being close to zero in traditional MAPE through symmetry processing, and at the same time can make a balanced assessment of the cases of overestimation and underestimation.

[0043] S3.2, based on the current fitness value, historical best fitness value and historical global best position of each particle, determine the global best position and the individual best position of each particle. The global best position is the position corresponding to the minimum fitness value of the particle determined by the particle swarm during the iteration process.

[0044] S3.3 Update the current velocity and current position of each particle based on the individual optimal position, the global optimal position, the velocity update formula of the particle swarm optimization algorithm, and the position update formula.

[0045] The expression for the velocity update formula is as follows:

[0046]

[0047] in, For the particle in the first The speed of the next iteration For the particle in the first The position of the next iteration. This refers to the optimal historical position of a particle determined during the iteration process of the particle swarm. This represents the historical global optimal position of the particle swarm determined during the iteration process. For inertial weights, For the first The speed of the next iteration and As a learning factor, and A random number between 0 and 1.

[0048] The expression for the position update formula is:

[0049] in, For the particle in the first The position of the next iteration.

[0050] Furthermore, based on each particle's current fitness value, historical best fitness value, and historical global best position, the global best position and each particle's individual best position are determined, including: For each particle, compare its current fitness value with the historical best fitness value. If the current fitness value is better, then the current position is determined as the particle's individual best position; otherwise, the original individual best position is retained. Based on the individual best positions and corresponding fitness values ​​of all particles, determine the target individual best position among the individual best positions of all particles. Compare the target individual best position with the historical global best position. If the target individual best position is better, then the target individual best position is determined as the global best position; otherwise, the historical global best position is retained. S3.4 Repeat S3.1~S3.3 until the preset maximum number of iterations is reached. Take the smoothing factor corresponding to the current global optimal position as the best smoothing factor, and build and train the GRNN model based on the best smoothing factor and the training set to obtain the trained GRNN model.

[0051] It should be noted that, as described in S3 regarding the GRNN model establishment process, the GRNN model obtained in this embodiment can quickly predict the corresponding electrical performance indicators of a given combination of geometric structural parameters of a CTSV array without performing full-wave simulation. This effectively solves the problem that the relationship between structural parameters and electrical performance indicators of CTSV arrays in the terahertz band is highly nonlinear, strongly coupled, and difficult to accurately describe analytically. Furthermore, it avoids frequent calls to three-dimensional full-wave electromagnetic simulation during the optimization process, thus significantly reducing computational complexity and simulation time overhead, and improving the overall efficiency of CTSV array parameter optimization.

[0052] It is understood that the GRNN model described above is used as a proxy model for full-wave electromagnetic simulation in this invention, in order to achieve rapid evaluation of electrical performance indicators while ensuring prediction accuracy.

[0053] Optionally, the above method is not limited to CTSV array structures of a specific size. The constructed GRNN model can be adjusted according to different array sizes and different application requirements, thus making it suitable for CTSV array optimization design in various sizes and application scenarios.

[0054] S4: Based on the genetic algorithm and the trained GRNN model, the combination of geometric structural parameters of the CTSV array is iteratively solved. When the preset iteration termination condition is met, the updated combination of geometric structural parameters is output and used as the design parameters of the CTSV array.

[0055] In this embodiment of the invention, based on a genetic algorithm and a trained GRNN model, the combination of geometric structural parameters of the CTSV array is iteratively solved. When a preset iteration termination condition is met, the updated combination of geometric structural parameters is output and used as the design parameters of the CTSV array. This includes the following four steps: S4.1: Use a genetic algorithm to encode the combination of geometric structure parameters and use the combination of geometric structure parameters as chromosome representation to construct an initial population. Each individual in the initial population corresponds to a set of geometric structure parameter combinations.

[0056] Specifically, a binary encoding method is used. The principle is to set the length of the chromosome (in binary form), map the range of geometric structure parameter combinations to the value range of the chromosome's binary representation, first randomly generate a binary chromosome, then decode it into decimal parameters, and perform subsequent calculations.

[0057] For example, setting , The chromosome lengths are 13, 13, and 12, respectively, so the total length of this chromosome is 38, which includes... , Three parameters. During decoding, the three segments are decoded separately, using the decoding formula (in...). (For example)

[0058] in, express The decimal value, express Chromosome values, The first chromosome Bit. and They represent The upper and lower limits, express The length of the chromosome form. The conversion operations for other parameters are the same as described above, and will not be repeated here.

[0059] It should be noted that after representing the combination of geometric structure parameters as chromosomes, each combination of geometric structure parameters can be represented as a real number vector, considered as a chromosome. Under the preset population size, for each individual in the population (i.e., each chromosome), the value of each parameter gene is generated through uniform random sampling within its corresponding value range. This yields a set of initial design schemes randomly distributed in the solution space, constituting the initial population for the evolutionary iteration of the genetic algorithm.

[0060] S4.2: Use the trained GRNN model to predict the electrical performance index corresponding to each individual in the initial population.

[0061] S4.3: Construct a multi-objective fitness function based on the predicted electrical performance index. The multi-objective fitness function is used to characterize the fitness of each individual.

[0062] The multi-objective fitness function is a function obtained by weighted summation of the mean values ​​of return loss, insertion loss, near-end crosstalk, and far-end crosstalk.

[0063] Specifically, the multi-objective fitness function is expressed as follows:

[0064] in, , and Indicates the weighting coefficient. , and They represent the first... The optimization criteria for return loss, insertion loss, near-end crosstalk, and far-end crosstalk of a CTSV element can be expressed as follows:

[0065]

[0066]

[0067]

[0068] in, and They are the first The S-parameters (in dB) of the return loss and insertion loss of each CTSV element are negative. The larger the absolute value or A higher value indicates better transmission performance of the CTSV unit. and They represent the first The average near-end crosstalk and average far-end crosstalk (in dB) of each CTSV cell. The larger their absolute values, the weaker the crosstalk experienced by the CTSV cell, and the better the performance of the CTSV array.

[0069] It is understandable that the above multi-objective fitness function can be used to comprehensively evaluate different configurations of geometric structure parameters and guide the optimization process to converge in the direction that meets the design objectives.

[0070] S4.4: Execute the genetic operations in the genetic algorithm to iteratively update the combination of geometric structure parameters in the initial population. When the preset iteration termination condition is met, output the updated combination of geometric structure parameters as the design parameters of the CTSV array.

[0071] Among them, genetic operations include selection operations based on roulette wheel strategy, crossover operations based on two-point crossover, and mutation operations based on random bit flipping; the iteration termination conditions include reaching the preset maximum number of iterations or the change in population fitness being less than a preset threshold.

[0072] It should be noted that during the evolutionary process of the genetic algorithm, selection operations are performed on the current population to retain individuals with better fitness; simultaneously, crossover operations generate new combinations of geometric structure parameters to expand the search space; and mutation operations randomly perturb some geometric structure parameters to improve population diversity and avoid getting trapped in local optima. In each generation of evolution, a pre-trained GRNN prediction model can be invoked to predict the electrical performance indicators of newly generated individuals, thus enabling rapid evaluation of candidate solution performance without repeatedly performing full-wave electromagnetic simulations.

[0073] Crossover operation: The probability of crossover is controlled by the crossover probability. The position of crossover is determined by random values, and the data at the corresponding positions of the two chromosomes are exchanged. Mutation operation: The probability of mutation is controlled by the mutation probability. The position of mutation is determined by random values, and the data at the corresponding positions on the chromosomes is inverted (i.e., 0 becomes 1, 1 becomes 0).

[0074] Optionally, during the iterative optimization process, the relevant strategies of the genetic algorithm can be dynamically adjusted according to the progress of the iterative optimization, such as adjusting the selection probability or mutation method, to further improve the optimization efficiency and search stability.

[0075] Furthermore, when the genetic algorithm reaches the preset iteration termination condition, such as the number of iterations reaching the set upper limit, the change in population fitness being less than the preset threshold, or the optimization result meeting the predetermined performance requirements, the optimal combination of structural parameters for the CTSV array that satisfies the multi-objective constraints can be determined. At this point, the updated combination of geometric structural parameters is output and used as the design parameters for the coaxial through-silicon via array, which can then be used for the physical structure design, layout implementation, or process parameter configuration of the CTSV array.

[0076] It should be noted that by combining the GRNN model with the genetic algorithm, this invention can significantly reduce the computational overhead caused by repeatedly calling full-wave simulation in traditional optimization methods while ensuring prediction accuracy. Furthermore, the multi-objective optimization method provided by this invention does not depend on a specific array size or structure and can be extended to the design of CTSV arrays of different sizes, interconnect densities, and application scenarios.

[0077] In summary, this invention provides a multi-objective optimization method for the electromagnetic transmission characteristics of a coaxial through-silicon via (CTSV) array. First, a full-wave simulation model of the CTSV array is constructed based on its physical structure, material parameters, optimizable geometric parameters, and scattering parameters. Then, a dataset including multiple combinations of geometric parameters and corresponding electrical performance indices is built based on this full-wave simulation model. Next, a Generalized Regression Neural Network (GRNN) model architecture is constructed using the dataset, and the optimal smoothing factor of the GRNN model architecture is determined using a particle swarm optimization algorithm. Based on this optimal smoothing factor and the dataset, the GRNN model is constructed and trained to obtain a well-trained GRNN model. Finally, based on a genetic algorithm and the trained GRNN model, the geometric parameter combinations of the CTSV array are iteratively solved, and the updated geometric parameter combinations are output as the design parameters for the CTSV array. Therefore, the GRNN model constructed in this invention can quickly predict electrical performance indicators based on the combination of geometric structural parameters. It effectively solves the problem that the relationship between geometric structural parameters and electrical performance indicators of CTSV arrays in the terahertz band is highly nonlinear, strongly coupled, and difficult to describe accurately by analytical methods. It also avoids frequent calls to three-dimensional full-wave electromagnetic simulation during the optimization process, thereby significantly reducing computational complexity and simulation time overhead, and improving the overall efficiency of CTSV array parameter optimization.

[0078] Furthermore, this invention leverages the global search capability of genetic algorithms to perform multi-objective collaborative optimization of the structural parameters of the CTSV array. Under conditions of multiple performance constraints, it can automatically optimize and obtain a combination of geometric structural parameters that meets the design requirements of low loss and low crosstalk, avoiding the problem of getting trapped in local optima in traditional empirical design and manual trial-and-error methods. Compared to traditional optimization methods that rely on extensive simulation calculations, this invention significantly shortens the design cycle and reduces design costs while ensuring design accuracy, demonstrating good engineering applicability and scalability.

[0079] In addition, the optimized design method proposed in this invention has good versatility and scalability, and can be flexibly adjusted according to the design requirements of different CTSV arrays and different application scenarios, making it suitable for various three-dimensional integrated circuit and high-speed interconnect design scenarios.

[0080] Another embodiment of the present invention provides a multi-objective optimization device for the electromagnetic transmission characteristics of a coaxial silicon via array, such as... Figure 3 As shown, the device includes: Module 401 is used to construct a full-wave simulation model of the coaxial through-silicon via array based on the physical structure, material parameters, optimizable geometric parameter combinations, and scattering parameters of the coaxial through-silicon via array to be optimized. The construction module 401 is also used to sample the optimizable geometric structure parameter combinations based on the full-wave simulation model, obtain multiple sets of geometric structure parameter combinations and electrical performance indicators corresponding to each set of geometric structure parameter combinations, and construct a dataset from the multiple sets of geometric structure parameter combinations and electrical performance indicators corresponding to each set of geometric structure parameter combinations. The model training module 402 is used to construct a generalized regression neural network model architecture by taking the combination of geometric structural parameters in the dataset as input and the corresponding electrical performance index as output, using the particle swarm optimization algorithm to determine the optimal smoothing factor of the generalized regression neural network model architecture, and constructing and training the generalized regression neural network model based on the optimal smoothing factor and the dataset to obtain the trained generalized regression neural network model. The optimization design module 403 is used to iteratively solve the combination of geometric structure parameters of the coaxial through silicon via array based on the genetic algorithm and the trained generalized regression neural network model. When the preset iteration termination condition is met, the updated combination of geometric structure parameters is output and used as the design parameters of the coaxial through silicon via array.

[0081] In the several embodiments provided by this invention, it should be understood that the apparatus and methods disclosed in this invention can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative. For example, the division of modules is merely a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed.

[0082] Furthermore, the functional modules in the various embodiments of the present invention can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module. The integrated module can be implemented in hardware or in the form of hardware plus software functional modules.

[0083] Another embodiment of the present invention provides a storage medium storing a computer program for executing the steps of the multi-objective optimization method for the electromagnetic transmission characteristics of the coaxial through-silicon via array described in the above embodiments. A further aspect of the present invention provides an electronic device including a memory and a processor. The memory stores a computer program, and the processor, when calling the computer program in the memory, implements the steps of the multi-objective optimization method for the electromagnetic transmission characteristics of the coaxial through-silicon via array described in the above embodiments. Specifically, the integrated modules implemented as software functional modules can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0084] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A multi-objective optimization method for the electromagnetic transmission characteristics of a coaxial silicon through-hole array, characterized in that, include: Based on the physical structure, material parameters, optimizable geometric parameter combinations, and scattering parameters of the coaxial through-silicon via array to be optimized, a full-wave simulation model of the coaxial through-silicon via array is constructed. Based on the full-wave simulation model, the optimizable geometric structure parameter combinations are sampled to obtain multiple sets of geometric structure parameter combinations and electrical performance indicators corresponding to each set of geometric structure parameter combinations. The multiple sets of geometric structure parameter combinations and electrical performance indicators corresponding to each set of geometric structure parameter combinations are then constructed into a dataset. Using the combination of geometric structural parameters in the dataset as input and the corresponding electrical performance index as output, a generalized regression neural network model architecture is constructed. The optimal smoothing factor of the generalized regression neural network model architecture is determined by the particle swarm optimization algorithm. Based on the optimal smoothing factor and the dataset, the generalized regression neural network model is constructed and trained to obtain the trained generalized regression neural network model. Based on the genetic algorithm and the trained generalized regression neural network model, the geometric structure parameter combination of the coaxial through silicon via array is iteratively solved. When the preset iteration termination condition is met, the updated geometric structure parameter combination is output and used as the design parameters of the coaxial through silicon via array.

2. The multi-objective optimization method for the electromagnetic transmission characteristics of coaxial silicon through-hole arrays according to claim 1, characterized in that, The full-wave simulation model of the coaxial through-silicon via array is constructed based on the physical structure, material parameters, optimizable geometric parameter combinations, and scattering parameters of the array to be optimized, including: Based on the physical structure, material parameters, and optimizable geometric parameter combinations of the coaxial silicon via array, an electromagnetic simulation model of a three-dimensional integrated circuit is established. The electromagnetic simulation model is calibrated based on the scattering parameters to obtain the full-wave simulation model of the coaxial silicon via array.

3. The multi-objective optimization method for the electromagnetic transmission characteristics of coaxial silicon through-hole arrays according to claim 1, characterized in that, Based on the full-wave simulation model, the optimizable geometric parameter combinations are sampled to obtain multiple sets of geometric parameter combinations and corresponding electrical performance indicators for each set of geometric parameter combinations, including: Based on the full-wave simulation model, the combination of geometric structure parameters is sampled to obtain multiple sets of sample parameter combinations; Full-wave simulation was performed on each set of sample parameter combinations to obtain the electrical performance indicators corresponding to each set of geometric structure parameter combinations.

4. The multi-objective optimization method for electromagnetic transmission characteristics of coaxial silicon through-hole arrays according to claim 1, characterized in that, The dataset is divided into a training set and a validation set according to a preset ratio; The process of determining the optimal smoothing factor for the generalized regression neural network model architecture using the particle swarm optimization algorithm, and constructing and training the generalized regression neural network model based on the optimal smoothing factor and the dataset to obtain the trained generalized regression neural network model includes: Initialize the particle swarm, set the search range of the smoothing factor of the initial generalized regression neural network model architecture, and randomly initialize the position and velocity of each particle in the particle swarm. The position of each particle represents a candidate smoothing factor. The particle swarm is iteratively optimized, and the following steps are performed in each iteration: S3.1, obtain the smoothing factor represented by the current position of each particle in the particle swarm, construct and train the corresponding generalized regression neural network model based on the smoothing factor corresponding to each particle and the training set; input the geometric structure parameters in the validation set into the generalized regression neural network model corresponding to each particle to obtain the electrical performance index predicted by each generalized regression neural network model, calculate the error between the electrical performance index predicted by each generalized regression neural network model and the corresponding real electrical performance index in the validation set, and use the error as the current fitness value of the corresponding particle; S3.2, Based on the current fitness value, historical best fitness value and historical global best position of each particle, determine the global best position and the individual best position of each particle. The global best position is the position corresponding to the minimum fitness value of the particle determined by the particle swarm during the iteration process. S3.3, based on the individual optimal position of each particle, the global optimal position, the velocity update formula of the particle swarm optimization algorithm, and the position update formula, update the current velocity and current position of each particle; S3.4, Repeat S3.1 to S3.3 until the preset maximum number of iterations is reached. Take the smoothing factor corresponding to the current global optimal position as the optimal smoothing factor, and construct and train a generalized regression neural network model based on the optimal smoothing factor and the training set to obtain the trained generalized regression neural network model.

5. The multi-objective optimization method for the electromagnetic transmission characteristics of a coaxial silicon through-hole array according to claim 4, characterized in that, The process of determining the global optimal position and the individual optimal position of each particle based on its current fitness value, historical best fitness value, and historical global best position includes: For each particle, the particle's current fitness value is compared with the historical best fitness value. If the current fitness value is better, the current position is determined as the individual best position of the particle; otherwise, the original individual best position is retained. Based on the individual optimal positions and corresponding fitness values ​​of all particles, the target individual optimal position is determined among the individual optimal positions of all particles. The target individual optimal position is compared with the historical global optimal position. If the target individual optimal position is better, it is determined as the global optimal position; otherwise, the historical global optimal position is retained.

6. The multi-objective optimization method for electromagnetic transmission characteristics of coaxial silicon through-hole arrays according to claim 1, characterized in that, The genetic algorithm and the trained generalized regression neural network model iteratively solve for the geometric structure parameter combination of the coaxial through-silicon via array. When a preset iteration termination condition is met, the updated geometric structure parameter combination is output and used as the design parameters of the coaxial through-silicon via array, including: The genetic algorithm is used to encode the combination of geometric structure parameters, and the combination of geometric structure parameters is used as a chromosome representation to construct an initial population, in which each individual corresponds to a set of geometric structure parameter combinations; The trained generalized regression neural network model is used to predict the electrical performance index corresponding to each individual in the initial population. A multi-objective fitness function is constructed based on the predicted electrical performance indicators, and the multi-objective fitness function is used to characterize the fitness of each individual. The genetic operation in the genetic algorithm is executed to iteratively update the combination of geometric structure parameters in the initial population. When the preset iteration termination condition is met, the updated combination of geometric structure parameters is output as the design parameters of the coaxial through-silicon via array.

7. The multi-objective optimization method for electromagnetic transmission characteristics of coaxial silicon through-hole arrays according to claim 6, characterized in that, The genetic operations include selection operations based on roulette wheel strategy, crossover operations based on two-point crossover, and mutation operations based on random bit flipping.

8. The multi-objective optimization method for electromagnetic transmission characteristics of coaxial silicon through-hole arrays according to claim 6, characterized in that, The electrical performance indicators include return loss, insertion loss, near-end crosstalk, and far-end crosstalk. The multi-objective optimization function is a function obtained by weighted summation of the return loss, the insertion loss, the mean of the near-end crosstalk, and the mean of the far-end crosstalk.

9. The multi-objective optimization method for electromagnetic transmission characteristics of coaxial silicon through-hole arrays according to claim 5, characterized in that, The iteration termination conditions include reaching a preset maximum number of iterations or the change in population fitness being less than a preset threshold.

10. A multi-objective optimization device for the electromagnetic transmission characteristics of a coaxial silicon through-hole array, characterized in that, include: A construction module is used to construct a full-wave simulation model of the coaxial through-silicon via array based on the physical structure, material parameters, optimizable geometric parameter combinations, and scattering parameters of the coaxial through-silicon via array to be optimized. The construction module is also used to sample the optimizable geometric structure parameter combinations based on the full-wave simulation model to obtain multiple sets of geometric structure parameter combinations and electrical performance indicators corresponding to each set of geometric structure parameter combinations, and to construct the multiple sets of geometric structure parameter combinations and electrical performance indicators corresponding to each set of geometric structure parameter combinations into a dataset. The model training module is used to construct a generalized regression neural network model architecture by taking the combination of geometric structure parameters in the dataset as input and the corresponding electrical performance index as output, using the particle swarm optimization algorithm to determine the optimal smoothing factor of the generalized regression neural network model architecture, and constructing and training the generalized regression neural network model based on the optimal smoothing factor and the dataset to obtain the trained generalized regression neural network model. The optimization design module is used to iteratively solve the combination of geometric structure parameters of the coaxial through-silicon via array based on the genetic algorithm and the trained generalized regression neural network model. When the preset iteration termination condition is met, the updated combination of geometric structure parameters is output and used as the design parameters of the coaxial through-silicon via array.

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