Parasitic parameter extraction method based on 3D Gaussian Splitting technology
Through the deep learning method based on 3D Gaussian Splatting technology, the problem of parasitic effect processing of three-dimensional structures in integrated circuit design is solved, efficient electromagnetic field solution and parasitic parameter extraction is achieved, design accuracy and speed are improved, and adaptability is strong.
Patent Information
- Application Number
- CN202411449911.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-17
- Publication Date
- 2025-01-14
AI Technical Summary
The prior art is difficult to accurately handle parasitic effects in three-dimensional structures in integrated circuit design, especially in multi-level integrated circuit design, and the electromagnetic field solution calculation is large and slow, making it difficult to adapt to more advanced process nodes.
The parasitic parameter extraction method based on 3D Gaussian Splatting technology is adopted to realize electromagnetic field solving through deep learning, randomly generate 3D circuit patterns, use electromagnetic field solver to solve electromagnetic field distribution, establish electromagnetic field data set, build a prediction model based on 3D Gaussian, and extract parasitic parameters. Parallel processing and model optimization are used with GPU.
It improves the accuracy of electromagnetic field solving and parasitic parameter extraction, shortens the design cycle, can adapt to various circuit layouts, has good versatility and calculation efficiency.
Smart Images
Figure CN119312762A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of electronic design automation, and in particular to a parasitic parameter extraction method based on 3D Gaussian Splatting in electronic design automation (EDA). Background Art
[0002] With the development of very large-scale integration technology, there are many layers of metal interconnects in integrated circuits. These interconnects can no longer be approximated as equipotential connections, and their parasitic effects under normal working conditions should be considered. In the field of integrated circuit design, the parasitic effects of interconnects determine key factors such as circuit delay, reliability, and power consumption. Accurately extracting and evaluating electromagnetic field parameters and parasitic parameters has become a key step, especially in high-frequency or high-speed applications. Figure 2 As shown in Figure 1, this process usually involves creating a physical model of the integrated circuit based on the layout information of the chip. In industrial applications, the layout information can be saved in a variety of different file formats, such as CFI, GDSII or OASIS. These files record the characteristics of conductors and dielectrics in detail, including their thickness, specific layout positions in the integrated circuit, and key parameters such as the relative dielectric constant of the dielectric.
[0003] By analyzing the layout data stored in the files, relevant information about conductors and dielectrics can be extracted, including not only their thickness and specific location in the chip, but also key parameters such as the relative dielectric constant of the dielectric, thereby building an integrated circuit geometric structure model. This model is the basis for subsequent electromagnetic field parameter extraction and is crucial to ensuring the accuracy of circuit performance analysis.
[0004] In integrated circuit design, accurate simulation and analysis of electromagnetic fields are essential for predicting and optimizing circuit performance. Modern electromagnetic field solvers, such as software tools based on the finite element method (FEM), boundary element method (BEM), or finite-difference time-domain method (FDTD), can help designers evaluate and optimize electromagnetic field effects in circuits, but they have problems such as large computational complexity and slow speed. For example, although the indirect boundary element method reduces the variables and the amount of original information in the problem, it generates a full coefficient matrix, which makes the extraction process time-consuming and difficult to adapt to more advanced process nodes; in addition, existing technologies may have difficulty in accurately handling parasitic effects in three-dimensional structures, especially in multi-faceted integrated circuit design. Summary of the invention
[0005] In order to solve the above problems, the present invention provides a parasitic parameter extraction method based on 3D Gaussian Splatting technology. The method uses deep learning to solve the electromagnetic field and can extract parasitic parameters quickly and accurately.
[0006] The technical solution of the present invention is specifically described as follows.
[0007] The present invention provides a parasitic parameter extraction method based on 3D Gaussian Splatting technology, comprising the following steps:
[0008] Step 1: Randomly generate 3D circuit patterns to simulate different layout structures in integrated circuits;
[0009] Step 2: Use an electromagnetic field solver to solve the electromagnetic field distribution of the generated 3D circuit pattern;
[0010] Step 3: Using the solved electromagnetic field distribution, an electromagnetic field data set is established to train the spatial characteristics of the radiation field and construct a prediction model based on 3D Gaussian;
[0011] Step 4: Use the trained 3D Gaussian-based prediction model to extract parasitic parameters; where:
[0012] In step 3, key features are extracted from the electromagnetic field distribution information at the corresponding coordinates of the 3D circuit pattern, including charge distribution, electromagnetic field, and parasitic capacitance C, resistance R, and inductance L of the interconnection line; these features are used to establish an electromagnetic field data set to train and construct a prediction model based on 3D Gaussian;
[0013] During the training process, the model generates a three-dimensional surface by learning the geometric structure and electromagnetic field distribution information in the data; it performs parallel processing on the GPU through differentiable rasterization, and calculates the loss function Loss for comparison and iteration to update the model parameters and achieve model optimization.
[0014] In the present invention, in step 1, the method for randomly generating a 3D circuit pattern to simulate an integrated circuit layout is as follows:
[0015] (1) Define the overall design parameters of the integrated circuit, including size, shape, and material properties;
[0016] (2) using computer-aided design (CAD) software to randomly generate an initial 3D pattern according to defined parameters;
[0017] (3) determining geometric parameters of the generated pattern to meet specific performance requirements; wherein: geometric parameters include line width, line spacing, and contact hole size; performance parameters include power consumption, area, and speed;
[0018] (4) Perform design rule checks to check for electrical problems in the design to ensure the manufacturability of the design;
[0019] (5) determining initial conditions and boundary conditions of the pattern in a finite domain model according to the designed 3D circuit pattern;
[0020] (6) If the pattern design rule check fails, review the design parameters and layout and make adjustments.
[0021] In the present invention, in step 2, the electromagnetic field solver is a software tool based on the finite element method FEM, the boundary element method BEM or the finite difference time domain method FDTD.
[0022] In the present invention, in step 3, during the radiation field training and learning process, the corresponding sparse point cloud is first generated, and each point is modeled as a 3D Gaussian distribution, which includes the mean μ of the sampling point, the covariance matrix Σ, the parasitic parameters (R, L, C), and the charge Q. μ defines the position of the Gaussian ellipsoid, and the covariance matrix Σ defines the shape and size of the Gaussian ellipsoid. For the main conductor, rays are emitted to the surroundings and sampling points are sampled. Each voxel obtained by sampling is represented by a Gaussian distribution, and the obtained parasitic parameter (R, L, C) information is integrated into the Gaussian function, which is expressed as:
[0023]
[0024] Among them, G is a Gaussian function that describes the electromagnetic field distribution at position x, μ is the mean of the Gaussian function, Σ is the covariance matrix of the Gaussian function, which is a 3×3 matrix that describes the distribution shape of the Gaussian ellipsoid, and c(x) is a vector used to represent the parasitic parameters (R, L, C) at position x. c(x) is calculated by spherical harmonics:
[0025]
[0026] Here, Y lm (θ, φ) are spherical harmonics, a lm are the corresponding coefficients, θ and φ are angles in spherical coordinates, representing the direction from the center of the Gaussian to x.
[0027] In the present invention, in step 3, after the point cloud is generated, the projection matrix is generated, as follows:
[0028] Through sampling parameters, the points are projected onto the image plane, and the parasitic parameter (R, L, C) information obtained by sampling is recorded as the attributes of the point cloud; through projection matrix generation, occlusion processing in 3D interconnected sampling is realized.
[0029] In the present invention, in step 3, the prediction model based on 3D Gaussian is a 3D Gaussian Splatting model, and the prediction model based on 3D Gaussian is used for electromagnetic field and charge distribution prediction.
[0030] In the present invention, in step 3, the loss function Loss is defined as follows:
[0031] L=(1-λ)L MSE +λL SSIM
[0032] Among them, L MSE It is used to measure the difference between the extracted parasitic parameters and the true values, L SSIM Used to measure the similarity of structures, defined as:
[0033]
[0034] L SSIM =1-SSIM(I pred -I true )
[0035] Among them, I i pred is the parasitic parameter characteristic of the i-th point cloud predicted by the model, I i true is the parasitic parameter characteristic of the real corresponding point cloud i, N is the total number of point clouds, and SSIM is the structural similarity index, which is used to evaluate the similarity between the predicted chip pattern structure and the real information.
[0036] In the present invention, in step 3, during the training process, the distribution mode of the point cloud is changed based on the gradient adaptive algorithm according to the calculated Loss, as follows:
[0037] According to the gradient transferred to the point, the 3D Gaussian is segmented or cloned, and the gradient is transferred to the 3D Gaussian to update its stored position μ, update the covariance matrix Σ, and the spherical harmonic function used to represent the parasitic parameters (R, L, C).
[0038] In the present invention, in step 3, one or more of the resistance R, inductance L, and capacitance C in the parasitic parameters may be extracted and solved separately or simultaneously.
[0039] In the present invention, in step 4, the charge distribution is obtained based on the electromagnetic field around the main conductor, and the resistance R, inductance L, and capacitance C are further solved through the gradient adaptive algorithm; the calculated loss and the gradient returned by the 3D Gaussian point cloud are adapted to obtain better rendering effects and calculation accuracy.
[0040] As described above, the present invention extracts the parasitic parameters of large-scale integrated circuits by sampling the local electromagnetic field and using the idea of 3D Gaussian Splatting rendering; compared with the prior art, the present invention has the following advantages:
[0041] (1) Improve the accuracy of electromagnetic field solution and parasitic parameter extraction.
[0042] (2) Improved solution speed and shortened design cycle.
[0043] (3) It can adapt to various circuit layouts and has good versatility. BRIEF DESCRIPTION OF THE DRAWINGS
[0044] Figure 1 : Flow chart of the parasitic parameter extraction method based on 3D Gaussian Splatting technology of the present invention.
[0045] Figure 2 : 3D integrated circuit layout diagram.
[0046] Figure 3 : 3D Gaussian sampling principle diagram.
[0047] Figure 4 : Schematic diagram of 3D Gaussian sparse point cloud generation.
[0048] Figure 5 : Schematic diagram of the pattern generation process.
[0049] Figure 6 : Schematic diagram of electromagnetic field information extraction and feature training process.
[0050] Figure 7 :Schematic diagram of parasitic parameter prediction process using 3D Gaussian Splatting technology. DETAILED DESCRIPTION
[0051] The present invention provides a parasitic parameter extraction method based on 3D Gaussian Splatting technology, the principle of which is as follows:
[0052] Radiation field training and learning generate the corresponding sparse point cloud. Each point is modeled as a 3D Gaussian distribution. These 3D Gaussian distributions include the mean μ of the sampling point, the covariance matrix Σ, parasitic parameters (R, L, C), the charge Q, etc. μ defines the position of the Gaussian ellipsoid, and the covariance matrix Σ defines the shape and size of the Gaussian ellipsoid. For the main conductor, rays are emitted to the surrounding area and sampling points are performed. Each voxel obtained by sampling is represented by a Gaussian distribution. By integrating the obtained parasitic parameters (R, L, C) into the Gaussian function, it can be expressed as:
[0053]
[0054] Among them, G is a Gaussian function that describes the electromagnetic field distribution at position x, μ is the mean of the Gaussian function, Σ is the covariance matrix of the Gaussian function, which is a 3×3 matrix that describes the distribution shape of the Gaussian ellipsoid, and c(x) is a vector that represents the parasitic parameters (R, L, C) at position x, which can be calculated by spherical harmonics:
[0055]
[0056] Here, Y lm (θ, φ) are spherical harmonics, a lm are the corresponding coefficients, θ and φ are angles in spherical coordinates, representing the direction from the center of the Gaussian to x.
[0057] like Figure 1 As shown, the present invention provides a parasitic parameter extraction method based on 3D Gaussian Splatting technology, comprising the following steps:
[0058] Randomly generate 3D circuit patterns to simulate different layout structures in integrated circuits;
[0059] Use the electromagnetic field solver to solve the electromagnetic field distribution of the generated 3D circuit pattern, obtain the solution results under the corresponding coordinates, establish a data set, and analyze the corresponding electromagnetic field data;
[0060] Extract key features from the established electromagnetic field data set and use these features to train a 3D Gaussian-based prediction model. During the training process, the model will generate a three-dimensional surface by learning the geometric structure and electromagnetic field distribution information in the data;
[0061] The parasitic capacitance, resistance and inductance of interconnects are estimated based on 3D Gaussian Splatting technology, and GPU is used to achieve parallel accelerated calculation and parasitic parameter extraction.
[0062] The specific implementation of the present invention is described below in conjunction with the accompanying drawings:
[0063] Example 1
[0064] In Example 1, Figure 4 As shown, pattern generation is the first step in integrated circuit design and simulation. This process usually includes the following key steps:
[0065] The method of randomly generating 3D patterns to simulate integrated circuit layout is as follows:
[0066] Define the overall design parameters of the integrated circuit, including size, shape, and material properties;
[0067] Using computer-aided design (CAD) software, the initial 3D pattern is randomly generated according to the defined parameters;
[0068] Determine the geometric parameters of the generated pattern, such as line width, line spacing, contact hole size, etc., to meet specific performance requirements, including power consumption, area and speed;
[0069] Perform design rule checks to check electrical problems in the design (electrical rule check ERC, design rule check DRC constraints) to ensure the manufacturability of the design;
[0070] According to the designed 3D circuit pattern, initial conditions and boundary conditions of the pattern are determined in a finite domain model;
[0071] If the pattern design rule check fails, review the design parameters and layout and make adjustments.
[0072] Example 2
[0073] like Figure 5 , Example 2 involves using dedicated analysis software to simulate and analyze the electromagnetic field distribution in an integrated circuit. This process generally includes the following steps:
[0074] Electromagnetic field analysis solves electromagnetic field distribution: Import the generated pattern data into the electromagnetic field analysis software. Set simulation parameters, frequency to define simulation boundary conditions (such as voltage, fixed charge), material properties (such as dielectric constant, magnetic permeability, electrical conductivity), simulation accuracy and other parameters. Run the simulation, start the simulation process, and the software will calculate the distribution of the electromagnetic field.
[0075] Get the solution result: Figure 6 ,By acquiring the electromagnetic field distribution information under the corresponding coordinates, key features such as charge distribution, electromagnetic field, etc., a data set is established for the subsequent ,training of radiation fields.
[0076] Training radiation field: Use the extracted features and known results to train the model. Perform model evaluation to assess the model’s prediction accuracy and make necessary adjustments. If the model’s prediction performance is poor and the convergence is not up to standard, the designer needs to collect data again or optimize the model parameters.
[0077] Optimization and expansion: For large-scale integrated circuits, use distributed training systems, such as Grendel, to parallelize computing on multiple GPUs to improve computing efficiency.
[0078] Example 3
[0079] like Figure 7 , Embodiment 3 is to apply the trained model to a new pattern to predict its electromagnetic field. This process usually includes the following steps:
[0080] The initialized sparse point cloud is obtained through Structure from motion (sfm): the rays emitted by the main body are sampled, the sampled feature points are detected, the sampling view is associated with the world coordinates, and the sampling motion is estimated by analyzing the matched feature points; the sampling information is combined with the results of sfm, and the feature points are projected from the two-dimensional image to the three-dimensional space to generate a sparse point cloud.
[0081] A set of 3D Gaussian ellipsoids is generated based on the initialized point cloud: each point cloud position is represented as a 3D Gaussian ellipsoid, whose center μ defines the position of the ellipsoid, the covariance matrix Σ defines the shape and size of the ellipsoid, and the spherical harmonic function is used to record the relevant parasitic parameter (R, L, C) information.
[0082] Projection matrix generation: Through sampling parameters, the points are projected onto the image plane, and the parasitic parameter (R, L, C) information obtained by sampling is recorded as the attributes of the point cloud; through projection matrix generation, occlusion processing in 3D interconnected sampling can be realized, which is a key step in achieving high-quality parasitic parameter extraction.
[0083] Differentiable rasterization: The entire scene is divided into fixed-size, independent tiles. The parasitic parameters (R, L, C) and charge distribution of each tile are stored in the GPU's on-chip cache. Each independent tile is rasterized in parallel, and the corresponding charge distribution and parasitic parameters (R, L, C) are calculated for each pixel. The loss function is calculated by comparing with the parasitic parameters (R, L, C) obtained or calculated through the electromagnetic field distribution that contain real information, and the gradient is returned.
[0084] According to the calculated Loss, the distribution of the point cloud is adaptively changed based on the gradient: according to the gradient transferred to the point, the 3D Gaussian is segmented or cloned, and the gradient is transferred to the 3D Gaussian to update its stored position, covariance matrix, spherical harmonics used to represent parasitic parameters (R, L, C) and other parameters.
[0085] Model prediction: Use the trained 3D Gaussian Splatting model to predict electromagnetic fields and charges.
[0086] Result analysis: Analyze the results predicted by the model, and perform circuit design or further simulation analysis based on the predicted results.
[0087] If the predicted results are significantly different from the actual values, you may need to retrain the model or adjust the prediction algorithm.
[0088] Example 4
[0089] Embodiment 4 is a Loss loss function calculation and verification method, which is used for gradient backpropagation to achieve point cloud optimization.
[0090] In 3D Gaussian Splatting, the initial conditions and boundary conditions are combined through the optimization process. To ensure that the model can accurately extract parasitic parameters (R, L, C) and electromagnetic field information from the 3D Gaussian ellipsoid set, the loss function can be defined as follows:
[0091] L=(1-λ)L MSE +λL SSIM
[0092] Among them, L MSE It is used to measure the difference between the extracted parasitic parameters and the true values, L SSIM It is used to measure the similarity of structures and can be defined as:
[0093]
[0094] Here, I i pred is the parasitic parameter characteristic of the i-th point cloud predicted by the model, I i true is the parasitic parameter characteristic of the real corresponding point cloud i, N is the total number of point clouds, and SSIM is the structural similarity index, which is used to evaluate the similarity between the predicted chip pattern structure and the real information.
[0095] Example 5
[0096] We perform capacitance tests on a 15nm process technology dataset, a 15nm process technology based on FreePDK15. For each process technology, we select some multi-layer metal layer combinations to generate 3-D patterns. With each pattern, we generate several sample structures to form a dataset, and then randomly split the dataset into a training subset (accounting for 90% of the samples) and a test subset (accounting for 10% of the samples). Using 3D Gaussian Splatting technology, based on A100 GPU, through the results of 6 minutes and 50 minutes of training, the model of the present invention has an accuracy of less than 7.5% on the capacitor test data set in 99% of the cases when training for 6 minutes, and has an accuracy of less than 7% on the capacitor test data set in 99% of the cases when training for 50 minutes, while the original loss function accuracy is less than 10% in 99% of the cases, which can provide accurate parasitic parameter prediction for 3-D mode structures with a variable number of conductors; in addition, the running time based on the present invention is greatly improved than the extraction rate under the multi-physics field solver, and the memory consumption is negligible, which further proves its effectiveness and practicality in full-chip parasitic parameter extraction.
Claims
1. A parasitic parameter extraction method based on 3D Gaussian Splatting technology, characterized in that: The following steps are involved: Step 1: Randomly generate 3D circuit patterns to simulate different layout structures in integrated circuits; Step 2: Use an electromagnetic field solver to solve the electromagnetic field distribution of the generated 3D circuit pattern; Step 3: Using the solved electromagnetic field distribution, an electromagnetic field data set is established to train the spatial characteristics of the radiation field and construct a prediction model based on 3D Gaussian; Step 4: Use the trained 3D Gaussian-based prediction model to extract parasitic parameters; where: In step 3, key features are extracted from the electromagnetic field distribution information at the corresponding coordinates of the 3D circuit pattern, including charge distribution, electromagnetic field, and parasitic capacitance C, resistance R, and inductance L of interconnects; these features are used to establish an electromagnetic field data set to train and construct a prediction model based on 3D Gaussian; During the training process, the model generates a three-dimensional surface by learning the geometric structure and electromagnetic field distribution information in the data; it performs parallel processing on the GPU through differentiable rasterization, and calculates the loss function Loss for comparison and iteration to update the model parameters and achieve model optimization.
2. The parasitic parameter extraction method based on 3D Gaussian Splatting technology according to claim 1, characterized in that: In step 1, the method of randomly generating a 3D circuit pattern to simulate an integrated circuit layout is as follows: (1) Define the overall design parameters of the integrated circuit, including size, shape, and material properties; (2) using computer-aided design (CAD) software to randomly generate an initial 3D pattern according to defined parameters; (3) determining geometric parameters of the generated pattern to meet specific performance requirements; wherein: geometric parameters include line width, line spacing, and contact hole size; performance parameters include power consumption, area, and speed; (4) Perform design rule checks to check for electrical problems in the design to ensure the manufacturability of the design; (5) determining initial conditions and boundary conditions of the pattern in a finite domain model according to the designed 3D circuit pattern; (6) If the pattern design rule check fails, review the design parameters and layout and make adjustments.
3. The parasitic parameter extraction method based on 3D Gaussian Splatting technology according to claim 1, characterized in that: In step 2, the electromagnetic field solver is a software tool based on the finite element method FEM, the boundary element method BEM or the finite difference time domain method FDTD.
4. The parasitic parameter extraction method based on 3D Gaussian Splatting technology according to claim 1, characterized in that: In step 3, during the radiation field training and learning process, the corresponding sparse point cloud is first generated, and each point is modeled as a 3D Gaussian distribution. These 3D Gaussian distributions contain the mean μ of the sampling point, the covariance matrix Σ, the parasitic parameters (R, L, C), and the charge Q. μ defines the position of the Gaussian ellipsoid, and the covariance matrix Σ defines the shape and size of the Gaussian ellipsoid. For the main conductor, rays are emitted to the surrounding area and sampling points are sampled. Each voxel obtained by sampling is represented by a Gaussian distribution, and the obtained parasitic parameter (R, L, C) information is integrated into the Gaussian function, which is expressed as: Among them, G is a Gaussian function that describes the electromagnetic field distribution at position x, μ is the mean of the Gaussian function, Σ is the covariance matrix of the Gaussian function, which is a 3×3 matrix that describes the distribution shape of the Gaussian ellipsoid, and c(x) is a vector used to represent the parasitic parameters (R, L, C) at position x. c(x) is calculated by spherical harmonics: Here, Y lm (θ, φ) are spherical harmonics, a lm are the corresponding coefficients, θ and φ are angles in spherical coordinates, representing the direction from the center of the Gaussian to x.
5. The parasitic parameter extraction method based on 3D Gaussian Splatting technology according to claim 1, characterized in that: In step 3, the rays emitted by the main conductor are first sampled, the sampled feature points are detected, and a sparse point cloud is generated. Then, a 3D Gaussian ellipsoid set is generated based on the initialized point cloud, and a projection matrix is generated. The steps for generating the projection matrix are as follows: Through sampling parameters, the points are projected onto the image plane, and the parasitic parameter (R, L, C) information obtained by sampling is recorded as the attributes of the point cloud; through projection matrix generation, occlusion processing in 3D interconnected sampling is realized.
6. The parasitic parameter extraction method based on 3D Gaussian Splatting technology according to claim 1, characterized in that: In step 3, the prediction model based on 3D Gaussian is a 3D Gaussian Splatting model, and the prediction model based on 3D Gaussian is used for electromagnetic field and charge distribution prediction.
7. The parasitic parameter extraction method based on 3D Gaussian Splatting technology according to claim 1, characterized in that: In step 3, the loss function Loss is defined as follows: L=(1-λ)L MSE +λL SSIM Among them, L MSE It is used to measure the difference between the extracted parasitic parameters and the true values, L SSIM Used to measure the similarity of structures, defined as: L SSIM =1-SSIM(I pred -I true ) in, is the parasitic parameter characteristic of the i-th point cloud predicted by the model, I i true is the parasitic parameter characteristic of the real corresponding point cloud i, N is the total number of point clouds, and SSIM is the structural similarity index, which is used to evaluate the similarity between the predicted chip pattern structure and the real information.
8. The parasitic parameter extraction method based on 3D Gaussian Splatting technology according to claim 7, characterized in that: In step 3, during the training process, the distribution of the point cloud is changed based on the calculated Loss based on the gradient adaptive algorithm, as follows: According to the gradient passed to the point, the 3D Gaussian is segmented or cloned, and the gradient is passed to the 3D Gaussian to update its stored position μ, update the covariance matrix Σ, and update the spherical harmonics used to represent the parasitic parameters (R, L, C).
9. The parasitic parameter extraction method based on 3D Gaussian Splatting technology according to claim 1, characterized in that: In step 4, the charge distribution is obtained based on the electromagnetic field around the main conductor, and the resistance R, inductance L, and capacitance C are further solved through the gradient adaptive algorithm.