Parasitic parameter extraction method based on random walk algorithm in EDA

Abstract

The invention discloses a parasitic parameter extraction method based on a random walk algorithm in EDA. The method comprises the following steps: firstly, carrying out spatial discretization on a to-be-processed region, dividing a target region into a plurality of grid units, and applying a boundary condition on a grid, so that a random walking path is converged under the boundary condition; thirdly, enabling the discrete region to be equivalent to a network model, and calculating the electric field distribution. Then, through a random walking process, starting from a grid node and randomly selecting an adjacent node to walk, and the path probability of each walking is based on a random transfer process of a Markov chain; the termination probability of the walking sample is used for constructing potential distribution of each node, so that parasitic parameters are extracted. And finally, performing convergence judgment on a walking result based on a statistical method of a large number law to obtain an expected parasitic parameter value. The method has high parallelism and low storage requirements, can keep efficient calculation performance in parameter extraction of a large-scale integrated circuit, and improves parasitic parameter extraction efficiency of an EDA tool.

Description

Technical Field

[0001] The present invention belongs to the technical field of electronic design automation (EDA), and in particular, relates to a parasitic parameter extraction method based on a random walk algorithm in EDA. Background Art

[0002] With the continuous advancement of integrated circuit technology, feature sizes are gradually shrinking, and signal frequencies are continuously increasing, resulting in the increasingly obvious impact of parasitic effects on circuit performance. Parameters such as parasitic capacitance and resistance can cause problems such as signal delay, crosstalk, and noise, posing a threat to the reliability and performance of high-frequency circuits. Especially in deep submicron and nanoscale processes, the delay of interconnects begins to dominate circuit speed, and parasitic parameters become a key factor affecting the overall performance of the chip. Therefore, quickly and accurately extracting these parasitic parameters is an important requirement in integrated circuit design.

[0003] Common parasitic parameter extraction methods, such as the finite element method (FEM), boundary element method (BEM), and moment method (MoM), have advantages in accuracy, but have great limitations when dealing with complex geometric structures and multimedia materials, especially for non-Manhattan structures. These methods usually require discretization of the entire target area, resulting in large storage and computational overhead. For large-scale integrated circuit design, traditional methods are difficult to adapt to the needs of high efficiency. The random walk method has the characteristics of high theoretical accuracy and no discrete error, and can be highly parallelized, making it particularly suitable for processing multi-node, large-scale computing tasks. However, its convergence speed is slow and its adaptability to complex geometric shapes and materials is poor. In the traditional framework, it is not efficient when dealing with complex geometric structures and multimedia, especially when a large number of suspended conductors are involved. Summary of the invention

[0004] In order to solve the problem of insufficient adaptability of the traditional random walk method to complex structures, the present invention provides a new parasitic parameter extraction method based on the random walk algorithm in EDA, which uses a discrete exterior differential method, a numerical method adapted to complex geometric structures and multimedia materials, which converts the physical field problem into a spatially discrete electrical network model to achieve an equivalent description of the complex system. Combined with the discrete exterior differential framework, the random walk method can extract parasitic parameters on the grid by constructing an equivalent network model; this combination can significantly improve the computational efficiency and solve the problem of insufficient adaptability of the traditional random walk method to complex structures. The present invention has high parallelism and low storage requirements, can maintain efficient computing performance in the parameter extraction of large-scale integrated circuits, and improve the parasitic parameter extraction efficiency of EDA tools, thereby laying the foundation for subsequent design processes.

[0005] The technical solution of the present invention is specifically described as follows.

[0006] The present invention provides a parasitic parameter extraction method based on a random walk algorithm in EDA, which is used for efficiently extracting parasitic capacitance and parasitic resistance parameters in complex geometric structures and multi-media environments in integrated circuits, and comprises the following steps:

[0007] (1) Establishing a spatial discrete grid

[0008] Performing spatial discretization on the target region in the integrated circuit and dividing it into grid cells;

[0009] (2) Setting boundary conditions and end points

[0010] Boundary conditions are imposed on the discrete grid, and nodes with known potential or stable boundary potential are set as the termination points of the random walk;

[0011] (3) Construct an equivalent network and calculate the electric potential

[0012] Using the discrete exterior differential framework, each grid unit is regarded as a node in the electrical network model. Each node represents the electric potential at a different position. The connection between adjacent nodes is equivalent to a resistor or capacitor element to represent the potential difference and construct an equivalent network. The equivalent network converts the physical field problem into an electrical network model, and then obtains the potential distribution through network calculation.

[0013] (4) Random walk process

[0014] The potential distribution is calculated by simulating the random movement of electrons or currents in the grid. Starting from a grid node, the adjacent nodes are randomly selected for walking until the preset end point is reached. Each walk follows the random transfer principle of the Markov chain, and the transfer probability between nodes is determined by their equivalent resistance or capacitance. The random walk process adopts the independence principle and uses parallel computing for multi-path random walks.

[0015] (5) Statistics and convergence judgment

[0016] The walking process is repeated many times, and the potential values ​​of the termination nodes are counted and the law of large numbers is used to ensure the convergence of the potential values ​​and obtain the desired parasitic parameter values.

[0017] In the present invention, in step (1), establishing a spatial discrete grid is the basis of the entire parasitic parameter extraction method, which does not require the grid to be orthogonal. Its main purpose is to divide the target area (such as a part of an integrated circuit) into a number of small units so that the subsequent random walk algorithm can calculate the physical parameters on each unit. The target area is discretized to convert the complex geometric structure into a plurality of regular small areas (grid units) for easy numerical calculation. In this way, the physical parameters (such as electric potential) of each unit can be calculated independently and share information with adjacent units. The division of the grid makes it possible to locally process complex geometry or material properties when calculating parasitic parameters without directly processing the entire large area. This division also provides a "walking path" for the random walk method, and each unit can be regarded as a walking node in the algorithm.

[0018] The grid unit types are divided into regular grids: usually rectangular or cubic grids are used, which can be easily implemented and suitable for geometrically simple structures. Irregular grids: When the target area has a complex shape or contains multiple media, the use of irregular grids (such as triangles or tetrahedron units) can more accurately describe the shape and material of the target structure. The present invention uses regular grids for some areas and irregular grids for complex areas, which can improve the calculation efficiency while ensuring accuracy.

[0019] Grid accuracy affects the accuracy and resource overhead of calculations. Finer grid division will improve the calculation accuracy, but it will also increase storage and calculation costs. Therefore, a trade-off needs to be made between accuracy and efficiency, and the grid density is usually adjusted according to the required parameter extraction accuracy. The present invention uses a local encrypted grid. In areas with strong interconnect parasitic effects (such as conductor boundaries and near suspended conductors), an encrypted grid can be used to improve local calculation accuracy, while a coarser grid is maintained in other areas to reduce the amount of calculation.

[0020] In the present invention, in step (2), boundary conditions and end points are set, and defining appropriate boundary conditions and walk end points is crucial to ensure the accuracy and efficiency of the algorithm. This step not only provides a control mechanism for the random walk method, avoiding invalid calculations, but also helps to achieve accurate electric field distribution calculations in the target area. The end point of the random walk is a node where the set potential is known or the boundary potential is stable. Each time the walk reaches such a node, the walk of the path will be stopped to avoid further calculation of invalid paths.

[0021] Dirichlet boundary conditions are set on the discrete grid, that is, fixed potentials are assigned to some nodes. For example, a known voltage value is set on the conductor boundary of the target area, so that the potential of these nodes becomes a fixed value. For some specific boundary nodes, such as floating conductors, this boundary condition ensures the termination of the walking algorithm.

[0022] In addition, the boundary conditions use nodes with known electric potential as absorbing states, which means that once the path reaches these nodes, the path calculation stops. This can control the termination of the walk and ensure that each path can reach the terminal state within a reasonable number of steps.

[0023] In the present invention, in step (3), an equivalent network is constructed and the potential is calculated, and boundary conditions and termination points are set. After meshing, each grid unit is regarded as a node in the electrical network model, and each node represents the potential at a different position. The connection between adjacent nodes is equivalent to a resistor or capacitor element to represent the potential difference. This equivalent network converts complex physical field problems into an electrical network model, so that the potential distribution can be obtained by network calculation.

[0024] According to the principle of discrete exterior differential method, combined with the electric field description of Maxwell equations, a linear equation of electric potential is established for each grid node. In this way, the electric potential calculation of the entire area is transformed into a problem of solving a linear equation system. In the linear equation, the unknown number of each equation corresponds to the electric potential value of a node, and the potential difference between adjacent nodes represents the electric field strength. The initial distribution of the initial electric potential is obtained.

[0025] In the present invention, in step (4), the "random walk process" is the core step of the method, which calculates the potential distribution by simulating the random movement of electrons or currents in the grid. The random walk starts from a node in the grid. The node is usually the target position of the potential to be solved, or a representative node of a specific area.

[0026] Each walk follows the random transfer principle of the Markov chain, moving from the current node to the adjacent node. The transfer probability between nodes is determined by their equivalent resistance or capacitance. The smaller the relative resistance or capacitance, the greater the probability of walking. This probability setting reflects the distribution of the potential difference between nodes. Each time starting from a node, the adjacent node is randomly selected according to the transfer probability, and the walking path forms a random process. The random walking process adopts the independence principle, that is, the walking of each path is independent and is not affected by other walks.

[0027] The walk continues until it reaches a preset boundary condition or end point. Boundary conditions are usually nodes with fixed potentials. Once these nodes are reached by the walk, they serve as the end points of the walk path. When the boundary condition is reached, the walk process stops immediately and the end position of the walk path is recorded. In this way, random walks will not be performed indefinitely, thereby reducing invalid walk paths. As the number of walks increases, the potential of each node will tend to stabilize, that is, it will reach a convergence state. When the calculated potential value changes less than the preset threshold, the result is considered to have converged and the number of walks will no longer increase.

[0028] In the present invention, in step (5), statistics and convergence judgment are performed to statistically analyze the results of multiple random walks to calculate the potential values ​​of the nodes and determine whether the results have reached the convergence condition. After each random walk, the state of the end point is recorded, including the position and potential value of its boundary node.

[0029] Record the frequency of each termination point being visited during multiple walks. The termination frequency of each boundary node will be used to weightedly calculate the potential of the node to be solved. Multiply the potential value of each boundary node by its corresponding termination frequency, and add up these weighted values ​​to obtain the average potential of the target node. This method ensures that the potential calculation not only reflects the boundary conditions, but also takes into account the probability distribution of the random walk path. The termination frequency of each boundary node is equivalent to the probability weight of the node. The node with a higher termination frequency contributes more to the potential of the target node, thereby ensuring the physical rationality of the potential calculation.

[0030] In the process of calculating the potential, the rate of change of the node potential is observed to determine whether convergence has been achieved. If the potential value changes less than the preset threshold in multiple consecutive calculations, it is considered to have converged. The node potential is updated after each walk and compared with the last calculation result. The change amplitude is dynamically monitored and the threshold of the convergence error is gradually lowered to ensure the accuracy of the final result. When the convergence of the target node potential meets the requirements, further walks are stopped to avoid unnecessary calculations. Controlling the number of walks in this way helps to balance the calculation accuracy and resource overhead.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] The method of the present invention uses the law of large numbers to ensure the convergence of the potential value. As the number of walks increases, the accuracy of the statistical results gradually improves, but once the convergence condition is reached, the number of walks will no longer increase. Multi-core or multi-node processors are used to record and count the walk results in parallel to speed up the judgment of the convergence process. Through the parallelized statistical mechanism, the convergence of the node potential can be quickly judged. As the number of walk samples increases, the tolerance of the convergence error is gradually reduced to balance the calculation speed and accuracy. A larger error tolerance is allowed in the early stage, and a smaller tolerance is required in the later stage, so that the accuracy of the results is gradually improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 The flow chart of overall parasitic extraction is described. DETAILED DESCRIPTION

[0034] The present invention provides a parasitic parameter extraction method based on a random walk algorithm in EDA, which comprises the following steps:

[0035] Step 1: The adaptive meshing algorithm dynamically adjusts the mesh density based on the geometric characteristics of the area. For areas with high parasitic effects (such as wire edges and near vias), denser mesh elements are used, while sparser meshes are used in other areas. This adaptive meshing method can improve calculation accuracy and reduce unnecessary calculations. The specific steps include:

[0036] 1. Identify areas of the circuit where the electric field strength or parasitic coupling effect is strong.

[0037] 2. Automatically refine the mesh in these areas to ensure that the details of complex structures are fully captured.

[0038] 3. Keep larger mesh cells in low coupling or empty areas to reduce computational overhead.

[0039] Step 2: Dirichlet boundary conditions are used to set boundaries with known potentials, such as boundary nodes of conductors. Assuming that the boundary potential of the conductor is known, fixed potential values ​​are set for these nodes so that the random walk terminates when it reaches these nodes. The end point of the walk is defined as an absorbing state, that is, the walk will stop immediately when it reaches this node. This setting of the absorbing state ensures that the walk will not enter a meaningless cycle area, reducing unnecessary calculations. For example, under the Dirichlet boundary condition, the boundary nodes are set to absorbing states. When the walking path reaches the absorbing state, it terminates to prevent the path from exceeding the actual calculation area. The setting of the absorbing state is achieved by assigning a specific state to each boundary node. Usually, the potential of the terminal node of the absorbing state is set to a fixed value to ensure that the walking path can converge to the boundary. After reaching the absorbing state in the Markov chain model, the transition probability is set to zero to ensure that the walk stops when it reaches the absorbing state and no longer transfers to other nodes.

[0040] Step 3: Each grid node is regarded as a node in the electrical network, and the connection relationship between adjacent grid nodes is represented by capacitors or resistors. Based on the equivalent electrical network, the potential of each node can be obtained by the potential of the adjacent nodes and the equivalent capacitance (or conductance). Assume that the potential of node i is V i , the potential of the adjacent node is V j , then according to Kirchhoff's current law (KCL), the potential at node i satisfies:

[0041] ∑ j G ij (V i -V j )=0

[0042] Among them G ij is the conductance between nodes. This equation indicates that the total current at node i is zero, and a set of linear equations for the entire network is established. In solving the node potential, the Poisson equation is an important equation to describe the electric field distribution. Its discretized form is:

[0043]

[0044] in is the Laplace operator of the potential at node i, ρ i represents the charge density on the node, and ε is the dielectric constant. This equation forms a linear equation at each node, and the potential distribution of the entire grid area can be obtained by solving this linear equation system. Although the random walk method is the main method in the present invention, the linear equation system for constructing the equivalent electrical network provides a more accurate initial distribution of potential for the random walk method.

[0045] Step 4: In the random walk method, Markov chain is used to describe the transition process from one node to another. Assuming that each node in the electrical network represents a state in the Markov chain, the transition between nodes is only related to the current position and has nothing to do with the previous state.

[0046] State transition probability: P(i→j)

[0047] The transition probability is the probability of going from node i to adjacent node j, calculated based on the conductance or capacitance between nodes. The formula is:

[0048]

[0049] Among them, G ij is the conductance between nodes i and j, G ik is the conductance between node i and all adjacent nodes. This formula ensures that the walk is more inclined to move along the path with lower resistance (i.e., higher conductance). The random walk method simulates the movement path of particles or electrons in an electrical network. Each walk starts from the starting node and randomly selects adjacent nodes according to the transition probability until the end node set by the boundary condition is reached. Assume that the walk starts from node i, and each step moves according to the transition probability P(i→j), and the next node j is randomly selected. The random walk process can be described by the following formula:

[0050]

[0051] Among them, (Random(0,1) is a random number used to determine the next node of the walk. The absorbing state is the terminal node of the walk. Once the walk reaches these nodes, it will not continue. This termination condition is achieved by setting boundary conditions (such as Dirichlet boundaries). When the walk reaches the node j of the absorbing state, the walk process ends. All absorbing state nodes in the transfer matrix P are set to 0, so that the walk can no longer transfer when it reaches the absorbing state, thereby ensuring that the random walk terminates within a reasonable range.

[0052] Step 5: Assume that the number of random walks performed by node i is N, where N j The walk ends at node j, and the potential of the ending node is V j The potential of node i is expected to be V i It can be calculated by weighted average:

[0053]

[0054] This formula indicates that the potential value of node i is the weighted average of the potentials of each terminal node, and the weight is determined by the frequency of occurrence of each terminal node. Let the potential of node i in the nth and n+1th iterations be V i (n) and V i (n+1) , the relative change rate convergence condition is used to judge convergence. If the relative change rate of the node potential is lower than the threshold, it is considered to be converged. The formula is:

[0055]

[0056] Where ∈ is the set relative rate of change threshold. This condition is more sensitive when the potential value is large and is suitable for calculations that require higher precision. According to the law of large numbers, when the number of random walks N→∞, the sample mean of the node potential will converge to its expected value. In order to improve the calculation efficiency, a strategy of dynamically adjusting the convergence threshold can be adopted. In the early stage, a larger error threshold is allowed to speed up the convergence speed; when the calculation tends to be stable, the threshold is gradually reduced to improve the accuracy. The dynamic threshold adjustment strategy allows the calculation to converge quickly in the early stage and accurately in the later stage.

[0057] Example 1

[0058] In this embodiment, a complex multi-layer interconnection structure is analyzed, which includes three horizontal wires (marked as wires A, B, C) and two vertical interconnection vias (marked as vias V1 and V2). Wires A, B, and C are located on different metal layers, placed horizontally and parallel, and vias V1 and V2 vertically connect wires of different layers. The width of the wire is 0.5 microns, the length is 20 microns, the wire spacing is 1 micron, the diameter of the via is 0.2 microns, and the material is copper. In order to accurately extract parasitic capacitance, the grid-based random walk method is used to analyze the structure.

[0059] Step 1: Create a spatial discrete grid

[0060] First, the interconnection area is spatially discretized and the target area is divided into three-dimensional grid cells. The size of each grid cell is 0.1 micron × 0.1 micron × 0.1 micron. In the area near the via and at the junction of the wire, a higher density grid is used to ensure accuracy, forming a grid structure containing thousands of nodes. The boundaries of the wires and vias are mapped as fixed potential nodes, while the remaining nodes are set to unknown potentials, waiting for subsequent calculations.

[0061] Step 2: Set boundary conditions and end points

[0062] Dirichlet boundary conditions are applied to the boundaries of the grid to ensure that the walking process terminates at the boundary where the potential is known. For example, the potential of wire A is set to 1V, the potential of wire B is set to 0.5V, and the potential of wire C and vias V1 and V2 is set to 0V. All boundary nodes are used as the termination points of random walking to prevent the walking path from continuing indefinitely and ensure that the walking process terminates within a finite number of steps.

[0063] Step 3: Construct an equivalent network and calculate the electric potential

[0064] The discrete grid is converted into an equivalent electrical network model. Each grid cell represents a node, and the connection between nodes is represented as a capacitive element. For example, the equivalent capacitance value between adjacent nodes is set to 0.5 femtofarad (fF). The physical properties of wires, vias, and insulating media are reflected in these capacitance values, thus forming a complex equivalent electrical network for simulating the potential distribution.

[0065] Step 4: Random walk process

[0066] Starting from the node where the electric potential is to be solved, a random walk is performed. The specific process is as follows:

[0067] 1. Walking path selection: Starting from a node, randomly select adjacent nodes to walk each time. The probability of selecting adjacent nodes is based on the capacitance value: the path with smaller capacitance has a higher probability, which ensures that walking is more inclined to the path with lower impedance.

[0068] 2. Random walk of the path: Assume that in a certain walk, the path goes from wire A to the upper node of via V1, and then to the end position of via V1, thus ending at the boundary node of wire C. This end position is recorded for subsequent statistical analysis.

[0069] 3. Independence of multiple walks: Each walk process does not interfere with each other, and parallel computing is used for multi-path random walks. Assume that 10,000 independent walks are performed at each node, and the end point of each walk is recorded. The end point of each walk is unknown. Parallelism means that multiple random walks are performed simultaneously without affecting each other. The number of parallel paths is selected according to performance, accuracy requirements and circuit complexity. For scenarios with good performance, high accuracy requirements and high circuit complexity, the number of parallel paths should be higher to improve efficiency.

[0070] Step 5: Statistics and convergence determination

[0071] By counting the walking results, the potential of each node is obtained. Assume that the result of a random walk at a node on wire A is as follows:

[0072] 6000 walks terminated at the boundary node of wire B (potential 0.5V)

[0073] ·3000 walks terminated at the boundary node of wire C (potential 0V)

[0074] 1000 walks terminated at the via V1 boundary node (potential 0V)

[0075] Based on these statistical results, the potential of the target node of wire A is calculated as:

[0076]

[0077] Repeat the walk several times and count the potential value changes. When the rate of change of the node potential is less than 1%, it is considered that the convergence standard has been reached. At this time, the potential of the target node of wire A is considered stable.

[0078] Final parasitic capacitance calculation

[0079] Using the distribution of node potential, calculate the equivalent parasitic capacitance between wire A and wire B and wire C. Assume that the following capacitance values ​​are obtained through further analysis:

[0080] The equivalent parasitic capacitance between wire A and wire B is 1.2fF;

[0081] The equivalent parasitic capacitance between wire A and wire C is 0.8fF;

[0082] The equivalent parasitic capacitance between vias V1 and V2 is 0.3fF.

[0083] Results Analysis

[0084] Through this random walk method, the parasitic capacitance values ​​between the wires A, B, C and the vias V1 and V2 are accurately extracted. This embodiment demonstrates the application of parasitic parameter extraction based on grid discretization and random walk method in complex interconnection structures. Compared with the finite element method, boundary element method and moment method, the present invention achieves higher accuracy and high efficiency parasitic parameter extraction, which is suitable for the analysis of multi-layer interconnection structures in large-scale integrated circuits.

Claims

1. A parasitic parameter extraction method based on random walk algorithm in EDA, which is used for efficient extraction of parasitic capacitance and parasitic resistance parameters in complex geometric structures and multi-media environments in integrated circuits, characterized in that: The following steps are involved: (1) Establishing a spatial discrete grid Performing spatial discretization on the target region in the integrated circuit and dividing it into grid cells; (2) Setting boundary conditions and end points Boundary conditions are imposed on the discrete grid, and nodes with known potential or stable boundary potential are set as the termination points of the random walk; (3) Construct an equivalent network and calculate the electric potential Using the discrete exterior differential framework, each grid unit is regarded as a node in the electrical network model. Each node represents the electric potential at a different position. The connection between adjacent nodes is equivalent to a resistor or capacitor element to represent the potential difference and construct an equivalent network. The equivalent network converts the physical field problem into an electrical network model, and then obtains the potential distribution through network calculation. (4) Random walk process The potential distribution is calculated by simulating the random movement of electrons or currents in the grid, starting from a grid node and randomly selecting adjacent nodes to walk until a preset end point is reached; Each walk follows the random transfer principle of the Markov chain, and the transfer probability between nodes is determined by their equivalent resistance or capacitance; the random walk process adopts the independence principle and uses parallel computing to perform multi-path random walks; (5) Statistics and convergence judgment The walking process is repeated many times, and the potential values ​​of the termination nodes are counted and the law of large numbers is used to ensure the convergence of the potential values ​​and obtain the desired parasitic parameter values.

2. The parasitic parameter extraction method based on random walk algorithm in EDA according to claim 1, characterized in that: In step (1), a local encrypted grid is used, and an encrypted grid is used in areas where the interconnect parasitic effect is strong.

3. The parasitic parameter extraction method based on random walk algorithm in EDA according to claim 1, characterized in that: In step (2), Dirichlet boundary conditions are set on the discrete grid, and the known potential nodes in the boundary conditions are regarded as absorbing states.

4. The parasitic parameter extraction method based on random walk algorithm in EDA according to claim 1, characterized in that: In step (3), according to the principle of discrete exterior differential method, combined with the electric field description of Maxwell equations, a linear equation of electric potential is established for each grid node; in this way, the electric potential calculation of the entire area is transformed into a problem of solving a linear equation system, in which the unknown number of each equation corresponds to the electric potential value of a node, and the potential difference between adjacent nodes represents the electric field strength, thereby obtaining a preliminary initial distribution of electric potential.

5. The parasitic parameter extraction method based on random walk algorithm in EDA according to claim 4, characterized in that: In step (3), assume that the potential of node i is V i , the potential of the adjacent node is V j , then according to Kirchhoff's current law KCL, the potential of node i satisfies: ∑ j G ij (V i -V j )=0 Among them G ij is the conductance between nodes; this equation indicates that the total current at node i is zero, and a set of linear equations for the entire network is established; in solving the node potential, Poisson's equation is an important equation to describe the electric field distribution; Its discretized form is: in is the Laplace operator of the potential at node i, ρ i represents the charge density on the node, ε is the dielectric constant; this equation forms a linear equation at each node, and the potential distribution of the entire grid area is obtained by solving this linear equation system.

6. The parasitic parameter extraction method based on random walk algorithm in EDA according to claim 1, characterized in that: In step (4), the random walk starts from a node in the grid, which is the target location of the electric potential to be solved, or a representative node of a specific area.

7. The parasitic parameter extraction method based on random walk algorithm in EDA according to claim 1, characterized in that: In step (4), the transition probability is the probability of transitioning from node i to adjacent node j, calculated according to the conductance or capacitance between nodes; the formula is: Among them, G ij is the conductance between nodes i and j, G ik is the sum of the conductances between node i and all adjacent nodes; this formula ensures that walking tends to move along paths with smaller resistance, i.e., larger conductance; Assume that we start walking from node i, move at each step according to the transition probability P(i→j), and randomly select the next node j; the random walk process is described by the following formula: Among them, (Random(0,1) is a random number used to determine the next node of the walk; the absorbing state is the terminal node of the walk. All absorbing state nodes in the transfer matrix P are set to 0, so that the walk cannot be transferred when it reaches the absorbing state, thereby ensuring that the random walk terminates within a reasonable range.

8. The parasitic parameter extraction method based on random walk algorithm in EDA according to claim 1, characterized in that: In step (5), the frequency of each terminal point being visited in multiple walks is recorded; the terminal frequency of each boundary node is used to weightedly calculate the potential of the node to be solved, the potential value of each boundary node is multiplied by its corresponding terminal frequency, and these weighted values ​​are accumulated to obtain the average potential of the target node; by observing the rate of change of the node potential, it is judged whether convergence has been achieved; if the potential value changes less than a preset threshold in multiple consecutive calculations, it is considered to have converged.

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