A floating random walk-based parasitic capacitance extraction method and a computer readable storage medium

Abstract

The present application relates to a kind of parasitic capacitance extraction method based on floating random walk, it is related to integrated circuit electronic design automation field, including: obtaining the conductor distribution information of target chip;In current walk step, the target distance of current walk particle to nearest conductor is obtained;In response to target distance greater than preset threshold, first transfer geometry is selected to perform jump sampling;In response to target distance less than or equal to preset threshold, second transfer geometry is selected to perform jump sampling;Wherein the maximum jump distance of first and second transfer geometry matches;Parasitic capacitance value is determined based on walk path termination state and path weight.The present application dynamically switches matching transfer geometry, considers far-field diffusion and near-field termination efficiency, significantly reduces walk step number and improves extraction speed.

Description

Technical Field

[0001] This invention relates to the field of integrated circuit electronic design automation technology, and in particular to a method for extracting parasitic capacitance based on floating random walk and a computer-readable storage medium. Background Technology

[0002] In the extraction of parasitic parameters of interconnects in very large-scale integrated circuit (VLSI) chips, the Floating Random Walk (FRW) algorithm is widely used due to its adaptability to complex three-dimensional geometries and its statistical unbiasedness. This algorithm solves the Laplace equation by simulating the random motion of particles in a dielectric region, and then calculates the coupling capacitance between conductors.

[0003] Existing FRW methods typically employ a single type of transfer geometry (such as a cube or sphere) for skip sampling throughout the process. However, a single transfer geometry cannot simultaneously satisfy the requirements of rapid spatial diffusion in the far field and efficient boundary termination in the near field: if an isotropic large-scale geometry (such as a sphere) is used, although it is beneficial for rapid spatial coverage in the far field, the termination efficiency is low near the conductor surface due to the lack of surface constraints; if a polyhedral geometry with surface constraints (such as a cube) is used, although efficient termination can be achieved in the near field using adaptive boundary conditions, the spatial diffusion rate is slow in the far field due to the directionality of the geometry.

[0004] The inherent contradiction between spatial coverage and boundary termination efficiency in this single geometry makes it difficult for existing FRW algorithms to further reduce the number of walks and total computation time while ensuring extraction accuracy. Summary of the Invention

[0005] To address the problem that existing technologies cannot simultaneously balance spatial coverage and boundary termination efficiency with a single transfer geometry, this invention proposes a parasitic capacitance extraction method based on floating random walks. This method dynamically selects different transfer geometries with matching maximum jump distances based on the distance from the wandering particle to the nearest conductor, thereby significantly reducing the number of walks and improving extraction efficiency while ensuring statistical unbiasedness.

[0006] To address the aforementioned technical problems, this invention provides a method for extracting parasitic capacitance based on floating random walks, comprising: acquiring conductor distribution information of a target chip; acquiring the target distance from the current wandering particle to the nearest conductor in the current walk step of the floating random walk; in response to the target distance being greater than a preset threshold, selecting a first transfer geometry to perform jump sampling on the current wandering particle; in response to the target distance being less than or equal to the preset threshold, selecting a second transfer geometry to perform jump sampling on the current wandering particle; wherein the maximum jump distance of the first transfer geometry matches the maximum jump distance of the second transfer geometry; and determining the parasitic capacitance value of the target chip based on the termination state of the walk path and the corresponding path weight.

[0007] The above scheme dynamically switches the transfer geometry based on the spatial position of the particle during a single walk. The far-field region, which is far from the conductor, adopts the first transfer geometry that emphasizes isotropic large-scale diffusion, while the near-field region, which is close to the conductor, switches to the second transfer geometry that emphasizes boundary constraints and surface sampling termination. By matching the maximum jump distance between the two, the efficiency degradation at the switching boundary is eliminated. Thus, the mean square displacement of each step is maximized without sacrificing accuracy, significantly reducing the number of walks and the total computation time.

[0008] In one embodiment of the present invention, the first transfer geometry is an isotropic geometry, and the second transfer geometry is a polyhedral geometry with surface constraints; the preset threshold is determined based on the basic size parameters of the first transfer geometry.

[0009] This implementation clarifies the complementarity of the two transfer geometries in terms of physical properties: isotropic geometries have the same jumping ability in any direction, making them suitable for rapid space exploration in far-field regions without conductor constraints; while polyhedral geometries with surface constraints can utilize the geometric alignment between their planar boundaries and conductor surfaces to achieve efficient absorption in the near-field region through harmonic metric sampling. The correlation between the preset threshold and the basic dimensional parameters of the first transfer geometry ensures the inherent consistency between the switching timing and the geometry's own spatial coverage capability.

[0010] In one embodiment of the present invention, the first transfer geometry is a sphere, and the second transfer geometry is a cube; the maximum jump distance of the first transfer geometry is the radius of the sphere, and the maximum jump distance of the second transfer geometry is the distance from the center to the vertex of the cube; the radius of the sphere and the distance from the center to the vertex of the cube are equal or on the same order of magnitude.

[0011] This implementation uses a sphere and a cube as the preferred geometric combination and solves the problem of degraded switching boundary efficiency caused by geometric scale imbalance by limiting the matching relationship between the radius of the sphere and the distance from the center to the vertex of the cube (i.e., the length of half the diagonal). When the maximum jump distances of the two are equal or on the same order of magnitude, the particles have comparable spatial coverage capabilities at the switching boundary regardless of which geometry is used, avoiding the overall performance degradation of the hybrid mode caused by the significantly weaker coverage capability of one side's geometry compared to the other side.

[0012] In one embodiment of the present invention, the first transfer geometry is a sphere, and selecting the first transfer geometry to perform jump sampling on the currently wandering particle includes: in the current wandering step, obtaining a three-dimensional direction vector from a pre-computed direction vector lookup table through a random index, the direction vector lookup table containing multiple direction vectors uniformly distributed on a unit sphere; and updating the position of the currently wandering particle based on the current position of the currently wandering particle, the radius of the sphere, and the three-dimensional direction vector.

[0013] This implementation eliminates the real-time computation overhead of trigonometric functions in uniform spherical sampling by pre-compiling a direction vector lookup table. During the execution phase, only one random integer generation and array indexing operation are needed to obtain the jump direction, reducing the time complexity of direction sampling to O(1). This makes the single-step time of spherical jumping comparable to that of cube jumping, ensuring that the performance gains of the hybrid mode come entirely from the reduction in the number of steps rather than the difference in single-step speed.

[0014] In one embodiment of the present invention, selecting a second transfer geometry to perform jump sampling on the current wandering particle includes: obtaining the constraint state of the current wandering particle being constrained by conductors along each axis of the polyhedral geometry; detecting the number of constrained axes through a bit mask, and selecting a target Green's function sub-table from multiple Green's function sub-tables based on the number of axes; and sampling the surface of the polyhedral geometry based on the target Green's function sub-table to determine the next jump position of the current wandering particle.

[0015] This implementation automatically detects the conductor constraint state along each axis of the polyhedron using a bitmasking mechanism, and selects the corresponding Green's function sub-table (such as full cube, half cube, quarter cube, etc.) for surface sampling probability correction accordingly. This mechanism ensures that in the near-field region, the sampling distribution of the transfer geometry always conforms to the harmonic measure under the absorbing boundary conditions, enabling particles to hit the conductor surface with the highest probability and maximizing near-field termination efficiency.

[0016] In one embodiment of the present invention, in response to the target distance being greater than a preset threshold, a first transfer geometry is selected to perform jump sampling on the currently wandering particle, including: in response to the target distance being greater than the preset threshold, the target distance is passed as a pre-calculated radius parameter to the transfer function of the first transfer geometry; and the transfer function is used to perform a jump based on the pre-calculated radius parameter to skip repeated distance queries inside the first transfer geometry.

[0017] This implementation utilizes distance prediction results to eliminate redundant calculations in the far-field step of the hybrid mode. Since the target distance has already been calculated when the first transfer geometry is used, it is directly passed as a pre-calculated radius parameter to the transfer function. This allows the first transfer geometry to skip the step of traversing the conductor again to calculate the nearest distance, reducing the number of conductor traversals per step from two to one, further reducing the time overhead per step.

[0018] In one embodiment of the present invention, prior to the current walk step of the floating random walk, the method further includes: randomly sampling the walk start point on the source conductor surface in an area-weighted manner; performing a first hop on the walk start point using a Poisson kernel hemispherical boundary estimator; projecting the current walking particle from the source conductor surface to the dielectric region; and calculating the corresponding Poisson weight coefficient.

[0019] This implementation uses area-weighted sampling and a Poisson kernel hemispherical boundary estimator to handle the first hop at the start of the walk, ensuring that the initial projection from the conductor surface to the dielectric region meets the mathematical requirements of the electrostatic boundary value problem, thus laying the foundation for the statistical unbiasedness of subsequent random walks.

[0020] In one embodiment of the present invention, determining the parasitic capacitance value of the target chip based on the termination state of the wandering path and the corresponding path weight includes: terminating the current wandering path in response to the current wandering particle being absorbed by the target conductor, exceeding the simulation domain boundary, or reaching the maximum number of steps; and calculating the coupling capacitance value from the source conductor to the target conductor based on the floating random walk capacitance formula, wherein the floating random walk capacitance formula is: ; in, Source conductor To the target conductor The coupling capacitance value, For the first Path weights of the second walk For the effective dielectric constant, Source conductor Surface area, The total number of visits, The radius of the first jump. For medium weight, To indicate whether the current travel path has hit the target conductor Indicator functions.

[0021] This implementation clarifies the mathematical expression of the walk termination condition and capacitance calculation, where the path weight integrates the first jump radius, dielectric weight, and hit indicator, ensuring that the statistical expectation of the final capacitance value converges to the true solution.

[0022] In one embodiment of the present invention, selecting a first transfer geometry or a second transfer geometry to perform jump sampling on the currently wandering particle includes: in each step of the walk, dynamically constructing the size of the first transfer geometry or the second transfer geometry based on the real-time distance of the currently wandering particle to the surrounding conductor; when dynamically constructing the size, forcing the set size of the first transfer geometry to be equal to the maximum spatial coverage scale of the currently constrained second transfer geometry, so as to keep the maximum jump distance of the two matched in real time.

[0023] This implementation proposes a real-time size alignment strategy for scenarios where the size of the transferred geometry dynamically changes with the particle position in the actual FRW algorithm. During each step of dynamic geometry construction, the set size of the first transferred geometry (e.g., the radius of a sphere) is forced to be equal to the maximum spatial coverage scale of the currently constrained second transferred geometry (e.g., the distance from the center to the vertex of a cube under the current constraint). This ensures that the maximum jump distance between the two remains matched in real-time even in dynamic size mode, guaranteeing that the hybrid mode maintains optimal spatial coverage efficiency throughout the entire walk.

[0024] In addition, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described above.

[0025] The parasitic capacitance extraction method based on floating random walks of the present invention achieves a smooth transition between rapid far-field spatial diffusion and efficient near-field boundary termination by dynamically selecting a first or second transfer geometry based on the target distance of the wandering particle to the nearest conductor and matching their maximum jump distances. The principle is as follows: In the far-field region, the isotropic first transfer geometry can rapidly cover the unconstrained space with a large step size, reducing ineffective small-step exploration; in the near-field region, the surface-constrained second transfer geometry can utilize the alignment characteristics of its geometric boundary with the conductor surface to guide particles to efficiently hit the conductor through harmonic metric sampling; and the matching of their maximum jump distances eliminates the efficiency degradation caused by unequal spatial coverage at the switching boundary, ensuring that the actual benefits of dynamic switching are fully realized. Therefore, while ensuring statistical unbiasedness in capacitance extraction, the average number of walk steps and total computation time are significantly reduced, improving the overall efficiency of chip parasitic capacitance extraction. Attached Figure Description

[0026] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a flowchart of the parasitic capacitance extraction method based on floating random walk according to the present invention. Detailed Implementation

[0028] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0029] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0030] It should be noted that the following description covers various aspects of embodiments within the scope of the appended claims. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number and aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0031] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The drawings only show the components related to this application and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0032] Additionally, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that practice can be carried out without these specific details.

[0033] Reference Figure 1 As shown, this invention provides a parasitic capacitance extraction method based on floating random walks. This method balances far-field spatial diffusion efficiency and near-field boundary termination efficiency by dynamically switching the transfer geometry. The method specifically includes the following steps: Step S100: Obtain the conductor distribution information of the target chip. Specifically, this step involves parsing the chip layout file (such as GDSII or JSON format) and constructing a three-dimensional data model containing the geometry of all conductors, dielectric layer properties, and network topology. The conductor distribution information is the physical basis for subsequent random walk simulations, and its accuracy directly determines the accuracy of parasitic capacitance extraction. It should be understood that, in addition to standard layout files, intermediate format data exported from other EDA tools can also be used, as long as it can completely characterize the three-dimensional spatial distribution of conductors inside the chip.

[0034] Step S200: In the current walk step of the floating random walk, obtain the target distance from the currently walking particle to the nearest conductor. Specifically, in each walk iteration, the system calculates in real time the minimum three-dimensional Euclidean distance between the current walking particle's location and all surrounding conductor surfaces, and uses this minimum distance as the target distance. This target distance is a key indicator for determining the type of spatial region in which the particle is located, used to quantify the degree to which the particle is moving away from or close to the conductor. In practical engineering implementations, to accelerate distance queries, spatial index structures (such as octrees or KD-trees) are usually used to manage conductor geometry data, thereby reducing the time complexity of a single distance query to logarithmic levels.

[0035] In step S300, in response to a target distance greater than a preset threshold, a first transfer geometry is selected to perform jump sampling on the currently wandering particle; in response to a target distance less than or equal to the preset threshold, a second transfer geometry is selected to perform jump sampling on the currently wandering particle. Specifically, the preset threshold defines the spatial boundary between the far-field region and the near-field region. When the target distance is greater than the preset threshold, it is determined that the particle is in the far-field region far from the conductor. At this time, the first transfer geometry is selected, utilizing its isotropic properties in unconstrained space to achieve large-scale rapid diffusion; when the target distance is less than or equal to the preset threshold, it is determined that the particle is in the near-field region close to the conductor. At this time, the algorithm switches to the second transfer geometry, utilizing the adaptability of its geometric boundary to the conductor surface to achieve efficient termination. This distance-based dynamic switching mechanism allows the algorithm to adaptively select the optimal sampling strategy according to the local environment of the particle, avoiding the defect that a single geometry cannot simultaneously consider diffusion and termination efficiency on a global scale.

[0036] In this design, the maximum jump distance of the first transfer geometry is matched with that of the second transfer geometry. "Matching maximum jump distances" is a functional constraint, essentially meaning that the two transfer geometries have continuous and comparable spatial coverage capabilities at the switching boundary. Specifically, the maximum jump distance characterizes the maximum spatial scale that a transfer geometry can traverse in a single sampling. If the two do not match, for example, if the maximum jump distance of the first transfer geometry is significantly smaller than that of the second, when a particle moves from the near field to the far field, although it switches to a geometry theoretically more suitable for the far field, its actual traversal capability weakens, leading to a deterioration in the overall efficiency of the hybrid mode, even lower than that of the single-geometry mode. Therefore, by matching the maximum jump distances of the two, it is ensured that regardless of whether the particle moves from the far field to the near field or from the near field to the far field, its spatial exploration capability before and after the switching point remains smooth, eliminating performance gaps caused by geometric scale imbalances. It should be understood that matching does not strictly require absolute equality of values; it also includes approximate equality within the same order of magnitude or a preset error range, as long as the efficiency continuity at the switching boundary is guaranteed.

[0037] Step S400 involves performing jump sampling based on the selected transfer geometry to update the position of the currently wandering particle. Specifically, on the surface of the selected transfer geometry constructed with the current particle position as the center, the next landing point is randomly sampled according to a harmonic measure distribution that satisfies the boundary conditions of the Laplace equation, and the particle is moved to that landing point. This process simulates the random walk trajectory of Brownian motion within the medium region, ensuring the unbiasedness of the final statistical results.

[0038] Step S500: Based on the termination state and corresponding path weight of the wandering path, determine the parasitic capacitance value of the target chip. Specifically, the current wandering path terminates when the wandering particle is absorbed by the target conductor, exceeds the simulation domain boundary, or reaches a preset maximum number of steps. The system records the termination state and accumulated weight of each path. After completing a predetermined number of wandering paths, the system uses the floating random wandering capacitance formula to statistically average the weights of all paths, thereby calculating the coupling capacitance value from the source conductor to the target conductor. Because the aforementioned steps employ dynamically switching and maximum jump distance matching transfer geometry, the average number of steps for each wandering path is significantly reduced, greatly improving the overall computational efficiency of capacitance extraction while ensuring statistical accuracy.

[0039] Furthermore, the specific shapes and dimensional matching relationships of the first and second transfer geometries are defined. The first transfer geometry is an isotropic geometry, and the second transfer geometry is a polyhedral geometry with surface constraints; the preset threshold is determined based on the basic dimensional parameters of the first transfer geometry. Specifically, an isotropic geometry refers to a geometric shape with the same spatial extension characteristics in any direction. Its advantage lies in its ability to diffuse outwards with equal probability in the far-field region far from the conductor, avoiding exploration lag in certain directions due to the geometry's own directional bias. A polyhedral geometry with surface constraints refers to a closed solid enclosed by multiple planes. Its planar boundaries can form a natural geometric alignment with the rectangular conductor surfaces commonly found in chips, thereby efficiently applying absorbing boundary conditions in the near-field region using this alignment characteristic. The correlation between the preset threshold and the basic dimensional parameters of the first transfer geometry ensures that the triggering timing for switching from far-field mode to near-field mode is inherently consistent with the spatial coverage capability of the geometry itself, avoiding the problem of insufficient utilization of far-field advantages due to switching too early, or decreased near-field termination efficiency due to switching too late.

[0040] Based on this, as a preferred implementation, the first transfer geometry is a sphere, and the second transfer geometry is a cube. A sphere is a typical example of isotropic geometry, where the distance from any point on its surface to the center is equal, making it ideal for unbiased, large-step jumps in dielectric regions. A cube is the optimal choice for a polyhedral geometry with surface constraints, because most conductors in integrated circuit layouts are orthogonal cuboid structures. The six faces of the cube are parallel or perpendicular to the conductor surfaces, allowing for maximum fit to the conductor boundaries when constructing a constrained transfer cube in the near-field region, thus increasing the probability of wandering particles hitting the conductor.

[0041] To ensure the actual gain of the dynamic switching mechanism, this application emphasizes a strict matching relationship in size between the two geometries. The maximum jump distance of the first transfer geometry is the radius of the sphere, and the maximum jump distance of the second transfer geometry is the distance from the center to the vertex of the cube; the radius of the sphere and the distance from the center to the vertex of the cube are equal or on the same order of magnitude. Specifically, let the half-side length of the cube be H, then the distance from its center to the vertex (i.e., the half-diagonal length) is... Let the radius of the sphere be R. In this application, it is mandatory to... Or the two are on the same order of magnitude. This specific mathematical relationship is not a simple geometric conversion, but a key technical parameter determined based on a deep understanding of the efficiency bottleneck of the floating random walk algorithm.

[0042] During the research and development verification process, it was found that if one were to rely solely on intuition and set the radius R of the sphere to be equal to the half-side length H of the cube (i.e., ... Although they appear similar on a visual scale, they exhibit a significant efficiency imbalance in actual movement performance. This is because the maximum traversal capability of a cube in three-dimensional space is determined by its diagonal. At that time, the maximum jump distance of the sphere is only about 57.7% of the maximum jump distance of the cube (i.e., This means that at the switching boundary near the preset threshold, when a particle moves from the near field to the far field and switches to a sphere, the spatial range that it can cover in a single jump is actually reduced by nearly half compared to the previous cube mode. This abrupt break in spatial coverage will cause the diffusion speed of the hybrid mode in the far field region to be significantly lower than expected, and even lead to the anomaly that the total time of the hybrid mode is higher than that of the pure cube mode, which is the so-called "switching boundary efficiency degradation".

[0043] Conversely, when strictly enforced When using a size-matching strategy, the radius of the sphere is exactly equal to half the diagonal length of the cube. In this case, regardless of whether a particle uses a sphere or a cube at the switching boundary, the theoretically farthest spatial point it can reach is statistically equivalent. This continuity in spatial coverage eliminates the performance dip caused by geometric scale asymmetry, allowing the hybrid mode to truly inherit the rapid diffusion advantage of the sphere in the far field and the efficient termination advantage of the cube in the near field. The experimental data trend shows that, under the premise of satisfying this size-matching relationship, the hybrid mode exhibits a significant nonlinear decrease in both the average number of walks and the total computation time compared to the single-geometry mode, demonstrating the non-obviousness and technical necessity of this parameter relationship.

[0044] It should be understood that, although this application is based on While this is explained as an optimal matching point, in practical engineering applications, considering manufacturing tolerances, mesh discretization errors, or the geometric characteristics of a specific layout, the radius of the sphere and the distance from the center to the vertex of the cube can also be on the same order of magnitude, for example, in... to Fluctuations within a certain range, as long as the spatial coverage capabilities of both can be roughly equivalent at the switching boundary without significant efficiency breaks, should be considered within the scope of protection of this application. Furthermore, the preset threshold T is typically set equal to the radius R of the sphere, i.e. Thus, when the target distance is greater than R, there must be a complete and safe sphere space around the particle that is not invaded by the conductor, thereby ensuring the physical legitimacy of the sphere jumping and the statistical unbiasedness of the sampling distribution.

[0045] Furthermore, the jump sampling process of the first transfer geometry in the far-field region is engineered and optimized to eliminate the additional computational overhead that may be introduced by the hybrid mode. When the first transfer geometry is a sphere, the specific process of selecting the first transfer geometry to perform jump sampling on the current wandering particle includes: in the current walking step, obtaining a three-dimensional direction vector from a pre-computed direction vector lookup table through a random index. This direction vector lookup table contains multiple direction vectors uniformly distributed on the unit sphere; subsequently, updating the position of the current wandering particle based on the current position of the current wandering particle, the radius of the sphere, and the obtained three-dimensional direction vector. Specifically, in the traditional spherical uniform sampling algorithm, each generation of jump direction requires real-time calculation of trigonometric functions such as sine and cosine, which constitutes a significant performance bottleneck in high-frequency random walk loops. This application constructs a direction vector lookup table by pre-compiling and storing a large number (e.g., ten thousand) of three-dimensional direction vectors uniformly distributed on the unit sphere during the algorithm initialization stage. During the actual walk execution phase, the system only needs to generate a random integer as an index to directly read the corresponding direction vector from memory in constant time O(1), completely avoiding the repeated calculation of trigonometric functions at runtime. This space-for-time strategy ensures that the single-step calculation time of the sphere jump is basically the same as that of the cube jump, thus guaranteeing that the performance gains brought by the hybrid mode are purely due to the reduction in the number of walk steps, rather than at the cost of sacrificing the single-step execution speed.

[0046] Building upon this, to further optimize the execution efficiency of the far-field mode, this application also introduces a distance prediction and deduplication mechanism. As one implementation, in response to a target distance exceeding a preset threshold, a first transfer geometry is selected to perform jump sampling on the currently wandering particle. This further includes: in response to a target distance exceeding the preset threshold, passing the target distance as a pre-calculated radius parameter to the transfer function of the first transfer geometry; and executing a jump based on this pre-calculated radius parameter through the transfer function to skip repeated distance queries within the first transfer geometry. Specifically, in the unoptimized hybrid mode implementation, the system first needs to traverse the surrounding conductors at the beginning of each wandering step to calculate the target distance d_min, used to determine whether to switch geometries; and when a sphere is determined to be used, the sphere's transfer builder typically traverses the conductors again to confirm the maximum safe radius. This double traversal leads to significant computational redundancy. This application directly passes the target distance calculated in step S200 as a parameter to the sphere transfer function, enabling the transfer function to directly use this known distance to determine the jump radius or verify spatial safety, thereby completely skipping the internal secondary distance query logic. This optimization reduces the number of conductor space traversals per step in the far-field mode from two to one, significantly reducing the constant factor in the single-step time complexity.

[0047] It should be understood that although the aforementioned direction vector lookup table mechanism and distance prediction deduplication mechanism target two different sub-stages—direction sampling and distance calculation—they work closely together technically to serve the unified technical goal of reducing the single-step time in the far field. In the floating random walk algorithm, the dynamic switching strategy can only truly translate into an overall speedup when the average single-step time of the hybrid mode is not higher than that of the single geometry mode. This application, through these two engineering defense measures, eliminates the performance penalty that may arise from the introduction of complex switching logic, ensuring that the hybrid mode can stably achieve the expected speedup effect in actual chip parasitic capacitance extraction applications, thus enabling the theoretical advantages of the algorithm to be implemented without loss in engineering practice.

[0048] Furthermore, the jump sampling process of the second transfer geometry in the near-field region is specifically defined. As one implementation, selecting the second transfer geometry to perform jump sampling on the current wandering particle includes: obtaining the constraint state of the current wandering particle under conductor constraints along each axis of the polyhedral geometry; detecting the number of constrained axes using a bitmask, and selecting a target Green's function sub-table from multiple Green's function sub-tables based on the number of axes; and sampling the surface of the polyhedral geometry based on the target Green's function sub-table to determine the next jump position of the current wandering particle.

[0049] Specifically, when a wandering particle enters the near-field region and switches to a second transition geometry (such as a cube), its surrounding space is often no longer a complete, isotropic free space, but is instead cut and restricted by one or more conductive surfaces. To maintain statistical unbiasedness in this asymmetric, confined space, the current geometric constraint environment must be accurately perceived. This application calculates whether the particle touches a conductive surface when it extends along each of the six orthogonal axes of three-dimensional space (i.e., +X, -X, +Y, -Y, +Z, -Z directions) to the cube boundary. If the extension distance along an axis is equal to half the theoretical side length of the cube, then that axis is considered constrained; conversely, if the extension distance is less than half the theoretical side length, it indicates that a closer conductive boundary exists in that direction, and the cube is truncated in that direction. The constraint states of these six axes are encoded into a six-bit binary bitmask, with each bit corresponding to a constraint flag for one axis (e.g., 1 indicates constrained, 0 indicates free). With this bitmask encoding method, the system can uniquely identify the local topological configuration of the current particle with extremely low computational overhead, such as complex situations where only one face is constrained, the edge formed by the intersection of two faces is constrained, or the corner point formed by the intersection of three faces is constrained.

[0050] After obtaining the bitmask, the system does not simply process it linearly based on the number of constraints. Instead, it uses it as an index key to directly match the target Green's function sub-table that best suits the current constraint configuration from multiple pre-set Green's function sub-tables. The Green's function sub-table essentially stores the sampling probability distribution (i.e., harmonic measure) of each point on the surface of the transfer geometry under different boundary conditions. For example, when the bitmask shows zero axial constraints, a full-cube Green's function sub-table is selected, with its sampling probability uniformly distributed across the six faces; when the bitmask shows one axial constraint, a half-cube Green's function sub-table is selected, where the probability distribution has been corrected for a single planar boundary, ensuring that the probability of a particle jumping to the constrained surface conforms to the absorption characteristics of an electrostatic field on a conductor surface; when the bitmask shows two or more axial constraints, a quarter-cube or other higher-order sub-table is selected accordingly. This adaptive lookup mechanism based on bitmasks ensures that regardless of the complexity of the asymmetric constraint environment in which the particle is located, the sampling distribution of its next-hop position always strictly satisfies the boundary conditions of the Laplace equation, thus guaranteeing the mathematical correctness and statistical unbiasedness of the final capacitance extraction result.

[0051] It should be understood that although this application uses a cube and its corresponding full / half / quarter Green's function sub-tables as examples, the bitmask constraint detection and sub-table adaptive selection mechanism has general engineering value. For other types of orthogonal polyhedral geometries, as long as a clear axial constraint state can be defined and the corresponding harmonic measure distribution table can be pre-calculated, a similar bitmask mapping strategy can be used to achieve efficient adaptation of near-field sampling. Compared with the traditional boundary processing logic based on multiple conditional branch judgments (if-else), the bitmask mechanism not only avoids the performance loss caused by cumbersome code branch prediction failures, but also transforms complex geometric topology recognition into deterministic memory access operations, significantly improving the execution efficiency of near-field walk steps. More importantly, this mechanism sinks the abstract physical concept of "adaptive surface constraint" into a concrete and verifiable algorithm implementation, effectively preventing it from being simply equated to conventional collision detection or boundary clipping in patent protection, highlighting the unique automated modeling capability and accuracy guarantee mechanism of this application when dealing with complex three-dimensional geometry of chip interconnects.

[0052] Furthermore, the complete lifecycle of the floating random walk algorithm is further explained, especially for scenarios involving dynamic changes in the size of transferred geometry in practical engineering applications, where a real-time size alignment strategy is proposed. As one implementation method, before the current walk step, the method further includes: randomly sampling the walk start point on the source conductor surface using area weighting; performing a first hop on the walk start point using a Poisson kernel hemispherical boundary estimator, projecting the current walking particle from the source conductor surface to the dielectric region, and calculating the corresponding Poisson weight coefficients. Specifically, since parasitic capacitance extraction focuses on the charge distribution on the conductor surface, it is not possible to simply scatter points uniformly in space during the initialization phase. Instead, weighted sampling must be performed based on the area of ​​each surface of the source conductor to ensure that the sampling probability is proportional to the physical charge quantity. Simultaneously, considering the singularity of the electric field at the conductor surface, directly initiating a random walk at this location would lead to numerical instability. Therefore, a Poisson kernel hemispherical boundary estimator is used to perform the first hop, instantaneously projecting the particle from the conductor surface onto a virtual hemispherical surface within the dielectric region. This process is not only mathematically equivalent to the limit behavior starting from the surface, but also eliminates the discretization error in the first hop region through analytically calculated Poisson weight coefficients, laying a solid foundation for the statistical unbiasedness of subsequent walks.

[0053] As one implementation method, the parasitic capacitance value of the target chip is determined based on the termination state of the walking path and the corresponding path weight. This includes: terminating the current walking path in response to the current walking particle being absorbed by the target conductor, exceeding the simulation domain boundary, or reaching the maximum number of steps; and calculating the coupling capacitance value from the source conductor to the target conductor based on the floating random walk capacitance formula. Specifically, the floating random walk capacitance formula is expressed as follows: ; in, Source conductor To the target conductor The coupling capacitance value, For the first Path weights of the second walk For the effective dielectric constant, Source conductor Surface area, Total number of visits. Path weight. It integrates the first-hop radius, dielectric weight, and indicators of whether the current travel path hits the target conductor. The indicator function. The physical essence of this formula is to transform the solution of the Laplace equation into the expected value of a stochastic process, approximating the true capacitance value through the statistical averaging of a large number of independent walks. As long as the transition probability distribution at each step satisfies the harmonic measure condition, regardless of the shape of the transition geometry or switching strategy used in the intermediate process, the final calculation result is statistically unbiased and convergent.

[0054] Based on this, and to adapt to the complex and ever-changing geometric environment of actual chip layouts, this application proposes a dynamic size real-time alignment strategy. As one implementation method, selecting a first transfer geometry or a second transfer geometry to perform jump sampling on the currently wandering particle includes: in each step of the walk, dynamically constructing the size of the first transfer geometry or the second transfer geometry based on the real-time distance from the currently wandering particle to surrounding conductors; while dynamically constructing the size, forcing the set size of the first transfer geometry to be equal to the maximum spatial coverage scale of the currently constrained second transfer geometry, so as to maintain the maximum jump distance of the two matching in real time.

[0055] Specifically, the matching relationship described in the application, where the radius of the sphere is equal to the distance from the center to the vertex of the cube, is based on a static ratio under an ideal, unconstrained state. However, in actual floating random walks, the size of the transferred geometry is not fixed but updates in real time with the particle's position: when the particle is far from the conductor, the geometry is larger to accelerate diffusion; when the particle is close to the conductor, the geometry automatically shrinks to avoid penetrating the conductor boundary. In this dynamic mode, mechanically applying the static ratio may lead to efficiency losses. For example, when the second transferred geometry (cube) is truncated in some axes due to its proximity to the conductor, the maximum spatial scale it can actually cover (i.e., the distance from the center to the farthest vertex) will be significantly smaller than the theoretical unconstrained diagonal length. In this case, if the first transferred geometry (sphere) is still constructed according to the theoretical maximum value under unconstrained conditions, it may not only lead to illegal sampling due to exceeding the safe space but also generate invalid repeated attempts in local narrow regions due to the sphere's excessive size; conversely, if the sphere is too small, it cannot fully utilize the currently available free space.

[0056] Therefore, the dynamic size real-time alignment strategy proposed in this application requires that, at each step of geometry construction, the actual maximum spatial coverage scale of the currently constrained second transfer geometry is first calculated, and then this scale is directly assigned to the set size (such as the radius of a sphere) of the first transfer geometry. This means that regardless of whether the particle is in an open far-field region or a narrow near-field gap, the spatial coverage capability of the two transfer geometries at the switching boundary remains dynamically consistent. This real-time alignment mechanism is essentially an equivalent implementation and generalization of the above-mentioned static matching principle in dynamic scenarios. It ensures that the hybrid mode can maintain optimal spatial exploration efficiency at every node of the entire walking path, completely eliminating performance fluctuations caused by local geometric constraints. It should be understood that this dynamic alignment is not limited to the combination of spheres and cubes. For any pair of transfer geometries with complementary characteristics, as long as the principle of "maximum jump distance being equal in real time" is followed during the dynamic construction process, a similar full-path efficiency optimization effect can be achieved.

[0057] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the parasitic capacitance extraction method based on floating random walk as described above.

[0058] Specifically, the computer-readable storage medium is a physical entity or logical carrier used to carry software program products, and its specific forms include, but are not limited to, read-only memory, random access memory, disk, optical disk, flash drive, or cloud storage server. When a processor loads and runs the computer program instructions stored on the medium, the processor will be configured to perform a series of operation steps, such as obtaining conductor distribution information, calculating target distance, dynamically selecting transfer geometry based on threshold, performing jump sampling, and determining parasitic capacitance values. This implementation solidifies the method flow into a distributable and tradable software product form, ensuring the portability of the technical solution across different hardware platforms and the integrity of the scope of protection. It should be understood that as long as the instruction sequence recorded on the storage medium enables a general-purpose computing device to reproduce the core logic of the method of this application during execution, regardless of the specific encoding format, compression method, or transmission protocol used, it falls within the protection scope of this application.

[0059] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for extracting parasitic capacitance based on floating random walks, characterized in that, include: Obtain conductor distribution information of the target chip; In the current step of the floating random walk, obtain the target distance from the current walking particle to the nearest conductor; In response to the target distance being greater than a preset threshold, a first transfer geometry is selected to perform jump sampling on the currently wandering particle; In response to the target distance being less than or equal to the preset threshold, a second transfer geometry is selected to perform jump sampling on the currently wandering particle; Wherein, the maximum jump distance of the first transfer geometry is matched with the maximum jump distance of the second transfer geometry; The parasitic capacitance value of the target chip is determined based on the termination state of the walking path and the corresponding path weight.

2. The parasitic capacitance extraction method based on floating random walk according to claim 1, characterized in that, The first transfer geometry is an isotropic geometry, and the second transfer geometry is a polyhedral geometry with surface constraints; The preset threshold is determined based on the basic size parameters of the first transfer geometry.

3. The parasitic capacitance extraction method based on floating random walk according to claim 2, characterized in that, The first transfer geometry is a sphere, and the second transfer geometry is a cube; The maximum jump distance of the first transfer geometry is the radius of the sphere, and the maximum jump distance of the second transfer geometry is the distance from the center to the vertex of the cube; The radius of the sphere is equal to or on the same order of magnitude as the distance from the center to the vertex of the cube.

4. The parasitic capacitance extraction method based on floating random walk according to claim 2, characterized in that, The first transfer geometry is a sphere. Selecting the first transfer geometry to perform jump sampling on the currently wandering particle includes: In the current walk step, a three-dimensional direction vector is obtained from a pre-computed direction vector lookup table by a random index. The direction vector lookup table contains multiple direction vectors uniformly distributed on a unit sphere. The position of the current wandering particle is updated based on its current position, the radius of the sphere, and the three-dimensional direction vector.

5. The parasitic capacitance extraction method based on floating random walk according to claim 2, characterized in that, Selecting the second transfer geometry to perform jump sampling on the currently wandering particle includes: Obtain the constraint state of the currently wandering particle under the conductor constraint in each axis of the polyhedral geometry; The number of constrained axes is detected by bitmask, and a target Green function sub-table is selected from multiple Green function sub-tables based on the number of axes. The surface of the polyhedral geometry is sampled based on the target Green's function sub-table to determine the next hop position of the currently wandering particle.

6. The parasitic capacitance extraction method based on floating random walk according to claim 1, characterized in that, In response to the target distance being greater than a preset threshold, a first transfer geometry is selected to perform jump sampling on the currently wandering particle, including: In response to the target distance being greater than the preset threshold, the target distance is passed as a pre-calculated radius parameter to the transfer function of the first transfer geometry; The transfer function performs a jump based on the pre-calculated radius parameter to skip repeated distance queries inside the first transfer geometry.

7. The parasitic capacitance extraction method based on floating random walk according to claim 1, characterized in that, Prior to the current walk step of the floating random walk, the method further includes: The starting point of the walk is randomly sampled on the surface of the source conductor using an area-weighted method. A Poisson kernel hemispherical boundary estimator is used to perform a first hop on the starting point of the walk, projecting the current wandering particle from the surface of the source conductor to the dielectric region, and calculating the corresponding Poisson weight coefficients.

8. The parasitic capacitance extraction method based on floating random walk according to claim 1, characterized in that, Based on the termination state of the walking path and the corresponding path weight, the parasitic capacitance value of the target chip is determined, including: The current wandering path is terminated in response to the current wandering particle being absorbed by the target conductor, exceeding the boundary of the simulation domain, or reaching the maximum number of steps. The coupling capacitance value from the source conductor to the target conductor is calculated based on the floating random walk capacitance formula, which is: ； in, Source conductor To the target conductor The coupling capacitance value, For the first Path weights of the second walk For the effective dielectric constant, Source conductor Surface area, The total number of visits, The radius of the first jump. For medium weight, To indicate whether the current travel path has hit the target conductor Indicator functions.

9. The parasitic capacitance extraction method based on floating random walk according to claim 1, characterized in that, Selecting either the first or second transfer geometry to perform jump sampling on the currently wandering particle includes: In each step of the journey, the dimensions of the first or second transfer geometry are dynamically constructed based on the real-time distance between the currently moving particle and the surrounding conductor. When dynamically constructing dimensions, the set size of the first transfer geometry is forced to be equal to the maximum spatial coverage scale of the currently constrained second transfer geometry, so as to keep the maximum jump distance of the two matched in real time.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the parasitic capacitance extraction method based on floating random walk as described in any one of claims 1 to 9.

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