Implicit diffusion model-based SRAF graph generation method and system

Abstract

The invention discloses an implicit diffusion model-based SRAF graph generation method and system, and the method comprises the steps: collecting training sample data, the training sample data comprises a graph of a target layout, an SRAF graph of the target layout and a photoetching simulation intensity graph of the target layout, the SRAF graph of the target layout is represented by a rectangle, and the SRAF graph of the target layout is represented by a photoetching simulation intensity graph of the target layout; a central point coordinate (xc, yc), a width w and a height h are adopted for expression; preprocessing the training sample data, and converting the SRAF graph of the target layout into a thermodynamic diagram; and inputting the preprocessed training sample data into a preset implicit diffusion model for training to obtain an SRAF generation model capable of automatically generating a thermodynamic diagram corresponding to the SRAF graph of the target layout according to the graph of the target layout and the photoetching simulation intensity graph of the target layout. By adopting the technical method provided by the invention, the generation efficiency and reliability of the SRAF graph can be improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of semiconductor manufacturing, and in particular to a SRAF pattern generation method and system based on an implicit diffusion model. BACKGROUND

[0002] Lithography is an indispensable core technology in modern semiconductor manufacturing, whose main purpose is to accurately transfer the design patterns onto the surface of a semiconductor substrate, thereby realizing the manufacturing of complex electronic devices. The basic flow of lithography includes several key steps: first, a layer of photoresist sensitive to light is uniformly coated on the substrate surface, forming a thin film. Then, through high-precision lithography equipment, the design pattern is projected from the mask to the photoresist. After exposure, the chemical properties of the photoresist change, and the development process will dissolve the exposed or unexposed part, thereby forming a specific pattern on the substrate surface. Subsequently, the substrate will undergo a series of subsequent process steps, such as etching, material deposition or ion implantation, to complete the construction of the entire micro-nano structure. This process will be repeated multiple times to stack complex circuit structures layer by layer, realizing the manufacturing of high-performance semiconductor chips.

[0003] With the continuous advancement of process technology to advanced nodes (such as 5nm and below), lithography technology is facing unprecedented challenges. In these nodes, during the projection of the mask pattern onto the wafer, limited by the resolution limit of the optical system, the actual pattern formed may deviate from the design target, resulting in problems such as blurred pattern edges and increased size errors. These phenomena are usually attributed to optical proximity effect (OPE), which manifests as the deviation between the actual image on the wafer surface and the design layout. This deviation not only affects the performance of the device, but also may lead to the narrowing of the process window, thereby significantly increasing the difficulty of yield control.

[0004] In order to overcome the optical proximity effect, optical proximity correction (OPC) technology is widely used. OPC technology adjusts the pattern in the design stage, so that the actual pattern formed after lithography is closer to the design target. In the OPC process, sub-resolution assist feature (SRAF) has been proven to be an effective solution. SRAF is a small auxiliary pattern that does not directly image itself, but through optimizing the distribution and phase of light energy, it improves the imaging quality of the target pattern and the stability of the process window. SRAF not only can reduce the edge placement error (EPE), but also can improve the tolerance to focus distance and exposure dose changes, thereby enhancing the robustness of the lithography system.

[0005] However, in practical applications, there are significant technical bottlenecks in the generation and optimization of SRAFs. Currently, SRAF generation methods mainly include rule-driven methods, model-driven methods, and machine learning-based methods. Rule-driven methods rely on a series of rules predefined by engineers to determine the position, shape, and size of SRAFs. Although this method is simple and direct, and is more efficient in standardized design, it lacks flexibility, especially when faced with complex or non-standardized designs, it is difficult to provide high-quality solutions. In addition, the formulation of rules is highly dependent on the experience of engineers, and the development and maintenance costs are high. When the process conditions change, the rules usually need to be adjusted, further increasing the design burden. Model-driven methods use optical simulation or inverse lithography technology (ILT) to optimize the generation of auxiliary patterns. This method can generate more accurate and complex SRAFs according to the imaging needs of the target pattern. However, the computational complexity of model-driven methods is extremely high, and in high-resolution simulation scenarios, it often requires a large amount of computing resources and time. Therefore, the application of model-driven methods is significantly limited in large-scale production. In recent years, machine learning technology has been introduced into SRAF generation, by extracting features from historical design data to predict the generation position of SRAFs in the target layout. Machine learning methods have a significant advantage in efficiency and can adapt to more complex design patterns. However, its performance is highly dependent on the quality and distribution of the training sample data. When faced with new process nodes or special design requirements, the model usually needs to be retrained. In addition, due to the bias or lack of training sample data, machine learning methods may generate unreasonable SRAF layouts in some cases, resulting in patterns that cannot pass mask rule check (MRC) or lithography compliance check (LCC). Overall, existing SRAF generation techniques face significant challenges in efficiency, versatility, and reliability. Especially in advanced processes, the complexity of design patterns and the strict requirements of process windows further exacerbate these technical bottlenecks. Current methods are difficult to balance between optimization speed and design quality, resulting in significant limitations in SRAF design in meeting the needs of advanced processes. SUMMARY

[0006] The purpose of the present application is to overcome the shortcomings of the prior art, and to provide an SRAF pattern generation method and system based on an implicit diffusion model, which can improve the generation efficiency and reliability of SRAF patterns.

[0007] In the embodiments of the present application, an SRAF pattern generation method based on an implicit diffusion model is provided, which comprises:

[0008] collecting training sample data, the training sample data comprising a target layout graph, a target layout SRAF graph and a target layout lithography simulation intensity map, wherein the target layout SRAF graph is represented by a rectangle, and is represented by a center point coordinate (xc, yc), a width w and a height h;

[0009] preprocessing the training sample data, and converting the target layout SRAF graph into a heat map;

[0010] inputting the preprocessed training sample data into a preset implicit diffusion model for training, to obtain an SRAF generation model capable of automatically generating a heat map corresponding to the target layout SRAF graph according to the target layout graph and the target layout lithography simulation intensity map.

[0011] In the embodiment of the present application, the target layout SRAF graph is converted into a heat map, which comprises:

[0012] each SRAF rectangle is converted into a two-dimensional Gaussian distribution heat map, in which the heat peak is located at the center point (xc, yc) of the rectangle, and the width and height of the Gaussian distribution function are determined by the width w and the height h of the SRAF graph, and for each pixel point (x, y) in the heat map, the heat value I (x, y) is calculated by the following formula:

[0013]

[0014] wherein,

[0015] In the embodiment of the present application, the loss function of the implicit diffusion model is as follows:

[0016]

[0017] wherein, I θ (i,j) represents the heat map prediction value of the model at the coordinate (i,j), I GT (i,j) is the true value of the heat map at the coordinate (i,j), and H and W represent the height and width of the heat map resolution size, respectively.

[0018] In the embodiment of the present application, the SRAF graph generation method based on the implicit diffusion model further comprises:

[0019] inputting the target layout graph and the target layout lithography simulation intensity map into the SRAF generation model, to obtain a heat map corresponding to the target layout SRAF graph.

[0020] In the embodiment of the present application, the SRAF graph generation method based on the implicit diffusion model further comprises:

[0021] decode the heat map corresponding to the SRAF pattern of the target layout to obtain the SRAF pattern of the target layout.

[0022] In the embodiment of the present application, the heat map corresponding to the SRAF pattern of the target layout is decoded to obtain the SRAF pattern of the target layout, comprising:

[0023] The center point detection identifies the peak position in the heat map as a candidate center point through a set high threshold value.

[0024] From the center point, the boundary is searched along the horizontal and vertical directions, and when the heat value drops to a set low threshold value, the rectangular boundary position of the SRAF pattern is determined.

[0025] The overlapped SRAF patterns are merged to generate regular rectangular SRAF patterns.

[0026] In the embodiment of the present application, a SRAF pattern generation system based on an implicit diffusion model is also provided, which automatically generates the optimized SRAF pattern by using the SRAF pattern generation method based on the implicit diffusion model.

[0027] Compared with the prior art, the SRAF pattern generation method and system based on the implicit diffusion model of the present application have the following beneficial effects:

[0028] 1. High-precision generation: By introducing the implicit diffusion model, the present application can generate sub-resolution auxiliary patterns (SRAF) that meet the requirements of the target layout under complex design rules and process conditions. Compared with traditional methods based on rules or physical models, the diffusion model can learn complex optical properties from historical data, significantly improving the precision of the generated results and ensuring that the edge position error (EPE) of the lithography simulation results is minimized.

[0029] 2. Automation and high efficiency: The present application combines the generation ability of the diffusion model with the optical simulation results, omits the tedious manual design and iterative optimization process in traditional methods, and significantly improves the efficiency of SRAF generation; at the same time, the step-by-step generation mechanism of the diffusion model can effectively reduce the computational complexity, adapt to diversified design modes, and significantly shorten the mask optimization period.

[0030] 3. High consistency and reliability: Through the generation consistency of the diffusion model and the sufficient learning of historical design patterns, highly consistent SRAF structures can be generated under similar design layouts, thereby improving the reliability in mass production and avoiding the inconsistency problems caused by manual design or model changes in traditional methods. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 is a flowchart of the SRAF pattern generation method based on an implicit diffusion model according to an embodiment of the present application.

[0032] Figure 2 is a schematic diagram of a RAF pattern according to an embodiment of the present application.

[0033] Figure 3 is a heat map of a SRAF pattern according to an embodiment of the present application.

[0034] Figure 4 is a schematic diagram of an implicit diffusion model according to an embodiment of the present application. DETAILED DESCRIPTION

[0035] As shown in Figure 1 , in an embodiment of the present application, a SRAF pattern generation method based on an implicit diffusion model is provided, which includes steps S1-S5. The following will be described respectively.

[0036] Step S1, collect training sample data.

[0037] Before model training, a high-quality training sample dataset needs to be constructed. These data mainly include target layout and its corresponding sub-resolution auxiliary pattern (SRAF) design results. The target layout is the basic unit of chip design, which contains various geometric structures under the constraints of design rules, such as lines, spacings, corners, T-shaped connections, and other complex features. In order to ensure the performance of the generated model, high-precision SRAF annotation samples need to be obtained from multiple lithography tools, which can be generated by commercial lithography simulation tools. During data collection, variations in multiple process conditions need to be covered, such as different process nodes (e.g. 7nm, 5nm), exposure dose, focal length deviation, etc., which directly affect the lithography imaging results. The collected target layout samples need to have high diversity, including dense layout, sparse layout, complex boundary, etc., in order to improve the generalization ability of the model. In order to simplify the complexity of model learning and improve the quality of the final SRAF, the shape of all SRAFs is limited to rectangular representation. This form can describe SRAF with fewer parameters, such as center point coordinates (xc, yc), width w, and height h, as shown in Figure 1 . Specifically, each rectangular SRAF can be represented and stored by the following structured data: 1. Center point coordinates: (xc, yc), representing the geometric center position of the rectangle; 2. Width and height: w and h, representing the horizontal and vertical length of the rectangle, respectively.

[0038] The training sample data will be stored in the form of images and structured parameters. The target layout as input, and the rectangular parameters of SRAF pattern as the labeled target result. To ensure the quality of data, a comprehensive inspection is required to eliminate abnormal data, such as misaligned target pattern and SRAF example, samples that do not meet the design rule (Design Rule Check, DRC), etc.

[0039] In addition to the pattern information of the target layout, the input of the diffusion model also includes the lithography simulation results, such as intensity images under specific exposure dose and focus deviation conditions. These simulation images can reflect the physical characteristics of the target layout in the actual lithography process, providing additional constraints for the model. The input data of the final model contains multiple channels: Channel 1: the pattern of the target layout, representing the geometric shape of the target layout; Channel 2: lithography simulation intensity map, representing the lithography imaging result under specific process conditions. The output of the model is the SRAF pattern. Through this multi-channel input design, the model can simultaneously utilize the geometric information of the target layout and the lithography simulation data, thereby more accurately designing and optimizing the SRAF.

[0040] Step S2: Preprocessing the training sample data, converting the SRAF pattern of the target layout into a heat map.

[0041] It should be noted that the image results generated by the diffusion model are based on the continuous distribution of pixels, so the output of the model often presents irregular contour features. However, the present application focuses on the design and optimization of rectangular SRAF. To overcome this contradiction, the present application proposes a coding scheme based on two-dimensional Gaussian function, which is used to convert rectangular SRAF into continuous heat map representation, as shown in Figure 3 The specific coding method is as follows: each SRAF rectangle is converted into a two-dimensional Gaussian distribution, with its peak value located at the center point (xc, yc) of the rectangle, as shown in Figure 2 The width and height of the Gaussian function are determined by the geometric dimensions w and h of the SRAF. For each pixel point (x, y), the heat value I(x, y) is calculated by the following formula:

[0042]

[0043] where, respectively. The expansion of the heat map can be controlled to ensure that the heat difference between the center point and the upper, lower, left and right boundaries is 0.5. In this way, the rectangular SRAF is effectively encoded into a smooth continuous heat map, which not only adapts to the generation characteristics of the diffusion model, but also accurately preserves the geometric information of the SRAF. In order to ensure the stability and standardization of the model input, all the intensity values of the heat map are normalized to the interval [0, 1]. Outside the rectangular boundary, i.e. in the non-SRAF region, all values are set to 0.

[0044] Step S3: input the preprocessed training sample data into the pre-set implicit diffusion model for training to obtain an SRAF generation model.

[0045] It should be noted that in the implementation of the present application, an implicit diffusion model is used as the generation framework, as shown in Figure 4 The core idea of the diffusion model is to recover the target SRAF heat map from random noise through a step-by-step reverse denoising process. By simulating the step-by-step reverse process from noise to data, the diffusion model can effectively capture complex data distribution. Compared with the generative adversarial network (GAN), the diffusion model generally performs more stably and is less likely to have mode collapse. In addition, the diffusion model has strong control ability and can accurately guide the generation result by adjusting each step in the noise process, thereby providing better flexibility and interpretability. Compared with traditional diffusion models, the innovation of the implicit diffusion model lies in that it first uses the encoder of the variational autoencoder (VAE) to compress high-dimensional data (such as images) from the pixel space to the low-dimensional latent space. This process can capture the basic semantic information in the image and obtain a low-dimensional implicit representation of the data. In this way, the subsequent operation in the latent space is significantly reduced, thereby improving the generation efficiency. Then, the diffusion process is performed on the compressed implicit representation in the latent space. At the same time, the model can better handle the conditional generation case, i.e. the image generation under a specific condition, i.e. the generation of the model is not random. During forward diffusion, noise is added to the latent variable Z0 according to the Markov chain to generate a series of latent variables Z1, Z2,..., Z T , the process of which is modeled by the transition probability q(Z t+1 |Z t ). The U-Net module composed of a residual network is used to denoise the noisy latent variables obtained by forward diffusion in the latent space. The U-Net learns a reverse denoising process to learn the denoising function p θ (Z t-1 |Z t; c) gradually restore the noisy latent variable to a close-to-original implicit representation, and θ is the parameter learned by the model during training. Finally, the decoder of the VAE is used to convert the de-noised implicit representation back to the data space, such as decoding the representation in the latent space to a high-dimensional image, to obtain the finally generated sample.

[0046] During training, in order to optimize the matching degree between the heat map generated by the model and the target heat map, the following loss function is designed: the pixel difference L between the heat map generated by the model and the target heat map mse As shown in the following formula:

[0047]

[0048] Where, I θ (i,j) represents the heat value of the heat map generated by the model at coordinate (i,j), I GT (i,j) is the heat value of the target heat map at coordinate (i,j), H and W represent the height and width in the resolution size of the heat map, respectively. During training, the target layout can be mirrored, translated, etc. to improve the robustness of the model. At the same time, the input data covers different exposure doses and focal length deviation conditions, so that the model has stronger generalization ability.

[0049] Step S4: input the current target layout pattern and the lithography simulation intensity map of the target layout into the SRAF generation model to obtain a heat map corresponding to the SRAF pattern of the current target layout.

[0050] It should be noted that after the SRAF generation model is trained, the pattern of the new target layout and the lithography simulation intensity map of the target layout can be input into the SRAF generation model to automatically generate a heat map corresponding to the SRAF pattern of the target layout.

[0051] Step S5: decoding the heat map corresponding to the SRAF pattern of the target layout to obtain the SRAF pattern of the target layout.

[0052] Since the diffusion model is generated at the pixel level, the obtained SRAF is not a regular rectangle, but a heat map, so the generated result needs to be decoded. The decoding process includes:

[0053] Center point detection, by setting a high threshold (for example, 0.98), identifying the peak position in the heat map as a candidate center point;

[0054] Starting from the center point, find the boundary along the horizontal and vertical directions, and when the heat value drops to a low threshold (for example, 0.5), determine it as the boundary position of the rectangle;

[0055] The overlapped SRAFs are merged, for example, taking the circumscribed rectangle of the overlapping region, or directly retaining the maximum coverage area. Through the above steps, regular rectangular SRAFs can be generated while avoiding redundancy and overlap problems.

[0056] Step S6: SRAF pattern verification.

[0057] Subsequently, the generated SRAFs are simulated using a photolithography simulation model to verify the matching degree of the generated mask pattern with the target layout in the photolithography process. Through simulation, it can be checked whether the generated SRAF pattern meets the design requirements and predicts its effect in actual manufacturing. If the error between the generated SRAF pattern and the target layout exceeds the preset threshold, the system will automatically feedback and adjust the input data or fine-tune the model until the error reaches an acceptable level.

[0058] Further, the embodiment of the present application also provides an SRAF pattern generation system based on an implicit diffusion model, which automatically generates SRAF patterns by using the above-mentioned SRAF pattern generation method based on an implicit diffusion model.

[0059] In summary, compared with the prior art, the SRAF pattern generation method and system based on an implicit diffusion model of the present application have the following beneficial effects:

[0060] 1. High-precision generation: By introducing an implicit diffusion model, the present application can generate sub-resolution auxiliary patterns (SRAFs) that meet the requirements of the target layout under complex design rules and process conditions. Compared with traditional methods based on rules or physical models, the diffusion model can learn complex optical characteristics from historical data, significantly improving the precision of the generated results and ensuring that the edge position error (EPE) of the pattern after photolithography simulation is minimized.

[0061] 2. Automation and high efficiency: The present application combines the generation capability of the diffusion model with the optical simulation results, eliminating the tedious manual design and iterative optimization process in traditional methods, greatly improving the efficiency of SRAF generation; at the same time, the step-by-step generation mechanism of the diffusion model can effectively reduce the computational complexity, adapt to diversified design modes, and significantly shorten the mask optimization period.

[0062] 3. High consistency and reliability: Through the generation consistency of the diffusion model and the sufficient learning of historical design patterns, highly consistent SRAF structures can be generated under similar design layouts, thereby improving the reliability in mass production and avoiding the inconsistency problems caused by manual design or model changes in traditional methods.

[0063] The above merely describes preferred embodiments of the present application, and is not used to limit the present application, any modification, equivalent replacement and improvement within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method for generating SRAF patterns based on an implicit diffusion model, characterized in that, The method comprises the following steps: Collecting training sample data, which comprises a target layout graph, a target layout SRAF graph and a target layout lithography simulation intensity graph, wherein the target layout SRAF graph is represented by a rectangle and stored by structured data of a center point coordinate (xc, yc), a width w and a height h; Preprocessing the training sample data to convert the target layout SRAF graph into a heat map; Inputting the preprocessed training sample data into a preset implicit diffusion model for training to obtain an SRAF generation model capable of automatically generating a heat map corresponding to the target layout SRAF graph according to the target layout graph and the target layout lithography simulation intensity graph.

2. The SRAF pattern generation method based on an implicit diffusion model according to claim 1, wherein, Converting the target layout SRAF graph into a heat map comprises the following steps: Converting each SRAF rectangle into a two-dimensional Gaussian distribution heat map, wherein the heat peak of the heat map is located at the center point (xc, yc) of the rectangle, the width and height of the Gaussian distribution function are determined by the width w and the height h of the SRAF graph, and the heat value I(x, y) of each pixel point (x, y) in the heat map is calculated by the following formula: wherein 3. The SRAF pattern generation method based on an implicit diffusion model according to claim 1, wherein, The loss function of the implicit diffusion model is as follows: wherein, wherein, θ (i,j) represents the heat value of the heat map generated by the model at coordinate (i,j), I GT (i,j) is the heat value of the target heat map at coordinate (i,j), H and W represent the height and width in the resolution size of the heat map, respectively.

4. The SRAF pattern generation method based on an implicit diffusion model according to claim 1, wherein, Further comprising the following steps: Inputting the target layout graph and the target layout lithography simulation intensity graph into the SRAF generation model to obtain a heat map corresponding to the target layout SRAF graph.

5. The SRAF pattern generation method based on an implicit diffusion model according to claim 1, wherein, Further comprising the following steps: Decoding the heat map corresponding to the target layout SRAF graph to obtain the target layout SRAF graph.

6. The SRAF pattern generation method based on an implicit diffusion model according to claim 1, wherein, Decoding the heat map corresponding to the target layout SRAF graph to obtain the target layout SRAF graph comprises the following steps: Center point detection, identifying the peak position in the heat map as a candidate center point by setting a high threshold value; Starting from the center point, finding the boundary along the horizontal and vertical directions, and determining the rectangular boundary position of the SRAF graph when the heat value drops to a set low threshold value; Merging the overlapped SRAF graphs to generate a regular rectangular SRAF graph.

7. An SRAF pattern generation system based on an implicit diffusion model, characterized by, The method comprises the following steps: The method comprises the following steps: Collecting training sample data, which comprises a target layout graph, a target layout SRAF graph and a target layout lithography simulation intensity graph, wherein the target layout SRAF graph is represented by a rectangle and stored by structured data of a center point coordinate (xc, yc), a width w and a height h; Preprocessing the training sample data to convert the target layout SRAF graph into a heat map; Inputting the preprocessed training sample data into a preset implicit diffusion model for training to obtain an SRAF generation model capable of automatically generating a heat map corresponding to the target layout SRAF graph according to the target layout graph and the target layout lithography simulation intensity graph. Converting the target layout SRAF graph into a heat map comprises the following steps: Converting each SRAF rectangle into a two-dimensional Gaussian distribution heat map, wherein the heat peak of the heat map is located at the center point (xc, yc) of the rectangle, the width and height of the Gaussian distribution function are determined by the width w and the height h of the SRAF graph, and the heat value I(x, y) of each pixel point (x, y) in the heat map is calculated by the following formula: The loss function of the implicit diffusion model is as follows: Further comprising the following steps: Inputting the target layout graph and the target layout lithography simulation intensity graph into the SRAF generation model to obtain a heat map corresponding to the target layout SRAF graph. Further comprising the following steps: Decoding the heat map corresponding to the target layout SRAF graph to obtain the target layout SRAF graph. Decoding the heat map corresponding to the target layout SRAF graph to obtain the target layout SRAF graph comprises the following steps: Center point detection, identifying the peak position in the heat map as a candidate center point by setting a high threshold value; Starting from the center point, finding the boundary along the horizontal and vertical directions, and determining the rectangular boundary position of the SRAF graph when the heat value drops to a set low threshold value; Merging the overlapped SRAF graphs to generate a regular rectangular SRAF graph. The method comprises the following steps: The method comprises the following steps: Collecting training sample data, which comprises a target layout graph, a target layout SRAF graph and a target layout lithography simulation intensity graph, wherein the target layout SRAF graph is represented by a rectangle and stored by structured data of a center point coordinate (xc, yc), a width w and a height h; Preprocessing the training sample data to convert the target layout SRAF graph into a heat map; Inputting the preprocessed training sample data into a preset implicit diffusion model for training to obtain an SRAF generation model capable of automatically generating a heat map corresponding to the target layout SRAF graph according to the target layout graph and the target layout lithography simulation intensity graph. Converting the target layout SRAF graph into a heat map comprises the following steps: Converting each SRAF rectangle into a two-dimensional Gaussian distribution heat map, wherein the heat peak of the heat map is located at the center point (xc, yc) of the rectangle, the width and height of the Gaussian distribution function are determined by the width w and the height h of the SRAF graph, and the heat value I(x, y) of each pixel point (x, y) in the heat map is calculated by the following formula: The loss function of the implicit diffusion model is as follows: Further comprising the following steps: Inputting the target layout graph and the target layout lithography simulation intensity graph into the SRAF generation model to obtain a heat map corresponding to the target layout SRAF graph. Further comprising the following steps: Decoding the heat map corresponding to the target layout SRAF graph to obtain the target layout SRAF graph. Decoding the heat map corresponding to the target layout SRAF graph to obtain the target layout SRAF graph comprises the following steps: Center point detection, identifying the peak position in the heat map as a candidate center point by setting a high threshold value; Starting from the center point, finding the boundary along the horizontal and vertical directions, and determining the rectangular boundary position of the SRAF graph when the heat value drops to a set low threshold value; Merging the overlapped SRAF graphs to generate a regular rectangular SRAF graph.

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