Rule-based mask pattern constraint method for non-Manhattan mask manufacturing

Abstract

The invention discloses a rule-based mask pattern constraint method for non-Manhattan mask manufacturing. The method comprises the following steps: constructing a binary mask image, scanning the mask image according to lines, distributing labels according to neighbor pixel conditions of each mask pattern pixel, repeatedly scanning to obtain final labels, and taking a region of the same final label as a final connected region; scanning each connected region, and performing neighborhood foreground pixel screening to obtain an extracted skeleton; carrying out a point sampling algorithm based on depth-first search on each obtained skeleton graph, and sampling to obtain the circle center of each connected region; a radius increasing strategy is used in a radius constraint range based on the circle center, and a circle capable of covering an original mask area to the maximum degree is obtained; and combining all the obtained circles, and outputting a final constraint mask result. The method is high in algorithm efficiency, and the manufacturability of the mask is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to photolithography technology, and in particular to a rule-based mask pattern constraint method for non-Manhattan mask manufacturing. BACKGROUND

[0002] As technology nodes continue to shrink, the pattern print shape and design deviation due to optical effects in photolithography processes become increasingly significant. Resolution enhancement techniques (RETs) such as optical proximity correction (OPC) are used to improve mask fidelity and printability. OPC can be divided into model-based methods and inverse lithography technology (ILT)-based methods: the former modifies the mask pattern and inserts auxiliary features to compensate for optical effects, but has the problems of limited solution space and poor performance; the latter optimizes the mask through lithography simulation, provides pixel-level flexibility, and generates a curve mask with a more optimal process window and key size uniformity. ILT has been widely used in mask pattern generation for 193 nm immersion lithography and extreme ultraviolet lithography.

[0003] Although ILT improves the quality of the curve mask, its manufacturing still faces challenges. Traditional variable shape beam (VSB) equipment uses different sizes of rectangular patterns, which need to be fragmented into non-overlapping rectangles or VSB exposure lenses through mask data preparation (MDP) to ensure printability. However, Manhattan-based curve patterns (especially sub-resolution auxiliary features (SRAFs)) can cause a significant increase in the number of exposure lenses, not only increasing the cost of mask manufacturing, but also affecting mask yield, thereby hindering large-scale wafer manufacturing. In addition, rectangular fragmented mask shapes are prone to writing errors due to short-range electron beam blur in the range of 20-40 nm. These factors limit the widespread application of curve masks, despite their excellent mask quality potential.

[0004] To solve the above problems, the prior art proposes a new type of annular electron beam mask writer, which can write variable radius circles in a single write and allows overlapping writing. This writer is more suitable for curve non-Manhattan mask manufacturing, as it requires much fewer exposure lenses than rectangular writers. In addition, fragmented curve masks are also easier to perform mask rule checking (MRC), as the distance can be easily checked by the position and radius of the circular exposure lens.

[0005] Traditional variable shape beam (VSB) equipment uses different sizes of rectangular patterns, which need to be fragmented into non-overlapping rectangles or VSB exposure lenses through mask data preparation (MDP) to ensure printability. However, Manhattan-based curve patterns (especially sub-resolution auxiliary features (SRAFs)) can cause a significant increase in the number of exposure lenses, such as Figure 1As shown, this not only increases mask manufacturing costs but also affects mask yield, thus hindering large-scale wafer fabrication. Furthermore, the rectangular fragmented mask shape is prone to writing errors due to short-range electron beam blurring in the 20-40 nm range. These factors limit the widespread application of curved masks, despite their superior mask quality potential. A comparison of writing techniques using variable-shape electron beam (VSB) devices and novel ring-shaped electron beam mask writers is provided. Figure 1 As shown.

[0006] While the new writer offers advanced manufacturing capabilities, it suffers from a critical flaw: it is merely a manufacturing device, lacking an efficient and adaptable manufacturing design. The specific flaws are as follows: Lack of intelligent integration with upstream design: While the writer can efficiently fabricate masks composed of circles, generating an optimal mask pattern of circles for a given target circuit pattern is a problem the writer itself cannot solve. Existing reverse lithography (ILT) techniques typically generate pixel-level or curved contour masks, which cannot be directly and efficiently adapted to circular writers.

[0007] Manufacturing efficiency potential is not fully realized: If the complex curve mask generated by ILT is simply broken into circles, the overlapping nature of circles may not be fully utilized, resulting in an excessive number of generated circles (i.e., the number of exposure shots #Shots), limiting the improvement in mask manufacturability and yield. In other words, the potential of the new writer is constrained by the inefficiency of the upstream pattern generation method. Summary of the Invention

[0008] The purpose of this invention is to address the shortcomings of existing technologies by proposing a rule-based mask pattern constraint method for non-Manhattan mask manufacturing. Its advantage is not to replace new writers, but to perfectly combine with them to form an efficient closed loop from design to manufacturing.

[0009] The objective of this invention is achieved through the following technical solution: a rule-based mask pattern constraint method for non-Manhattan mask manufacturing, the method comprising: constructing a binary mask image, scanning the mask image row by row, assigning labels according to the neighboring pixels of each mask pattern pixel, repeatedly scanning to obtain the final label, and taking the region with the same final label as the final connected region.

[0010] Scan each connected region and perform neighborhood foreground pixel screening to obtain the extracted skeleton;

[0011] For each obtained skeleton graph, a point sampling algorithm based on depth-first search is used to sample the center of each connected region. Based on the center, a radius growth strategy is used within the radius constraint to obtain a circle that can cover the original mask region to the greatest extent. All the obtained circles are merged, and the final constrained mask result is output.

[0012] Furthermore, the step of assigning labels based on the neighboring pixels of each mask pattern pixel specifically includes:

[0013] If there are no foreground pixels above or to the left of a pixel, then assign a new label to that pixel;

[0014] If there is only one foreground pixel above or to the left, then that pixel is labeled with the same label as its neighbor;

[0015] If there are foreground pixels above and to the left, and the labels are the same, then the pixel is labeled with the same label;

[0016] If there are foreground pixels above and to the left, but with different labels, then mark them as one of the labels and record that the two labels are equivalent. Then, merge the pixels with equivalent but different labels into the smallest label value among these labels.

[0017] Further, the neighborhood foreground pixel screening specifically includes: deleting pixels that simultaneously meet screening conditions A, B, and C, and deleting pixels that simultaneously meet screening conditions A, B, and D, wherein the screening conditions include:

[0018] Condition A: The number of foreground pixels in the neighborhood of P1 is between 2 and 6;

[0019] Condition B: In the pixel sequence, the number of changes from the background to the foreground is exactly 1;

[0020] Condition C: P2×P4×P6 = 0 and P4×P6×P8 = 0, the binary mask only has two pixel values, 0 and 1, the background is 0 and the foreground is 1;

[0021] Condition D: P2 * P4 * P8 = 0 and P2 * P6 * P8 = 0.

[0022] Furthermore, the extracted skeleton is obtained by repeatedly screening neighboring foreground pixels until no pixels are deleted in a complete iteration, and the remaining pixels are the extracted skeleton.

[0023] Furthermore, the point sampling algorithm based on depth-first search specifically includes:

[0024] A depth-first search is performed on the skeleton graph starting from the starting point, and a point is collected at fixed sampling distances as the center of the circle. The starting point is the first node of the skeleton graph that is randomly specified. The traversal direction is selected according to the starting point position. If the starting point is the end point of the skeleton, there is only one traversal direction. If the starting point is the middle node, there are two directions, until the entire skeleton is traversed and all sampling points are obtained.

[0025] Furthermore, the radius growth strategy specifically includes:

[0026] The initial radius is set to the minimum radius within the radius constraints. The coverage of the current circle is calculated, and the radius is gradually increased. The increase scale is a fixed value that is proportional to the key dimensions of the mask layout.

[0027] When the coverage rate first drops below the preset threshold, or when the radius reaches the maximum radius in the radius constraint, growth stops, and the radius before growth stops is selected as the final radius.

[0028] Furthermore, the coverage rate is defined as the ratio of the number of pixels that are simultaneously connected regions within a single circle to the total number of pixels contained within the circle.

[0029] Furthermore, the radius constraint is: the maximum radius is 1.5 times the critical dimension, and the minimum radius is 0.8 times the critical dimension.

[0030] According to another aspect of the specification, a rule-based mask pattern constraint device for non-Manhattan mask fabrication is also provided, including a memory and one or more processors, wherein the memory stores executable code, and when the processor executes the executable code, it implements the aforementioned rule-based mask pattern constraint method for non-Manhattan mask fabrication.

[0031] According to another aspect of the specification, a computer-readable storage medium is also provided, on which a program is stored, which, when executed by a processor, implements the rule-based mask pattern constraint method for non-Manhattan mask fabrication.

[0032] The beneficial effects of this invention are:

[0033] Based on connected component extraction, skeleton extraction, and DFS depth-first sampling algorithm to obtain the center sampling point, the algorithm can easily and effectively find the center of each patch (connected region) on the binary mask, and the algorithm is highly efficient.

[0034] The circular radius growth scheme and coverage calculation method after obtaining the center sampling point can gradually scan and select a circle of appropriate size through the circular radius growth method, and then select a circle that fits the original mask pattern through coverage calculation. This ensures that the generated circular constraint mask fits the original mask to the maximum extent, thus ensuring the quality of the mask lithography results (good ILT index) and improving the mask manufacturability.

[0035] This invention addresses the mask manufacturing constraint (which must consist of circles) at the mask generation stage. The method directly processes the initial mask generated by the ILT (Integrated Photonic Transformer), outputting a mask represented by a set of circles that can be directly used in the manufacture of novel ring-shaped electron beam writers. This approach avoids the disconnect between the traditional process of "generating the mask first, then breaking it down into manufacturing patterns," achieving integration of mask generation and breaking down the process. Attached Figure Description

[0036] Figure 1 Schematic diagrams showing rectangular decomposition based on a traditional variable-shape electron beam writer and circular decomposition based on a novel ring-shaped electron beam mask writer;

[0037] Figure 2 A flowchart of a rule-based SRAF constraint method for reverse lithography technology provided in an embodiment of the present invention;

[0038] Figure 3 This is a flowchart of the connected region and skeleton extraction scheme provided in an embodiment of the present invention;

[0039] Figure 4 This is a schematic diagram of pixel distribution provided in an embodiment of the present invention;

[0040] Figure 5 This is a schematic diagram of skeleton extraction provided in an embodiment of the present invention;

[0041] Figure 6 This is a schematic diagram of the DFS algorithm sampling provided in an embodiment of the present invention;

[0042] Figure 7 A schematic diagram of the radius growth method provided in an embodiment of the present invention;

[0043] Figure 8 The diagram shows the ILT target layout, the circularly constrained mask pattern, and the result of the photolithography simulation of the constrained mask, provided for embodiments of the present invention.

[0044] Figure 9 This invention provides a rule-based mask pattern constraint device for non-Manhattan mask fabrication. Detailed Implementation

[0045] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0046] like Figure 2 As shown, the present invention provides a rule-based SRAF constraint method for reverse lithography technology, comprising:

[0047] S1: Input the original binary mask, DFS sampling distance m, and maximum and minimum circular radii R. max R min Coverage threshold I;

[0048] Specifically, in step S1, the original binary mask is generated by any ILT method, and the DFS (depth-first search-based) algorithm samples the distance m and the maximum radius R. max With the minimum circular radius R min The specified relationship is: m=3, R max =1.5×CD, R min =0.8×CD, where CD is the key dimension corresponding to the mask layout; the coverage threshold is specified as 0.9, and the coverage is defined as a single circle. The interior is also a connected region The number of pixels (expressed as) ) and the total number of pixels contained within the circle (represented as The ratio of ) to:

[0049] ;

[0050] S2: Divide the mask into multiple connected regions A in S1, and extract the skeleton G of the connected regions; the textual flowchart of the connected region and skeleton extraction scheme in step S2 is as follows: Figure 3 As shown:

[0051] S21: Scan the mask image row by row and assign labels based on the neighboring pixels above and to the left of each mask pattern pixel;

[0052] Specifically, in step S21, the assignment of labels based on neighboring pixels falls into the following four categories:

[0053] Case 1: If there are no foreground pixels above and to the left (foreground pixels refer to pixels on the mask pattern that belong to the mask pattern rather than the background), then assign a new label to the pixel;

[0054] Case 2: If there is only one foreground pixel above or to the left, then mark that pixel with the same label as its neighbor;

[0055] Case 3: If there are foreground pixels on the top and left sides, and the labels are the same, then mark it with that label;

[0056] Case 4: If there are foreground pixels on the top and left sides, but with different labels, then mark them as one of the labels (e.g., the one on the left), and record that the two labels are equivalent (belonging to the same area).

[0057] S22: Based on the equivalence relationship recorded in the first scan, pixels belonging to the same connected region but temporarily assigned different labels are uniformly merged into the smallest label value;

[0058] Specifically, in step S22, pixels belonging to the same connected region but temporarily assigned different labels are uniformly merged into the smallest label value among these labels. A connected region refers to a region composed of foreground pixels that are connected to each other.

[0059] S23: Rescan the image once, replace the temporary labels with the final labels, and obtain all connected regions;

[0060] Specifically, in step S23, each label in the final label corresponds to a different connected region, and pixels with the same label belong to the same connected region.

[0061] S24: Scan all connected spatial regions of the mask, mark all pixels that simultaneously satisfy conditions A, B, and C as to be deleted, and delete these pixels;

[0062] Specifically, in step S24, conditions A, B, and C are defined as follows:

[0063] Condition A: The neighborhood of P1 (the surrounding eight pixels, such as...) Figure 4 The number of foreground pixels in the diagram is between 2 and 6 (to ensure that the endpoints are not deleted and are not excessively eroded).

[0064] Condition B: such as Figure 4 In the corresponding pixel cycle sequence P2, P3, P4, P5, P6, P7, P8, P9, P2, the number of changes from 0 (background) to 1 (foreground) is exactly 1 (ensuring connectivity).

[0065] Under the premise that conditions A and B are satisfied, conditions C and D are applied in different iterations. The purpose is to "thin" the graph in a directional manner to avoid unnecessary deviation of the skeleton and eventually converge to the center line.

[0066] Condition C: The product of the values ​​corresponding to pixels P2, P4, and P6 is 0 (P2 × P4 × P6 = 0), and the product of the values ​​corresponding to pixels P4, P6, and P8 is 0 (P4 × P6 × P8 = 0) (a binary mask only has two pixel values, 0 and 1; if 0 exists, the result of the expression is 0). Condition C focuses on the pixels in the four cardinal directions (P2: top, P4: right, P6: bottom, P8: left). It indirectly determines the pixel situation on the right (P4) and below (P6) by checking whether the product of P2, P4, and P6, and the product of P4, P6, and P8, are 0.

[0067] Design Principle: Condition C is primarily used to delete boundary pixels in the lower right corner of a graphic. For example, if a pixel is surrounded by background to the right and below (i.e., P4=0 or P6=0), it is likely located at the lower right edge of the graphic and can be safely deleted. This directional deletion ensures that the skeletonization process is orderly and uniform, preventing the skeleton from shifting in one direction. It prioritizes removing the boundaries in the "southeast" direction of the graphic.

[0068] S25: Scan all connected spatial regions of the mask, mark all pixels that simultaneously satisfy conditions A, B, and D as to be deleted, and delete these pixels;

[0069] Specifically, in step S25, condition D is defined as follows:

[0070] Condition D: The product of the values ​​corresponding to each pixel P2, P4, and P8 is 0 (P2×P4×P8 = 0) and the product of the values ​​corresponding to each pixel P2, P6, and P8 is 0 (P2×P6×P8 = 0).

[0071] Condition D also focuses on the pixels in the four cardinal directions (P2, P4, P6, P8). It indirectly determines the situation of the pixels above (P2) and to the left (P8) by checking whether the product of P2, P4, and P8, as well as the product of P2, P6, and P8, is 0.

[0072] Design Principle: Condition D is complementary to Condition C and is primarily used to remove boundary pixels in the upper left corner of the graphic. For example, if a pixel is surrounded by background above and to the left (i.e., P2=0 or P8=0), it is likely located at the upper left edge of the graphic. By applying Conditions C and D in alternating iterations, the algorithm can alternately "thin" the graphic from two main directions (lower right and upper left), thus ensuring that the final skeleton is located at the geometric center of the graphic.

[0073] The core reason for not selecting symbols at corner positions (such as P3, P5, P7, P9) is to maintain connectivity and avoid breaking diagonal connections.

[0074] Corner pixels (P3, P5, P7, P9) represent diagonal connections. If deletion rules are primarily based on these diagonal neighbors, a serious risk arises: diagonal connections of a single pixel width may be severed.

[0075] Consider a simple 2x2 pixel cube connected diagonally. If deletion rules rely too heavily on corner pixels, they can easily misjudge and break these connections, thus disrupting the topology of the graphic. Deletion rules based on pixels along the positive directions (top, bottom, left, right) are more robust because positive connectivity is 4-connected (more stringent), while diagonal connectivity is 8-connected. Prioritizing 4-connectivity ensures that the skeleton maintains its single-pixel width without creating unnecessary branches or breaks due to the presence of diagonals.

[0076] In theory, different Boolean functions can be designed to combine the neighboring pixel values ​​of P1 to create new deletion conditions. However, any new combination must meet the following basic requirements:

[0077] Topology preservation: Connected regions cannot be disconnected.

[0078] Endpoint preservation: The endpoints of a line segment cannot be deleted.

[0079] Center the skeleton: The final skeleton should be located as far as possible in the center of the original area.

[0080] Convergence: The algorithm must converge to a result of a single pixel width within a finite number of steps.

[0081] S26: Repeat steps S24 and S25 until no pixels are deleted in a complete iteration. The remaining pixels are the extracted skeleton, such as... Figure 5 The extracted skeleton shown is a single pixel wide.

[0082] S3: For each skeleton graph G obtained in S2, perform a point sampling algorithm based on depth-first search (DFS);

[0083] like Figure 6 As shown, the DFS algorithm performs a depth-first search on the skeleton graph (a graph composed of skeleton pixels), starting from the starting point, and samples a point as the center at fixed sampling intervals m=3. Figure 6 As shown. The starting point is the first node of the randomly specified skeleton graph. Traverse the skeleton graph from both directions (if the starting point is an endpoint of the skeleton, there is only one direction; if it is an intermediate node, there are two directions) until the entire skeleton is traversed and all sampling points are obtained.

[0084] S4: Find a radius for each circle center sampled in S3, such that the circle can cover the original mask area to the maximum extent, while the radius is within [R]. min Rmax Within the range;

[0085] Specifically, in step S4, in [R min R max Try circles with different radii within the range. The method is a radius growth strategy, such as... Figure 7 As shown:

[0086] 1. Initialize radius r = R min .

[0087] 2. Calculate the current coverage of the circle. That is, the number of pixels within the circle that belong to the mask area divided by the total number of pixels within the circle.

[0088] 3. Gradually increase r (set to increase by a fixed value x each time, where x is in a fixed proportion to CD, set as needed).

[0089] 4. When When it first drops below the threshold I, or when r reaches R max When the radius stops growing, the radius before growth stops is chosen as the final radius R.

[0090] The principle is that when the circle is small, it is completely inside the mask, with a coverage rate of 1. As the radius increases, the circle begins to extend beyond the mask boundary, and the coverage rate decreases. The coverage rate threshold I controls the degree to which the circle fits the original mask shape.

[0091] S5: Merge all the circles obtained in S4, specifically by taking the union of the pixels of all the circles and outputting the final constraint mask result.

[0092] at last, Figure 8 The circular constraint mask effect generated by this invention is demonstrated, including the ILT target pattern, the circularly constrained mask pattern, and the printed image of the constrained mask lithography simulation. Tables 1 and 2 verify the effectiveness of this invention on some ILT schemes, including comparisons of squared L2 loss, process variation band (PVB), edge placement error (EPE), and number of exposure lenses (#Shots).

[0093] The squared L2 loss is used for the nominal photoresist (photoresist profile under standard process conditions) image Z. nom With target image Z t Differences in L2 norm (Euclidean norm):

[0094] ;

[0095] .

[0096] The process fluctuation band is used to evaluate the robustness of the mask to different process conditions, that is, the sensitivity of the mask image to process fluctuations under different process conditions, through the maximum process angle Z. max and minimum process angle Z min The L2 distance between the printed image (corresponding to the maximum and minimum contours of the image) is calculated, and the smaller the value, the stronger the stability.

[0097] .

[0098] The edge placement error is used to evaluate the geometric distortion of the photoresist image. The target shape edge points are sampled and the number of points whose distance exceeds the constraint is counted. The fewer the number of points, the higher the mask quality.

[0099] The number of exposure lenses constitutes the basic shape (circle) of the mask pattern, representing the manufacturability of the mask; the smaller the number, the stronger the manufacturability.

[0100] Based on the above explanation of the evaluation parameters, the parameters in the table demonstrate that the present invention significantly improves the effectiveness of reducing the number of mask exposure lenses and enhancing mask manufacturability at the cost of only a small portion of performance indicators.

[0101] Table 1. Mask constraint effect of the present invention on the Neutal-ILT scheme.

[0102]

[0103] Table 2 Mask constraint effect of the present invention on the Multi-ILT scheme.

[0104] Corresponding to the aforementioned embodiment of a rule-based mask pattern constraint method for non-Manhattan mask fabrication, the present invention also provides an embodiment of a rule-based mask pattern constraint device for non-Manhattan mask fabrication.

[0105] See Figure 9 The present invention provides a rule-based mask pattern constraint device for non-Manhattan mask manufacturing, comprising a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it implements a rule-based mask pattern constraint method for non-Manhattan mask manufacturing as described in the above embodiment.

[0106] The present invention provides an embodiment of a rule-based mask pattern constraint device for non-Manhattan mask fabrication, which can be applied to any device with data processing capabilities, such as a computer. The device embodiment can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution. From a hardware perspective, such as... Figure 9 The diagram shown is a hardware structure diagram of any device with data processing capabilities, which includes a rule-based mask pattern constraint device for non-Manhattan mask manufacturing provided by the present invention. (Except for...) Figure 9 In addition to the processor, memory, network interface, and non-volatile memory shown, any data processing device in the embodiment may also include other hardware depending on the actual function of the data processing device, which will not be described in detail here.

[0107] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0108] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0109] This invention also provides a computer-readable storage medium storing a program that, when executed by a processor, implements a rule-based mask pattern constraint method for non-Manhattan mask fabrication as described in the above embodiments.

[0110] The computer-readable storage medium can be an internal storage unit of any data processing device described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be an external storage device of any data processing device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units and external storage devices of any data processing device. The computer-readable storage medium is used to store the computer program and other programs and data required by the data processing device, and can also be used to temporarily store data that has been output or will be output.

[0111] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the aforementioned rule-based mask pattern constraint method for non-Manhattan mask fabrication.

[0112] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0113] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this application. This application is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A rule-based mask pattern constraint method for non-Manhattan mask fabrication, characterized in that, The method includes: constructing a binary mask image, scanning the mask image row by row, assigning labels according to the neighboring pixels of each mask pattern pixel, repeatedly scanning to obtain the final label, and taking the region with the same final label as the final connected region; Scan each connected region and perform neighborhood foreground pixel screening to obtain the extracted skeleton; For each obtained skeleton graph, a point sampling algorithm based on depth-first search is used to sample the center of each connected region. Based on the center, a radius growth strategy is used within the radius constraint to obtain a circle that can cover the original mask region to the greatest extent. All the obtained circles are merged, and the final constrained mask result is output.

2. The rule-based mask pattern constraint method for non-Manhattan mask fabrication according to claim 1, characterized in that, The specific steps of assigning labels based on the neighboring pixels of each mask pattern pixel include: If there are no foreground pixels above or to the left of a pixel, then assign a new label to that pixel; If there is only one foreground pixel above or to the left, then that pixel is labeled with the same label as its neighbor; If there are foreground pixels above and to the left, and the labels are the same, then the pixel is labeled with the same label; If there are foreground pixels above and to the left, but with different labels, then mark them as one of the labels and record that the two labels are equivalent. Then, merge the pixels with equivalent but different labels into the smallest label value among these labels.

3. The rule-based mask pattern constraint method for non-Manhattan mask fabrication according to claim 1, characterized in that, The neighborhood foreground pixel screening specifically includes: deleting pixels that simultaneously meet the screening conditions, wherein the screening conditions include: The number of foreground pixels in the 8 neighboring pixels of the pixel to be screened is between 2 and 6; In the cyclic sequence of neighboring pixels of the pixel to be screened, the number of changes from background to foreground is 1; Background pixels exist in the four neighboring pixels in the four directions (up, down, left, and right) of the pixel to be screened.

4. The rule-based mask pattern constraint method for non-Manhattan mask fabrication according to claim 3, characterized in that, The extracted skeleton is obtained by repeatedly screening neighboring foreground pixels until no pixels are deleted in a complete iteration, and the remaining pixels are the extracted skeleton.

5. The rule-based mask pattern constraint method for non-Manhattan mask fabrication according to claim 1, characterized in that, The point sampling algorithm based on depth-first search specifically includes: A depth-first search is performed on the skeleton graph starting from the starting point, and a point is collected at fixed sampling distances as the center of the circle. The starting point is the first node of the skeleton graph that is randomly specified. The traversal direction is selected according to the starting point position. If the starting point is the end point of the skeleton, there is only one traversal direction. If the starting point is the middle node, there are two directions, until the entire skeleton is traversed and all sampling points are obtained.

6. The rule-based mask pattern constraint method for non-Manhattan mask fabrication according to claim 1, characterized in that, The radius growth strategy specifically includes: The initial radius is set to the minimum radius within the radius constraints. The coverage of the current circle is calculated, and the radius is gradually increased. The increase scale is a fixed value that is proportional to the key dimensions of the mask layout. When the coverage rate first drops below the preset threshold, or when the radius reaches the maximum radius in the radius constraint, growth stops, and the radius before growth stops is selected as the final radius.

7. A rule-based mask pattern constraint method for non-Manhattan mask fabrication according to claim 6, characterized in that, The coverage rate is defined as the ratio of the number of pixels that are simultaneously connected regions within a single circle to the total number of pixels contained within the circle.

8. The rule-based mask pattern constraint method for non-Manhattan mask fabrication according to claim 1, characterized in that, The radius constraints are: the maximum radius is 1.5 times the critical dimension, and the minimum radius is 0.8 times the critical dimension.

9. A rule-based mask pattern constraint apparatus for non-Manhattan mask fabrication, comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that, When the processor executes the executable code, it implements a rule-based mask pattern constraint method for non-Manhattan mask fabrication as described in any one of claims 1-8.

10. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements a rule-based mask pattern constraint method for non-Manhattan mask fabrication as described in any one of claims 1-8.

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