Sub-resolution assist feature pattern generation method for improving lithographic pattern resolution

Abstract

The application belongs to the field of chip manufacturing, and proposes a sub-resolution auxiliary feature pattern generation method which can improve the definition of photolithography pattern. The method uses continuous transmittance mask to accurately guide the generation position of sub-resolution auxiliary feature pattern. In addition to considering the layout design rule constraints and the influence of the interaction range of transmitted light, an optimization objective is introduced to represent the final effect of the sub-resolution auxiliary feature pattern. Through the continuous relaxation of the intractable discrete solution space problem, a better balance between the image generation quality and complexity of the mask after adding auxiliary features is achieved. Process deviation modeling and optimization are performed, and the generated mask can more effectively resist process deviation. The mask for chip manufacturing is optimized, so that the pattern after photolithography has high fidelity.

Description

Technical Field

[0001] This invention belongs to the field of chip manufacturing and relates to a sub-resolution auxiliary feature pattern generation method that can improve the clarity of photolithography patterns. Background Technology

[0002] As the feature size of integrated circuits continues to shrink, existing manufacturing technologies face significant challenges. Because the pattern size of the circuit and the wavelength of the light source used in photolithography are similar, interference effects are inevitable, leading to lithographic pattern distortion and impacting integrated circuit manufacturing capacity. The application of resolution enhancement techniques is a crucial step in improving capacity. With further shrinking feature sizes, the improvement achieved by applying optical proximity correction techniques solely to the target pattern mask is limited. In production, the generation of sub-resolution auxiliary feature patterns becomes increasingly important for compensating for optical scattering and improving the clarity of lithographic patterns. The first type is design rule-based methods, which are simple and fast, handling simple designs well. However, the design rules for large-scale designs at advanced technology nodes grow exponentially, thus limiting the quality of sub-resolution auxiliary features generated by design rule-based methods. Another type is model-based methods, which have a very large solution space, making it very time-consuming to obtain high-quality results. As the complexity of circuit designs increases, both design rule-based and model-based methods face efficiency or output quality issues. Therefore, analytical methods are becoming a new trend. Another type is based on machine learning. These methods are computationally fast, but their effectiveness depends excessively on the number and quality of the training samples used. When faced with advanced technology nodes, their results are not reliable enough.

[0003] Classical sub-resolution auxiliary feature generation methods rely on binary mask information for layout. However, much of the light transmittance information inherent in this mask is lost during the binary process, resulting in limited guidance for generating sub-resolution feature patterns. Consequently, the generated sub-resolution auxiliary features do not adequately improve the quality of the final photolithography mask. Furthermore, after generating candidate sub-resolution auxiliary features using classical methods, significant manual checks are required to ensure they conform to complex design rules, necessitating subsequent cleaning and shape refinement. Summary of the Invention

[0004] To overcome the problems existing in the prior art, this invention fundamentally differs from sub-resolution auxiliary feature generation methods based on binary mask information. It uses a continuous transmittance mask as the guiding basis for the generation position of sub-resolution auxiliary features. The scenario of selecting high-quality sub-resolution auxiliary feature seeds under design rules is extracted as an NP-hard optimization problem of finding the maximum value of the objective function. An efficient and accurate calculation method based on approximation and relaxation is proposed. Information on violations of the minimum distance rule between sub-resolution auxiliary feature seeds is recorded using a conflict matrix. The values ​​of the elements in the binary matrix represent whether any sub-resolution auxiliary feature seed is selected. Weights are assigned based on the transmittance on the corresponding continuous transmittance mask at the seed location. In each loop, the selection of sub-resolution auxiliary feature seeds is guided by comparing the magnitude of the objective function before and after optimization. After selection, a probe method and fine-tuning coefficients are used to control the shape evolution of the final sub-resolution auxiliary feature. Because this method automatically drives the selection of sub-resolution auxiliary feature positions and automatically performs shape evolution by a high-precision continuous transmittance mask and optimization objective, the entire process does not require manual adjustment by professionals or subsequent cleaning and shape correction.

[0005] The specific technical solution of this invention is as follows:

[0006] A sub-resolution auxiliary feature pattern generation method that can improve the sharpness of lithographic patterns includes the following steps:

[0007] Step 1: Generate a continuous transmittance mask based on the target image;

[0008] Step 2: Use the transmittance distribution of the continuous transmittance mask generated in Step 1 to accurately guide the distribution of candidate seeds for sub-resolution auxiliary feature images, form a safe generation region for sub-resolution auxiliary feature images, and construct a candidate set of sub-resolution auxiliary feature image seeds.

[0009] Step 3: Based on the minimum distance requirement between sub-resolution auxiliary feature images, select the most valuable sub-resolution auxiliary feature image seed from the sub-resolution auxiliary feature image seed candidate set in Step 2, and construct the sub-resolution auxiliary feature image seed set.

[0010] Step 4: By performing graphic evolution on the sub-resolution auxiliary feature graphic seeds in the sub-resolution auxiliary feature graphic seed set in Step 3, sub-resolution auxiliary feature graphics that can improve the clarity of lithographic patterns are generated.

[0011] Further, in step 1, a continuous transmittance mask based on the target image is generated, specifically including the following steps:

[0012] Step 1.1, calculate the initial continuous transmittance mask M0 using the continuous transmittance mask calculation formula (1).

[0013]

[0014] In the formula, P is a continuous auxiliary variable, randomly initialized to an unrestricted continuous auxiliary variable P0; θ P The steepness is 0.1 to 0.2 times that of the binary value mask transformation function;

[0015] Step 1.2: After photolithography simulation, the loss function L is obtained according to formula (2);

[0016]

[0017] In the formula, L is the loss function, R is the lithographic pattern under standard conditions, and R0 is the lithographic pattern under standard conditions. v For the lithographic pattern under the v-th offset condition, R * For the target image, α represents the weight of lithographic accuracy under the offset condition; N p The number of different photolithography conditions considered;

[0018] Step 1.3: Compare the loss function calculated in Step 1.2 with the pre-set maximum allowable threshold. If it is not less than the threshold, then use the gradient of the loss function calculated in Step 1.2 to backpropagate and update the continuous auxiliary variable P, as shown in Equation (3).

[0019]

[0020] In the formula, Δt is the iteration step size. The gradient of the loss function;

[0021] Then, the continuous transmittance mask M is iteratively updated using formula (1);

[0022] The optimization is considered complete when the loss function is less than the preset maximum allowable threshold, and the final continuous transmittance mask is output.

[0023] Furthermore, in step 2, the safe generation region of the sub-resolution auxiliary feature graphic refers to the sub-resolution auxiliary feature safe distance D extending outward from the boundary of the shape in the target image. OPC and the effective range D of sub-resolution auxiliary features SRAF , in D OPC and D SRAF The area between two boundaries.

[0024] Furthermore, in step 2, the sub-resolution auxiliary feature image candidate seed refers to selecting the part with the highest local transmittance in the safe generation area; the seed is a square of the same size.

[0025] Furthermore, step 3 specifically includes the following steps:

[0026] Step 3.1, construct the optimization and update objective function g k (z (k) u (k) As shown in formula (4):

[0027]

[0028] In the formula, z is the selection vector, u is the auxiliary vector, z and u have the same vector length and are both equal to the number n of candidate seeds in the sub-resolution auxiliary feature image seed candidate set; w is the value of the sub-resolution auxiliary feature image seed, which is equal to the average transmittance of all pixels in the square area; H is the conflict matrix, which is an n×n symmetric matrix; λ is the conflict penalty coefficient; k is the kth cycle.

[0029] Step 3.2: Initialize the auxiliary vector u as a vector with elements randomly selected as 0 or 1, where an element being 1 represents selecting the corresponding sub-resolution auxiliary feature image seed, and an element being 0 represents discarding the corresponding sub-resolution auxiliary feature image seed; initialize the selection vector z with each element being 0, which is the current optimal selection vector z. * ;

[0030] Step 3.3, determine the selection vector z (k) As shown in formula (5):

[0031]

[0032] In the formula, i is the i-th element in the selection vector;

[0033] Step 3.4, update the auxiliary vector u (k) and the optimal choice vector z * ;

[0034] If we choose vector z (k) The corresponding objective function g k (z (k) u (k) The value is greater than the auxiliary vector u. (k) , then u (k) Updated to u (k +1) ←z (k) Conversely, the step size weight θ is calculated. k u is calculated using linear interpolation. (k+1) As shown in formulas (6) and (7):

[0035]

[0036] u (k+1) ←θ k z(k) +(1-θ k )u (k) (7)

[0037] If we choose vector z (k) The corresponding objective function g k (z (k) u (k) () is greater than the current optimal choice vector z * The objective function value, i.e. Then use z (k) Replace z * It becomes the new optimal choice vector;

[0038] Step 3.5: Repeat steps 3.3 to 3.4 until, in two consecutive iterations, u (k) with u (k+1) The objective function value g k (z (k) u (k) ) and g k (z (k) u (k+1) The difference is less than a pre-set threshold; the final optimal selection vector z is used. * The i-th element is set to either 0 or 1 to determine whether to discard or select the i-th sub-resolution auxiliary feature image seed, thereby constructing the sub-resolution auxiliary feature image seed set.

[0039] Furthermore, the side length of the conflict matrix H is equal to the length of the selection vector z and the auxiliary vector u, respectively. If the i-th sub-resolution auxiliary feature image seed and the j-th sub-resolution auxiliary feature image seed are too close to each other on the mask, less than the set minimum distance, and a conflict occurs, then the (i,j) elements and (j,i) elements of this matrix are 1, and the rest are 0.

[0040] Furthermore, step 4 includes the following specific steps:

[0041] Step 4.1: According to the probe growth method, extend the probe from the center of the sub-resolution auxiliary feature image seed outwards to the left, right, up, and down until the continuous transmittance is less than the threshold I. evo The lengths extending to the left, right, up, and down are l respectively. l '、l r '、l u '、l d ';

[0042] Step 4.2: Calculate the fine-tuning coefficient c, which is used to compress the extended graph from step 4.1;

[0043] (8)

[0044] Step 4.3: Calculate the actual length extending from the center of the sub-resolution auxiliary feature image seed to the left, right, up, and down using the fine-tuning coefficient c. Specifically:

[0045] l l =c·l′ l

[0046] l r =c·l′ r

[0047] l u =(1-c)·l′ u

[0048] l d =(1-c)·l′ d (9)

[0049] Generate the final sub-resolution auxiliary feature map

[0050] The beneficial effect of this invention is that it proposes a sub-resolution auxiliary feature pattern generation method that can improve the sharpness of lithographic patterns. In addition to considering the influence of design rule constraints and the range of interaction between transmitted rays, an optimization objective function representing the effect of sub-resolution auxiliary feature generation is introduced. This invention has the following characteristics:

[0051] 1. By using a continuous transmittance mask to guide the selection of the sub-resolution auxiliary feature generation position, the generated sub-resolution auxiliary features can significantly improve the photolithography mask effect.

[0052] 2. A novel sub-resolution auxiliary feature location optimization objective is proposed, which has high algorithm efficiency and good final results;

[0053] 3. A new sub-resolution auxiliary feature shape generation scheme is proposed to improve the effect of sub-resolution auxiliary features;

[0054] 4. The design rules are automatically incorporated into the reference, and the complete sub-resolution auxiliary feature generation is performed without the need for manual post-processing;

[0055] 5. It can support the expansion of other optimization objectives. Attached Figure Description

[0056] Figure 1 This is a schematic diagram of the target mask according to an embodiment of the present invention.

[0057] Figure 2 The diagram shows a comparison of photolithography simulation effects. (a) is a traditional mask, and (b) is the continuous transmittance mask used in the embodiment of the present invention.

[0058] Figure 3The final sub-resolution auxiliary feature image is shown in (a) of the present invention, (b) is the result image using the first prior art, and (c) is the result image using the second prior art. Detailed Implementation

[0059] The technical solution of the present invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0060] Example

[0061] A sub-resolution auxiliary feature pattern generation method that can improve the sharpness of lithographic patterns includes the following steps:

[0062] Step 1: Generate a continuous transmittance mask based on the target image;

[0063] Step 1.1, calculate the initial continuous transmittance mask M0 using the continuous transmittance mask calculation formula (1).

[0064]

[0065] In the formula, P is a continuous auxiliary variable, randomly initialized to an unrestricted continuous auxiliary variable P0; θ P The steepness is 0.1 to 0.2 times that of the binary value mask transformation function;

[0066] Step 1.2: After photolithography simulation, the loss function L is obtained according to formula (2);

[0067]

[0068] In the formula, L is the loss function, R is the lithographic pattern under standard conditions, and R0 is the lithographic pattern under standard conditions. v For the lithographic pattern under the v-th offset condition, R * For the target image, α represents the weight of lithographic accuracy under the offset condition; N p The number of different photolithography conditions considered;

[0069] Step 1.3: Compare the loss function calculated in Step 1.2 with the pre-set maximum allowable threshold. If it is not less than the threshold, then use the gradient of the loss function calculated in Step 1.2 to backpropagate and update the continuous auxiliary variable P, as shown in Equation (3).

[0070]

[0071] In the formula, Δt is the iteration step size. The gradient of the loss function;

[0072] Then, the continuous transmittance mask M is iteratively updated using formula (1);

[0073] The optimization is considered complete when the loss function is less than the preset maximum allowable threshold, and the final continuous transmittance mask is output.

[0074] Step 2: Using the transmittance distribution of the continuous transmittance mask generated in Step 1, guide the distribution of candidate seeds for sub-resolution auxiliary feature graphics to form a safe generation region for sub-resolution auxiliary feature graphics. The safe generation region for sub-resolution auxiliary feature graphics refers to the sub-resolution auxiliary feature safe distance D extending outwards from the boundary of the shape in the target image. OPC and the effective range D of sub-resolution auxiliary features SRAF , in D OPC and D SRAF The region between the two boundaries. The sub-resolution auxiliary feature image candidate seed refers to the part with the highest local transmittance in the safe generation region; the seed is a square of the same size. A sub-resolution auxiliary feature image candidate set is then constructed.

[0075] Step 3: Based on the minimum distance requirement between sub-resolution auxiliary feature images, select the most valuable sub-resolution auxiliary feature image seed from the sub-resolution auxiliary feature image seed candidate set in Step 2, and construct the sub-resolution auxiliary feature image seed set.

[0076] Step 3.1, construct the optimization and update objective function g k (z (k) u (k) As shown in formula (4):

[0077] In the formula, z is the selection vector, u is the auxiliary vector, and the vector lengths of z and u are equal and both equal to the number of candidate seeds n in the candidate set of sub-resolution auxiliary feature image seeds; w is the value of the sub-resolution auxiliary feature image seed, which is equal to the average transmittance of all pixels in the square area; H is the conflict matrix, which is an n×n symmetric matrix; the side length of the conflict matrix H is equal to the length of the selection vector z and the auxiliary vector u, respectively. If the i-th sub-resolution auxiliary feature image seed and the j-th sub-resolution auxiliary feature image seed are too close on the mask, less than the set minimum distance, a conflict occurs, then the (i,j) elements and (j,i) elements of this matrix are 1, and the rest are 0. λ is the conflict penalty coefficient; k is the k-th loop;

[0078] Step 3.2: Initialize the auxiliary vector u as a vector with elements randomly selected as 0 or 1, where an element being 1 represents selecting the corresponding sub-resolution auxiliary feature image seed, and an element being 0 represents discarding the corresponding sub-resolution auxiliary feature image seed; initialize the selection vector z with each element being 0, which is the current optimal selection vector z. * ;

[0079] Step 3.3, determine the selection vector z (k) As shown in formula (5):

[0080]

[0081] In the formula, i is the i-th element in the selection vector;

[0082] Step 3.4, update the auxiliary vector u (k) and the optimal choice vector z * ;

[0083] If we choose vector z (k) The corresponding objective function g k (z (k) u (k) The value is greater than the auxiliary vector u. (k) , then u (k) Updated to u (k +1) ←z (k) Conversely, the step size weight θ is calculated. k u is calculated using linear interpolation. (k+1) As shown in formulas (6) and (7):

[0084]

[0085] u (k+I) ←θ k z (k) +(1-θ k )u (k) (7)

[0086] If we choose vector z (k) The corresponding objective function g k (z (k) u (k) The objective function value is greater than the current optimal choice vector z*, i.e. Then use z (k) Replace z * It becomes the new optimal choice vector;

[0087] Step 3.5: Repeat steps 3.3 to 3.4 until, in two consecutive iterations, u (k) with u (k+1) The objective function value g k (z (k) u (k) ) and g k (z (k) u (k+1)If the difference is less than a pre-set threshold, the i-th sub-resolution auxiliary feature image seed is abandoned or selected by determining whether the i-th element in the final optimal selection vector z* is 0 or 1, thereby constructing a sub-resolution auxiliary feature image seed set.

[0088] Step 4: The sub-resolution auxiliary feature pattern seeds from the sub-resolution auxiliary feature pattern seed set in Step 3 are subjected to pattern evolution to generate sub-resolution auxiliary feature patterns that can improve the clarity of the lithographic pattern. Step 4.1: According to the probe growth method, the probe extends from the center of the sub-resolution auxiliary feature pattern seed outwards and outwards until the continuous transmittance is less than the threshold I. evo The lengths extending to the left, right, up, and down are l respectively. l '、l r '、l u '、l d ';

[0089] Step 4.2: Calculate the fine-tuning coefficient c, which is used to compress the extended graph from step 4.1;

[0090]

[0091] Step 4.3: Calculate the actual length extending from the center of the sub-resolution auxiliary feature image seed to the left, right, up, and down using the fine-tuning coefficient c. Specifically:

[0092] l l =c·l′ l

[0093] l r =c·l′ r

[0094] l u =(1-c)·l′ u

[0095] l d =(1-c)·l′ d (9)

[0096] Generate the final sub-resolution auxiliary feature map.

[0097] The lithography kernel function and image evaluation module used in this embodiment were provided by the ICCAD 2013 CAD competition organizing committee (Banerjee S, Li Z, Nassif S R. ICCAD-2013CAD contest in mask optimization and benchmark suite [C] / / 2013IEEE / ACM International Conference on Computer-Aided Design (ICCAD). IEEE, 2013: 271-274.).

[0098] pass Figure 3 As shown in (a), the sub-resolution pattern obtained by the method optimized by this invention can ensure that the size of the sub-resolution auxiliary feature pattern is limited, and the distances between sub-resolution auxiliary features and between them and the target graphic meet the minimum distance limit. In contrast, Figure 3 (b) The method of using only a continuous transmittance mask without optimizing the selection of sub-resolution auxiliary feature positions and shapes may result in sub-resolution auxiliary features that are too close to the main graphic (within the blue circle), or that are too close to each other (within the yellow circle), or that exceed the design rule limits in shape (within the red circle). Figure 3 (c) is a method for generating sub-resolution auxiliary features based on dictionary learning, which is currently the highest level of machine learning. Compared with the method in this embodiment, this method still results in sub-resolution auxiliary features being too close together (yellow inside), and it can only generate a few pre-set fixed-size sub-resolution auxiliary features, which affects the improvement effect of photolithography.

[0099] Figure 3 (b) Paper: Gao, Pengzheng, Libin Zhang, and Ya Yi Wei. "SRAF generationbased on SGM / CTM contour line." Optical Microlithography XXXIV.Vol.11613.SPIE, 2021.

[0100] Figure 3 (c) Paper: Geng, Hao, et al. "SRAF insertion via supervised dictionary learning." Proceedings of the 24th Asia and South Pacific Design AutomationConference.2019.

Claims

1. A sub-resolution auxiliary feature pattern generation method that can improve the clarity of photolithographic patterns, characterized in that, The steps include the following: Step 1: Generate a continuous transmittance mask based on the target image; Step 2: Use the transmittance distribution of the continuous transmittance mask generated in Step 1 to guide the distribution of candidate seeds for sub-resolution auxiliary feature graphics, form a safe generation region for sub-resolution auxiliary feature graphics, and construct a candidate set of sub-resolution auxiliary feature graphics seeds. Step 3: Based on the minimum distance requirement between sub-resolution auxiliary feature images, select the most valuable sub-resolution auxiliary feature image seed from the sub-resolution auxiliary feature image seed candidate set in Step 2, and construct the sub-resolution auxiliary feature image seed set. Step 4: By performing graphic evolution on the sub-resolution auxiliary feature graphic seeds in the sub-resolution auxiliary feature graphic seed set in Step 3, sub-resolution auxiliary feature graphics that can improve the clarity of lithographic patterns are generated.

2. The sub-resolution auxiliary feature pattern generation method for improving the clarity of photolithographic patterns according to claim 1, characterized in that, Step 1: Generate a continuous transmittance mask based on the target image. Specific steps include: Step 1.1, calculate the initial continuous transmittance mask M0 using the continuous transmittance mask calculation formula (1). In the formula, P is a continuous auxiliary variable, randomly initialized to an unrestricted continuous auxiliary variable P0; θ P The steepness is 0.1 to 0.2 times that of the binary value mask transformation function; Step 1.2: After photolithography simulation, the loss function L is obtained according to formula (2); In the formula, L is the loss function, R is the lithographic pattern under standard conditions, and R0 is the lithographic pattern under standard conditions. v For the lithographic pattern under the v-th offset condition, R * For the target image, α represents the weight of lithographic accuracy under the offset condition; N p The number of different photolithography conditions considered; Step 1.3: Compare the loss function calculated in Step 1.2 with the pre-set maximum allowable threshold. If it is not less than the threshold, then use the gradient of the loss function calculated in Step 1.2 to backpropagate and update the continuous auxiliary variable P, as shown in Equation (3). In the formula, Δt is the iteration step size. The gradient of the loss function; Then, the continuous transmittance mask M is iteratively updated using formula (1); The optimization is considered complete when the loss function is less than the preset maximum allowable threshold, and the final continuous transmittance mask is output.

3. The sub-resolution auxiliary feature pattern generation method for improving the clarity of photolithographic patterns according to claim 1, characterized in that, In step 2, the safe generation region of the sub-resolution auxiliary feature graphic refers to the sub-resolution auxiliary feature safe distance D extending outward from the boundary of the shape in the target image. OPC and the effective range D of sub-resolution auxiliary features SRAF , in D OPC and D SRAF The area between two boundaries.

4. The sub-resolution auxiliary feature pattern generation method for improving the clarity of photolithographic patterns according to claim 1, characterized in that, In step 2, the sub-resolution auxiliary feature image candidate seed refers to the part with the highest local transmittance in the safe generation area; the seed is a square of the same size.

5. The sub-resolution auxiliary feature pattern generation method for improving the clarity of photolithographic patterns according to claim 1, characterized in that, Step 3 is specifically implemented as follows: Step 3.1, construct the optimization and update objective function gk(z) (k) u (k) As shown in formula (4): In the formula, z is the selection vector, u is the auxiliary vector, z and u have the same vector length and are both equal to the number n of candidate seeds in the sub-resolution auxiliary feature image seed candidate set; w is the value of the sub-resolution auxiliary feature image seed, which is equal to the average transmittance of all pixels in the square area; H is the conflict matrix, which is an n×n symmetric matrix; λ is the conflict penalty coefficient; k is the kth cycle. Step 3.2: Initialize the auxiliary vector u as a vector with elements randomly selected as 0 or 1, where an element with a value of 1 represents selecting the corresponding sub-resolution auxiliary feature image seed, and an element with a value of 0 represents discarding the corresponding sub-resolution auxiliary feature image seed. The initialization of the selection vector z is such that each element is 0, which is the current optimal selection vector z. * ; Step 3.3, determine the selection vector z (k) As shown in formula (5): In the formula, i is the i-th element in the selection vector; Step 3.4, update the auxiliary vector u (k) and the optimal choice vector z * ; If we choose vector z (k) The corresponding objective function g k (z (k) u (k) The value is greater than the auxiliary vector u. (k) , then u (k) Updated to u (k+1) ←z (k) Conversely, the step size weight θ is calculated. k u is calculated using linear interpolation. (k+1) As shown in formulas (6) and (7): u (k+1) ←θ k z (k) +(1-θ k )u (k) (7) If we choose vector z (k) The corresponding objective function g k (z (k) u (k) () is greater than the current optimal choice vector z * The objective function value, i.e. Then use z (k) Replace z * It becomes the new optimal choice vector; Step 3.5: Repeat steps 3.3 to 3.4 until, in two consecutive iterations, u (k) with u (k+1) The objective function value g k (z (k) u (k) ) and g k (z (k) u (k+1) The difference is less than a pre-set threshold; the final optimal selection vector z is used. * The i-th element is set to either 0 or 1 to determine whether to discard or select the i-th sub-resolution auxiliary feature image seed, thereby constructing the sub-resolution auxiliary feature image seed set.

6. The sub-resolution auxiliary feature pattern generation method for improving the clarity of photolithographic patterns according to claim 5, characterized in that, The side length of the conflict matrix H is equal to the length of the selection vector z and the auxiliary vector u, respectively. If the i-th sub-resolution auxiliary feature image seed and the j-th sub-resolution auxiliary feature image seed are too close to each other on the mask, less than the set minimum distance, and a conflict occurs, then the (i,j) elements and (j,i) elements of this matrix are 1, and the rest are 0.

7. The sub-resolution auxiliary feature pattern generation method for improving the clarity of photolithographic patterns according to claim 1, characterized in that, Step 4 includes the following specific steps: Step 4.1: According to the probe growth method, extend the probe from the center of the sub-resolution auxiliary feature image seed outwards to the left, right, up, and down until the continuous transmittance is less than the threshold I. evo The lengths extending to the left, right, up, and down are l respectively. l '、l r '、l u '、l d '; Step 4.2: Calculate the fine-tuning coefficient c, which is used to compress the extended graph from step 4.1; Step 4.3: Calculate the actual length extending from the center of the sub-resolution auxiliary feature image seed to the left, right, up, and down using the fine-tuning coefficient c. Specifically: l l ＝c·l′ l l r ＝c·l′ r l u ＝(1-c)·l′ u l d ＝(1-c)·l′ d (9) Generate the final sub-resolution auxiliary feature map.

Images