Curved reverse lithography method based on sub-resolution auxiliary pattern seed insertion

Abstract

A curve-type reverse lithography method based on sub-resolution auxiliary pattern seed insertion. The method uses pixels to characterize the mask pattern, and each pixel in the mask pattern represents the transmittance of the position. In the background area of ​​the target pattern, sub-resolution auxiliary pattern seeds are inserted around the main pattern at equal intervals, and the width of the sub-resolution auxiliary pattern seeds and the minimum offset relative to the main pattern are set according to the characteristic size of the target pattern. The target pattern with the sub-resolution auxiliary pattern seeds inserted in the background area is used as the initial mask pattern, and the weighted sum of the pattern errors between the photoresist pattern and the target pattern under different exposure dose deviations and defocus conditions is used as the evaluation function, and the mask is optimized with the help of an optimization algorithm. Directly inserting sub-resolution auxiliary pattern seeds according to the target pattern is simple to operate, is not constrained by lithography process conditions and lithography imaging models, and improves the convergence efficiency of reverse lithography and the performance of mask optimization.

Description

Technical Field

[0001] The invention belongs to the field of integrated circuit manufacturing, and in particular relates to a curved reverse photolithography method based on sub-resolution auxiliary pattern seed insertion. Background Art

[0002] Photolithography is one of the key technologies in the manufacture of very large-scale integrated circuits. The resolution of photolithography determines the critical dimension (CD) of integrated circuit graphics. As the feature size of integrated circuit graphics continues to shrink, the mask diffraction effect gradually becomes non-negligible, resulting in a decline in the quality of photolithography imaging. Therefore, the industry has proposed a series of photolithography resolution enhancement techniques (RETs). Inverse lithography (ILT) was first used in the manufacture of integrated circuits at the 65nm node. After continuous development, it has become one of the resolution enhancement technologies that has attracted much attention in the manufacture of advanced node integrated circuits. Inverse lithography uses the lithography imaging model to reversely calculate the mask graphics with the best imaging quality under given process conditions. The optimal solution search space for inverse lithography is very large, and the mask optimization process is not constrained by the target graphics. Since it can flexibly generate sub-resolution auxiliary graphics (Sub-Resolution Assist Feature, SRAF) and optimize both the main graphics and the auxiliary graphics at the same time, the optimal mask graphics calculated by reverse lithography technology can obtain graphic fidelity and process window that cannot be achieved by optical proximity correction (Optical Proximity Correction, OPC) and sub-resolution auxiliary graphics.

[0003] Early reverse lithography technology had problems such as low optimization efficiency and poor manufacturability of optimized masks. In order to avoid the loss of imaging performance caused by improving mask manufacturability with the help of regularization methods, the industry has successively proposed technologies such as Curvilinear Mask Process Correction (CLMPC), Curvilinear Mask Rule Check (CLMRC), and Model-Based Mask Data Preparation (MBMDP) to generate curved mask patterns with the help of reverse lithography. Due to the limiting factors such as electron beam shape, photoresist sensitivity, and lithography machine resolution, the real mask pattern and the pattern transferred to the silicon wafer are both curved. Compared with the Manhattan mask pattern generated by optical proximity effect correction, the imaging quality of the curved mask pattern is better. However, in order to accurately manufacture the curved mask pattern, more electron beam bombardment times are required, which increases the mask direct writing time and mask manufacturing cost. Multi-beam mask writer (MBMW) can produce mask patterns of any shape by bombarding a large number of independently controlled electron beams in a single attack, so that the mask writing time depends only on the mask area and is no longer affected by the shape of the mask pattern. The industry believes that the introduction of multi-beam mask writing has greatly improved the efficiency of curved mask writing and removed the biggest obstacle to mass production of masks. In recent years, the introduction of graphics processing units (GPUs) has promoted the development of full-chip reverse lithography technology, providing an alternative to the traditional full-chip reverse lithography technology of first optimizing blocks and then integrating the optimization results, avoiding multiple optimization rule adjustments and global verifications, and improving the efficiency of full-chip reverse lithography. Therefore, it is particularly important to use efficient optimization strategies for reverse lithography.

[0004] By using the inverse lithography technology, a sub-resolution auxiliary pattern is inserted into the sparse background area of ​​the mask pattern, which effectively increases the lithography process window. However, the existing inverse lithography method (prior art 1, W. Lv, Q. Xia, and S. Liu, "Mask-filtering-based inverse lithography," J. Micro / Nanolith. MEMS MOEMS, 12 (4), 043003 (2013)) uses the target pattern as the initialization mask pattern, and it takes a lot of time to determine the insertion position, shape and size of the sub-resolution auxiliary pattern during the mask optimization process, which reduces the convergence efficiency of the inverse lithography and the mask optimization performance. Existing sub-resolution auxiliary graphics insertion methods (prior art 2, S. Jayaram, P. LaCour, J. Word, and A. Tritchkov, "Effective model-based SRAF placement for full chip 2D layouts," Proc. SPIE 8683, 86830H (2013)) include rule-based sub-resolution auxiliary graphics insertion methods and model-based sub-resolution auxiliary graphics insertion methods. The rule-based sub-resolution auxiliary graphics insertion method has high operating efficiency, but the insertion rules are difficult to cover all graphic structures and lithography process conditions, and are less applicable to complex graphic layouts in advanced node integrated circuits. The model-based sub-resolution auxiliary graphics insertion method defines an objective function that seeks to maximize the process window, and uses the position where the objective function obtains the maximum gradient as the insertion position of the sub-resolution auxiliary graphics. Multiple sub-resolution auxiliary graphics candidate solutions are generated based on the gradient signal, and the sub-resolution auxiliary graphics corresponding to the maximum objective function value are selected as the insertion solution, which is subsequently jointly optimized with the main graphics. The model-based sub-resolution auxiliary graphics insertion method is relatively complex to operate and has poor applicability to scenarios where complex lithography imaging models are used, resulting in high gradient calculation complexity.

[0005] In summary, using the target graphic without sub-resolution auxiliary graphics as the initial mask graphic reduces the convergence efficiency and mask optimization performance of the inverse lithography method, while the rule-based sub-resolution auxiliary graphics insertion method is difficult to cover all graphic structures and lithography process conditions, and the model-based sub-resolution auxiliary graphics insertion method is complex to operate and has poor applicability to scenarios using complex lithography imaging models. Summary of the invention

[0006] The present invention provides a curve-type reverse lithography method based on the insertion of sub-resolution auxiliary pattern seeds, which uses pixels to characterize mask patterns, and each pixel in the mask pattern represents the transmittance of the position. In the background area of ​​the target pattern, sub-resolution auxiliary pattern seeds are inserted around the main pattern at equal intervals, and the width of the sub-resolution auxiliary pattern seeds and the minimum offset relative to the main pattern are set according to the characteristic size of the target pattern. The target pattern with the sub-resolution auxiliary pattern seeds inserted in the background area is used as the initial mask pattern, and the weighted sum of the pattern errors between the photoresist pattern and the target pattern under different exposure dose deviations and defocus conditions is used as an evaluation function, and mask optimization is achieved with the help of an optimization algorithm. Directly inserting sub-resolution auxiliary pattern seeds according to the target pattern is simple to operate, is not constrained by lithography process conditions and lithography imaging models, and improves the convergence efficiency of reverse lithography and the mask optimization performance.

[0007] The technical solution of the present invention is as follows:

[0008] The curved reverse lithography method based on sub-resolution auxiliary pattern insertion has the following specific steps:

[0009] 1. Initialize light source graphics J 0 , pupil function H 0 , photoresist sensitivity α, photoresist threshold t r , mask threshold t m , Development threshold t dev , the value of exposure dose deviation and the corresponding weight, the value of defocus amount and the corresponding weight.

[0010] Initialize T values ​​of exposure dose deviation t, with corresponding weight p t , initialize H values ​​of the defocus amount h, and the corresponding weight is p h Initialize the light source graph J according to the value of the defocus h 0 and pupil function H 0 , pre-calculate the TCC kernel corresponding to the defocus amount h in the Hopkins imaging model, TCC (Transmission Cross Coefficient) represents the transmission cross coefficient, and retain the first K TCC kernels.

[0011] 2. Set the target pattern TP, insert sub-resolution auxiliary pattern seeds around the main pattern at equal intervals in the background area of ​​the target pattern TP, and obtain the initial mask pattern M 0 .

[0012] Set the size of the target graphic TP to N V ×N H , where N V and N HRespectively represent the number of elements contained in each row and column of the target graph TP, both are odd numbers. Set the transmittance of the light-transmitting pixels on the target graph TP to 1, the transmittance of the light-shielding pixels to 0, and the pixel side length of the target graph TP to a.

[0013] The width L of the sub-resolution auxiliary graphics seed SRAF =c 1 ×CD, where CD is the characteristic size of the target graphic, And 0.2≤c 1 ≤1, c 1 Coefficient used to adjust the width L of the sub-resolution auxiliary graphic seed SRAF .

[0014] The minimum offset D of the sub-resolution auxiliary graphic seed relative to the main graphic SRAF =c 2 ×CD, And 1≤c 2 ≤2, c 2 is a coefficient used to adjust the minimum offset D of the sub-resolution auxiliary graphic seed relative to the main graphic SRAF .

[0015] Set the transmittance of the sub-resolution auxiliary graphics seed to And 0<t SRAF <1.

[0016] In the background area of ​​the target graphic, insert sub-resolution auxiliary graphic seeds around the main graphic at equal intervals. The specific steps are as follows:

[0017] 2.1 Constructing the convolution kernel K 1 and convolution kernel K 2 :

[0018] Convolution kernel K 1 =ones(N 1 ,N 1 ) indicates the size is N 1 ×N 1 , a matrix whose elements are all 1, where symbol Indicates rounding up;

[0019] Convolution kernel K 2 =ones(N 2 ,N 2 ) indicates the size is N 2 ×N 2 , a matrix whose elements are all 1, where

[0020] A temporary variable tmp=TP is set to record the mask pattern of the sub-resolution auxiliary pattern seed insertion process.

[0021] 2.2 Calculate temporary variables tmp and convolution kernel K 1 Convolution, as well as temporary variables tmp and convolution kernel K 2 The convolution formula is as follows:

[0022] symbol Represents a convolution operation.

[0023] 2.3 Two logic matrices index1 and index2 are calculated based on the two convolution results, thereby determining the insertion position of the sub-resolution auxiliary graphic seed.

[0024] index1=convR1==0,index2=convR2>0,the symbol “==” indicates the logical judgment of the equal relationship. The element with the value of 1 in the logic matrix index1 indicates that the distance between the background area of ​​the current mask pattern and the light-transmitting area is greater than D SRAF The position index of the logic matrix index2, the element with a value of 1 indicates that the distance between the background area of ​​the current mask pattern and the light-transmitting area is less than or equal to D SRAF +L SRAF The position index of .

[0025] The logic matrix index=index1&index2 represents the intersection of two logic matrices, wherein the elements with a value of 1 correspond to the insertion position of the sub-resolution auxiliary graphic seed.

[0026] If there is a non-zero element in the logical matrix index, the temporary variable tmp is updated and the sub-resolution auxiliary graphic seed is inserted at the corresponding position, that is, tmp(index) = t SRAF , return to step 2.2 and continue to insert the sub-resolution auxiliary pattern seeds; otherwise, if the values ​​of the elements in the logic matrix index are all 0, the insertion of the sub-resolution auxiliary pattern seeds is completed, and the initial mask pattern M is obtained. 0 =tmp, go to step 3.

[0027] 3. Constructing the evaluation function for the inverse lithography problem

[0028] 3.1 With the help of mask filtering and binarization processing, a binary mask pattern M is obtained according to the mask pattern M B .

[0029] In order to improve the manufacturability of the mask pattern, the present invention uses a mask filtering method to process the mask pattern M to obtain a blurred mask pattern M. blur ,

[0030]

[0031] Among them, r 0 Indicates the center position, ||rr 0 || represents point r to point r 0 The distance, σ GF is the standard deviation of the Gaussian function, and Ω represents the number of elements contained in the Gaussian convolution kernel.

[0032] Using the mask threshold t m For the blurred mask pattern M blur Perform binarization to obtain the final binary mask pattern M B , that is, M B =Γ(M blur -t m ). Γ(x)={1|x≥0∪0|x<0}, the function Γ(x) converts M blur Medium transmittance is greater than or equal to the mask threshold t m The pixel value of M is 1. blur Medium transmittance is less than the mask threshold t m The pixel value is 0.

[0033] 3.2 According to the Hopkins imaging model, calculate the spatial image AI when the defocus amount is h,

[0034]

[0035] in, is the binary mask pattern M B The mask diffraction spectrum is calculated by Fourier transform, (x, y) is the spatial coordinate of the mask pattern, and (f′, g′) is the normalized spatial frequency coordinate of the mask diffraction spectrum. Φ i (f′, g′; h) represents the i-th frequency domain TCC kernel when the defocus amount is h, S i is the coefficient corresponding to the i-th TCC core, which is shared by K TCC cores. IFFT{} represents inverse Fourier transform.

[0036] 3.3 According to the spatial image AI and sigmoid photoresist model, the photoresist image RI is calculated when the defocus amount is h and the exposure dose deviation is t.

[0037]

[0038] Where α is the photoresist sensitivity, t r is the photoresist threshold. In addition to the sigmoid photoresist model used here, a constant threshold photoresist model, a variable threshold photoresist model or a three-dimensional photoresist model can also be selected according to actual needs.

[0039] 3.4 In the positive development process, if the photoresist image RI is greater than or equal to the development threshold tdev , the photoresist at that position is removed; otherwise, if the photoresist image RI is less than the developing threshold t dev , the photoresist at this position is retained. Thus, the developed photoresist pattern RC is obtained, that is, RC(x,y;h,t)=Γ(RI(x,y;h,t)-t dev ).

[0040] 3.5 The evaluation function f is constructed by using the weighted sum of the graphic errors between the photoresist pattern and the target pattern under different exposure dose deviations t and defocus amounts h.

[0041]

[0042] 4. According to the initial mask pattern M 0 , with the goal of minimizing the evaluation function value, the mask pattern M is optimized using the optimization algorithm. During the optimization process, the elements of the mask pattern M satisfy And 0≤M(p,q)≤1, where p and q are the element indices of the mask pattern M, And 1≤p≤N V , And 1≤q≤N H . The optimized mask pattern M * Substitute into step 3.1 to obtain the binary mask pattern with the best imaging quality

[0043] Compared with the prior art, the present invention has the following advantages:

[0044] The present invention uses the target pattern of inserting sub-resolution auxiliary pattern seeds in the background area as the initial mask pattern, thereby improving the convergence efficiency and mask optimization capability of reverse lithography. In addition, directly inserting sub-resolution auxiliary pattern seeds according to the target pattern is simple to operate and is not constrained by lithography process conditions and lithography imaging models. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 This is a schematic diagram of the target mask pattern used in the present invention.

[0046] Figure 2 The schematic diagram of the initial mask pattern after inserting the sub-resolution auxiliary pattern seed by the method of the present invention is shown in FIG.

[0047] Figure 3 The present invention adopts Figure 1 Schematic diagram of photoresist patterns produced under different process conditions when used as initial mask patterns

[0048] Figure 4 The present invention adopts Figure 1 Schematic diagram of the binary mask pattern obtained after optimization when used as the initial mask pattern

[0049] Figure 5 The present invention adopts Figure 4 Schematic diagram of photoresist patterns produced by binary mask patterns under different process conditions

[0050] Figure 6 The present invention adopts Figure 2 Schematic diagram of photoresist patterns produced under different process conditions when used as initial mask patterns

[0051] Figure 7 The present invention adopts Figure 2 Schematic diagram of the binary mask pattern obtained after optimization when used as the initial mask pattern

[0052] Figure 8 The present invention adopts Figure 7 Schematic diagram of photoresist patterns produced by binary mask patterns under different process conditions

[0053] Fig. 9 The present invention adopts Figure 1 and Figure 2 Schematic diagram of the comparison of convergence curves of reverse lithography using two initial mask patterns

[0054] Fig.10 Flow chart of reverse lithography using the method of the present invention DETAILED DESCRIPTION

[0055] The present invention will be further described below in conjunction with embodiments and drawings, but the protection scope of the present invention should not be limited by these embodiments.

[0056] 1. Initialize light source graphics J 0 , pupil function H 0 , photoresist sensitivity α, photoresist threshold t r , mask threshold t m , Development threshold t dev , the value of exposure dose deviation and the corresponding weight, the value of defocus amount and the corresponding weight.

[0057] In this embodiment, the illumination wavelength of the lithography machine is 193.368 nm, and the partial coherence factor σ is used. in =0.7,σ out = 0.9 annular light source, light source polarization type is tPol, projection lens numerical aperture NA = 1.35, zoom factor R = 4, immersion liquid refractive index is 1.44. T = 3, the three values ​​of exposure dose deviation t are {-10%, 0, 10%}, and the corresponding weights are {1, 1, 1}, H = 2, the defocus h values ​​are {0nm, 60nm}, and the corresponding weights are {1, 1.2}. Photoresist sensitivity α = 150, photoresist threshold t r=0.2, mask threshold t m =0.48, development threshold t dev = 0.5. According to the value of the defocus amount h, initialize the light source graph J 0 and pupil function H 0 , pre-calculate the TCC cores corresponding to the defocus amount h in the Hopkins imaging model, and retain the first 10 TCC cores, that is, the number of TCC cores is K=10.

[0058] 2. Set the target pattern TP, insert sub-resolution auxiliary pattern seeds around the main pattern at equal intervals in the background area of ​​the target pattern TP, and obtain the initial mask pattern M 0 .

[0059] Figure 1 The target graph TP is set to have a size of 405×405, that is, the number of elements contained in each row and column of the target graph TP is N. V =405,N H = 405. Set the transmittance of the light-transmitting pixels on the target pattern TP to 1, the transmittance of the light-shielding pixels to 0, and the pixel side length a of the target pattern TP to 3 nm.

[0060] The width L of the sub-resolution auxiliary graphics seed SRAF =c 1 ×CD, where CD is the characteristic size of the target graphic, And 0.2≤c 1 ≤1, c 1 Coefficient used to adjust the width L of the sub-resolution auxiliary graphic seed SRAF .

[0061] The minimum offset D of the sub-resolution auxiliary graphic seed relative to the main graphic SRAF =c 2 ×CD, And 1≤c 2 ≤2, c 2 is a coefficient used to adjust the minimum offset D of the sub-resolution auxiliary graphic seed relative to the main graphic SRAF .

[0062] Set the transmittance of the sub-resolution auxiliary graphics seed to t SRAF , And 0<t SRAF <1.

[0063] In this embodiment, CD = 45 nm, and c 2 =1, that is, the width of the sub-resolution auxiliary graphic seed L SRAF =30nm, the minimum offset D relative to the main pattern SRAF=45nm, the transmittance of the sub-resolution auxiliary pattern seed is t SRAF =0.5.

[0064] In the background area of ​​the target graphic, insert sub-resolution auxiliary graphic seeds around the main graphic at equal intervals. The specific steps are as follows:

[0065] 2.1 Constructing the convolution kernel K 1 and convolution kernel K 2 :

[0066] Convolution kernel K 1 =ones(N 1 ,N 1 ) indicates the size is N 1 ×N 1 , a matrix whose elements are all 1, where symbol Indicates rounding up;

[0067] Convolution kernel K 2 =ones(N 2 ,N 2 ) indicates the size is N 2 ×N 2 , a matrix whose elements are all 1, where

[0068] A temporary variable tmp=TP is set to record the mask pattern of the sub-resolution auxiliary pattern seed insertion process.

[0069] 2.2 Calculate temporary variables tmp and convolution kernel K 1 Convolution, as well as temporary variables tmp and convolution kernel K 2 The convolution formula is as follows:

[0070] symbol Represents a convolution operation.

[0071] 2.3 Two logic matrices index1 and index2 are calculated based on the two convolution results, thereby determining the insertion position of the sub-resolution auxiliary graphic seed.

[0072] index1=convR1==0,index2=convR2>0,the symbol “==” indicates the logical judgment of the equal relationship. The element with the value of 1 in the logic matrix index1 indicates that the distance between the background area of ​​the current mask pattern and the light-transmitting area is greater than D SRAF The position index of the logic matrix index2, the element with a value of 1 indicates that the distance between the background area of ​​the current mask pattern and the light-transmitting area is less than or equal to D SRAF +L SRAF The position index of .

[0073] The logic matrix index=index1&index2 represents the intersection of two logic matrices, wherein the elements with a value of 1 correspond to the insertion position of the sub-resolution auxiliary graphic seed.

[0074] If there is a non-zero element in the logical matrix index, the temporary variable tmp is updated and the sub-resolution auxiliary graphic seed is inserted at the corresponding position, that is, tmp(index) = t SRAF Return to step 2.2 and continue to insert the sub-resolution auxiliary pattern seeds. On the contrary, if the values ​​of the elements in the logic matrix index are all 0, the insertion of the sub-resolution auxiliary pattern seeds is completed, and the initial mask pattern M is obtained. 0 =tmp, go to step 3.

[0075] Figure 2 It is a schematic diagram of an initial mask pattern after inserting a sub-resolution auxiliary pattern seed using the method of the present invention.

[0076] 3. Constructing the evaluation function for the inverse lithography problem

[0077] 3.1 With the help of mask filtering and binarization processing, a binary mask pattern M is obtained according to the mask pattern M B .

[0078] In order to improve the manufacturability of the mask pattern, the present invention uses a mask filtering method to process the mask pattern M to obtain a blurred mask pattern M. blur ,

[0079]

[0080] Among them, r 0 Indicates the center position, ||rr 0 || represents point r to point r 0 The distance, σ GF is the standard deviation of the Gaussian function, Ω represents the number of elements contained in the Gaussian convolution kernel. In this embodiment, the Gaussian convolution kernel is a 21×21 matrix, σ GF =18nm.

[0081] Using the mask threshold t m For the blurred mask pattern M blur Perform binarization to obtain the final binary mask pattern M B , that is, M B =Γ(M blur -t m ). Γ(x)={1|x≥0∪0|x<0}, the function Γ(x) converts M blur Medium transmittance is greater than or equal to the mask threshold t m The pixel value of M is 1.blur Medium transmittance is less than the mask threshold t m The pixel value is 0.

[0082] 3.2 According to the Hopkins imaging model, calculate the spatial image AI when the defocus amount is h,

[0083]

[0084] in, is the binary mask pattern M B The mask diffraction spectrum is calculated by Fourier transform, (x, y) is the spatial coordinate of the mask pattern, and (f′, g′) is the normalized spatial frequency coordinate of the mask diffraction spectrum. Φ i (f′, g′; h) represents the i-th frequency domain TCC kernel when the defocus amount is h, S i is the coefficient corresponding to the i-th TCC core, which is shared by K TCC cores. IFFT{} represents inverse Fourier transform.

[0085] 3.3 According to the spatial image AI and sigmoid photoresist model, the photoresist image RI is calculated when the defocus amount is h and the exposure dose deviation is t.

[0086]

[0087] Where α is the photoresist sensitivity, t r is the photoresist threshold. In addition to the sigmoid photoresist model used here, a constant threshold photoresist model, a variable threshold photoresist model or a three-dimensional photoresist model can also be selected according to actual needs.

[0088] 3.4 In the positive development process, if the photoresist image RI is greater than or equal to the development threshold t dev , the photoresist at that position is removed; otherwise, if the photoresist image RI is less than the developing threshold t dev , the photoresist at this position is retained. Thus, the developed photoresist pattern RC is obtained, that is, RC(x,y;h,t)=Γ(RI(x,y;h,t)-t dev ).

[0089] 3.5 The evaluation function f is constructed by using the weighted sum of the graphic errors between the photoresist pattern and the target pattern under different exposure dose deviations t and defocus amounts h.

[0090]

[0091] According to the above calculation process, the developed photoresist pattern RC can be calculated according to the mask pattern M, thereby obtaining the corresponding evaluation function value.

[0092] 4. According to the initial mask pattern M0 , with the goal of minimizing the evaluation function value, the mask pattern M is optimized using the optimization algorithm. During the optimization process, the elements of the mask pattern M satisfy And 0≤M(p,q)≤1, where p and q are the element indices of the mask pattern M, And 1≤p≤N V , And 1≤q≤N H . The optimized mask pattern M * Substitute into step 3.1 to obtain the binary mask pattern with the best imaging quality In this embodiment, the fast covariance matrix adaptive evolution strategy is selected as the optimization algorithm, and the relevant algorithm parameters are set as follows: the initial search step size is 0.33, the algebraic interval of the low-rank matrix update is 50, the iteration termination condition parameters include the evaluation function threshold of 200, the maximum number of evaluation function calls is 15000, and the change amplitude of the evaluation function value for 50 consecutive iterations cannot be less than 10.

[0093] Figure 3 The present invention adopts Figure 1 Schematic diagram of photoresist patterns generated under different process conditions when used as initial mask patterns. When the mask is not optimized, the photoresist patterns under different process conditions are significantly different from the target patterns, and the pattern fidelity is very poor. Figure 4 The present invention adopts Figure 1 The schematic diagram of the binary mask pattern obtained after optimization as the initial mask pattern generates auxiliary patterns in the sparse pattern area. The contours of the optimized main pattern and auxiliary patterns are relatively smooth, and there is no excessively small pattern width and pattern interval. Figure 5 The present invention adopts Figure 4 Schematic diagram of the photoresist pattern produced by the binary mask pattern under different process conditions. Figure 6 The present invention adopts Figure 2 Schematic diagram of photoresist patterns produced under different process conditions as initial mask patterns. Figure 3 and Figure 6 It can be found that whether or not to insert a sub-resolution auxiliary pattern seed at the initial moment has little effect on the generated binary mask pattern, so the photoresist patterns generated under different process conditions using two initial mask patterns are basically the same. Figure 7 The present invention adopts Figure 2 Schematic diagram of the binary mask pattern obtained after optimization when used as the initial mask pattern. Figure 2 and Figure 7It can be found that some auxiliary graphics contained in the optimized binary mask graphic are similar to the sub-resolution auxiliary graphic seeds inserted at the initial moment, indicating that the sub-resolution auxiliary graphic seeds inserted in the background sparse area of ​​the target graphic at the initial moment contain some potential sub-resolution auxiliary graphic insertion positions, which is equivalent to artificially improving the search space for the optimal solution in the optimization problem. Figure 8 The present invention adopts Figure 7 Schematic diagram of the photoresist pattern produced by the binary mask pattern under different process conditions. Figure 5 and Figure 8 It can be seen that the reverse lithography method using two initial mask patterns has good process robustness. Fig. 9 The present invention adopts Figure 1 and Figure 2 Schematic diagram of the convergence curve comparison of two initial mask patterns for reverse lithography. Figure 1 When used as the initial mask pattern, the iteration is terminated after 15,000 evaluation function calls, and the final evaluation function value is 5129.79. The whole process takes 585.51 seconds. Figure 2 When used as the initial mask pattern, convergence is reached after 12,600 evaluation function calls, the iteration is terminated, and the final evaluation function value is 4691.81. The whole process takes 500.44 seconds. Obviously, inserting the target pattern of the sub-resolution auxiliary pattern seed in the background area as the initial mask pattern improves the convergence efficiency and mask optimization performance of reverse lithography. Fig.10 The present invention is a flowchart of reverse lithography.

[0094] In addition, the method of the present invention can be extended to computational lithography technologies such as source mask optimization (SMO) and source mask projector optimization (SMPO), and the quality of lithography imaging can be further improved by increasing the degree of freedom of optimization.

[0095] The present embodiment and the accompanying drawings are only used to describe the specific implementation method of the present invention, and are not intended to limit the present invention. The present invention may also have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding deformations, substitutions and improvements according to the present invention, but these corresponding deformations, substitutions and improvements shall all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A curved reverse lithography method based on sub-resolution auxiliary pattern insertion, characterized in that: The method comprises the following steps: Step 1. Initialize the light source pattern J0, pupil function H0, photoresist sensitivity α, and photoresist threshold t r , mask threshold t m , Development threshold t dev ; Initialize T values ​​of exposure dose deviation t, with corresponding weight p t , initialize H values ​​of the defocus amount h, and the corresponding weight is p h ; According to the value of the initial defocus h, the light source graph J0 and the pupil function H0 are initialized, and the TCC kernel corresponding to the defocus h in the Hopkins imaging model is pre-calculated. TCC (Transmission Cross Coefficient) represents the transmission cross coefficient, and the first K TCC kernels are retained; Step 2. Insert sub-resolution auxiliary pattern seeds around the main pattern at equal intervals in the background area of ​​the target pattern TP to obtain the initial mask pattern M0: Set the size of the target graphic TP to N V ×N H , where N V and N H Respectively represent the number of elements contained in each row and each column of the target graph TP, both of which are odd numbers; set the transmittance of the light-transmitting pixels on the target graph TP to 1, the transmittance of the light-shielding pixels to 0, and the pixel side length of the target graph TP to a; The width L of the sub-resolution auxiliary graphics seed SRAF =c1×CD, where CD is the characteristic size of the target pattern, And 0.2≤c1≤1, c1 is a coefficient used to adjust the width L of the sub-resolution auxiliary graphic seed SRAF ; The minimum offset D of the sub-resolution auxiliary graphic seed relative to the main graphic SRAF =c2×CD, And 1≤c2≤2, c2 is a coefficient used to adjust the minimum offset D of the sub-resolution auxiliary graphic seed relative to the main graphic SRAF ; Set the transmittance t of the sub-resolution auxiliary graphics seed SRAF , And 0<t SRAF <1; In the background area of ​​the target graphic, insert sub-resolution auxiliary graphic seeds around the main graphic at equal intervals. The specific steps are as follows: 2.1 Construct convolution kernel K1 and convolution kernel K2: The convolution kernel K1=ones(N1,N1) represents a matrix of size N1×N1 with all elements set to 1, where symbol Indicates rounding up; The convolution kernel K2=ones(N2,N2) represents a matrix of size N2×N2 with all elements set to 1, where Set a temporary variable tmp=TP to record the mask pattern of the sub-resolution auxiliary pattern seed insertion process; 2.2 Calculate the convolution of the temporary variable tmp and the convolution kernel K1, and the convolution of the temporary variable tmp and the convolution kernel K2. The formula is as follows: symbol Represents the convolution operation; 2.3 Two logical matrices index1 and index2 are calculated based on the two convolution results, thereby determining the insertion position of the sub-resolution auxiliary graphic seed: index1=convR1==0,index2=convR2>0,the symbol "==" indicates the logical judgment of the equal relationship. The element with the value of 1 in the logic matrix index1 indicates that the distance between the background area of ​​the current mask pattern and the light-transmitting area is greater than D SRAF The position index of the logic matrix index2, the element with a value of 1 indicates that the distance between the background area of ​​the current mask pattern and the light-transmitting area is less than or equal to D SRAF +L SRAF The position index of The logic matrix index=index1&index2 represents the intersection of two logic matrices, where the elements with a value of 1 correspond to the insertion position of the sub-resolution auxiliary graphic seed; If there is a non-zero element in the logical matrix index, the temporary variable tmp is updated and the sub-resolution auxiliary graphic seed is inserted at the corresponding position, that is, tmp(index) = t SRAF , return to step 2.2, and continue to insert the sub-resolution auxiliary pattern seeds; otherwise, if the values ​​of the elements in the logic matrix index are all 0, the insertion of the sub-resolution auxiliary pattern seeds is completed, and the initial mask pattern M0 = tmp is obtained, and step 3 is entered; Step 3. Construct the evaluation function of the inverse lithography problem: 3.1 With the help of mask filtering and binarization processing, a binary mask pattern M is obtained according to the mask pattern M B : The mask image M is processed by the mask filtering method to obtain the blurred mask image M. blur , the formula is as follows: Among them, r0 represents the center position, ||r-r0|| represents the distance from point r to point r0, σ GF is the standard deviation of the Gaussian function, and Ω represents the number of elements contained in the Gaussian convolution kernel; Binarization processing obtains the binary mask pattern M B , the formula is as follows: M B =Γ(M blur -t m ) Among them, Γ(x)={1|x≥0∪0|x<0}, the function Γ(x) converts M blur Medium transmittance is greater than or equal to the mask threshold t m The pixel value of M is 1. blur Medium transmittance is less than the mask threshold t m The pixel value of is 0; 3.2 Calculate the spatial image AI when the defocus amount is h, the formula is as follows: in, is the binary mask pattern M B The mask diffraction spectrum is calculated by Fourier transform, (x, y) is the spatial coordinate of the mask pattern, (f′, g′) is the normalized spatial frequency coordinate of the mask diffraction spectrum, Φ i (f′, g′; h) represents the i-th frequency domain TCC kernel when the defocus amount is h, S i is the coefficient corresponding to the i-th TCC core, shared by K TCC cores, IFFT{} represents inverse Fourier transform; 3.3 Calculate the RI of the photoresist image when the defocus amount is h and the exposure dose deviation is t. The formula is as follows: Where α is the photoresist sensitivity, t r is the photoresist threshold; 3.4 In the positive development process, if the photoresist image RI is greater than or equal to the development threshold t dev , the photoresist at that position is removed; otherwise, if the photoresist image RI is less than the developing threshold t dev , then the photoresist at this position is retained; Thus, the developed photoresist pattern RC is obtained, that is, RC(x, y; h, t) = Γ(RI(x, y; h, t)-t dev ); 3.5 The evaluation function f is constructed by using the weighted sum of the graphic errors between the photoresist pattern and the target pattern under different exposure dose deviations t and defocus amounts h. The formula is as follows: Step 4. Based on the initial mask pattern M0, the mask pattern M is optimized using an optimization algorithm with the goal of minimizing the evaluation function value. During the optimization process, the elements of the mask pattern M satisfy And 0≤M(p,q)≤1, where p and q are the element indices of the mask pattern M, And 1≤p≤N V , And 1≤q≤N H , get the optimized mask pattern M * Substitute into step 3.1 to obtain the binary mask pattern with the best imaging quality

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