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Abstract
Source and mask optimization (SMO) is one of the most important resolution enhancement techniques for integrated circuit manufacturing in 2X nm technology node and beyond. Nowadays full-chip SMO is alternatively realized by applying SMO to limited number of selected critical patterns instead of to full-chip area, since it is too computational expensive to be apply SMO in full-chip area directly. The critical patterns are selected by a pattern selection method which enables SMO in full-chip application by balancing the performance and computation consumption. A novel diffraction-based pattern selection method has been proposed in this paper. In this method, diffraction-signatures are sufficiently described with widths in eight selected directions. Coverage rules between the diffraction-signatures are specifically designed. Diffraction-signature grouping method and pattern selection strategy are proposed based on the diffraction-signatures and coverage rules. A series of simulations and comparisons performed using ASML’s Tachyon software, which is one of the state of the art commercial SMO platforms, verify the validity of the proposed method.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Lithography is an important part of very-large-scale integrated circuits (VLSI) manufacturing. As the technology node continues to shrink, SMO as one of resolution enhancement techniques (RETs) becomes important for 2X nm technology node and beyond [1–3]. Many good researches have been carried out on new method or algorithm development, technique improvement, experiment demonstration, application, theories behind the technique, and SMO for extreme ultraviolet lithography, etc. [1–14]. With the number of designed patterns increasing to over hundreds or even thousands of patterns, the time consumption would be unacceptable if SMO was applied to the full-chip layout directly. It is a common consensus that there is limitation of SMO area [1]. In nowadays full-chip SMO application [2,3], SMO and mask optimization are performed in turn to obtain the largest common process window with acceptable runtime. SMO is used to generate the source for full-chip mask optimization using a representative set of patterns. Mask optimization, including optical proximity correction (OPC) and Sub-resolution assist feature (SRAF) technique, is performed on all patterns to achieve process window, mask error enhancement factor (MEEF) and mask complexity [15]. OPC pre-distorts mask patterns such that the printed patterns are as close to the desired shapes as possible [16]. Sub-resolution assist feature (SRAF) is an important technique used with OPC that addresses process window [16,17]. SRAF creates a dense environment for sparse patterns, which makes sparse patterns appear dense to the projection system but print as sparse patterns [16]. It is used to improve the common process windows of sparse patterns and dense patterns.
To balance the performance and time consumption of full-chip SMO, pattern selection technique is used to select critical patterns from the input pattern set before performing SMO. The selected critical patterns make up a representative pattern set. The number of patterns in the representative pattern set is much smaller than that in the input pattern set, while the representative pattern set catches most of the characteristics of the input pattern set. SMO is performed on the representative pattern set instead of on all of the input patterns to speed up the full-chip SMO. It is easy to see that pattern selection significantly affects the time consumption and the final process window of today’s full-chip SMO. It is one of the most important steps of full-chip SMO.
IBM CO. LTD. has proposed a pattern selection method base on clustering [18]. However, the representative patterns of different clusters may contain patterns whose spectrums have coverage relationship. The method may bring redundant patterns. ASML CO. LTD. has proposed a diffraction based pattern selection method [2,15]. The method has been involved in the commercial software Tachyon, which is one of the state of the art computational lithography tools in the world. As reported in their publications, diffraction-signatures are identified for each pattern. Critical patterns are selected according to the coverage relationship of diffraction-signatures. The coverage relationship is described by the designed cover rules. The diffraction-signatures and the cover rules are two of the key parts which determine the result of pattern selection. They will affect the optimized source by SMO, which will affect the process window directly. ASML’s method describes the diffraction-signatures with two widths in x and y directions. As we found during the research, only two widths are insufficient to describe the diffraction-signatures. Cover rules which are set base on diffraction-signatures with two widths are not profitable enough to describe the coverage relationship between patterns. Therefore, better performance can be predicted by improving ASML’s method. Because of the significance of the pattern selection in full-chip SMO and commercial reasons there may be, there are quite limited technical information in literatures but only the results and brief introduction of their in-house methods.
In this paper, we propose a critical pattern selection method for full-chip SMO application. This method contains three phases: diffraction-signature extraction, diffraction-signature grouping and critical pattern selection. The diffraction-signature extraction base on diffraction-signatures with widths in eight directions (0°, 45°, 90°, 135°, 180°, 225°, 270° and 315°). Diffraction-signature grouping method and critical pattern selection method are proposed. Diffraction-signature with widths in eight directions brings more information of the diffraction order, which will be highly profitable for diffraction-signature grouping and critical pattern selection. Comparison between the proposed method and ASML’s method is conducted. Critical patterns selected by the two methods from pattern sets are used to perform SMO to generate optimized sources. Mask optimization are performed to all patterns using the optimized sources. Comparisons between the common process windows are given. The critical parameters, such as depth of focus (DOF), MEEF, and image log slop (ILS) are shown. The results verify the validity and effectiveness of the proposed method.
2. Methodology
For a lithography imaging system, the intensity of the aerial image is given by [17]:
The full set of patterns are generated from design layout (GDS files). The spectrums of different patterns are different, but there is coverage relationship between their diffraction orders. For each pattern, diffraction orders can be used as diffraction-signatures for the pattern. After diffraction-signatures are extracted, diffraction-signatures are grouped base on defined grouping method. Finally, a representative set of patterns are selected to be the critical patterns, which cover all diffraction-signature groups. The proposed method contains three phases: diffraction-signature extraction, diffraction-signature grouping and critical patterns selection.
2.1 Diffraction-signature extraction
Because diffraction map of patterns depends on their patterns, diffraction orders can be used as the signature of patterns. Due to the finite size of projection lens of lithography tools, only those portions of diffraction orders that fall inside the aperture contribute to forming the image [20]. Therefore, the diffraction-signatures are extracted from diffraction orders that fall inside the aperture.
The diffraction order peaks of non-array patterns are continuous, after removing the zeroth-order, all the continuous peaks are treated as diffraction-signatures for non-array patterns. An example is shown in Fig. 1(a). The diffraction order peaks of array patterns are discrete. Their spectrums consist of 1st-order and the harmonics. When an array pattern contains a single pitch, the 1st-order contains the pitch information, which is useful for the critical pattern selection. Therefore, the 1st-order is the diffraction-signature for single pitch array patterns. In the case of an array pattern contains multiple pitches, the diffraction-signature extraction method is as follow. At the beginning, the zeroth-order are removed. The strongest diffraction order peak is identified and added to the diffraction-signature group. The identified diffraction order peak and its harmonics are removed from the diffraction map. Repeat the identification step until all diffraction orders have been removed. Finally, the diffraction-signatures are extracted for a pattern. An example is shown in Fig. 1(b). The 2nd-order is identified and added to the diffraction-signature group, which is the strongest peak and corresponding to pitch1. Then the 2nd-order and its harmonics (4th-order) are removed. Next, the 1st-order, which is the strongest peak of remain peaks, is identified and added to the diffraction-signature group. The 1st-order corresponds to pitch2. Then, 1st-order and its harmonics (3rd-order) are removed. After that, all diffraction orders were removed and the signature extraction terminated. Finally, the 1st-order and 2nd-order are extracted as the diffraction-signature of the array pattern.
Fig. 1. Schematic diagram of diffraction-signature extraction: (a) diffraction-signature extraction for non-array pattern, (b) diffraction-signature extraction for array pattern.
Diffraction-signatures are described as $S({\hat{f}^{\prime}_\textrm{o}},{\hat{g^{\prime}}_\textrm{o}},{w_1}\textrm{,}{w_2}\textrm{,}{w_3}\textrm{,}{w_4}\textrm{,}{w_5}\textrm{,}{w_6}\textrm{,}{w_7},{w_8})$, where $({\hat{f}^{\prime}_\textrm{o}},{\hat{g^{\prime}}_\textrm{o}})$ is the peak’s location of the diffraction-signature in frequency space, ${w_1}{\sim }{w_8}$ are the widths in eight directions, which are 0°, 45°, 90°, 135°, 180°, 225°, 270° and 315°. The width is the distance from the peak’s location to the edge of the contour of diffraction-signature’s distribution in frequency space. The diffraction orders of array patterns are discrete peaks, so the widths are zero. For non-array patterns, their diffraction orders are continuous peaks with different widths in eight directions. As shown in Fig. 2, the widths in eight directions describe the distribution of diffraction-signature more accurate than only two widths in x and y directions.
Fig. 2. Diffraction-signature: (a) diffraction-signature described by ASML’s method, (b) diffraction-signature described by the proposed method.
The contour of the diffraction-signature can be sufficiently constructed using widths in eight directions. As shown in Fig. 3, the widths in directions 0°, 90°, 180° and 270°, which are ${w_1}\textrm{,}{w_3},{w_5}\textrm{,}{w_7}$, respectively, describe a rectangular contour, as shown in Fig. 3(b). The widths in directions 45°, 135°, 225° and 315°, which are ${w_2}\textrm{,}{w_4},{w_6}\textrm{,}{w_8}$, respectively, describe an oblique rectangular contour, as shown in Fig. 3(c). As shown in Fig. 3(d), the two rectangular contours sufficiently and effectively describe the contour of the diffraction-signature.
Fig. 3. Contours of diffraction-signature constructed by eight widths: (a) the distribution of a diffraction-signature and its widths in eight directions, (b) the rectangular contour constructed by widths in directions 0°, 90°, 180° and 270°, (c) the rectangular contour constructed by widths in directions 45°, 135°, 225° and 315°, (d) the two rectangular contours constructed by eight widths of the diffraction-signature.
2.2 Diffraction-signature grouping
After diffraction-signature extraction, many diffraction-signatures are generated for all patterns. There is coverage relationship between the diffraction-signatures. The diffraction-signatures should be divided into different groups according to predefined coverage rules. In this paper, the coverage rules are defined using the eight-width description method of diffraction-signatures stated in the last section.
- 1) In the case of diffraction-signatures ${S_A}$ and ${S_B}$ are continuous peaks, the coverage rule is defined by the situation that whether the location of a diffraction-signature is covered by the contour of another diffraction-signature. If the peak’s location of ${S_A}$ is covered by the contour of ${S_B}$, ${S_A}$ is covered by ${S_B}$. The coverage rule is given by:$$\begin{array}{l} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {d_i}({S_A},{S_B}) \le {w_i} + {R_{blur}},{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} (i = 1,3,5,7),\\ or{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {d_j}({S_A},{S_B}) \le {w_j} + {R_{blur}},{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} (j = 2,4,6,8). \end{array}$$where i and j are the number of the eight directions, using 1∼8 as direction number of the 0°, 45°, 90°, 135°,180°, 225°, 270°and 315°; $d({S_A},{S_B})$ is distance between the peaks’ locations of ${S_A}$ and ${S_B}$; ${d_i}$ and ${d_j}$ are the projections of the distance onto the direction i and j; ${w_i}$ and ${w_j}$are the widths of ${S_A}$ in directions i and j; ${R_{blur}}$ is the source blur radius of the illumination system of lithography tools [21]. If the ${d_i}$ or ${d_j}$ is less than or equals to the sum of the widths of ${S_A}$ and ${R_{blur}}$, it means the peak’s location of ${S_B}$ is covered by the contour of ${S_A}$, so ${S_B}$ is covered by ${S_A}$. Examples are shown in Fig. 4, when peak’s location of ${S_B}$ is covered by the rectangular contour constructed by ${w_1}\textrm{,}{w_3},{w_5}\textrm{,}{w_7}$ of ${S_A}$, as shown in Fig. 4(a), the projections of the distance d onto these directions (0°, 90°, 180° and 270°) are not greater than the sum of the width and ${R_{blur}}$ in corresponding directions. As shown in Fig. 4(b), when peak’s location of ${S_B}$ is covered by the rectangular contour constructed by ${w_2}\textrm{,}{w_4},{w_6}\textrm{,}{w_8}$ of ${S_A}$, the projections of the distance d onto these directions (45°, 135°, 225° and 315°) are not greater than the sum of the width and ${R_{blur}}$ in corresponding directions.
- 2) In the case of diffraction-signatures ${S_A}$ and ${S_B}$ are discrete peaks, their widths are zeros. The coverage rule is given by: where d is the distance between two discrete peaks. When the distance of the two discrete peaks is smaller than ${R_{blur}}$, they are insolvable illuminated by source with blur radius ${R_{blur}}$, and there is coverage relationship between them. When ${S_A}$ covers the harmonics of ${S_B}$, it means pitch of ${S_A}$ is smaller than that of ${S_B}$. SRAFs can be used to create a dense environment for the pattern of ${S_B}$, which makes the pattern of ${S_B}$ appear dense to the projection system but print as a sparse pattern. Therefore, when ${S_A}$ covers the harmonics of ${S_B}$, ${S_B}$ is also covered by ${S_A}$.
- 3) In the case of ${S_A}$ is discrete peak and ${S_B}$ is continuous peak, the coverage rule is given by Eq. (3). When the distance between ${S_A}$ and the peak’s location of ${S_B}$ is smaller than ${R_{blur}}$, ${S_A}$ covers ${S_B}$. However, ${S_B}$ cannot cover ${S_A}$, because array pattern is preferred in SMO application.
Fig. 4. Two cases of diffraction-signature ${S_A}$covers ${S_B}$: (a) the peak’s location of ${S_B}$ is covered by the rectangular contour constructed by w1, w3, w5 and w7, (b) the peak’s location of ${S_B}$ is covered by the rectangular contour constructed by w2, w4, w6 and w8.
In this paper, diffraction-signatures grouping method is based on the coverage relationship expressed by the coverage rules. The flowchart of the grouping method is shown in Fig. 5. At the beginning, coverage relationship is determined for all diffraction-signatures. Diffraction-signatures covered by the same diffraction-signature are grouped into a group. In other words, a diffraction-signature and the diffraction-signatures covered by it are grouped into a group. The diffraction-signature that covers all members of the selected groups is the representative diffraction-signature. Then, all diffraction-signatures are marked as unvisited. The biggest diffraction-signature group is identified, which the representative diffraction-signature is from the unvisited diffraction-signatures. The members of the identified group are marked as visited. Repeat this step until all diffraction-signatures are visited. After the identification step, several diffraction-signature groups are generated but with intersections. Finally, the diffraction-signatures of these intersections are grouped into the group whose representative diffraction-signature is the nearest to them. After the grouping step, diffraction-signature groups are generated. It worthy to note that there may be more than one representative diffraction-signatures in each group, since there may be more than one signatures who cover all the members of a group.
2.3 Critical patterns selection
The representative diffraction-signatures cover all diffraction-signatures. We select one representative diffraction-signatures from each group. When the patterns corresponding to these representative diffraction-signatures are used as critical patterns to perform SMO, all the diffraction-signature groups are naturally included in SMO. There can be more than one representative diffraction-signature for each group, so the critical pattern set that cover all the representative diffraction-signatures is not unique. In order to reduce the runtime of SMO, the number of critical patterns in critical pattern set should be as less as possible. So, we need to select critical patterns to guarantee the speed of SMO is as high as possible, especially in full-chip application.
In this paper, the critical pattern selection method is proposed to select critical patterns that cover all the diffraction-signature groups, while keep the number of patterns as small as possible. The flowchart of the proposed pattern selection method is shown in Fig. 6, which is designed base on greedy algorithm [22]. At the beginning, all the representative diffraction-signatures are marked as unvisited. The numbers of representative diffraction-signatures covered by each pattern are counted. The pattern that covers most unvisited representative diffraction-signatures is selected as critical pattern. The groups related to the covered representative diffraction-signatures are covered by the critical pattern. The representative diffraction-signatures in these groups are marked as visited. Repeat the selection step until all representative diffraction-signatures are visited. Finally, the critical pattern set is generated.
3. Results
In order to verify the validity of the proposed method, comparison between the proposed method and ASML’s method is conducted. For the same pattern set, pattern selection results of two methods are used to perform SMO to obtain different optimized sources for all patterns. After sources are generated, mask optimization is performed to all patterns using the optimized sources. Process windows are obtained using the same cut-lines. Finally, the process windows of the two methods are compared to show which results is better for full-chip SMO. All of the simulations and comparisons were performed by using Tachyon software. Two pattern sets are used in the simulations. For clear and convincing verification, the simulations are performed under “repeating” and “unrepeating” cases for each pattern set. In the repeating case, the array patterns are set as “repeating” in Tachyon, while the non-array patterns are treated as isolated patterns. In the unrepeating case, all the array and non-array patterns are treated as isolated patterns. The simulation settings are shown in Table 1.
Table 1. Simulation settings.
3.1 SMO using pattern set A
Pattern set A contains 34 patterns, including one dimensional line and space patterns, contact hole patterns and two-dimensional patterns. This pattern set is designed based on test pattern set in Ref. [23], which is GLOBALFOUNDRIES’s test pattern set.
3.1.1 Repeating case
In the repeating case, both the proposed method and ASML's method selected 15 critical patterns. As shown in Fig. 7 and Fig. 8, the selection results are slightly different, there are 4 different patterns between them.
The selected critical patterns are used to perform SMO using Tachyon software. The optimized sources are shown in Fig. 9. Because the selected patterns are different, the optimized sources of the two methods are different. As shown in Fig. 9(a), the source of the proposed method has four strong source points along the diagonal regions of the source, while ASML’s method’s source has four strong source points along the horizontal and vertical axes, as shown in Fig. 9(b). Mask optimizations were performed to all patterns using the two sources. The final process windows are compared. The common process windows and exposure latitude (EL) vs. DOF plots are shown in Fig. 10. It is obvious that the process window obtained by the proposed method is larger than that obtained by ASML’s method. Table 2 shows the DOF (the larger the better), maximum MEEF (the smaller the better) and worst ILS (the larger the better) obtained by the two methods at 5% EL and 10% critical dimension (CD) variation. The results show that an improved process window in all measures has been obtained by the proposed method.
Fig. 9. Optimized sources by using critical patterns selected by (a) the proposed method, and (b) ASML’ method. (Pattern set A, repeating case).
Fig. 10. The process windows obtained after MO is performed on all patterns by using the two sources: (a) the common process windows, (b) the EL vs. DOF plots. (Pattern set A, repeating case).
Table 2. DOF, maximum MEEF and worst ILS, calculated at 5% EL and 10% CD variation. (Pattern set A, repeating case).
3.1.2 Unrepeating case
In the unrepeating case, both the proposed method and ASML's method selected 12 critical patterns, as shown in Fig. 11 and Fig. 12, respectively. There are only 6 identical patterns.
The selected critical patterns are used to perform SMO using Tachyon software. The optimized sources are shown in Fig. 13. Because the selected patterns are different, the optimized sources of two methods are different. Mask optimizations were performed to all patterns using the two sources. The final process windows are compared. The common process windows and EL vs. DOF plots are shown in Fig. 14. It is obvious that the process window obtained by the proposed method is much larger than that obtained by ASML’s method. Table 3 shows the DOF, maximum MEEF and worst ILS obtained by the two methods at 5% EL and 10% CD variation. 87.82 nm DOF was obtained by the proposed method, while no DOF is obtained by ASML’s method. As 5% EL and 10% CD variation are criteria usually used in process evaluation, no overlap process window was obtained by ASML’s method, while process window was obtained by the proposed method. The proposed method shows better performance.
Fig. 13. Optimized sources by using critical patterns selected by (a) the proposed method, and (b) ASML’ method. (Pattern set A, unrepeating case).
Fig. 14. The process windows obtained after MO is performed on all patterns by using the two sources: (a) the common process windows, (b) the EL vs. DOF plots. (Pattern set A, unrepeating case).
Table 3. DOF, maximum MEEF and worst ILS, calculated at 5% EL and 10% CD variation. (Pattern set A, unrepeating case).
3.2 SMO with pattern set B
Pattern set B contains 60 patterns, much more than pattern set A. There are array patterns and non-array patterns in pattern set B. The patterns are selected randomly from the designs of INV, AND, NAND, BUF, OR, NOR, MUX, etc. in a 45 nm standard Cell Library [24]. Compare to pattern set A, pattern set B contains complex 2D patterns. The selection results are shown in Table 4. In the repeating case, both the proposed method and ASML's method selected 11 critical patterns. In the unrepeating case, both the proposed method and ASML's method selected 10 critical patterns.
Table 4. Pattern selection result (Pattern set B).
The selected critical patterns are used to perform SMO using Tachyon software. The optimized sources are shown in the third row of Table 5. Mask optimizations were performed to all patterns using the optimized sources. The common process window comparison and EL vs. DOF plot comparison are shown in the fourth row of Table 5. DOF, maximum MEEF and worst ILS are calculated at 5% EL and 10% CD variation. DOF obtained by the proposed method is larger than that obtained by ASML's method, which means the process windows obtained by the proposed method is larger than that by ASML's method. The MEEF and ILS obtained by the two methods are almost the same. The results verified the validity of the proposed method. As shown in Table 4, there are only two identical patterns in the repeating case while the selection results are absolutely different in the unrepeating case. The differences and simulation results denote that pattern selection is a multiple solution problem, and the proposed method provides a better solution than ASML's method. The increase of the directionality with respect to diffraction-signature description is one of the reasons for the improvement of the SMO performance. It is one of the reasons why the proposed method shows better performance than ASML's method. However, 8 directions seem sufficient enough to describe diffraction-signatures' distribution of the mask patterns, since the mask patterns are usually Manhattan patterns [25].
Table 5. Simulation results (Pattern set B).
4. Summary
Pattern selection techniques is one of the most important techniques for full-chip SMO, as it enables SMO in full-chip application by balancing the performance and time consumption. A diffraction-based pattern selection method has been proposed in this paper. Effective pattern selection is realized by sufficient description of diffraction-signatures with widths in eight selected directions, specifically designed coverage rules between diffraction-signatures and diffraction-signature grouping method and pattern selection method presented based on the first two. Comparisons between the proposed method and ASML's method were conducted using ASML's Tachyon software, which is one of the state of the art computational lithography tools. In some cases, such as the "unrepeating" case of pattern set A as stated in the third section in this paper, process window is obtained by the proposed method, while no process window is achieved by ASML's method. The results verified the advancement of the proposed method. It can be noted from the simulation results that pattern selection is a multiple solution problem. Future researches are worthy to be conducted to see whether there is a best solution or not, to find out the best solution if there is one, and to find out the theories behind the solution.
Funding
National Major Science and Technology Projects of China (2017ZX02101004-002, 2017ZX02101004); Natural Science Foundation of Shanghai (17ZR1434100).
Disclosures
The authors declare no conflicts of interest.
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