基于卷积运算的嵌段共聚物自组装图像缺陷分析统计方法

doi:10.19894/j.issn.1000-0518.210121

摘要/Abstract

摘要： 嵌段共聚物引导自组装是制备sub-10 nm尺寸半导体器件的潜在技术方案之一。然而由于缺少高效准确的实验室分析工具,难以对嵌段共聚物自组装/引导自组装的结构进行深入定量分析,特别是对其组装结构的缺陷密度及线边粗糙度等进行定量研究。本文参考图形分析中的图像增强算法和模板匹配算法,采用二值化和骨架化算法对嵌段共聚物自组装/引导自组装图像进行处理,构建相应的卷积核并利用卷积运算分析和定位组装结构中的缺陷,并对缺陷密度进行统计。经验证,该算法能够减少噪点对统计结果的影响,区分图像边缘截断所产生的断点和组装缺陷,快速准确地自动统计自组装/引导自组装图像中的端点、分叉和岛缺陷结构。同时对分析所需的图片放大倍率和幅面尺寸极限进行了探索,结果表明嵌段共聚物本征相分离周期与像素尺寸的比值至少为6.69, 有效统计嵌段共聚物自组装缺陷所需的视场面积至少为1.5 μm²。缺陷分析速度测试表明,本文算法相较于邻近像素判断法快136~147倍。

关键词: 嵌段共聚物, 自组装, 引导自组装, 卷积, 缺陷统计

Abstract: Directed self-assembly (DSA) of block copolymers (BCP) is one of the potential methods to manufacture sub-10 nm structures for semiconductors. However, the lack of tools in labs makes it difficult to quantitatively analyze defects and defect densities in BCP films prepared by self-assembly and DSA. Inspired by the general image processing method, image enhancement and template matching, a convolution algorithm was developed to detect defects in the scanning electron microscopy (SEM) images of BCP films and count the densities of each types of defects. Defects and artificial noises are accurately distinguished as verified by hand. The dot, terminal point and junction defects are automatically counted without any error in most SEM images by this algorithm. In order to get the reliable and reproducible results, the ratio of the BCP period (L₀) to nanometers per pixel (NPP) needs to be ＞6.69 and the smallest image area is 1.5 μm². Finally, direct comparison of the two algorithms on our workstation shows that the compute speed of the convolution algorithm is about 136~147 times faster than that of the adjacent pixel determination algorithm.

Key words: Block copolymer, Self-assembly, Directed self-assembly, Convolution, Defect statistics

中图分类号:

O631

田昕, 赖翰文, 刘亚栋, 季生象. 基于卷积运算的嵌段共聚物自组装图像缺陷分析统计方法[J]. 应用化学, 2021, 38(9): 1199-1208.

TIAN Xin, LAI Han-Wen, LIU Ya-Dong, JI Sheng-Xiang. Analysis of Defects in Block Copolymer Films by a Convolution Algorithm[J]. Chinese Journal of Applied Chemistry, 2021, 38(9): 1199-1208.

参考文献

[1] LEIBLER L. Theory of microphase separation in block co-polymers[J]. Macromolecules, 1980, 13(6): 1602-1617.
[2] COULON G, RUSSELL T P, DELINE V R, et al. Surface-induced orientation of symmetric, diblock copolymers-a secondary ion mass-spectrometry study[J]. Macromolecules, 1989, 22(6): 2581-2589.
[3] RUSSELL T P, COULON G, DELINE V R, et al. Characteristics of the surface-induced orientation for symmetric diblock PS/PMMA copolymers[J]. Macromolecules, 1989, 22(12): 4600-4606.
[4] COULON G, COLLIN B, AUSSERRE D, et al. Islands and holes on the free-surface of thin diblock copolymer films.1.Characteristics of formation and growth[J]. J Phys, 1990, 51(24): 2801-2811.
[5] PICKETT G T, WITTEN T A, NAGEL S R. Equilibrium surface orientation of lamellae[J]. Macromolecules, 1993, 26(12): 3194-3199.
[6] JIN X S, PANG Y Y, JI S X. From self-assembled monolayers to chemically patterned brushes: controlling the orientation of block copolymer domains in films by substrate modification[J]. Chinese J Polym Sci, 2016, 34(6): 659-678.
[7] STEIN G E, MAHADEVAPURAM N, MITRA I. Controlling interfacial interactions for directed self assembly of block copolymers[J]. J Polym Sci, 2015,53 (2): 96-102.
[8] MANSKY P, LIU Y, HUANG E, et al. Controlling polymer-surface interactions with random copolymer brushes[J]. Science, 1997, 275(5305): 1458-1460.
[9] IN I, LA Y H, PARK S M, et al. Side-chain-grafted random copolymer brushes as neutral surfaces for controlling the orientation of block copolymer microdomains in thin films[J]. Langmuir, 2006, 22(18): 7855-7860.
[10] KIM B H, LEE D H, KIM J Y, et al. Mussel-inspired block copolymer lithography for low surface energy materials of teflon, graphene, and gold[J]. Adv Mater, 2011, 23(47): 5618-5622.
[11] JI S X, LIU G L, ZHENG F, et al.Preparation of neutral wetting brushes for block copolymer films from homopolymer blends[J]. Adv. Mater, 2008, 20(16): 3054-3060.
[12] LIU G L, JI S X, STUEN K O, et al. Modification of a polystyrene brush layer by insertion of poly(methyl methacrylate) molecules[J]. J Vac Sci Technol, 2009, 27(6): 3038-3042.
[13] SHE M S, LO T Y, HO R M. Long-range ordering of block copolymer cylinders driven by combining thermal annealing and substrate functionalization[J]. ACS Nano, 2013, 7(3): 2000-2011.
[14] CERESOLI M, PALERMO M, FERRARESE LUPI F, et al. Neutral wetting brush layers for block copolymer thin films using homopolymer blends processed at high temperatures[J]. Nanotechnology, 2015, 26(41):1-12.
[15] JI S X, LIAO W, NEALEY P F. Block cooligomers: a generalized approach to controlling the wetting behavior of block copolymer thin films[J]. Macromolecules, 2010, 43(16): 6919-6922.
[16] HUANG E, PRUZINSKY S, RUSSELL T P, et al. Neutrality conditions for block copolymer systems on random copolymer brush surfaces[J]. Macromolecules, 1999, 32(16): 5299-5303.
[17] HUANG E, RUSSELL T P, HARRISON C, et al. Using surface active random copolymers to control the domain orientation in diblock copolymer thin films[J]. Macromolecules, 1998, 31(22): 7641-7650.
[18] MANSKY P, RUSSELL T P, HAWKER C J, et al. Ordered diblock copolymer films on random copolymer brushes[J]. Macromolecules, 1997, 30(22): 6810-6813.
[19] YANG X M, PETERS R D, NEALEY P F, et al. Guided self-assembly of symmetric diblock copolymer films on chemically nanopatterned substrates[J]. Macromolecules, 2000, 33(26): 9575-9582.
[20] KIM S O, SOLAK H H, STOYKOVICH M P, et al. Epitaxial self-assembly of block copolymers on lithographically defined nanopatterned substrates[J]. Nature, 2003, 424(6947): 411-414.
[21] LIU C C, HAN E, ONSES M S, et al. Fabrication of lithographically defined chemically patterned polymer brushes and mats[J]. Macromolecules, 2011, 44(7): 1876-1885.
[22] LIU C C, RAMIREZ-HERNANDEZ A, HAN E, et al. Chemical patterns for directed self-assembly of lamellae-forming block copolymers with density multiplication of features[J]. Macromolecules, 2013, 46(4): 1415-1424.
[23] LIU C C,FRANKE E, MIGNOT Y, et al. Directed self-assembly of block copolymers for 7 nanometre FinFET technology and beyond[J]. Nat Electron, 2018, 1(10): 562-569.
[24] JI S X, WAN L, LIU C C, et al. Directed self-assembly of block copolymers on chemical patterns: a platform for nanofabrication[J]. Prog Polym Sci, 2016, 54/55: 76-127.
[25] PIETROY D, GEREIGE I, GOURGON C. Automatic detection of NIL defects using microscopy and image processing[J]. Microelectron Eng, 2013, 112: 163-167.
[26] MURPHY J N, HARRIS K D, BURIAK J M. Automated defect and correlation length analysis of block copolymer thin film nanopatterns[J]. PLoS One,2015, 10(7): 1-32.
[27] GRONHEID R, HOHLE C K, CHEVALIER X, et al. Automated lamellar block copolymer process characterization[C]. Adv Pattern Mater Proc XXXV, 2018: 1-6.
[28] ROBERTS L. Machine perception of three-dimensional solids[M]. MIT Press, 1963: 25-36.
[29] HANY F, EERO P S. Optimally rotation-equivariant directional derivative kernels[J]. Comput Anal Im Pattern, 1997: 207-214.
[30] CANNY J. A computational approach to edge-detection[J]. IEEE Tran Pattern Anal Mach Intell,1986, 8(6): 679-698.
[31] BRIECHLE K, HANEBECK U D. Template matching using fast normalized cross correlation[J]. Opt Pattern Rec XII, 2001, 4387: 95-102.
[32] ZHANG K, LU J B, LAFRUIT G, et al. Robust stereo matching with fast normalized cross-correlation over shape-adaptive regions[J]. IEEE Int Conf IM Proc, 2009(1/2/3/4/5/6): 2357-2360.
[33] CHAUDHARI R E, DHOK S B. An optimized approach to pipelined architecture for fast 2d normalized cross-correlation[J]. J Circuits Sys Comput, 2019, 28(12):1-17.
[34] HAN E, STUEN K O, LA Y H, et al. Effect of composition of substrate-modifying random copolymers on the orientation of symmetric and asymmetric diblock copolymer domains[J]. Macromolecules, 2008, 41(23): 9090-9097.
[35] MERMIN N D. Points, lines and walls in liquid-crystals, magnetic systems, and various ordered media- Kleman, M[J]. Am J Phys, 1984, 52(2): 188-189.
[36] GLASBEY C A. An analysis of histogram-based thresholding algorithms[J]. Graph Mod Im Proc,1993, 55(6): 532-537.
[37] LI C H, TAM P K S. An iterative algorithm for minimum cross entropy thresholding[J]. Patt Rec Lett, 1998, 19(8): 771-776.
[38] LI C H, LEE C K. Minimum cross entropy thresholding[J]. Patt Rec, 1993, 26(4): 617-625.
[39] REINHARD E. High dynamic range imaging, Computer vision: a reference guide[M]. Springer International Publishing, 2020: 1-6.
[40] ZHANG T Y, SUEN C Y. A fast parallel algorithm for thinning digital patterns[J]. Commun ACM, 1984, 27(3): 236-239.
[41] LEE T C, KASHYAP R L, CHU C N. Building skeleton models via 3-D medial surface axis thinning algorithms[J]. Graph Mod Im Proc, 1994, 56(6): 462-478.
[42] WU K S, OTOO E, SUZUKI K. Optimizing two-pass connected-component labeling algorithms[J]. Patt Anal App, 2009, 12(2): 117-135.
[43] WU K S, OTOO E, SHOSHANI A. Optimizing connected component labeling algorithms[J]. Med Imaging, 2005, 5747: 1965-1976.
[44] FIORIO C, GUSTEDT J. Two linear time union-find strategies for image processing[J].Theor Comput.Sci,1996, 154(2): 165-181.
[45] WILLIAM E. LORENSEN H E C. Marching cubes: a high resolution 3D surface construction algorithm[J]. ACM Siggraph Comput Graph, 1987, 21: 163-169.
[46] ELLIOTT W D, BOARD J A. Fast Fourier transform accelerated fast multipole algorithm[J]. SIAM J Sci, Comput, 1996, 17(2): 398-415.
[47] CHEN F, SUTER D. Using a fast multipole method to accelerate spline evaluations[J]. IEEE Comput Sci Eng, 1998, 5(3): 24-31.
[48] CECKA C, DARVE E. Fourier-based fast multipole method for the helmholtz equation[J]. SIAM J Sci, Comput, 2013, 35(1): A79-A103.