{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T23:03:39Z","timestamp":1771628619063,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,14]],"date-time":"2023-01-14T00:00:00Z","timestamp":1673654400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11675169"],"award-info":[{"award-number":["11675169"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["XDA25020314"],"award-info":[{"award-number":["XDA25020314"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Strategic Priority Research Program of the Chinese Academy of Sciences, China","award":["11675169"],"award-info":[{"award-number":["11675169"]}]},{"name":"Strategic Priority Research Program of the Chinese Academy of Sciences, China","award":["XDA25020314"],"award-info":[{"award-number":["XDA25020314"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Ion bombardment (IB) is a promising nanofabrication tool for self-organized nanostructures. When ions bombard a nominally flat solid surface, self-organized nanoripples can be induced on the irradiated target surface, which are called intrinsic nanoripples of the target material. The degree of ordering of nanoripples is an outstanding issue to be overcome, similar to other self-organization methods. In this study, the IB-induced nanoripples on bilayer systems with enhanced quality are revisited from the perspective of guided self-organization. First, power spectral density (PSD) entropy is introduced to evaluate the degree of ordering of the irradiated nanoripples, which is calculated based on the PSD curve of an atomic force microscopy image (i.e., the Fourier transform of the surface height. The PSD entropy can characterize the degree of ordering of nanoripples). The lower the PSD entropy of the nanoripples is, the higher the degree of ordering of the nanoripples. Second, to deepen the understanding of the enhanced quality of nanoripples on bilayer systems, the temporal evolution of the nanoripples on the photoresist (PR)\/antireflection coating (ARC) and Au\/ARC bilayer systems are compared with those of single PR and ARC layers. Finally, we demonstrate that a series of intrinsic IB-induced nanoripples on the top layer may act as a kind of self-organized template to guide the development of another series of latent IB-induced nanoripples on the underlying layer, aiming at improving the ripple ordering. The template with a self-organized nanostructure may alleviate the critical requirement for periodic templates with a small period of ~100 nm. The work may also provide inspiration for guided self-organization in other fields.<\/jats:p>","DOI":"10.3390\/e25010170","type":"journal-article","created":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T02:29:55Z","timestamp":1673836195000},"page":"170","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Can One Series of Self-Organized Nanoripples Guide Another Series of Self-Organized Nanoripples during Ion Bombardment: From the Perspective of Power Spectral Density Entropy?"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7371-7772","authenticated-orcid":false,"given":"Hengbo","family":"Li","sequence":"first","affiliation":[{"name":"National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hezuohua South Road 42, Hefei 230029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinyu","family":"Li","sequence":"additional","affiliation":[{"name":"National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hezuohua South Road 42, Hefei 230029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gaoyuan","family":"Yang","sequence":"additional","affiliation":[{"name":"National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hezuohua South Road 42, Hefei 230029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8768-3155","authenticated-orcid":false,"given":"Ying","family":"Liu","sequence":"additional","affiliation":[{"name":"National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hezuohua South Road 42, Hefei 230029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4043-6314","authenticated-orcid":false,"given":"Frank","family":"Frost","sequence":"additional","affiliation":[{"name":"Leibniz Institute of Surface Engineering (IOM), Permoserstra\u00dfe 15, 04318 Leipzig, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yilin","family":"Hong","sequence":"additional","affiliation":[{"name":"National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hezuohua South Road 42, Hefei 230029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2418","DOI":"10.1126\/science.1070821","article-title":"Self-Assembly at All Scales","volume":"295","author":"Whitesides","year":"2002","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"6553","DOI":"10.1002\/anie.202017016","article-title":"An Efficient Turing-Type Ag2Se-CoSe2 Multi-Interfacial Oxygen Evolving Electrocatalyst","volume":"60","author":"Zhang","year":"2021","journal-title":"Angew. Chem. Int. Ed."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"e2206888119","DOI":"10.1073\/pnas.2206888119","article-title":"Bridging scales in a multiscale pattern-forming system","volume":"119","author":"Brauns","year":"2022","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1126\/science.abn1459","article-title":"Growth rules for irregular architected materials with programmable properties","volume":"377","author":"Liu","year":"2022","journal-title":"Science"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1038\/s41467-021-26985-3","article-title":"Megaripple mechanics: Bimodal transport ingrained in bimodal sands","volume":"13","author":"Tholen","year":"2022","journal-title":"Nat. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"287","DOI":"10.2976\/1.3233933","article-title":"Guided self-organization","volume":"3","author":"Prokopenko","year":"2009","journal-title":"HFSP J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5232","DOI":"10.3390\/e16105232","article-title":"Entropy Methods in Guided Self-Organisation","volume":"16","author":"Prokopenko","year":"2014","journal-title":"Entropy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2845","DOI":"10.1002\/adma.200500717","article-title":"Lateral Templating for Guided Self-Organization of Sputter Morphologies","volume":"17","author":"Cuenat","year":"2005","journal-title":"Adv. Mater."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.optlaseng.2018.10.005","article-title":"Guided self-organization of nanodroplets induced by nanosecond IR laser radiation of molybdenum fifilms on sapphire","volume":"113","author":"Zagoranskiy","year":"2019","journal-title":"Opt. Lasers Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1038\/s41563-020-00885-1","article-title":"Guiding tissue-scale self-organization","volume":"20","author":"Gartner","year":"2021","journal-title":"Nat. Mater."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Ara\u00fajo, N.A.M., Janssen, L.M.C., Barois, T., Boffetta, G., Cohen, I., Corbetta, A., Dauchot, O., Dijkstra, M., Durham, W.M., and Dussutour, A. (2022). Steering self-organisation through confinement. arXiv.","DOI":"10.1039\/D2SM01562E"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2390","DOI":"10.1116\/1.575561","article-title":"Theory of ripple topography induced by ion bombardment","volume":"6","author":"Bradley","year":"1988","journal-title":"J. Vac. Sci. Technol. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4116","DOI":"10.1103\/PhysRevLett.85.4116","article-title":"Roughness Evolution of Ion Sputtered Rotating InP Surfaces: Pattern Formation and Scaling Laws","volume":"85","author":"Frost","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"245412","DOI":"10.1103\/PhysRevB.89.245412","article-title":"Evolution of ion beam induced patterns on Si(001)","volume":"89","author":"Engler","year":"2014","journal-title":"Phys. Rev. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"011311","DOI":"10.1063\/1.5043438","article-title":"Ion-induced nanopatterning of silicon: Toward a predictive model","volume":"6","author":"Norris","year":"2019","journal-title":"Appl. Phys. Rev."},{"key":"ref_16","first-page":"085301","article-title":"Designing self-organized nanopatterns on Si by ion irradiation and metal co-deposition","volume":"25","author":"Zhang","year":"2014","journal-title":"New. J. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"180902","DOI":"10.1063\/5.0021308","article-title":"A perspective on nanoscale pattern formation at surfaces by ion-beam irradiation","volume":"128","author":"Cuerno","year":"2020","journal-title":"J. Appl. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"333002","DOI":"10.1088\/1361-648X\/ac75a1","article-title":"Surface nanopatterning by ion beam irradiation: Compositional effects","volume":"34","author":"Lorenz","year":"2022","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"063004","DOI":"10.1088\/1367-2630\/10\/6\/063004","article-title":"Minimization of topological defects in ion-induced ripple patterns on silicon","volume":"10","author":"Keller","year":"2008","journal-title":"New. J. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2437","DOI":"10.1038\/s41467-019-10095-2","article-title":"Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy","volume":"10","author":"Huang","year":"2019","journal-title":"Nat. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2000653","DOI":"10.1002\/adom.202000653","article-title":"Evidence of Plasmon Enhanced Charge Transfer in Large-Area Hybrid Au\u2013MoS2 Metasurface","volume":"8","author":"Camellini","year":"2020","journal-title":"Adv. Opt. Mater."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Yang, Y., and Keller, A. (2021). Ion Beam Nanopatterning of Biomaterial Surfaces. Appl. Sci., 11.","DOI":"10.3390\/app11146575"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"385301","DOI":"10.1088\/1361-6528\/ac074e","article-title":"Enhancing the quality of self-organized nanoripples by Ar-ion bombardment of a bilayer system","volume":"32","author":"Li","year":"2021","journal-title":"Nanotechnology"},{"key":"ref_24","unstructured":"Li, H.B., Li, J.Y., Yang, G.Y., Liu, Y., Frost, F., and Hong, Y.L. (2022). Superimposition of ion-induced nanoripples: The erosion of a bilayer with a generalized varied-incidence-condition ion bombardment strategy, in preparation."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1117\/12.209287","article-title":"A sub-half micron i-line photolithography process using AZ BARLi","volume":"2440","author":"Johnson","year":"1995","journal-title":"Proc. Optical\/Laser Microlithography VIII SPIE"},{"key":"ref_26","unstructured":"(2023, January 13). MicroChemicals. Available online: http:\/\/microchemicals.com."},{"key":"ref_27","unstructured":"(2023, January 13). Image Analysis Software for Microscopy. Available online: http:\/\/imagemet.com."},{"key":"ref_28","unstructured":"Pelliccione, M., and Lu, T.M. (2008). Evolution of Thin Film Morphology, Springer."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"111410","DOI":"10.1016\/j.fusengdes.2019.111410","article-title":"Small-scale self-focusing assessment using PSD Shannon entropy of a 3\u03c9 process in a high-power laser facility","volume":"151","author":"Huang","year":"2020","journal-title":"Fusion Eng. Des."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"152267","DOI":"10.1016\/j.apsusc.2021.152267","article-title":"Role of the metal supply pathway on silicon patterning by oblique ion beam sputtering, Appl","volume":"580","author":"Palomares","year":"2022","journal-title":"Surf. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"032804","DOI":"10.1103\/PhysRevE.96.032804","article-title":"Emergence and detailed structure of terraced surfaces produced by oblique-incidence ion sputtering","volume":"96","author":"Harrison","year":"2017","journal-title":"Phys. Rev. E"},{"key":"ref_33","first-page":"63","article-title":"Sputtering by Ion Bombardment theoretical concepts","volume":"Volume 47","author":"Behrisch","year":"1981","journal-title":"Sputtering by Particle Bombardment I: Physical Sputtering of Single-Element Solids"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"146510","DOI":"10.1016\/j.apsusc.2020.146510","article-title":"Energy dependence of morphologies on photoresist surfaces under Ar+ ion bombardment with normal incidence","volume":"523","author":"Yang","year":"2020","journal-title":"Appl. Surf. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"147515","DOI":"10.1016\/j.apsusc.2020.147515","article-title":"Nanohole morphologies on photoresist surface produced by low-energy Ar+ ion bombardment under normal and near-normal incidence","volume":"523","author":"Yang","year":"2020","journal-title":"Appl. Surf. Sci."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/170\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:06:19Z","timestamp":1760119579000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/170"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,14]]},"references-count":35,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["e25010170"],"URL":"https:\/\/doi.org\/10.3390\/e25010170","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,14]]}}}