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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2025-16-6-785-790</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-1618</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PHYSICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИЗИКА</subject></subj-group></article-categories><title-group><article-title>Multilevel physical unclonable function based on silver nanostructures randomly integrated into the crystalline silicon wafer</article-title><trans-title-group xml:lang="ru"><trans-title>Многоуровневая физически неклонируемая функция, основанная на наноструктурах из серебра, случайным образом интегрированных в кристаллическую кремниевую пластину</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0002-5213-5217</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Федорова</surname><given-names>М. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Fedorova</surname><given-names>M.</given-names></name></name-alternatives><bio xml:lang="en"><p>Maria Fedorova – School of Physics and Engineering, Faculty of Physics</p><p>St. Petersburg</p></bio><email xlink:type="simple">mariya.fedorova@metalab.ifmo.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-1435-0274</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Петрова</surname><given-names>Е. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Petrova</surname><given-names>E.</given-names></name></name-alternatives><bio xml:lang="en"><p>Elena Petrova – School of Physics and Engineering, Faculty of Physics</p><p>St. Petersburg</p></bio><email xlink:type="simple">elena.petrova@metalab.ifmo.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-8609-9851</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ларин</surname><given-names>А. О.</given-names></name><name name-style="western" xml:lang="en"><surname>Larin</surname><given-names>A.</given-names></name></name-alternatives><bio xml:lang="en"><p>Artem Larin – School of Physics and Engineering, Faculty of Physics</p><p>St. Petersburg</p></bio><email xlink:type="simple">artem.larin@metalab.ifmo.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3115-1739</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Сандомирский</surname><given-names>М. П.</given-names></name><name name-style="western" xml:lang="en"><surname>Sandomirskii</surname><given-names>M.</given-names></name></name-alternatives><bio xml:lang="en"><p>Martin Sandomirskii – School of Physics and Engineering, Faculty of Physics</p><p>St. Petersburg</p></bio><email xlink:type="simple">m.sandomirskii@metalab.ifmo.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-9010-7482</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ермина</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Ermina</surname><given-names>A.</given-names></name></name-alternatives><bio xml:lang="en"><p>Anna Ermina</p><p>194021, St. Petersburg</p></bio><email xlink:type="simple">annaermina@mail.ioffe.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-9589-8017</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Павлов</surname><given-names>С. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Pavlov</surname><given-names>S.</given-names></name></name-alternatives><bio xml:lang="en"><p>Sergey Pavlov</p><p>194021, St. Petersburg</p></bio><email xlink:type="simple">pavlov_sergey@mail.ioffe.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-7002-5084</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Жарова</surname><given-names>Ю. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Zharova</surname><given-names>Yu.</given-names></name></name-alternatives><bio xml:lang="en"><p>Yuliya Zharova</p><p>St. Petersburg</p></bio><email xlink:type="simple">piliouguina@mail.ioffe.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-2708-9140</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Пермяков</surname><given-names>Д. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Permyakov</surname><given-names>D.</given-names></name></name-alternatives><bio xml:lang="en"><p>Dmitry Permyakov – School of Physics and Engineering, Faculty of Physics</p><p>St. Petersburg</p></bio><email xlink:type="simple">d.permyakov@metalab.ifmo.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-2034-4962</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ярошенко</surname><given-names>В. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Yaroshenko</surname><given-names>V.</given-names></name></name-alternatives><bio xml:lang="en"><p>Vitaly Yaroshenko – School of Physics and Engineering, Faculty of Physics</p><p>St. Petersburg</p></bio><email xlink:type="simple">v.yaroshenko@metalab.ifmo.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-9157-5683</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Зуев</surname><given-names>Д. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Zuev</surname><given-names>D.</given-names></name></name-alternatives><bio xml:lang="en"><p>Dmitry Zuev – School of Physics and Engineering, Faculty of Physics</p><p>St. Petersburg</p></bio><email xlink:type="simple">d.zuev@metalab.ifmo.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>ITMO University</institution><country>Russian Federation</country></aff><aff xml:lang="en" id="aff-2"><institution>Ioffe Institute</institution><country>Russian Federation</country></aff><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>06</day><month>01</month><year>2026</year></pub-date><volume>16</volume><issue>6</issue><fpage>785</fpage><lpage>790</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Fedorova M., Petrova E., Larin A., Sandomirskii M., Ermina A., Pavlov S., Zharova Y., Permyakov D., Yaroshenko V., Zuev D., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Федорова М.В., Петрова Е.А., Ларин А.О., Сандомирский М.П., Ермина А.А., Павлов С.И., Жарова Ю.А., Пермяков Д.В., Ярошенко В.В., Зуев Д.А.</copyright-holder><copyright-holder xml:lang="en">Fedorova M., Petrova E., Larin A., Sandomirskii M., Ermina A., Pavlov S., Zharova Y., Permyakov D., Yaroshenko V., Zuev D.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/1618">https://nanojournal.ifmo.ru/jour/article/view/1618</self-uri><abstract><p>We present an optical physical unclonable function (PUF) based on silver nanostructures randomly formed on a crystalline silicon wafer through galvanic displacement and thermal annealing. The process produces nanostructures with stochastic spatial distribution and morphology, resulting in unpredictable nonlinear optical responses. The hybrid Ag–Si interface generates two independent signals: photoluminescence (PL) and second-harmonic generation (SHG). Spatial PL and SHG maps were binarized and analyzed using standard PUF metrics. SHG demonstrated higher entropy and more balanced bit distribution, making it the preferred encoding channel, while PL provides an additional verification layer. The fabrication method is scalable, lithography-free, and compatible with standard silicon processing.</p></abstract><trans-abstract xml:lang="ru"><p>В этой статье представлена оптическая физически неклонируемая функция (ФНФ), основанная на серебряных (Ag) наноструктурах, случайным образом сформированных на кристаллической кремниевой (Si) пластине путем гальванического смещения и термического отжига. В результате этого процесса образуются наноструктуры со стохастическим пространственным распределением и морфологией, что приводит к непредсказуемым нелинейным оптическим характеристикам. Гибридный интерфейс Ag–Si создает два независимых сигнала: фотолюминесценцию (ФЛ) и генерацию второй гармоники (ГВГ). Пространственные карты ФЛ и ГВГ были бинаризованы и проанализированы с использованием стандартных показателей ФНФ. ГВГ продемонстрировала более высокую энтропию и более сбалансированное распределение битов, что делает ее предпочтительным каналом кодирования, в то время как ФЛ обеспечивает дополнительный уровень верификации. Метод изготовления является масштабируемым, не требует литографии и совместим со стандартными методами изготовления.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>серебряные наноструктуры</kwd><kwd>кремний</kwd><kwd>ГВГ</kwd><kwd>фотолюминесценция</kwd><kwd>физическая неклонируемая функция</kwd></kwd-group><kwd-group xml:lang="en"><kwd>silver nanostructures</kwd><kwd>silicon</kwd><kwd>SHG</kwd><kwd>photoluminescence</kwd><kwd>physical unclonable function</kwd></kwd-group><funding-group><funding-statement xml:lang="en">Part of this work related to the photoluminescence measurements was supported by Russian Science Foundation project # 25-72-20030, https://rscf.ru/en/project/25-72-20030/ Part of this work related to the PUF labels creation and studies is supported by the Russian Science Foundation # 25-12-00310, https://rscf.ru/en/project/25-12-00310/</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Kikerkova I., Toshevska Trpchevska K., Kikerkov I. 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