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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">10.17586/2220-8054-2026-17-3-291-296</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-1834</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>Calculation of characteristics of subnanometer delta-doped layers in diamond in the quasi-classical approach</article-title><trans-title-group xml:lang="ru"><trans-title>Вычисление характеристик субнанометровых дельта-легированных слоёв в алмазе в квазиклассическом приближении</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-8528-3884</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кукушкин</surname><given-names>В. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Kukushkin</surname><given-names>V. A.</given-names></name></name-alternatives><bio xml:lang="en"><p>Vladimir A. Kukushkin – Federal Research Center A. V. Gaponov-Grekhov Institute of Applied Physics of the RAS, Nizhny Novgorod, Russia; National Research Lobachevsky SU of Nizhny Novgorod.</p><p>Nizhny Novgorod</p></bio><email xlink:type="simple">vakuk@ipfran.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кукушкин</surname><given-names>Ю. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Kukushkin</surname><given-names>Yu. V.</given-names></name></name-alternatives><bio xml:lang="en"><p>Yuriy V. Kukushkin</p><p>Nizhny Novgorod</p></bio><email xlink:type="simple">yuriy.kukushkinn@gmail.com</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>Federal Research Center A. V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences; National Research Lobachevsky State University of Nizhny Novgorod</institution><country>Russian Federation</country></aff><aff xml:lang="en" id="aff-2"><institution>National Research Lobachevsky State University of Nizhny Novgorod</institution><country>Russian Federation</country></aff><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>18</day><month>07</month><year>2026</year></pub-date><volume>17</volume><issue>3</issue><fpage>291</fpage><lpage>296</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Kukushkin V.A., Kukushkin Y.V., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Кукушкин В.А., Кукушкин Ю.В.</copyright-holder><copyright-holder xml:lang="en">Kukushkin V.A., Kukushkin Y.V.</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/1834">https://nanojournal.ifmo.ru/jour/article/view/1834</self-uri><abstract><p>It is shown that subnanometer boron delta-doped layers characteristics in chemically vapor deposited diamond films can be calculated in the quasi-classical approximation both in equilibrium and in an external electromagnetic field ionizing doping boron atoms. The corresponding solutions are found, in the first case – analytically, in the second – numerically. The use of the quasi-classical approximation allows one to simplify significantly the mathematical modeling of diamond structures with subnanometer delta-doped layers, necessary for their application in nanoelectronics, for example in high-speed field-effect transistors.</p></abstract><trans-abstract xml:lang="ru"><p>Показано, что характеристики субнанометровых дельта-легированных бором слоёв в химически осаждённых из газовой фазы алмазных плёнках могут быть вычислены в квазиклассическом приближении как в равновесии, так и во внешнем электромагнитном поле, ионизирующем легирующие атомы бора. Найдены соответствующие решения, в первом случае – аналитически, во втором – численно. Использование квазиклассического приближения позволяет существенно упростить математическое моделирование алмазных структур с субнанометровыми дельта-легированными слоями, необходимое для их использования в наноэлектронике, например в быстродействующих полевых транзисторах.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>дельта-легированные слои</kwd><kwd>квазиклассическое приближение</kwd><kwd>химически осаждённый из газовой фазы алмаз</kwd></kwd-group><kwd-group xml:lang="en"><kwd>chemically vapor deposited diamond</kwd><kwd>delta-doped layers</kwd><kwd>quasi-classical approximation</kwd></kwd-group><funding-group><funding-statement xml:lang="en">The work is fulfilled in the frame of the state assignment of Federal Research Center A.V. 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