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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">10.17586/2220-8054-2018-9-2-206-211</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-693</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>MATHEMATICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>МАТЕМАТИКА</subject></subj-group></article-categories><title-group><article-title>Kinetic model of electron transport in cylindrical nanowire with rough surface</article-title><trans-title-group xml:lang="ru"><trans-title></trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Botman</surname><given-names>S. A.</given-names></name></name-alternatives><bio xml:lang="en"><p>ul. Aleksandra Nevskogo, 14, Kaliningrad, 236016</p></bio><email xlink:type="simple">sbotman@innopark.kantiana.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Leble</surname><given-names>S. B.</given-names></name></name-alternatives><bio xml:lang="en"><p>ul. Aleksandra Nevskogo, 14, Kaliningrad, 236016</p></bio><email xlink:type="simple">sleble@kantiana.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>Immanuel Kant Baltic Federal University</institution><country>Russian Federation</country></aff><pub-date pub-type="collection"><year>2018</year></pub-date><pub-date pub-type="epub"><day>12</day><month>08</month><year>2025</year></pub-date><volume>9</volume><issue>2</issue><elocation-id>206–211</elocation-id><permissions><copyright-statement>Copyright &amp;#x00A9; Botman S.A., Leble S.B., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Botman S.A., Leble S.B.</copyright-holder><copyright-holder xml:lang="en">Botman S.A., Leble S.B.</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/693">https://nanojournal.ifmo.ru/jour/article/view/693</self-uri><abstract><p>In this work, the problem of electron transport in cylindrical nanowires is considered. A model of nanowire is proposed with the irregularities/scatterers concentrated mainly in the vicinity of the surface. It is treated as a waveguide with some scattering indicatrix introduced to describe specular and nonspecular scattering. Employing the kinetic approach, Kolmogorov equation is used to calculate subsequently aproximate nonequlibrium distribution function and derive explicit formula for the resistivity of the system.</p></abstract><kwd-group xml:lang="en"><kwd>resistivity</kwd><kwd>kinetic equation</kwd><kwd>scattering</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Dresselhaus M. S. et al. Springer Handbook of Nanotechnology. Springer, 2010.</mixed-citation><mixed-citation xml:lang="en">Dresselhaus M. S. et al. Springer Handbook of Nanotechnology. Springer, 2010.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Dingle R. B. The electrical conductivity of thin wires. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1950, 201(1067), P. 545–560.</mixed-citation><mixed-citation xml:lang="en">Dingle R. B. The electrical conductivity of thin wires. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1950, 201(1067), P. 545–560.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Lin Y., Sun X., and Dresselhaus M. S. Theoretical investigation of thermoelectric transport properties of cylindrical Bi nanowires. Physical Review B, 2000, 62(7), P. 4610–4623.</mixed-citation><mixed-citation xml:lang="en">Lin Y., Sun X., and Dresselhaus M. S. Theoretical investigation of thermoelectric transport properties of cylindrical Bi nanowires. Physical Review B, 2000, 62(7), P. 4610–4623.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Pavlov B. S. and Strepetov A. V. Exactly solvable model of electron scattering by an inhomogeneity in a thin conductor Theoretical and Mathematical Physics, 1992, 90(2), P. 152–156.</mixed-citation><mixed-citation xml:lang="en">Pavlov B. S. and Strepetov A. V. Exactly solvable model of electron scattering by an inhomogeneity in a thin conductor Theoretical and Mathematical Physics, 1992, 90(2), P. 152–156.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Leble S. B. Kolmogorov equation for Bloch electrons and electrical resistivity models for nanowires. Nanosystems: Physics, Chemistry, Mathematics, 2017, 8(2), P. 247–259.</mixed-citation><mixed-citation xml:lang="en">Leble S. B. Kolmogorov equation for Bloch electrons and electrical resistivity models for nanowires. Nanosystems: Physics, Chemistry, Mathematics, 2017, 8(2), P. 247–259.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Kolmogoroff A. Uber die analytischen Methoden in der Wahrscheinlichkeitsrechnung.¨ Mathematische Annalen, 1931, 104(1), P. 415–458.</mixed-citation><mixed-citation xml:lang="en">Kolmogoroff A. Uber die analytischen Methoden in der Wahrscheinlichkeitsrechnung.¨ Mathematische Annalen, 1931, 104(1), P. 415–458.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Lobanov I. S., Popov I. Yu. Scattering by a junction of zig-zag and armchair nanotubes. Nanosystems: Physics, Chemistry, Mathematics, 2012, 3(2), P. 6–28.</mixed-citation><mixed-citation xml:lang="en">Lobanov I. S., Popov I. Yu. Scattering by a junction of zig-zag and armchair nanotubes. Nanosystems: Physics, Chemistry, Mathematics, 2012, 3(2), P. 6–28.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Botman S. A. and Leble S. B. Electrical conductivity model for quasi-one-dimensional structures. Nanosystems: Physics, Chemistry, Mathematics, 2017, 8(2), P. 231–235.</mixed-citation><mixed-citation xml:lang="en">Botman S. A. and Leble S. B. Electrical conductivity model for quasi-one-dimensional structures. Nanosystems: Physics, Chemistry, Mathematics, 2017, 8(2), P. 231–235.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Fuchs K. The conductivity of thin metallic films according to the electron theory of metals. In Mathematical Proceedings of the Cambridge Philosophical Society, 1938, 34(1), P. 100–108.</mixed-citation><mixed-citation xml:lang="en">Fuchs K. The conductivity of thin metallic films according to the electron theory of metals. In Mathematical Proceedings of the Cambridge Philosophical Society, 1938, 34(1), P. 100–108.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Chaplik A. V. and Entin M. V. Energy spectrum and electron mobility in a thin film with non-ideal boundary. Soviet Journal of Experimental and Theoretical Physics, 1969, 28(3), P. 514–517.</mixed-citation><mixed-citation xml:lang="en">Chaplik A. V. and Entin M. V. Energy spectrum and electron mobility in a thin film with non-ideal boundary. Soviet Journal of Experimental and Theoretical Physics, 1969, 28(3), P. 514–517.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Krokhin A., Makarov N. M., and Yampolskii V. A. Theory of the surface scattering of electrons in metals with gently sloping surface irregularities. Soviet Physics-JETP, 1991, 72(2), P. 289–294.</mixed-citation><mixed-citation xml:lang="en">Krokhin A., Makarov N. M., and Yampolskii V. A. Theory of the surface scattering of electrons in metals with gently sloping surface irregularities. Soviet Physics-JETP, 1991, 72(2), P. 289–294.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Makarov N. M., Moroz A. V., and Yampolskii V. A. Classical and quantum size effects in electron conductivity of films with rough boundaries. Physical Review B, 1995, 52(8), P. 6087–6101.</mixed-citation><mixed-citation xml:lang="en">Makarov N. M., Moroz A. V., and Yampolskii V. A. Classical and quantum size effects in electron conductivity of films with rough boundaries. Physical Review B, 1995, 52(8), P. 6087–6101.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Manjirov A. V. and Polyanin A. D. Reference book on integral equation. Factorial press, 2000.</mixed-citation><mixed-citation xml:lang="en">Manjirov A. V. and Polyanin A. D. Reference book on integral equation. Factorial press, 2000.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Ashcroft N., Mermin N., Wei D. Solid State Physics: Revised Edition. Amazon press, 2016.</mixed-citation><mixed-citation xml:lang="en">Ashcroft N., Mermin N., Wei D. Solid State Physics: Revised Edition. Amazon press, 2016.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
