Prof. Konstantin Nemchenko 1

Talk: "Diffusive boundary reflection as a factor in formation of heat flows in conductors of different dimensions and cross-sections"

Co-workers: J. Amrit2, Ye. Niemchenko1, S. Rogova1, T. Vikhtynska1
1 V.N.Karazin Kharkiv National University, 61022, Kharkiv, Ukraine
2 LISN, Université Paris-Saclay, CNRS, 91405, Orsay, France

The report presents the results of studies of the phonon flows formation in conductors of different shapes and dimensions. The main attention is paid to the diffuse reflection of phonons from the boundaries, as the main factor that determines the presence of thermal resistance of samples [1]. As a result of solving the integral equations for phonon flows in the ballistic mode [2], the influence of the conductor sizes on the temperature distribution inside along the samples was determined. This made it possible to determine the dependences of heat flows and, consequently, thermal conductivity coefficients on the sizes of conductors of different dimensions and different cross-sections. In particular, two-dimensional conductors of nanoribbons and graphene films, and three-dimensional conductors with a circular and rectangular cross-section were considered. In addition, two physically different experimental settings were considered. In the first case, the situation was studied when an external temperature gradient was applied along the conductor. Such an experimental setting takes place in conductors that are on massive substrates that form an external temperature gradient. In the second setting, external temperatures are specified at the ends of the conductor. This approach is used to describe suspended conductors, for example, when studying nanowires, nanoribbons, graphene films, or three-dimensional conductors with a given temperature difference at their end.

The results obtained are valid for the ballistic mode of phonon motion, which assumes that phonons do not interact with each other, and the thermal resistance is determined only by diffuse scattering of phonons on the walls, which allows for back reflection of phonons. This situation is realized for samples at low temperatures, when the phonon-phonon interaction is very weak. It is also possible at sufficiently high temperatures, including room temperatures, for nanofilms or nanowires, as well as semiconductors of sufficiently small sizes.

The report discusses the comparison of the results of previous theoretical [3 – 5] and numerical studies, carried out with experimental data [6], and discusses alternative approaches to describing the thermal conductivity of these systems.

  • [1] J. Amrit, K.E.Nemchenko, T.G.Vikhtinskaya, J. Appl. Phys., 129, 085105 (2021).
  • [2] J. Amrit, T. Medintseva, Ye. Nemchenko, K. Nemchenko, M. Spotar, S. Rogova, T. Vikhtinskaya, Low Temp. Phys., 49, 961 (2023).
  • [3] H.B.G. Casimir, Physica, 5, 495 (1938).
  • [4] T. Klitsner, J. E. VanCleve, H. E. Fischer, and R. O. Pohl, Phys. Rev. B, 38, 7576 (1988).
  • [5] M. Perlmutter, R. Siegel, J. Heat Transfer, 85, 55-62 (1963).
  • [6] X. Xu, L. Pereira, Y. Wang, et al. Nat Commun., 5, 3689 (2014).

Acknowledgements: This work was supported by the project “Remote Research Grants for Ukrainian Researchers” that has received funding through the EURIZON project, which is funded by the European Union under grant agreement No.871072.