Estimation of phonon relaxation time for silicon by means of using the velocity autocorrelation function of atoms in molecular dynamics

• Autorzy: Andriyevsky Bohdan , Maliński M. , Buryło Ł. , Stadnyk V. Y. , Romanuk M. O. , Piekarski J. , Andriyevska L.

Identyfikatory

DOI

10.24425/bpasts.2019.129663

• Języki publikacji: EN

Abstrakty

EN

Results of the ab initio molecular dynamics calculations of silicon crystals are presented by means of analysis of the velocity autocorrelation function and determination of mean phonon relaxation time. The mean phonon relaxation time is crucial for prediction of the phonon-associated coefficient of thermal conductivity of materials. A clear correlation between the velocity autocorrelation function relaxation time and the coefficient of thermal diffusivity has been found. The analysis of the results obtained has indicated a decrease of the velocity autocorrelation function relaxation time t with increase of temperature. The method proposed may be used to estimate the coefficient of ther-mal diffusivity and thermal conductivity of the materials based on silicon and of other wide-bandgap semiconductors. The correlation between kinetic energy fluctuations and relaxation time of the velocity autocorrelation function has been calculated with the relatively high coefficient of determination R2 = 0.9396. The correlation obtained and the corresponding approach substantiate the use of kinetic energy fluctuations for the calculation of values related to heat conductivity in silicon-based semiconductors (coefficients of thermal conductivity and diffusivity).

Słowa kluczowe

EN

silicon; molecular dynamics; relaxation time of the velocity autocorrelation function; coefficient of thermal diffusivity

PL

krzem; dynamika molekularna

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2019
• Tom: Vol. 67, nr 3
• Strony: 651--656
• Opis fizyczny: Bibliogr. 40 poz., tab., rys.

Twórcy

autor

Andriyevsky Bohdan

• Faculty of Electronics and Computer Sciences, Koszalin University of Technology, 2 Śniadeckich St., 75-453 Koszalin, Poland

autor

Maliński M.

• Faculty of Electronics and Computer Sciences, Koszalin University of Technology, 2 Śniadeckich St., 75-453 Koszalin, Poland

autor

Buryło Ł.

• Faculty of Electronics and Computer Sciences, Koszalin University of Technology, 2 Śniadeckich St., 75-453 Koszalin, Poland

autor

Stadnyk V. Y.

• Faculty of Physics, Ivan Franko National University of Lviv, 8 Kyryla i Mefodiya St., 79005 Lviv, Ukraine

autor

Romanuk M. O.

• Faculty of Physics, Ivan Franko National University of Lviv, 8 Kyryla i Mefodiya St., 79005 Lviv, Ukraine

autor

Piekarski J.

• Faculty of Civil Engineering, Environmental and Geodetic Sciences, Koszalin University of Technology, 2 Śniadeckich St., 75-453 Koszalin, Poland

autor

Andriyevska L.

• Faculty of Civil Engineering, Environmental and Geodetic Sciences, Koszalin University of Technology, 2 Śniadeckich St., 75-453 Koszalin, Poland

Bibliografia

• [1] Y. Liang, J. Zhang, M. Li, Y. Guo, and J. Yuan, “Thermal analysis of the heat exchanger for power electronic device with higher power density”, Przegląd Elektrotechniczny, 12a, 328‒332 (2012).
• [2] A. Miaskowski, B. Sawicki, and M. Subramanian, “Single-domain nanoparticle magnetic power losses calibrated with calorimetric measurements”, Bull. Pol. Ac.: Tech., 66, 509‒516 (2018).
• [3] M. Chmielewski and W. Weglewski, “Comparison of experimental and modelling results of thermal properties in Cu-AlN composite materials”, Bull. Pol. Ac.: Tech., 61, 507‒514 (2013).
• [4] K. Gnidzinska, G. De Mey, and A. Napieralski, “Heat dissipation and temperature distribution in long interconnect lines”, Bull. Pol. Ac.: Tech., 58, 119‒124 (2010).
• [5] A. Lidow, J. Strydom, M. de Rooij, and D. Reusch, GaN Transistors for Efficient Power Conversion, WILEY, 2015.
• [6] J. Millan, “IET Circuits”, Devices & System, 1, 372–379, (2007).
• [7] F. Ren and J.C. Zolper (Eds.), Wide Band Gap Electronic Devices, World Scientific, Singapore, 2003.
• [8] L.E. Bell, “Cooling, heating, generating power, and recovering waste heat with thermoelectric systems” Science, 321, 1457‒1461 (2008).
• [9] X. Zhang and L.-D. Zhao, “ Thermoelectric materials: Energy conversion between heat and electricity”, J. Materiomics, 1 92‒105 (2015).
• [10] B. Sothmann, R. Sanchez and A.N. Jordan, “Thermoelectric energy harvesting with quantum dots”, Nanotechnology, 26 032001 (2015).
• [11] E. Guilmeau, A. Maignan, C. Wan, and K. Koumoto, “On the effects of substitution, intercalation, non-stoichiometry and block layer concept in TiS2 based thermoelectrics”, Phys. Chem. Chem. Phys. 17, 24541‒24555 (2015).
• [12] B.C.J. Vineis, A. Shakouri, A. Majumdar, and M.G. Kanatzidis “Nanostructured thermoelectrics: big efficiency gains from small features”, Adv. Mater,. 22, 3970‒3980 (2010.)
• [13] Li. Guanpeng, D. Guangqian, and G. Guoying “ Thermoelectric properties of SnSe2 monolayer” J. Phys.: Condens. Matter, 29 015001‒015007 (2017).
• [14] C. Wan, Y. Wang, W. Norimatsu, M. Kusunoki, and K. Koumoto, “Nanoscale stacking faults induced low thermal conductivity in thermoelectric layered metal sulfides”, 2012 Appl. Phys. Lett., 100, 101913 (2012).
• [15] A.J.H. McGaughey, M. Kaviany, “Phonon Transport in Molecular Dynamics Simulations: Formulation and Thermal Conductivity Prediction”, Advances in Heat Transfer (Edited by George A. Greene, James P. Hartnett†, Avram Bar-Cohen, Young I. Cho), 39 169‒255 (2006).
• [16] S. Stackhouse and L. Stixrude, “Theoretical Methods for Calculating the Lattice Thermal Conductivity of Minerals”, Reviews in Mineralogy & Geochemistry, 71, 253‒269 (2010).
• [17] M.S. Green, “Markoff random processes and the statistical mechanics of time-dependent phenomena. 2. Irreversible processes in fluids”, J. Chem. Phys., 22, 398‒413 (1954).
• [18] R. Kubo, “Statistical-mechanical theory of irreversible processes. 1. General theory and simple applications to magnetic and conduction problems”, J. Phys. Soc. Japan, 12, 570‒586 (1957).
• [19] D.A. McQuarrie, Statistical Mechanics, University Science Books, Sausalito, 2000.
• [20] J. Callaway, “Model for lattice thermal conductivity at low temperature”, Phys. Rev.,113,1046‒51 (1959).
• [21] Y. Zhang, “First-principles Debye-Callaway approach to lattice thermal conductivity”, J Materiomics, 2, 237‒247 (2016).
• [22] B. Andriyevsky, “Comparative molecular dynamics studies of Si, GaN and SiC thermal conductivity”, Przegląd Elektrotechniczny, 9, 5‒8 (2015).
• [23] B. Andriyevsky and V. Stadnyk, “Thermal conductivity of silicon: theoretical first principles study”, Przegląd Elektrotechniczny, 9, 95‒97 (2016).
• [24] B. Andriyevsky, W. Janke, V.Yo. Stadnyk, and M.O. Romanyuk, “Thermal conductivity of silicon doped by phosphorus: ab initio study”, Materials Science-Poland, 35, 717‒724 (2017).
• [25] J.M. Ziman, Electrons and Phonons, Oxford University Press, Oxford, 2001.
• [26] C.J. Glassbrenner and G.A. Slack, “Thermal conductivity of silicon and germanium from 3 K to the melting point”, Phys. Rev., 134, A1058- A1069 (1964).
• [27] B. Andriyevsky, W. Janke, A. Patryn, M. Maliński, V. Stadnyk, and M. Romanyuk, “Ab initio molecular dynamics calculations of heat conductivity for silicon related materials”, Przegląd Elektrotechniczny, 8, 61‒63 (2017).
• [28] G. Kresse and D. Joubert, “From ultrasoft pseudopotentials to the projector augmented-wave method”, Phys. Rev. B, 59, 1758‒1775 (1999);G. Kresse, M. Marsman, and J. Furthmüller, http://cms.mpi.univie.ac.at/vasp/vasp/vasp.html, Vienna, October, 2015.
• [29] P.E. Blöchl, “Projector augmented-wave method”, Phys. Rev. B, 50, 17953‒17979 (1994).,
• [30] T. Róg, K. Murzyn, K. Hinsen, and G. R. Kneller, “nMoldyn: A program package for a neutron scattering oriented analysis of Molecular Dynamics simulations”, J. Comput Chem., 24, 657‒667 (2003).
• [31] O. Madelung, U. Rössler, and M. Schulz (ed.), SpringerMaterials, Silicon (Si) sound velocities, Landolt-Börnstein – Group III Condensed Matter 41A1α (Group IV Elements, IV-IV and III-V Compounds. Part a – Lattice Properties), Springer-Verlag Berlin Heidelberg, 2001.
• [32] B. Abeles, D.S. Beers, G.D. Cody, and J.P. Dismukes, “Thermal conductivity of Ge-Si alloys at high temperature”, Phys. Rev., 125, 44-& (1962).
• [33] H.R. Shanks, P.D. Maycock, P.H. Sidles, and G.C. Danielson, “Thermal conductivity of silicon from 300 to 1400 degrees K”, Phys. Rev., 130, 1743‒1748 (1963).
• [34] H.J. McSkimin, “Measurement of elastic constants at low temperatures by means of ultrasonic waves – data for silicon and germanium single crystals, and for fused silica”, J. Appl. Phys., 24, 988‒997 (1953).
• [35] F.J. Morin and J.P. Maita, “Electrical properties of silicon containing arsenic and boron”, Phys. Rev., 96, 28‒35 (1954).
• [36] S.P. Nikanorov, Yu.A. Burenkov, and A.V. Stepanov, “Elastic properties of silicon”, Sov. Phys. Solid State, 13, 2516‒2519 (1972).
• [37] Z. Tian, K. Esfarjani, J. Shiomi, A.S. Henry, and G. Chen, “On the importance of optical phonons to thermal conductivity in nanostructures”, Appl. Phys. Lett., 99, 053122‒3 (2011).
• [38] D.M. Olsen Heggø, “Ab initio molecular dynamics simulation of phosphorus diffusion in silicon”, MSc thesis, University of Oslo, 2012.
• [39] M.E. Tuckerman, Statistical Mechanics: Theory and Molecular Simulations, Oxford University Press, 2010.
• [40] D. Frenkel, Understanding Molecular Simulation: from algorithms to applications, Academic Press, 1996.