周晓,杨凯科,周光辉

• 1:湖南师范大学物理系

摘要(Abstract)：

后摩尔时代微纳电子器件尺寸不断缩小和厚度逐渐减薄，研究固体材料热管理和理解热传导微观物理机制具有极其重要的意义。本文介绍晶格热导率的四种计算方法，从理论上综合分析了Slack模型、Boltzmann方程、Wigner热输运和Green-Kubo方法。在考虑晶格非谐效应和声子散射作用情况下，结合第一性原理计算，分别获得了温度依赖的半导体硅(Si)和热电材料碲化铅(PbTe)的热导率，并与相应实验结果进行了比较，讨论了上述四种方法产生误差的原因。该研究可为理解和探索一些晶体和非晶材料热输运性质提供理论依据。

关键词(KeyWords)： 声子;非谐效应;热传导;晶格热导率;第一性原理计算

Abstract:

Keywords:

基金项目(Foundation): 湖南师范大学教学改革研究项目(2024年资助)

作者(Author): 周晓,杨凯科,周光辉

参考文献(References)：

• [1] MOORE G E.Cramming more components onto integrated circuits[J].Proceedings of the IEEE 1998,86(1):82-85.
• [2] WALDROP M M.The chips are down for Moore's law[J].Nature,2016,530(7589):144-147.
• [3] GIRI A,HOPKINS P E.Achieving a better heat conductor[J].Nature Materials,2020,19(5):482-484.
• [4] GU X,WEI Y,YIN X,LI B,YANG R.Phononic thermal properties of two-dimensional materials[J].Review of Modern Physics,2018,90(4):041002.
• [5] GEBAUER R,CAR R.Kinetic theory of quantum transport at the nanoscale[J].Physical Review B,2004,70(12):125324.
• [6] KANG J S,LI M,WU H,et al.Experimental observation of high thermal conductivity in boron arsenide[J].Science,2018,361(6402):575-578.
• [7] ZHAO L D,LO S H,ZHANG Y,et al.Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals[J].Nature,2014,508(7496):373-377.
• [8] LEE S,ESFARJANI K,LUO T,et al.Resonant bonding leads to low lattice thermal conductivity[J].Nature Communications,2014,5(1):3525.
• [9] FRENKEL J.On the transformation of light into heat in solids[J].Physical Review,1931,37(10):17-44.
• [10] DEBYE P.Zur theorie der spezifischen warmen[J].Annalen der Physik,1912,344(14):789-839.
• [11] ZIMAN J M.Electrons and phonons:The theory of transport phenomena in solids[M].New York:Oxford University Press,2001.
• [12] 黄昆，韩汝琦.固体物理学[M].北京：高等教育出版社，1988.
• [13] WANG B,Ge W.Historical survey on Born-Huang equations:In memory of 100 anniversary of professor Kun Huang' Birthday[J].Physics and Engineering,2019,29 (5):3-7.
• [14] PAN Z,LU G,LI X,et al.Remarkable heat conduction mediated by non-equilibrium phonon polaritons[J].Nature,2023,623(7986):307-312.
• [15] TOGO A,CHAPUT L,TANAKA I.Distributions of phonon lifetimes in Brillouin zones[J].Physical Review B,2015,91(9):094306.
• [16] WARD A,BROIDO D A.Intrinsic phonon relaxation times from first-principles studies of the thermal conductivities of Si and Ge[J].Physical Review B,2010,81(8):085205.
• [17] OMINI M,SPARAVIGNA A.Beyond the isotropic-model approximation in the theory of thermal conductivity[J].Physical Review B,1996,53(14):9064.
• [18] WANG A,SHENG Y.-F,BAO H.Recent advances in thermal transport theory of metals[J].Acta Physica Sinica 2024,73(3):037201.
• [19] FANG Y,SHEN H,CUI X,HUANG Z,FENG R,LIAO D,PANG X.Heat conductivity of poor heat conductor by plane heat source method with constant heating rate under quasi-steady state and its COMSOL simulation[J].Physics and Engineering,2023,33(5):87-94.
• [20] SLACK G A.Nonmetallic crystals with high thermal conductivity[J].Journal of Physics and Chemistry of Solids,1973,34(2):321-335.
• [21] LI W,CARRETE J,KATCHO N A,et al.ShengBTE:A solver of the Boltzmann transport equation for phonons[J].Computer Physics Communications,2014,185(6):1747-1758.
• [22] HAN Z,YANG X,LI W,FENG T,RUAN X.FourPhonon:An extension module to ShengBTE for computing four-phonon scattering rates and thermal conductivity[J].Computer Physics Communications,2022,270:108179.
• [23] SHI H.-X,YANG K.-K,LUO J.-W.Origin of abnormal thermal conductivity in group III-V boron compound semiconductors[J].Acta Physica Sinica 2021,70(14):147302.
• [24] SIMONCELLI M,MARZARI N,MAURI F.Unified theory of thermal transport in crystals and glasses[J].Nature Physics,2019,15(8):809-813.
• [25] SIMONCELLI M,MARZARI N,MAURI F.Wigner Formulation of thermal transport in solids[J].Physical Review X,2022,12(4):041011.
• [26] CARBOGNO C,RAMPRASAD R,SCHEFFLER M,Ab initio Green-Kubo approach for the thermal conductivity of solids[J].Physical Review Letters,2017,118(17):175901.
• [27] MARCOLONGO A,UMARI P,BARONI S,Microscopic theory and quantum simulation of atomic heat transport[J].Nature Physics,2016,12(1):80-84.
• [28] GIANNOZZI P,BARONI S,BONINI N,et al.QUANTUM ESPRESSO:A modular and open-source software project for quantum simulations of materials[J].Journal of Physics:Condensed Matter,2009,21(39):395502.
• [29] KOHN W,SHAM L J.Self-consistent equations including exchange and correlation effects[J].Physical Review,1965,140(4A):A1133-A1138.
• [30] PERDEW J P,BURKE K,ERNZERHOF M.Generalized gradient approximation made simple[J].Physical Review Letters,1996,77(18):3865-3868.
• [31] GUO F,WANG Y,YIN G.The influence of the different pseudopotentials on calculations of the phonon spectrum for graphene:A first-principles study[J].Physics and Engineering,2016,26(5):66-70.
• [32] MONKHORST H J,PACK J D.Special points for Brillouin-zone integrations[J].Physical Review B,1976,13(12):5188.
• [33] BARONI S,DE GIRONCOLI S,DAL CORSO A,et al.Phonons and related crystal properties from density-functional perturbation theory[J].Reviews of Modern Physics,2001,73(2):515.
• [34] BORN M,HUANG K.Dynamical theory of crystal lattices[M].London:Oxford University Press,1954.
• [35] GLASSBRENNER C J,SLACK G.A.Thermal conductivity of silicon and germanium from 3°K to the melting point[J].Physical Review,1964,134(4A):A1058-A1069.
• [36] QIU B,BAO H,ZHANG G,et al.Molecular dynamics simulations of lattice thermal conductivity and spectral phonon mean free path of PbTe:Bulk and nanostructures[J].Computational Materials Science,2012,53(1):278-285.
• [37] ZHANG Y,KE X,CHEN C,et al.Thermodynamic properties of PbTe,PbSe,and PbS:First-principles study[J].Physical Review B,2009,80(2):024304.
• [38] MORELLI D T,JOVOVIC V,HEREMANS J P.Intrinsically minimal thermal conductivity in cubic I-V-VI2 semiconductors[J].Physical Review Letters,2008,101(3):035901.
• [39] HE J,GIRARD S N,KANATZIDIS M G,et al.Microstructure-lattice thermal conductivity correlation in nanostructured PbTe0.7S0.3 thermoelectric materials[J].Advanced Functional Materials,2010,20(5):764-772.