本研究主要以非平衡態分子動力學模擬方法探討奈米碳管、矽及矽鍺奈米線的介面熱阻與聲子平均自由徑。於奈米碳管的研究中，首先設定不同自由層長度之奈米碳管，觀察其長度對熱傳導係數及熱阻的影響，並探討奈米碳管的熱傳行為。接著調整控溫層及自由層原子質量以研究介面熱阻隨原子質量的變化，最後以介面熱阻及熱傳導係數計算奈米碳管之聲子平均自由徑。於矽奈米線的研究中，首先觀察自由層長度對矽奈米線熱傳導係數及熱阻造成的影響，再調整熱流控制區及自由層的原子質量並探討原子質量對介面熱阻造成的變化。接著於矽奈米線中以不同濃度摻雜鍺原子，並調整熱流控制區及自由層原子質量以探討不同摻雜濃度下原子質量對介面熱阻造成的影響。最後再以介面熱阻及熱傳導係數計算矽及矽鍺奈米線之聲子平均自由徑。
於奈米碳管的研究中發現其熱傳導係數與熱阻隨長度增加而上升，並發現存在彈道型傳輸，且藉由調整控溫區及自由層原子質量發現介面熱阻及聲子平均自由徑皆隨原子質量的變化而上升，且介面熱阻變化趨勢與聲學不匹配模型計算之反射率相近。於矽及矽奈米線的研究中也發現了熱傳導係數與熱阻隨自由層長度增加而上升的情形，同樣存在彈道型傳輸，矽及矽鍺奈米線之介面熱阻及聲子平均自由徑也隨熱流控溫區及自由層原子質量改變而增加，此外聲子平均自由徑也隨著摻雜濃度上升而增加，介面熱阻的變化趨勢也與聲學不匹配模型計算之反射率相近，可見聲學不匹配模型可以解釋本研究中介面熱阻的變化。

In this study, the interface thermal resistance and phonon mean free path of carbon nanotubes (CNTs), silicon nanowires (Si NWs), and silicon-germanium nanowires (SiGe NWs) were investigated using the non-equilibrium molecular dynamics simulation method.
For the investigation of CNTs, CNTs with charity of (4, 4) were created, and CNTs of different lengths were set up to observe the relationship between length and thermal conductivity, as well as thermal resistance. and to study the thermal transport behavior. Subsequently, the variation of interfacial thermal resistance was investigated by changing the atomic mass of atoms in the temperature-controlled and free regions, and the reflectivity calculated by the acoustic mismatch model (AMM) was used to compare with the interfacial thermal resistance.
In the study of Si NWs and SiGe NWs, nanowires of different lengths were first set up to observe the relationship between length and thermal conductivity as well as thermal resistance. Subsequently, the variation of interfacial thermal resistance was investigated by changing the atomic mass in the temperature-controlled and free regions, and the reflectivity was compared with the interfacial thermal resistance. Then, Ge atoms were doped into the Si NWs, and the interfacial thermal resistance was calculated using the same method, comparing the variation of interfacial thermal resistance under different doping concentrations, and then comparing the interfacial thermal resistance with the reflectivity.
In the studies of CNTs, Si NWs, and SiGe NWs, it was found that the thermal conductivity and thermal resistance increased with the length. Ballistic transport was observed in these structures. Calculations revealed that the interfacial thermal resistance and phonon mean free path increased with the atomic mass. The trend of interfacial thermal resistance variation was found to be similar to the reflectance calculated from the acoustic mismatch model, indicating that the interfacial thermal resistance values can be predicted using reflectance. Additionally, it was observed that the phonon mean free path increased with the doping concentration of Ge atoms.

[1] S. Lepri, R. Livi, and A. Politi, "Heat conduction in chains of nonlinear oscillators," Physical Review Letters, vol. 78, pp. 1986, 1997.
[2] A. Dhar, "Heat transport in low-dimensional systems," Advances in Physics, vol. 57, pp. 457-537, 2008.
[3] A. Dhar, "Heat conduction in the disordered harmonic chain revisited," Physical Review Letters, vol. 86, pp. 5882, 2001.
[4] B. W. Li, H. Zhao, and B. B. Hu, "Can disorder induce a finite thermal conductivity in 1D lattices?" Physical Review Letters, vol. 86, pp. 63, 2001.
[5] K. Aoki and D. Kusnezov, "Fermi-Pasta-Ulam β model: boundary jumps, Fourier's law, and scaling" Physical Review Letters, vol. 86, pp. 4029, 2001.
[6] M. Khalkhali, F. Khoeini, and A. Rajabpour, "Thermal transport in silicene nanotubes: Effects of length, grain boundary and strain," International Journal of Heat and Mass Transfer, vol. 134, pp. 503-510, 2019.
[7] J. Wang and H. Xie, "Molecular dynamic investigation on the structures and thermal properties of carbon nanotube interfaces," Applied Thermal Engineering, vol. 88, pp. 347-352, 2015.
[8] S. Maruyama, "A molecular dynamics simulation of heat conduction in finite length SWNTs," Physica B, vol. 323, pp. 193-195, 2002.
[9] J. F. Moreland, "The disparate thermal conductivity of carbon nanotubes and diamond nanowires studied by atomistic simulation," Microscale Thermophysical Engineering, vol. 8, pp. 61-69, 2004.
[10] G. Zhang and B. Li, "Thermal conductivity of nanotubes revisited: Effects of chirality, isotope impurity, tube length, and temperature," The Journal of Chemical Physics, vol. 123, no. 11, pp. 114714, 2005.
[11] J. A. Thomas, R. M. Iutzi, and A. J. H. McGaughey, "Thermal conductivity and phonon transport in empty and water-filled carbon nanotubes," Physical Review B, vol. 81, pp. 045413, 2010.
[12] X. Zhang, J. Zhang, and M. Yang, "Molecular dynamics study on the thermal conductivity of bilayer graphene with nitrogen doping," Solid State Communications, vol. 309, pp. 113845, 2020.
[13] H. Zhong and J. R. Lukes, "Interfacial thermal resistance between carbon nanotubes: Molecular dynamics simulations and analytical thermal modeling," Physical Review B, vol. 74, pp. 125403, 2006.
[14] I.-L. Chang, C.-S. Li, G.-S. Wang, C.-L. Wu, and C.-W. Chang, "Does equilibrium or nonequilibrium molecular dynamics correctly simulate thermal transport properties of carbon nanotubes? "Physical Review Materials, vol. 4, pp. 036001, 2020.
[15] H. Dong, Z. Fan, P. Qian, T. Ala-Nissila, and Y. Su, "Thermal conductivity reduction in carbon nanotube by fullerene encapsulation: A molecular dynamics study," Carbon, vol. 161, pp. 800-808, 2020.
[16] C. Sevik, H. Sevinçli, G. Cuniberti, and T. Çağın, "Phonon engineering in carbon nanotubes by controlling defect concentration," Nano Letters, vol. 11, pp. 4505-5098, 2011.
[17] C.-W. Zhang, H. Zhou, Y. Zeng, L. Zheng, Y.-L. Zhan, and K.-D. Bi, "A reduction of thermal conductivity of non-periodic Si/Ge superlattice nanowire: Molecular dynamics simulation," Progress in Polymer Science, vol. 132, pp. 681-688, 2019.
[18] Z. Han and A. Fina "Thermal conductivity of carbon nanotubes and their polymer nanocomposites: A review," Progress in Polymer Science, vol. 36, pp. 914-944, 2011.
[19] Y. Chen, D. Li, J. Yang, Y. Wu, J. R. Lukes, and A. Majumdar, "Molecular dynamics study of the lattice thermal conductivity of Kr/Ar superlattice nanowires," Physica B: Condensed Matter, vol. 349, Issues 1-4, pp. 270-280, 2004.
[20] M. Hu and D. Poulikakos, "Si/Ge superlattice nanowires with ultralow thermal conductivity, " Nano Letters, vol. 12, Issues 11, pp. 5487-5494, 2012.
[21] X.-W. Zhou, R. E. Jones, C. J. Kimmer, J. C. Duda, and P. E. Hopkins, "Relationship of thermal boundary conductance to structure from an analytical model plus molecular dynamics simulations," Physical Review B, vol. 87, pp. 094303, 2013s.
[22] B. J. Alder and T. E. Wainwright, "Studies in molecular dynamics. I. General method," The Journal of Chemical Physics, vol. 31, no. 2, pp. 459-466, 1959.
[23] J. E. Jones, "On the determination of molecular fields.—II. From the equation of state of a gas," Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, vol. 106, no. 738, pp. 463-477, 1924.
[24] R. Saito, R. Matsuo, T. Kimura, G. Dresselhaus, and M. Dresselhaus, "Anomalous potential barrier of double-wall carbon nanotube," Chemical Physics Letters, vol. 348, no. 3-4, pp. 187-193, 2001.
[25] L. Lindsay and D. Broido, "Optimized Tersoff and Brenner empirical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene," Physical Review B, vol. 81, no. 20, pp. 205441, 2010.
[26] J. Haile, I. Johnston, A. J. Mallinckrodt, and S. McKay, "Molecular dynamics simulation: elementary methods," Computers in Physics, vol. 7, no. 6, pp. 625-625, 1993.
[27] P. H. Hünenberger, "Thermostat algorithms for molecular dynamics simulations," Advanced Computer Simulation, pp. 105-149, 2005.
[28] T. Dumitrica, "Trends in Computational Nanomechanics: Transcending Length and Time Scales," Springer Science & Business Media, 2010.
[29] G. Bussi, D. Donadio, and M. Parrinello, "Canonical sampling through velocity rescaling," The Journal of Chemical Physics, vol. 126, no. 1, pp. 014101, 2007.
[30] S. Nosé, "A unified formulation of the constant temperature molecular dynamics methods," The Journal of Chemical Physics, vol. 81, no. 1, pp. 511-519, 1984.
[31] D. J. Evans and B. L. Holian, "The nose–hoover thermostat," The Journal of Chemical Physics, vol. 83, no. 8, pp. 4069-4074, 1985.
[32] W. G. Hoover, "Canonical dynamics: Equilibrium phase-space distributions," Physical Review A, vol. 31, no. 3, pp. 1695, 1985.
[33] H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, and J. R. Haak, "Molecular dynamics with coupling to an external bath," The Journal of Chemical Physics, vol. 81, pp. 3684-3690, 1984.
[34] S. Adelman and J. Doll, "Generalized Langevin equation approach for atom/solid‐surface scattering: General formulation for classical scattering off harmonic solids," The Journal of Chemical Physics, vol. 64, no. 6, pp. 2375-2388, 1976.
[35] T. Schneider and E. Stoll, "Molecular-dynamics study of a three-dimensional one-component model for distortive phase transitions," Physical Review B, vol. 17, no. 3, pp. 1302, 1978.
[36] T. Schlick, "Molecular modeling and simulation: an interdisciplinary guide," Springer, 2010.
[37] G.-J. Hu and B.-Y. Cao, "Molecular dynamics simulations of heat conduction in multi-walled carbon nanotubes," Molecular Simulation, vol. 38, no. 10, pp. 823-829, 2012.
[38] L. Verlet, "Computer" experiments" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules," Physical Review, vol. 159, no. 1, pp. 98, 1967.
[39] W. C. Swope, H. C. Andersen, P. H. Berens, and K. R. Wilson, "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters," The Journal of Chemical Physics, vol. 76, no. 1, pp. 637-649, 1982.
[40] B. Quentrec and C. Brot, "New method for searching for neighbors in molecular dynamics computations," Journal of Computational Physics, vol. 13, no. 3, pp. 430-432, 1973.
[41] T. N. Heinz and P. H. Hünenberger, "A fast pairlist‐construction algorithm for molecular simulations under periodic boundary conditions," Journal of Computational Chemistry, vol. 25, no. 12, pp. 1474-1486, 2004.
[42] K.-C. Fang, C.-I. Weng, and S.-P. Ju, "An investigation into the structural features and thermal conductivity of silicon nanoparticles using molecular dynamics simulations," Nanotechnology, vol. 17, no. 15, pp. 3909, 2006.
[43] J.-P. Hansen and I. R. McDonald, "Theory of simple liquids: with applications to soft matter," Academic Press, 2013.
[44] D. Frenkel, B. Smit, and M. A. Ratner, "Understanding molecular simulation: from algorithms to applications," Academic Press, 1996.
[45] T. Ikeshoji and B. Hafskjold, "Non-equilibrium molecular dynamics calculation of heat conduction in liquid and through liquid-gas interface," Molecular Physics, vol. 81, no. 2, pp. 251-261, 1994.
[46] P. K. Schelling, S. R. Phillpot, and P. Keblinski, "Comparison of atomic-level simulation methods for computing thermal conductivity," Physical Review B, vol. 65, no. 14, pp. 144306, 2002.
[47] E. T. Swartz and R. O. Pohl, "Thermal boundary resistance," Reviews of Modern Physics, vol. 61, pp. 605, 1989.
[48] I. M. Khalitnikov, "Heat exchange between a solid body and helium I," Journal of Experimental and Theoretical Physics, vol. 22, pp.687, 1952.
[49] S. J. Stuart, A. B. Tutein, and J. A. Harrison, "A reactive potential for hydrocarbons with intermolecular interactions," Journal of Chemical Physics, vol. 112, pp. 6472-6486, 2000.