氧化鋁(Al₂O₃)因其卓越的力學強度、高硬度、化學穩定性與良好電絕緣性，已成為電子封裝高頻絕緣介質、硬質合金切削刀具塗層、催化劑載體及生醫陶瓷等多領域的關鍵材料。薄膜形式的氧化鋁更具備優異的熱穩定性與耐磨性，可應用於微電子器件的散熱層與高溫環境下的熱屏障。
本研究採用非平衡態分子動力學方法，並基於開源模擬軟體LAMMPS，模擬中選用Streitz–Mintmire 勢能確切描述鋁和氧原子間相互作用，通過在薄膜兩端施加溫度梯度誘發熱流，對氧化鋁薄膜進行熱傳導係數計算，分別考慮溫度及尺度效應下熱傳導係數的變化，結果發現溫度在600 K左右出現轉折，低溫區隨溫度上升，高溫區則因聲子散射增強而下降，在25〜100 nm尺度下呈彈道型傳輸，當尺度超過125 nm後則轉為擴散型傳輸，並將模擬的數據與文獻比較，以驗證模擬結果的準確。
研究揭示熱傳導係數嚴重受到缺陷率的影響，當缺陷率增至10 %時，無論是α型還是γ型氧化鋁，熱傳導係數皆顯著下降，而在低缺陷率下熱傳導係數對溫度的敏感性提高，且低溫300 K時10 %缺陷率的下降幅度比高溫900 K時更為明顯，代表在低溫下缺陷率的增加對熱傳導係數的影響遠大於高溫時的影響。

Aluminium oxide (Al₂O₃) due to its outstanding mechanical strength, high hardness, chemical stability, and excellent electrical insulation, has become a key material in various fields such as high-frequency dielectric insulation in electronic packaging, hard alloy cutting tool coatings, catalyst supports, and biomedical ceramics. In thin-film form, Al₂O₃ exhibits superior thermal stability and wear resistance, making it suitable for use as a heat dissipation layer in microelectronic devices and as a thermal barrier in high-temperature environments.
In this study, the non-equilibrium molecular dynamics (NEMD) method is employed based on the open-source simulation software LAMMPS. The Streitz–Mintmire potential is chosen to accurately describe the interactions between aluminum and oxygen atoms. By imposing a temperature gradient across both ends of the thin film to induce heat flux, the thermal conductivity of aluminium oxide thin films is calculated. The effects of temperature and scale on the thermal conductivity are investigated. The results reveal a turning point around 600 K: in the low-temperature region, the thermal conductivity increases with temperature, while in the high-temperature region it decreases due to enhanced phonon scattering. At thicknesses between 25 and 100 nm, transport exhibits ballistic behavior, but transitions to diffusive transport when the scale exceeds 125 nm. Simulation data are compared with literature values to verify the accuracy of the results.
The study demonstrates that thermal conductivity is significantly affected by defect content. When the defect rate increases to 10 %, the thermal conductivity drops considerably for both α and γ phase Al₂O₃. At lower defect rates, the sensitivity of thermal conductivity to temperature increases. Notably, at 300 K, an increase in defect rate to 10 % leads to a greater decline in thermal conductivity than at 900 K, indicating that the impact of defect rate on thermal conductivity is much more pronounced at low temperatures than at high temperatures.

[1] H. Wang and M. Sen, “Analysis of the 3-omega method for thermal conductivity measurement,” International Journal of Heat and Mass Transfer, vol.52, no. 7–8, pp.2102–2109, Mar. 2009.
[2] Y. Kogure and Y. Hiki, “Simultaneous measurement of low-temperature specific heat and thermal conductivity by temperature-wave method,” Japanese Journal of Applied Physics, vol.12, no. 6, pp.814–822, Jun. 1973.
[3] D. G. Cahill, “Analysis of heat flow in layered structures for time-domain thermoreflectance,” Review of Scientific Instruments, vol.75, no. 12, pp.5119–5122, Dec. 2004.
[4] J.-U. Lee, D. Yoon, H. Kim, S. W. Lee, and H. Cheong, “Thermal conductivity of suspended pristine graphene measured by Raman spectroscopy,” Physical Review B, vol.83, no. 8, p.081419, Feb. 2011.
[5] G. P. Celata, Heat transfer and fluid flow in microchannels. Begell House Inc., 2004.
[6] C. Schröder, V. Vikhrenko, and D. Schwarzer, “Molecular dynamics simulation of heat conduction through a molecular chain,” The Journal of Physical Chemistry A, vol.113, no. 51, pp.14039–14051, Dec. 2009.
[7] Y. Ran and V. Bertola, “Achievements and prospects of molecular dynamics simulations in thermofluid sciences,” Energies, vol.17, no. 4, p.888, Feb. 2024.
[8] M. Puligheddu, Y. Xia, M. Chan, and G. Galli, “Computational prediction of lattice thermal conductivity: a comparison of molecular dynamics and Boltzmann transport approaches,” Physical Review Materials, vol.3, no. 8, p.085401, Aug. 2019.
[9] S.-N. Li and B.-Y. Cao, “Fractional-order heat conduction models from generalized Boltzmann transport equation,” Philosophical Transactions of the Royal Society A, vol.378, no. 2172, p.20190280, May 2020.
[10] H. Wang, Y. Xu, M. Shimono, Y. Tanaka, and M. Yamazaki, “Molecular dynamics simulation of thermal conductivity of silicon thin film,” Materials Transactions, vol.48, no. 9, pp.2419–2421, 2007.
[11] I. Levin and D. Brandon, “Metastable alumina polymorphs: crystal structures and transition sequences,” Journal of the American Ceramic Society, vol.81, no. 8, pp.1995–2012, Aug. 1998.
[12] G. C. Kennedy, “Phase relations in the system Al_2 O_3-H_2 O at high temperatures and pressures,” American Journal of Science, vol.257, pp.563–573, 1959.
[13] X. Krokidis, P. Raybaud, A.-E. Gobichon, B. Rebours, P. Euzen, and H. Toulhoat, “Theoretical study of the dehydration process of boehmite to γ-alumina,” The Journal of Physical Chemistry B, vol.105, no. 22, pp.5121–5130, Jun. 2001.
[14] R. B. Bagwell, G. L. Messing, and P. R. Howell, “The formation of α-Al_2 O_3 from θ-Al_2 O_3: the relevance of a "critical size" and: diffusional nucleation or "synchro-shear"?,” Journal of Materials Science, vol.36, no. 7, pp.1833–1841, 2001.
[15] Y. M. Chiang, D. P. Birnie, III, and W. D. Kingery, Physical ceramics-principles for ceramic science and engineering. John Wiley & Sons Inc., New York, 1997.
[16] E.-L. Andreici Eftimie and N. M. Avram, “Absorption spectra, ligand field parameters and g factors of Cr^(3+)doped α-Al_2 O_3 laser crystal: ab initio calculations,” Physica Scripta, vol.95, no. 4, p.044005, Feb. 2020.
[17] H. P. Pinto, R. M. Nieminen, and S. D. Elliott, “Ab initio study of γ - Al_2 O_3 surfaces,” Physical Review B, vol.70, no. 12, p.125402, Sep. 2004.
[18] H. O. Ayoola, S. D. House, C. S. Bonifacio, K. Kisslinger, W. A. Saidi, and J. C. Yang, “Evaluating the accuracy of common γ - Al_2 O_3 structure models by selected area electron diffraction from high-quality crystalline γ - Al_2 O_3,” Acta Materialia, vol.182, pp.257–266, Jan. 2020.
[19] S. Chen, L. Tao, L. Zeng, and R. Hong, “RF magnetron sputtering aluminum oxide film for surface passivation on crystalline silicon wafers,” International Journal of Photoenergy, vol.2013, pp.1–5, 2013.
[20] K. Tadaszak, K. Nitsch, T. Piasecki, and W. M. Posadowski, “Properties of aluminium oxide thin films deposited in high effective reactive pulsed magnetron sputtering process,” Mater Sci-Pol, vol.30, no. 4, pp.323–328, Dec. 2012.
[21] J. A. García-Valenzuela, R. Rivera, A. B. Morales-Vilches, L. G. Gerling, A. Caballero, J. M. Asensi, C. Voz, J. Bertomeu, and J. Andreu, “Main properties of Al_2 O_3 thin films deposited by magnetron sputtering of an Al_2 O_3 ceramic target at different radio-frequency power and argon pressure and their passivation effect on p-type c-Si wafers,” Thin Solid Films, vol.619, pp.288–296, Nov. 2016.
[22] Y. Zhao, W. Wu, Y. Cheng, and W. Yan, “Optimization of processing parameters and adhesive properties of aluminum oxide thin-film transition layer for aluminum substrate thin-film sensor,” Micromachines, vol.13, no. 12, p.2115, Nov. 2022.
[23] B. A. Sperling, B. Kalanyan, and J. E. Maslar, “Atomic layer deposition of Al_2 O_3 using trimethylaluminum and H_2 O: the kinetics of the H_2 O half-cycle,” The Journal of Physical Chemistry C, vol.124, no. 5, pp.3410–3420, Feb. 2020.
[24] S.-C. Lin, C.-C. Wang, C.-L. Tien, F.-C. Tung, H.-F. Wang, and S.-H. Lai, “Fabrication of aluminum oxide thin-film devices based on atomic layer deposition and pulsed discrete feed method,” Micromachines, vol.14, no. 2, p.279, Jan. 2023.
[25] H.-Y. Li, Y.-F. Liu, Y. Duan, Y.-Q. Yang, and Y.-N. Lu, “Method for aluminum oxide thin films prepared through low temperature atomic layer deposition for encapsulating organic electroluminescent devices,” Materials, vol.8, no. 2, pp.600–610, Feb. 2015.
[26] N. Ozer, J. P. Cronin, and A. P. Tomsia, “Preparation of amorphous Al_2 O_3 films by the sol-gel process,” SPIE’s International Symposium on Optical Science, Engineering, and Instrumentation, pp.77–83, Oct. 1999.
[27] Y. Kobayashi, T. Ishizaka, and Y. Kurokawa, “Preparation of alumina films by the sol-gel method,” J Mater Sci, vol.40, no. 2, pp.263–283, Jan. 2005.
[28] Balakrishnan G, Priyatosh Kumar Ray, Ranjeet Kumar, Ranjeet Kumar Chaudhary, Ramesh Kumar, Praveen Kumar roy, and Gopinath R, “Preparation of alumina 〖(Al〗_2 O_3) thin films by sol-gel dip coating and characterization,” International Journal of Current Advanced Research, vol.6, no. 9, pp.6099–6103, Sep. 2017.
[29] 武鼎铭, “Analysis on influencing factors of α-phase transformation of alumina,” JAPC, vol.11, no. 01, pp.14–20, 2022.
[30] M. Stokey, R. Korlacki, M. Hilfiker, S. Knight, S. Richter, V. Darakchieva, R. Jinno, Y. Cho, H. G. Xing, D. Jena, Y. Oshima, K. Khan, E. Ahmadi, and M. Schubert, “Infrared dielectric functions and Brillouin zone center phonons of α - Ga_2 O_3 compared to α -Al_2 O_3,” Physical Review Materials, vol.6, no. 1, p.014601, Jan. 2022.
[31] M.-Y. Lee, “Nano-2D (γ-)Al_2 O_3 powder prepared using boehmite as the starting material.,” Department of Resources Engineering, National Cheng Kung University, pp.1–112, 2023.
[32] G. L. Harris, Properties of silicon carbide. IET, 1995.
[33] M. Asheghi, Y. K. Leung, S. S. Wong, and K. E. Goodson, “Phonon-boundary scattering in thin silicon layers,” Applied Physics Letters, vol.71, no. 13, pp.1798–1800, Sep. 1997.
[34] C. J. Glassbrenner and G. A. Slack, “Thermal conductivity of silicon and germanium from 3°K to the melting point,” Physical Review, vol.134, no. 4A, pp.A1058–A1069, May 1964.
[35] B. Latour and Y. Chalopin, “Distinguishing between spatial coherence and temporal coherence of phonons,” Physical Review B, vol.95, no. 21, p.214310, Jun. 2017.
[36] L. J. Sham and J. M. Ziman, “The electron-phonon interaction,” Solid State Physics, vol.15, Elsevier, 1963, pp.221–298.
[37] P. L. Bhatnagar, E. P. Gross, and M. Krook, “A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component systems,” Physical Review, vol.94, no. 3, pp.511–525, May 1954.
[38] R. F. Pawula, “Approximation of the linear boltzmann equation by the Fokker-Planck equation,” Physical Review, vol.162, no. 1, pp.186–188, Oct. 1967.
[39] F. X. Alvarez and D. Jou, “Memory and nonlocal effects in heat transport: From diffusive to ballistic regimes,” Applied Physics Letters, vol.90, no. 8, p.083109, Feb. 2007.
[40] C.-W. Wu, “The study on thermal conductivity of perfect and defective silicon carbide nanofilms and the influence of phonon transport behavior using non- equilibrium molecular dynamics,” Department of Mechanical Engineering, National Cheng Kung University, pp.1–135, 2020.
[41] T. Yamamoto and K. Watanabe, “Nonequilibrium Green’s function approach to phonon transport in defective carbon nanotubes,” Physical Review Letters, vol.96, no. 25, p.255503, Jun. 2006.
[42] C. Ren, Z. Xu, W. Zhang, Y. Li, Z. Zhu, and P. Huai, “Theoretical study of heat conduction in carbon nanotube hetero-junctions,” Physics Letters A, vol.374, no. 17–18, pp.1860–1865, Apr. 2010.
[43] R. L. Xu, M. Muñoz Rojo, S. M. Islam, A. Sood, B. Vareskic, A. Katre, N. Mingo, K. E. Goodson, H. G. Xing, D. Jena, and E. Pop, “Thermal conductivity of crystalline AlN and the influence of atomic-scale defects,” Journal of Applied Physics, vol.126, no. 18, p.185105, Nov. 2019.
[44] 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, Aug. 1959.
[45] H. A. L. Filipe and L. M. S. Loura, “Molecular dynamics simulations: advances and applications,” Molecules, vol.27, no. 7, p.2105, Mar. 2022.
[46] T. Arima, S. Yamasaki, Y. Inagaki, and K. Idemitsu, “Evaluation of thermal properties of UO_2 and PUO_2 by equilibrium molecular dynamics simulations from 300 to 2000 K,” Journal of Alloys and Compounds, vol.400, no. 1–2, pp.43–50, Sep. 2005.
[47] N. Galamba, C. A. Nieto De Castro, and J. F. Ely, “Thermal conductivity of molten alkali halides from equilibrium molecular dynamics simulations,” The Journal of Chemical Physics, vol.120, no. 18, pp.8676–8682, May 2004.
[48] 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, Feb. 1994.
[49] 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, Apr. 2002.
[50] J. E. Lennard-Jones, “Cohesion,” Proc. Phys. Soc., vol.43, no. 5, pp.461–482, Sep. 1931.
[51] P. M. Morse, “Diatomic molecules according to the wave mechanics. II. vibrational levels,” Physical Review, vol.34, no. 1, pp.57–64, Jul. 1929.
[52] J. Tersoff, “Empirical interatomic potential for silicon with improved elastic properties,” Physical Review B, vol.38, no. 14, pp.9902–9905, Nov. 1988.
[53] M. S. Daw and M. I. Baskes, “Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals,” Physical Review B, vol.29, no. 12, pp.6443–6453, Jun. 1984.
[54] M. I. Baskes, J. S. Nelson, and A. F. Wright, “Semiempirical modified embedded-atom potentials for silicon and germanium,” Physical Review B, vol.40, no. 9, pp.6085–6100, Sep. 1989.
[55] F. H. Streitz and J. W. Mintmire, “Electrostatic potentials for metal-oxide surfaces and interfaces,” Physical Review B, vol.50, no. 16, pp.11996–12003, Oct. 1994.
[56] D. Wolf, P. Keblinski, S. R. Phillpot, and J. Eggebrecht, “Exact method for the simulation of coulombic systems by spherically truncated, pairwise r−1 summation,” The Journal of Chemical Physics, vol.110, no. 17, pp.8254–8282, May 1999.
[57] S. Alavi, J. W. Mintmire, and D. L. Thompson, “Molecular dynamics simulations of the oxidation of aluminum nanoparticles,” The Journal of Physical Chemistry B, vol.109, no. 1, pp.209–214, Jan. 2005.
[58] P. Puri and V. Yang, “Thermo-mechanical behavior of nano aluminum particles with oxide layers during melting,” J Nanopart Res, vol.12, no. 8, pp.2989–3002, Oct. 2010.
[59] W. G. Hoover, “Canonical dynamics: equilibrium phase-space distributions,” Physical Review A, vol.31, no. 3, pp.1695–1697, Mar. 1985.
[60] J. M. Haile, I. Johnston, A. J. Mallinckrodt, and S. McKay, “Molecular dynamics simulation: elementary methods,” Computers in Physics, vol.7, no. 6, pp.625–625, Nov. 1993.
[61] J. W. Gibbs, “On the equilibrium of heterogeneous substances,” 2012.
[62] S. Nosé, “A molecular dynamics method for simulations in the canonical ensemble,” Molecular Physics, vol.100, no. 1, pp.191–198, Jan. 2002.
[63] J. M. Haile, Molecular dynamics simulation: elementary methods. John Wiley & Sons, Inc., 1992.
[64] H. Hernandez, “Standard Maxwell-Boltzmann distribution: definition and properties,” 2017.
[65] G. Bussi, D. Donadio, and M. Parrinello, “Canonical sampling through velocity rescaling,” The Journal of Chemical Physics, vol.126, no. 1, p.014101, Jan. 2007.
[66] 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, no. 8, pp.3684–3690, Oct. 1984.
[67] W. G. Hoover, “Computational statistical mechanics,” Elsevier, 2012.
[68] S. A. Adelman and J. D. 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, Mar. 1976.
[69] H. C. Andersen, “Molecular dynamics simulations at constant pressure and/or temperature,” The Journal of Chemical Physics, vol.72, no. 4, pp.2384–2393, Feb. 1980.
[70] 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, no. 8, pp.3684–3690, Oct. 1984.
[71] M. Parrinello and A. Rahman, “Polymorphic transitions in single crystals: a new molecular dynamics method,” Journal of Applied Physics, vol.52, no. 12, pp.7182–7190, Dec. 1981.
[72] S. Nosé, “A unified formulation of the constant temperature molecular dynamics methods,” The Journal of Chemical Physics, vol.81, no. 1, pp.511–519, Jul. 1984.
[73] F. Müller-Plathe, “A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity,” The Journal of Chemical Physics, vol.106, no. 14, pp.6082–6085, Apr. 1997.
[74] 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, Feb. 1994.
[75] L. Verlet, “Computer "experiments" on classical fluids. I. thermodynamical properties of Lennard-Jones molecules,” Physical Review, vol.159, no. 1, pp.98–103, Jul. 1967.
[76] 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, Jan. 1982.
[77] C. W. Gear, “The automatic integration of ordinary differential equations,” Communications of the ACM, vol.14, no. 3, pp.176–179, Mar. 1971.
[78] A. Cai, L. Yang, J. Chen, T. Xi, S. Xin, and W. Wu, “Thermal conductivity of anodic alumina film at (220 to 480) K by laser flash technique,” Journal of Chemical & Engineering Data, vol.55, no. 11, pp.4840–4843, Nov. 2010.
[79] I. Stark, M. Stordeur, and F. Syrowatka, “Thermal conductivity of thin amorphous alumina films,” Thin Solid Films, vol.226, no. 1, pp.185–190, Apr. 1993.
[80] M. E. DeCoster, K. E. Meyer, B. D. Piercy, J. T. Gaskins, B. F. Donovan, A. Giri, N. A. Strnad, D. M. Potrepka, A. A. Wilson, M. D. Losego, and P. E. Hopkins, “Density and size effects on the thermal conductivity of atomic layer deposited TiO_2 and Al_2 O_(3 )thin films,” Thin Solid Films, vol.650, pp.71–77, Mar. 2018.
[81] J.-T. Yang, “Study on measuring thermal conductivity for atomic layer deposition of aluminium oxide thin films by temperature wave analysis method,” Department of Mechanical Engineering, National Cheng Kung University, pp.1–113, 2024.
[82] B. Dongre, J. Carrete, N. Mingo, and G. K. H. Madsen, “Ab initio lattice thermal conductivity of bulk and thin-film α-Al_2 O_(3 ),” MRS Communications, vol.8, no. 3, pp.1119–1123, Sep. 2018.