本研究採用分子動力學（molecular dynamics, MD）模擬，利用 LAMMPS 搭配 Tersoff 多體勢能函數建立非晶態氮化矽模型，並透過熔融–淬火程序製備非晶態結構，再藉由徑向分布函數（radial distribution function, RDF）及密度分析驗證模型之合理性。其後，採用非平衡態分子動力學（non-equilibrium molecular dynamics, NEMD）建立穩態溫度梯度，依據傅立葉定律計算熱傳導係數，系統性探討不同薄膜厚度（尺寸效應）及不同溫度（溫度效應）對熱傳導特性之影響，並結合速度自相關函數（velocity autocorrelation function, VACF）與聲子狀態密度（phonon density of states, PDOS）分析振動模態特性，以探討其對熱傳輸之貢獻。
研究結果顯示，所建立之非晶態氮化矽模型密度約為 3.14 g/cm³，室溫熱傳導係數約為 2.54 W/(m·K)，與文獻中緻密無氫非晶態氮化矽之量測結果相符。在尺寸效應方面，薄膜厚度由 10 nm 增加至 70 nm 時，熱傳導係數由 2.54 W/(m·K) 緩升至 2.76 W/(m·K)，增幅約 8.9%，呈現微弱但一致之正向尺寸效應，PDOS 分析顯示此趨勢主要源自低頻傳播子振動模態隨厚度增加而增多。在溫度效應方面，100～700 K 範圍內熱傳導係數介於 2.46～2.63 W/(m·K)，整體僅呈現小幅波動，近乎與溫度無關；此平坦特徵反映非晶態氮化矽之熱傳輸以擴散子主導，同時亦為古典分子動力學模擬之結果，而真實材料於低溫下熱傳導係數之下降則須引入量子修正方能重現。
本研究藉由分子動力學模擬排除界面熱阻及製程差異等實驗因素之影響，在受控條件下系統性分析非晶態氮化矽薄膜之熱傳導特性，建立尺寸效應、溫度效應與微觀振動模態間之關聯性，增進對非晶態氮化矽熱傳輸機制之理解，並可作為後續非晶態薄膜熱傳輸研究與熱管理應用之基礎。

Amorphous silicon nitride (a-Si3N4) is widely used as a dielectric and passivation material in microelectronic devices, where efficient heat dissipation is essential for reliability. However, the thermal conductivity reported for a-Si3N4 varies considerably because of interfacial thermal resistance and differences in film composition and density. In this study, molecular dynamics (MD) simulations were performed to determine the intrinsic thermal conductivity of a-Si3N4 thin films under well-controlled conditions. A stoichiometric, hydrogen-free amorphous model was constructed in LAMMPS using a Tersoff many-body potential and the melt–quench method, and validated by the radial distribution function (RDF) and mass density. Non-equilibrium molecular dynamics (NEMD) was then used to establish a steady-state temperature gradient, and the thermal conductivity was calculated from Fourier’s law. The effects of film thickness and temperature were systematically investigated, and the heat-transport mechanisms were analyzed using the velocity autocorrelation function (VACF) and the phonon density of states (PDOS). The model exhibited a density of about 3.14 g/cm³ and a room-temperature thermal conductivity of about 2.5 W/m·K, consistent with dense hydrogen-free amorphous silicon nitride. As the thickness increased from 10 to 70 nm, the thermal conductivity rose only slightly, from 2.54 to 2.76 W/m·K, and remained nearly constant over 100～700 K. These results indicate that heat transport in amorphous silicon nitride is dominated by diffusons.

[1] G. T. Barkema and N. Mousseau, “High-quality continuous random networks,” Phys. Rev. B, vol. 62, no. 8, pp. 4985–4990, 2000.
[2] M. F. Thorpe, “Continuous deformations in random networks,” J. Non-Cryst. Solids, vol. 57, no. 3, pp. 355–370, 1983.
[3] G. Chen, Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons, Oxford, UK: Oxford Univ. Press, 2005.
[4] C. Kittel, Introduction to Solid State Physics, 8th ed., Hoboken, NJ, USA: John Wiley & Sons, 2005.
[5] P. B. Allen and J. L. Feldman, “Thermal conductivity of amorphous silicon,” Phys. Rev. B, vol. 48, no. 17, pp. 12581–12597, 1993.
[6] E. H. Sondheimer, “The mean free path of electrons in metals,” Adv. Phys., vol. 1, no. 1, pp. 1–42, 1952.
[7] S. Bai, Z. Tang, Z. Huang, and J. Yu, “Thermal characterization of Si3N4 thin films using transient thermoreflectance technique,” IEEE Trans. Ind. Electron., vol. 56, no. 8, pp. 3238–3243, 2009.
[8] M. Bogner, A. Hofer, G. Benstetter, H. Gruber, and R. Y. Q. Fu, “Differential 3ω method for measuring thermal conductivity of AlN and Si3N4 thin films,” Thin Solid Films, vol. 591, pp. 267–270, 2015.
[9] W. Zhu, G. Zheng, S. Cao, and H. He, “Thermal conductivity of amorphous SiO2 thin film: A molecular dynamics study,” Sci. Rep., vol. 8, Art. no. 10537, 2018.
[10] J. L. Braun et al., “Hydrogen effects on the thermal conductivity of delocalized vibrational modes in amorphous silicon nitride (a-SiNx:H),” Phys. Rev. Mater., vol. 5, no. 3, Art. no. 035604, 2021.
[11] Y. Wang, Z. Fan, P. Qian, M. A. Caro, and T. Ala-Nissila, “Quantum-corrected thickness-dependent thermal conductivity in amorphous silicon predicted by machine-learning molecular dynamics simulations,” Phys. Rev. B, vol. 107, no. 5, Art. no. 054303, 2023.
[12] S.-M. Lee and D. G. Cahill, “Heat transport in thin dielectric films,” J. Appl. Phys., vol. 81, no. 6, pp. 2590–2595, 1997.
[13] H. Ftouni, C. Blanc, D. Tainoff, A. D. Fefferman, M. Defoort, K. J. Lulla, J. Richard, E. Collin, and O. Bourgeois, “Thermal conductivity of silicon nitride membranes is not sensitive to stress,” Phys. Rev. B, vol. 92, no. 12, Art. no. 125439, 2015.
[14] T. Liang, P. Ying, K. Xu, Z. Ye, C. Ling, Z. Fan, and J. Xu, “Mechanisms of temperature-dependent thermal transport in amorphous silica from machine-learning molecular dynamics,” Phys. Rev. B, vol. 108, no. 18, Art. no. 184203, 2023.
[15] M. S. Green, “Markoff random processes and the statistical mechanics of time-dependent phenomena. II. Irreversible processes in fluids,” J. Chem. Phys., vol. 22, no. 3, pp. 398–413, 1954.
[16] R. Kubo, “Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems,” J. Phys. Soc. Jpn., vol. 12, no. 6, pp. 570–586, 1957.
[17] T. Ikeshoji and B. Hafskjold, “Non-equilibrium molecular dynamics calculation of heat conduction in liquid and through liquid-gas interface,” Mol. Phys., vol. 81, no. 2, pp. 251–261, 1994.
[18] F. Müller-Plathe, “A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity,” J. Chem. Phys., vol. 106, no. 14, pp. 6082–6085, 1997.
[19] J. Tersoff, “New empirical approach for the structure and energy of covalent systems,” Phys. Rev. B, vol. 37, no. 12, pp. 6991–7000, 1988.
[20] M. Ippolito and S. Meloni, “Atomistic structure of amorphous silicon nitride from classical molecular dynamics simulations,” Phys. Rev. B, vol. 83, no. 16, p. 165209, 2011.
[21] X. Yang, B. Tian, M. Jian, M. Wu, W. Li, J. Jiang, Z. Guo, and L. Yang, “Molecular dynamics simulation of uniaxial stretching for silicon nitride deposited by PECVD,” Appl. Surf. Sci., vol. 682, p. 161696, 2025.
[22] J. M. Haile, I. Johnston, A. J. Mallinckrodt, and S. McKay, “Molecular dynamics simulation: elementary methods,” Comput. Phys., vol. 7, no. 6, p. 625, 1993.
[23] J. W. Gibbs, “On the equilibrium of heterogeneous substances,” Am. J. Sci., vol. s3-16, no. 96, pp. 441–458, 1878.
[24] G. Bussi, D. Donadio, and M. Parrinello, “Canonical sampling through velocity rescaling,” J. Chem. Phys., vol. 126, no. 1, p. 14101, 2007.
[25] 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,” J. Chem. Phys., vol. 81, no. 8, pp. 3684–3690, 1984.
[26] S. Nosé, “A unified formulation of the constant temperature molecular dynamics methods,” J. Chem. Phys., vol. 81, no. 1, pp. 511–519, 1984.
[27] W. G. Hoover, “Canonical dynamics: equilibrium phase-space distributions,” Phys. Rev. A, vol. 31, no. 3, pp. 1695–1697, 1985.
[28] P. Langevin, “Sur la théorie du mouvement brownien,” C. R. Acad. Sci. (Paris), vol. 146, pp. 530–533, 1908.
[29] M. Parrinello and A. Rahman, “Polymorphic transitions in single crystals: a new molecular dynamics method,” J. Appl. Phys., vol. 52, no. 12, pp. 7182–7190, 1981.
[30] H. C. Andersen, “Molecular dynamics simulations at constant pressure and/or temperature,” J. Chem. Phys., vol. 72, no. 4, pp. 2384–2393, 1980.
[31] L. Verlet, “Computer ‘experiments’ on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules,” Phys. Rev., vol. 159, no. 1, pp. 98–103, 1967.
[32] 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,” J. Chem. Phys., vol. 76, no. 1, pp. 637–649, 1982.
[33] S. Plimpton, “Fast parallel algorithms for short-range molecular dynamics,” J. Comput. Phys., vol. 117, no. 1, pp. 1–19, 1995.
[34] A. P. Thompson et al., “LAMMPS – a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales,” Comput. Phys. Commun., vol. 271, Art. no. 108171, 2022.
[35] A. Stukowski, “Visualization and analysis of atomistic simulation data with OVITO – the Open Visualization Tool,” Modelling Simul. Mater. Sci. Eng., vol. 18, no. 1, Art. no. 015012, 2010.
[36] L. Beliaev, E. Shkondin, A. Laurynenka, and O. Takayama, “Optical, structural and composition properties of silicon nitride films deposited by reactive radio-frequency sputtering, low pressure and plasma-enhanced chemical vapor deposition,” Thin Solid Films, vol. 763, Art. no. 139568, 2022.
[37] F. de Brito Mota, J. F. Justo, and A. Fazzio, “Structural properties of amorphous silicon nitride,” Phys. Rev. B, vol. 58, no. 13, pp. 8323–8328, 1998.
[38] A. Dasmahapatra and P. Kroll, “Modeling amorphous silicon nitride: A comparative study of empirical potentials,” Comput. Mater. Sci., vol. 148, pp. 165–175, 2018.
[39] S. Cai, J. Mou, L. Zhang, and B. Cheng, “X-ray radial distribution function study of the bonding structure of nanometer amorphous silicon nitride,” Acta Phys. Sin., vol. 41, no. 10, pp. 1608–1613, Oct. 1992.
[40] P. E. Hopkins, J. R. Serrano, L. M. Phinney, S. P. Kearney, T. W. Grasser, and C. T. Harris, “Criteria for cross-plane dominated thermal transport in multilayer thin film systems during modulated laser heating,” J. Heat Transfer, vol. 132, no. 8, Art. no. 081302, Aug. 2010.
[41] N. Tambo, Y. Liao, C. Zhou, E. M. Ashley, K. Takahashi, P. F. Nealey, Y. Naito, and J. Shiomi, “Ultimate suppression of thermal transport in amorphous silicon nitride by phononic nanostructure,” Sci. Adv., vol. 6, no. 39, p. eabc0075, 2020.