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随着微电子器件尺寸的减小、 工作频率的提高, 金属薄膜中电子与声子将处于非平衡状态, 这将导致微电子器件的热阻增大. 为准确地对这些微电子器件进行热管理, 电子-声子耦合系数的测量变得越来越重要. 本文采用飞秒激光抽运-探测热 反射法研究了不同厚度的金属纳米薄膜的非平衡传热过程. 通过抛物两步模型对实验数据进行拟合, 在拟合过程中引入电子温度与声子温度对反射率影响的比例关系, 从而优化了拟合结果. 通过对不同厚度的Ni膜与Al膜的电子-声子耦合系数的研究, 表明金属薄膜中的电子-声子耦合系数并不随薄膜厚度的改变发生变化. 实验结果还验证了探测光的反射率同时受到电子温度和声子温度的影响, 并通过数据分析量化了电子温度和声子温度对反射率的影响系数.The reduction in size and the increase in speed of microelectronic device make the probability of nonequilibrium electron-phonon phenomena become greater, leading to the increase of thermal resistance in the device. The measurement of electron-phonon coupling factor in material resistance increasingly becomes important for accurate thermal treatment. The femtosecond laser pump and probe method is used for studing the nonequilibrium heat transfer in nano metal films with different thicknesses. Exploring parabolic two-step model (PTS) to fit the experimental data. During the fitting process, we considered the proportional relationship between the changes of electron temperature and phonon temperature, which affects the reflectivity. By studying the different thicknesses of Ni and Al films electron-phonon coupling factors, we find that the electron-phonon coupling factor does not change with film thickness. In addition, the experimental result verifies that the reflectivity of probe laser is affected by electron temperature and phonon temperature at the same time. Through the data analysis, we also get the influence coefficients of electron temperature and phonon temperature on reflectivity.
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Keywords:
- nano metal film /
- electron-phonon coupling /
- femtosecond laser /
- thermoreflectance
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[22] Wang H D, Ma W G, Zhang X, Wang W 2010 Acta Phys. Sin. 59 3856 (in Chinese) [王海东, 马维刚, 张兴, 王玮 2010 物理学报 59 3856]
[23] [24] Ma W G, Wang H D, Zhang X, Wang W 2011 Acta Phys. Sin. 60 064401 (in Chinese) [马维刚, 王海东, 张兴, 王玮 2011 物理学报 60 064401]
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[34] Qiu T Q, Tien C L 1994 Int. J. Heat Mass Transf. 37 2789
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[38] Park W J, Jenkins R J, Butler C P, Abbott G L 1961 J. Appl. Phys. 32 1679
[39] [40] [41] Cahill D G, 1990 Rev. Sci. Instrum. 61 802
[42] [43] Qiu T Q, Tien C L 1993 J. Heat Ttransf. 11 5842
[44] [45] Rosei R, Lynch D W 1972 Phys. Rev. B 5 3883
[46] [47] Brorson S D, Kazeroonian A, Moodera J S, Face D W, Cheng T K, Ippen E P, Dresselhaus M S, Dresselhaus G 1990 Phys. Rev. Lett. 64 2171
[48] Hostetler J L 2001 Ph.D Dissertation (Virginia: University of Virginia)
[49] [50] Hostetler J L, Smith A N, Norris P M 1997 Microsc Thermophys. Eng. 9 237
[51] [52] Zhu J 2011 Ph.D. Dissertation (Beijing: Graduate School of the Chinese Academy of Sciences) (in Chinese) [祝捷 2011 博士学位论文 (北京: 中国科学院研究生院)]
[53] [54] Hanus J, Feinleib J, Scouler W J 1967 Phys. Rev. Lett. 19 16
[55] -
[1] Smith A N, Calame J P 2004 Int. J. Thermophysics 25 409
[2] Chen J K, Latham W P, Beraun J E 2005 J. Laser Appl. 17 63
[3] [4] [5] Miura K, Qiu J R, Inouye H 1997 Appl. Phys. Lett. 77 3329
[6] Kaganov M I, Lifshitz I M, Tanatarov L V 1957 Sov. Phys. JETP 4 173
[7] [8] [9] Anisimov S I, Kapeliovich B L, Perelman T L 1974 Sov. Phys. JETP 39 375
[10] Paddock C A, Eeslay G L 1986 J. Appl. Phys. 60 285
[11] [12] Qiu T Q, Tian C L 1993 J. Heat Transf. Trans. ASME 115 835
[13] [14] [15] Hostetler J L, Smith A N, Czajkowsky D M, Norris P M 1999 Appl. Optics 38 3614
[16] Hopkins P E, klopf J M, Norris P M 2007 Appl. Optics 46 2076
[17] [18] [19] Hang P, Tang D W, Chen G H, Zhu J, Zhao W 2008 J. Eng. Thermophys. 29 297 (in Chinese) [韩鹏, 唐大伟, 程光华, 祝捷, 赵卫 2008 工程热物理学报 29 297]
[20] [21] Zhu J, Tang D W, Chen G H, Hang P, Zhao W, Zhang X 2008 J. Eng. Thermophys. 29 1227 (in Chinese) [祝捷, 唐大伟, 程光华, 韩鹏, 赵卫, 张兴 2008 工程热物理学报 29 1227]
[22] Wang H D, Ma W G, Zhang X, Wang W 2010 Acta Phys. Sin. 59 3856 (in Chinese) [王海东, 马维刚, 张兴, 王玮 2010 物理学报 59 3856]
[23] [24] Ma W G, Wang H D, Zhang X, Wang W 2011 Acta Phys. Sin. 60 064401 (in Chinese) [马维刚, 王海东, 张兴, 王玮 2011 物理学报 60 064401]
[25] [26] Hartland G V 2004 Int. J. Nanotechnol. 1 307
[27] [28] Orlande H R B, Ozisik M N, Tzou D Y 1995 J. Appl. Phys. 78 1843
[29] [30] [31] Hohlfeld J, Wellershoff S S, Gdde J, Conrad U, Jhnke V, Matthias E 2000 Chem. Phys. 251 237
[32] [33] Hopkins P E, Kassebaum J L, Norris P M 2009 J. Appl. Phys. 105 023710
[34] Qiu T Q, Tien C L 1994 Int. J. Heat Mass Transf. 37 2789
[35] [36] [37] Qiu T Q, Tien C L 1994 Int. J. Heat Mass Transf. 37 2799
[38] Park W J, Jenkins R J, Butler C P, Abbott G L 1961 J. Appl. Phys. 32 1679
[39] [40] [41] Cahill D G, 1990 Rev. Sci. Instrum. 61 802
[42] [43] Qiu T Q, Tien C L 1993 J. Heat Ttransf. 11 5842
[44] [45] Rosei R, Lynch D W 1972 Phys. Rev. B 5 3883
[46] [47] Brorson S D, Kazeroonian A, Moodera J S, Face D W, Cheng T K, Ippen E P, Dresselhaus M S, Dresselhaus G 1990 Phys. Rev. Lett. 64 2171
[48] Hostetler J L 2001 Ph.D Dissertation (Virginia: University of Virginia)
[49] [50] Hostetler J L, Smith A N, Norris P M 1997 Microsc Thermophys. Eng. 9 237
[51] [52] Zhu J 2011 Ph.D. Dissertation (Beijing: Graduate School of the Chinese Academy of Sciences) (in Chinese) [祝捷 2011 博士学位论文 (北京: 中国科学院研究生院)]
[53] [54] Hanus J, Feinleib J, Scouler W J 1967 Phys. Rev. Lett. 19 16
[55]
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