Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Deep learning molecular dynamics simulation on microwave high-temperature dielectric function of silicon nitride

Li Zhi-Qiang Tan Xiao-Yu Duan Xin-Lei Zhang Jing-Yi Yang Jia-Yue

Citation:

Deep learning molecular dynamics simulation on microwave high-temperature dielectric function of silicon nitride

Li Zhi-Qiang, Tan Xiao-Yu, Duan Xin-Lei, Zhang Jing-Yi, Yang Jia-Yue
PDF
HTML
Get Citation
  • Silicon nitride (β-Si3N4) is a most promising thermal wave-transparent material. The accurate measurement of its high-temperature dielectric function is essential to solving the “black barrier” problem of hypersonic vehicles and accelerating the design of silicon nitride-based thermal wave-transparent materials. Direct experimental measurement at high temperature is a difficult job and the accuracy of classical molecular dynamics (CMD) simulations suffers the choice of empirical potential. In this work, we build a β-Si3N4 model on a nanoscale, train the deep learning potential (DLP) by using first-principles data, and apply the deep potential molecular dynamics (DPMD) to simulate the polarization relaxation process. The predicted energy and force by DLP are excellently consistent with first-principles calculations, which proves the high accuracy of DLP. The RMSEs for β-Si3N4 are quite low (0.00550 meV/atom for energy and 7.800 meV/Å for force). According to the Cole-Cole formula, the microwave dielectric function in the temperature range of 300–1000 K is calculated by using the deep learning molecular dynamics method. Compared with the empirical potential, the computational results of the DLP are consistent with the experimental results in the sense of order of magnitude. It is also found that the DPMD performs well in terms of computational speed. In addition, a mathematical model of the temperature dependence of the relaxation time is established to reveal the pattern of relaxation time varying with temperature. The high-temperature microwave dielectric function of silicon nitride is calculated by implementing large-scale and high-precision molecular dynamics simulations. It provides fundamental data for promoting the application of silicon nitride in high-temperature thermal transmission.
      Corresponding author: Yang Jia-Yue, jy_yang@sdu.edu.cn
    [1]

    Mehra N, Singh R K, Bera S C 2015 Prog. Electromagn. Res. B 63 161Google Scholar

    [2]

    Hartunian R A, Stewart G E, Fergason S D 2007 Aerospace Corp. 5309 1

    [3]

    Jayaraman B, Shyy W 2008 Prog. Aerosp. Sci. 44 139Google Scholar

    [4]

    钟汶帆, 吴孟强 2014 压电与声光 36 1004

    Zhong W F, Wu M Q 2014 Piezoelectr. Acoustoopt. 36 1004

    [5]

    Zhang T, Zhang S R, Wu M Q, Sang W J, Gao Z P, Li Z P 2007 J. Electron. Sci. Technol. 5 4

    [6]

    Neumann M 1983 Mol. Phys. 50 841Google Scholar

    [7]

    Neumann M, Steinhauser O 1983 Chem. Phys. Lett. 102 508Google Scholar

    [8]

    Neumann M, Steinhauser O 1984 Chem. Phys. Lett. 106 563Google Scholar

    [9]

    Afify N D, Sweatman M B 2018 J. Chem. Phys. 148 024508Google Scholar

    [10]

    Cardona J, Fartaria R, Sweatman M B, Lue L 2016 Mol. Simul. 42 370Google Scholar

    [11]

    Blank T B, Brown S D, Calhoun A W, Doren D J 1998 J. Chem. Phys. 103 4129

    [12]

    Behler J, Parrinello M 2007 Phys. Rev. Lett. 98 146401Google Scholar

    [13]

    Bartók A P, Payne M C, Kondor R, Csányi G 2010 Phys. Rev. Lett. 104 136403Google Scholar

    [14]

    Behler J 2011 J. Chem. Phys. 134 074106Google Scholar

    [15]

    Novikov I S, Gubaev K, Podryabinkin E V, Shapeev A V 2021 Mach. Learn. Sci. Technol. 2 025002Google Scholar

    [16]

    Zhang L, Han J, Wang H, Car R, Weinan E 2018 Phys. Rev. Lett. 120 143001Google Scholar

    [17]

    Chen W, Li L S 2021 J. Appl. Phys. 129 244104Google Scholar

    [18]

    Kühne T D, Iannuzzi M, Del Ben M, Rybkin V V, Seewald P, Stein F, Laino T, Khaliullin R Z, Schütt O, Schiffmann F, Golze D, Wilhelm J, Chulkov S, Bani-Hashemian M H, Weber V, Borštnik U, Taillefumier M, Jakobovits A S, Lazzaro A, Pabst H, Müller T, Schade R, Guidon M, Andermatt S, Holmberg N, Schenter G K, Hehn A, Bussy A, Belleflamme F, Tabacchi G, Glöß A, Lass M, Bethune I, Mundy C J, Plessl C, Watkins M, VandeVondele J, Krack M, Hutter J 2020 J. Chem. Phys. 152 194103Google Scholar

    [19]

    VandeVondele J, Krack M, Mohamed F, Parrinello M, Chassaing T, Hutterc J 2005 Comput. Phys. Commun. 167 103Google Scholar

    [20]

    Del Ben M, Hutter J, VandeVondele J 2012 J. Chem. Theory Comput. 8 4177Google Scholar

    [21]

    Wang H, Zhang L, Han J, E W 2018 Comput. Phys. Commun. 228 178Google Scholar

    [22]

    Abadi M, Barham P, Chen J, Chen Z, Davis A, Dean J, Devin M, Ghemawat S, Irving G, Isard M, Kudlur M, Levenberg J, Monga R, Moore S, Murray D G, Steiner B, Tucker P, Vasudevan V, Warden P, Wicke M, Yu Y, Zheng X 2015 arXiv:1605.08695 [cs.DC]

    [23]

    Behler J 2011 Phys. Chem. Chem. Phys. 13 17930Google Scholar

    [24]

    Jia W, Wang H, Chen M, Lu D, Car R, E W, Zhang L 2018 Adv. Neural Inf. Process. Syst. 31 1Google Scholar

    [25]

    Kingma DP, Ba J 2017 arXiv. 1412 6980

    [26]

    Plimpton S 1995 J. Comput. Phys. 117 1Google Scholar

    [27]

    Martyna G J, Klein M L, Tuckerman M 1992 J. Chem. Phys. 97 2635Google Scholar

    [28]

    Evans D J, Holian B L 1985 J. Chem. Phys. 83 4069Google Scholar

    [29]

    Tersoff J 1989 Phys. Rev. B 39 5566Google Scholar

    [30]

    Tersoff J 1988 Phys. Rev. B 37 6991Google Scholar

    [31]

    Cole K S, Cole R H 1941 J. Chem. Phys. 9 341Google Scholar

    [32]

    Petousis I, Mrdjenovich D, Ballouz E, Liu M, Winston D, Chen W, Graf T, Schladt T D, Persson K A, Prinz F B 2017 Sci. Data 4 160134Google Scholar

    [33]

    Wang M, Zhang Y, Liu X, Wang X 2013 Ceram. Int. 39 2069Google Scholar

    [34]

    Shao S, Luo H, Deng L, He J, Huang S 2018 AIP Adv. 8 075127Google Scholar

    [35]

    Saleem A, Zhang Y J, Gong H Y, Majeed M K, Lin X, Jing J, Sheng M M, Zhao C C 2020 J. Mater. Sci. Mater. Electron. 31 2918Google Scholar

    [36]

    Yang J Y, Xu M, Liu L H 2016 J. Quant. Spectrosc. Radiat. Transf. 184 111Google Scholar

  • 图 1  深度学习势训练流程: 主要包含AIMD计算采样、深度神经网络训练以及深度学习分子动力学模拟三部分

    Figure 1.  DLP training process: AIMD computational sampling, DNN training, and DPMD simulation.

    图 2  β-Si3N4的晶体结构 (a) 用于第一性原理分子动力学计算的体系(原子个数为140个); (b) 用于深度学习分子动力学模拟的体系(原子个数为2200个), 其中绿色原子代表硅原子, 红色原子代表氮原子

    Figure 2.  Crystal structure of β-Si3N4: (a) The system for first-principles molecular dynamics calculations (140 atoms); (b) the system for deep potential molecular dynamics simulations (2200 atoms). The green atoms represent silicon atoms and the red atoms for nitrogen atoms.

    图 3  (a) 第一性原理计算体系能量和深度学习势计算体系能量对比关系图; (b)—(d) 第一性原理计算原子受力和深度学习势计算原子受力对比关系图. 其中图中直线代表y=x

    Figure 3.  (a) Comparison between the energy calculated by first-principles and that by the deep learning potential; (b)–(d) comparison between the forces on the atoms calculated by first-principles and those by the deep learning potential. The straight line in the figure represents y = x.

    图 4  (a)—(c) 300 K温度下DPMD与AIMD计算径向分布函数对比图; (d)—(f) 1000 K温度下DPMD与AIMD模拟径向分布函数对比图

    Figure 4.  (a)−(c) Comparison of radial distribution function between DPMD and AIMD simulations at 300 K; (d)−(f) comparison of radial distribution function between DPMD and AIMD simulations at 1000 K.

    图 5  运用深度学习分子动力学计算的700 K温度下氮化硅偶极矩自相关函数 (a) 偶极矩自相关函数随时间的变化; (b) 偶极矩自相关极值点对数值随时间的变化

    Figure 5.  Silicon nitride dipole moment autocorrelation function at 700 K calculated by the deep learning potential: (a) Dipole moment autocorrelation function versus time; (b) dipole moment autocorrelation polar point logarithm versus time.

    图 6  (a) β-Si3N4在不同温度时的频率相关介电函数实部; (b) β-Si3N4在不同温度时的频率相关介电函数虚部. 其中文献[34]仅给出了实部值, 未给出虚部值. 文献[35]给出了8—12 GHz频率范围内的介电函数实验测量值

    Figure 6.  (a) Real part and (b) imaginary part of frequency-dependent dielectric function of β-Si3N4 at varying temperatures. Note that only the real part is given in Ref. [34]. The values of dielectric function in the frequency range of 8–12 GHz are given in Ref. [35]

    图 7  弛豫时间随温度变化曲线, 其中蓝色直线代表弛豫时间温度依变性模型, 红色散点代表不同温度下弛豫时间变化曲线

    Figure 7.  Relaxation time variation curves with temperature. The blue straight line corresponds to relaxation time temperature dependence model, and the red scattered points represent relaxation time variation curves at different temperatures.

    图 8  DPMD (Nvidia RTX 3080 GPU计算)与AIMD (48个Intel Xeon Platinum 9242 CPU计算)计算速度结果

    Figure 8.  Computational speed of DPMD (running with a Nvidia RTX 3080 GPU) and AIMD calculations (running with 48 Intel Xeon Platinum 9242 CPU cores).

    表 1  不同温度条件下的弛豫时间

    Table 1.  Relaxation time under different temperatures by DLP and Tersoff potential.

    温度/K弛豫时间/ps
    DLPTersoff potential
    30029.2752.89
    40026.4833.17
    50016.1436.08
    60014.3927.87
    7007.1416.76
    8006.0420.05
    9004.150.88
    10002.830.27
    DownLoad: CSV
  • [1]

    Mehra N, Singh R K, Bera S C 2015 Prog. Electromagn. Res. B 63 161Google Scholar

    [2]

    Hartunian R A, Stewart G E, Fergason S D 2007 Aerospace Corp. 5309 1

    [3]

    Jayaraman B, Shyy W 2008 Prog. Aerosp. Sci. 44 139Google Scholar

    [4]

    钟汶帆, 吴孟强 2014 压电与声光 36 1004

    Zhong W F, Wu M Q 2014 Piezoelectr. Acoustoopt. 36 1004

    [5]

    Zhang T, Zhang S R, Wu M Q, Sang W J, Gao Z P, Li Z P 2007 J. Electron. Sci. Technol. 5 4

    [6]

    Neumann M 1983 Mol. Phys. 50 841Google Scholar

    [7]

    Neumann M, Steinhauser O 1983 Chem. Phys. Lett. 102 508Google Scholar

    [8]

    Neumann M, Steinhauser O 1984 Chem. Phys. Lett. 106 563Google Scholar

    [9]

    Afify N D, Sweatman M B 2018 J. Chem. Phys. 148 024508Google Scholar

    [10]

    Cardona J, Fartaria R, Sweatman M B, Lue L 2016 Mol. Simul. 42 370Google Scholar

    [11]

    Blank T B, Brown S D, Calhoun A W, Doren D J 1998 J. Chem. Phys. 103 4129

    [12]

    Behler J, Parrinello M 2007 Phys. Rev. Lett. 98 146401Google Scholar

    [13]

    Bartók A P, Payne M C, Kondor R, Csányi G 2010 Phys. Rev. Lett. 104 136403Google Scholar

    [14]

    Behler J 2011 J. Chem. Phys. 134 074106Google Scholar

    [15]

    Novikov I S, Gubaev K, Podryabinkin E V, Shapeev A V 2021 Mach. Learn. Sci. Technol. 2 025002Google Scholar

    [16]

    Zhang L, Han J, Wang H, Car R, Weinan E 2018 Phys. Rev. Lett. 120 143001Google Scholar

    [17]

    Chen W, Li L S 2021 J. Appl. Phys. 129 244104Google Scholar

    [18]

    Kühne T D, Iannuzzi M, Del Ben M, Rybkin V V, Seewald P, Stein F, Laino T, Khaliullin R Z, Schütt O, Schiffmann F, Golze D, Wilhelm J, Chulkov S, Bani-Hashemian M H, Weber V, Borštnik U, Taillefumier M, Jakobovits A S, Lazzaro A, Pabst H, Müller T, Schade R, Guidon M, Andermatt S, Holmberg N, Schenter G K, Hehn A, Bussy A, Belleflamme F, Tabacchi G, Glöß A, Lass M, Bethune I, Mundy C J, Plessl C, Watkins M, VandeVondele J, Krack M, Hutter J 2020 J. Chem. Phys. 152 194103Google Scholar

    [19]

    VandeVondele J, Krack M, Mohamed F, Parrinello M, Chassaing T, Hutterc J 2005 Comput. Phys. Commun. 167 103Google Scholar

    [20]

    Del Ben M, Hutter J, VandeVondele J 2012 J. Chem. Theory Comput. 8 4177Google Scholar

    [21]

    Wang H, Zhang L, Han J, E W 2018 Comput. Phys. Commun. 228 178Google Scholar

    [22]

    Abadi M, Barham P, Chen J, Chen Z, Davis A, Dean J, Devin M, Ghemawat S, Irving G, Isard M, Kudlur M, Levenberg J, Monga R, Moore S, Murray D G, Steiner B, Tucker P, Vasudevan V, Warden P, Wicke M, Yu Y, Zheng X 2015 arXiv:1605.08695 [cs.DC]

    [23]

    Behler J 2011 Phys. Chem. Chem. Phys. 13 17930Google Scholar

    [24]

    Jia W, Wang H, Chen M, Lu D, Car R, E W, Zhang L 2018 Adv. Neural Inf. Process. Syst. 31 1Google Scholar

    [25]

    Kingma DP, Ba J 2017 arXiv. 1412 6980

    [26]

    Plimpton S 1995 J. Comput. Phys. 117 1Google Scholar

    [27]

    Martyna G J, Klein M L, Tuckerman M 1992 J. Chem. Phys. 97 2635Google Scholar

    [28]

    Evans D J, Holian B L 1985 J. Chem. Phys. 83 4069Google Scholar

    [29]

    Tersoff J 1989 Phys. Rev. B 39 5566Google Scholar

    [30]

    Tersoff J 1988 Phys. Rev. B 37 6991Google Scholar

    [31]

    Cole K S, Cole R H 1941 J. Chem. Phys. 9 341Google Scholar

    [32]

    Petousis I, Mrdjenovich D, Ballouz E, Liu M, Winston D, Chen W, Graf T, Schladt T D, Persson K A, Prinz F B 2017 Sci. Data 4 160134Google Scholar

    [33]

    Wang M, Zhang Y, Liu X, Wang X 2013 Ceram. Int. 39 2069Google Scholar

    [34]

    Shao S, Luo H, Deng L, He J, Huang S 2018 AIP Adv. 8 075127Google Scholar

    [35]

    Saleem A, Zhang Y J, Gong H Y, Majeed M K, Lin X, Jing J, Sheng M M, Zhao C C 2020 J. Mater. Sci. Mater. Electron. 31 2918Google Scholar

    [36]

    Yang J Y, Xu M, Liu L H 2016 J. Quant. Spectrosc. Radiat. Transf. 184 111Google Scholar

  • [1] Jian Chao-Chao, Ma Xiang-Chao, Zhao Zi-Han, Zhang Jian-Qi. Temperature dependence of MXenes plasmons induced hot carrier generation and transport. Acta Physica Sinica, 2024, 73(11): 117801. doi: 10.7498/aps.73.20231924
    [2] Wang Wei, Li Jin-Yang, Mao Guo-Pei, Yang Yan, Gao Zhi-Qiang, Ma Cong, Zhong Xiang-Yu, Shi Qing. Optical fiber high-temperature pressure sensor with weak temperature sensitivity. Acta Physica Sinica, 2024, 73(1): 014208. doi: 10.7498/aps.73.20231155
    [3] Zhang Mao-Lin, Ma Wan-Yu, Wang Lei, Liu Zeng, Yang Li-Li, Li Shan, Tang Wei-Hua, Guo Yu-Feng. Investigation of high-temperature performance of WO3/β-Ga2O3 heterojunction deep-ultraviolet photodetectors. Acta Physica Sinica, 2023, 72(16): 160201. doi: 10.7498/aps.72.20230638
    [4] Li Ming-Zhu, Cai Xiao-Wu, Zeng Chuan-Bin, Li Xiao-Jing, Li Duo-Li, Ni Tao, Wang Juan-Juan, Han Zheng-Sheng, Zhao Fa-Zhan. Effect of high-temperature on holding characteristics in MOSFET ESD protecting device. Acta Physica Sinica, 2022, 71(12): 128501. doi: 10.7498/aps.71.20220172
    [5] Dong Jiu-Feng, Deng Xing-Lei, Niu Yu-Juan, Pan Zi-Zhao, Wang Hong. Research progress of polymer based dielectrics for high-temperature capacitor energy storage. Acta Physica Sinica, 2020, 69(21): 217701. doi: 10.7498/aps.69.20201006
    [6] Song Ting, Sun Xiao-Wei, Wei Xiao-Ping, Ouyang Yu-Hua, Zhang Chun-Lin, Guo Peng, Zhao Wei. High-pressure structure prediction and high-temperature structural stability of periclase. Acta Physica Sinica, 2019, 68(12): 126201. doi: 10.7498/aps.68.20190204
    [7] Zhang Xing, Zhang Yi, Zhang Jian-Wei, Zhang Jian, Zhong Chu-Yu, Huang You-Wen, Ning Yong-Qiang, Gu Si-Hong, Wang Li-Jun. 894 nm high temperature operating vertical-cavity surface-emitting laser and its application in Cs chip-scale atomic-clock system. Acta Physica Sinica, 2016, 65(13): 134204. doi: 10.7498/aps.65.134204
    [8] Gao Ying-Jun, Qin He-Lin, Zhou Wen-Quan, Deng Qian-Qian, Luo Zhi-Rong, Huang Chuang-Gao. Phase field crystal simulation of grain boundary annihilation under strain strain at high temperature. Acta Physica Sinica, 2015, 64(10): 106105. doi: 10.7498/aps.64.106105
    [9] Han Yong, Long Xin-Ping, Guo Xiang-Li. Prediction of methane PVT relations at high temperatures by a simplified virial equation of state. Acta Physica Sinica, 2014, 63(15): 150505. doi: 10.7498/aps.63.150505
    [10] Song Yun-Fei, Yu Guo-Yang, Yin He-Dong, Zhang Ming-Fu, Liu Yu-Qiang, Yang Yan-Qiang. Temperature dependence of elastic modulus of single crystal sapphire investigated by laser ultrasonic. Acta Physica Sinica, 2012, 61(6): 064211. doi: 10.7498/aps.61.064211
    [11] Wang Li-Hong, You Jing-Lin, Wang Yuan-Yuan, Zheng Shao-Bo, Simon Patrick, Hou Min, Ji Zi-Fang. Temperature dependent Raman spectra and micro-structure study of hexagonal MgTiO3 crystal. Acta Physica Sinica, 2011, 60(10): 104209. doi: 10.7498/aps.60.104209
    [12] Yu Feng, Wang Pei-Ji, Zhang Chang-Wen. Electronic structure and optical properties of Al-doped SnO2. Acta Physica Sinica, 2011, 60(2): 023101. doi: 10.7498/aps.60.023101
    [13] Lu Yao, Wang Pei-Ji, Zhang Chang-Wen, Feng Xian-Yang, Jiang Lei, Zhang Guo-Lian. First-principles calculation on electronic structure and optical properties of iron-doped SnO2. Acta Physica Sinica, 2011, 60(11): 113101. doi: 10.7498/aps.60.113101
    [14] Yu Feng, Wang Pei-Ji, Zhang Chang-Wen. First-principles study of optical and electronic properties of N-doped SnO2. Acta Physica Sinica, 2010, 59(10): 7285-7290. doi: 10.7498/aps.59.7285
    [15] Fan Zhen-Jun, Geng Xue-Wen, Kong Wen-Jie, Jin Yi-Rong. Measurement of anisotropy thermopower of decagonal AlCuCo quasicrystal. Acta Physica Sinica, 2009, 58(10): 7119-7123. doi: 10.7498/aps.58.7119
    [16] Song Xiao-Shu, Cheng Xin-Lu, Yang Xiang-Dong, Linghu Rong-Feng. Line intensities of 3000—0200 and 1001—0110 transition bands of 14N216O at high temperature. Acta Physica Sinica, 2007, 56(8): 4428-4434. doi: 10.7498/aps.56.4428
    [17] Li Gong-Ping, Zhang Mei-Ling. Energetics and structures of high-temperature copper cluster studied by Monte Carlo method. Acta Physica Sinica, 2005, 54(6): 2873-2876. doi: 10.7498/aps.54.2873
    [18] Zhang Yong, Tang Chao-Qun, Dai Jun. Ab inition studies on the electric and optical properties of Rb2TeW3O12. Acta Physica Sinica, 2005, 54(2): 868-874. doi: 10.7498/aps.54.868
    [19] Lu Wei, Liu Pu-Lin, Shen Xue-Chu, MvonOrtenberg. . Acta Physica Sinica, 1995, 44(4): 666-672. doi: 10.7498/aps.44.666
    [20] SHI HANG, CAI JIAN-HUA. ELECTROMAGNETIC MODES IN SUPERLATTICES WITH NONLOCAL DIELECTRIC FUNCTION. Acta Physica Sinica, 1988, 37(4): 589-597. doi: 10.7498/aps.37.589
Metrics
  • Abstract views:  13350
  • PDF Downloads:  183
  • Cited By: 0
Publishing process
  • Received Date:  19 May 2022
  • Accepted Date:  20 July 2022
  • Available Online:  08 December 2022
  • Published Online:  24 December 2022

/

返回文章
返回