-
The amorphous hafnia has a wide range of applications in microelectronic devices, and understanding its microscopic thermal transport mechanism is crucial for improving the performance and reliability of electronic devices. Most previous studies are based on molecular dynamics and the single quasi-harmonic Green-Kubo method, which makes it difficult to accurately consider the contribution of low-frequency vibrational modes to thermal conductivity. In this paper, based on the quasi-harmonic Green-Kubo method combined with hydrodynamic extrapolation, the heat transport mechanism of amorphous hafnia structures with different degrees of ordering is comprehensively investigated. The method effectively overcomes the finite size issue inherent in the single quasi-harmonic Green-Kubo method. Theoretical predictions show that the thermal conductivity of amorphous hafnia exhibits a weak correlation with the degree of microstructural ordering. Modal analysis reveals that low- and mid-frequency vibrational modes significantly contribute to thermal conductivity, which is the main reason for the underestimation of the thermal conductivity of amorphous hafnia in the single quasi-harmonic Green-Kubo method. Furthermore, this paper separates the contributions of propagons and diffusons to the thermal conductivity of amorphous hafnia using the anharmonic dynamic structure factor, revealing that diffusons dominate the thermal conductivity of all amorphous hafnia structures. However, the contribution of the propagons to thermal conductivity remains significant, reaching over 20% and increasing with the degree of ordering.
-
Keywords:
- thermal conductivity /
- amorphous hafnia /
- quasi-harmonic Green-Kubo theory /
- hydrodynamic extrapolation method
-
图 1 生成非晶结构过程中势能和均方位移累计值随模拟时间的变化, 图中灰色虚线之前为熔融过程, 灰色虚线与黑色实线之间为在温度4000 K下的弛豫过程, 红色点划线之后为退火过程
Figure 1. Variation of potential energy and accumulated mean square displacement with simulation time during the generation of amorphous structures, the melting process is before the gray dashed line, the relaxation process at 4000 K is between the gray dashed line and the black solid line, and the annealing process is after the red dotted line.
图 2 非晶HfO2在不同淬火速度下的(a)径向分布函数和(b)环数分布
Figure 2. (a) Radial distribution function and (b) ring distribution of amorphous HfO2 at different quenching rates.
图 3 有限尺寸(2592个原子)和流体动力学外推法的非晶HfO2随温度变化的热导率, 图中图例的下标表示淬火速度, 误差棒为热导率标准差
Figure 3. Thermal conductivity of amorphous HfO2 with temperature for finite size (2592 atoms) and the hydrodynamic extrapolation. The subscripts of the legend denote the quenching rate, error bar is standard deviations of thermal conductivity.
图 4 非晶HfO2热导率随温度变化关系, 图中散点是Panzer等[37]、Lee等[38]、Scott等[4]和Chaubey等[39]报道的非晶HfO2实验数据
Figure 4. Temperature-dependent thermal conductivity of amorphous HfO2, scattered points in the figure are experimental data for amorphous HfO2 reported by Panzer et al.[37], Lee et al.[38], Scott et al.[4] and Chaubey et al.[39].
图 5 300 K温度下不同淬火速度非晶HfO2 (a) 热容量; (b) 弛豫时间; (c) 模态扩散率; (d) 参与比
Figure 5. (a) Heat capacity; (b) lifetime; (c) modal diffusivity; (d) participation ratio of amorphous HfO2 with different quenching rates at 300 K.
图 6 (a)—(e) 淬火速度分别为5×1012, 1×1012, 5×1011, 1×1011, 5×1010 K/s的非晶HfO2的纵向非谐动态结构因子; (f)—(j) 为对应淬火速度下的横向非谐动态结构因子; 图中颜色条是根据(8)式计算的非谐动态结构因子强度, 蓝色直线是非谐动态结构因子在低频部分的线性拟合, 红色虚线是选取的截止频率
Figure 6. (a)–(e) Longitudinal anharmonic dynamic structure factors of amorphous HfO2 with different quenching rates of 5×1012, 1×1012, 5×1011, 1×1011, and 5×1010 K/s; (f)–(j) transverse anharmonic dynamic structure factors at corresponding quenching rates. The colorbar indicates the strength of the anharmonic dynamic structure factor calculated by Eq. (8), the blue straight line is a linear fit of the anharmonic dynamic structure factor in the low frequency part, and the red dashed line is the selected cut-off frequency.
图 7 300 K温度下不同淬火速度非晶HfO2的传播子和扩散子对热导率的贡献, 图中的蓝色文字代表传播子对总热导率的贡献百分比
Figure 7. Contributions of propagon and diffuson to thermal conductivity of amorphous HfO2 with different quenching rates at 300 K, the blue text in the figure represents the percentage contribution of propagon to the total thermal conductivity.
-
[1] Wilk G D, Wallace R M, Anthony J 2001 J. Appl. Phys. 89 5243
Google Scholar
[2] Wang Y, Zahid F, Wang J, Guo H 2012 Phys. Rev. B 85 224110
Google Scholar
[3] McKenna K, Shluger A, Iglesias V, Porti M, Nafría M, Lanza M, Bersuker G 2011 Microelectron. Eng. 88 1272
Google Scholar
[4] Scott E A, Gaskins J T, King S W, Hopkins P E 2018 APL Mater. 6 058302
Google Scholar
[5] Lu S X, Cebe P 1996 Polymer 37 4857
Google Scholar
[6] 何宇亮, 周衡南, 刘湘娜, 程光煦 1990 39 1796
Google Scholar
He Y L, Zhou H N, Liu X N, Cheng G X, Yu S D 1990 Acta Phys. Sin. 39 1796
Google Scholar
[7] Wang S, Wang C, Li M, Huang L, Ott R, Kramer M, Sordelet D, Ho K 2008 Phys. Rev. B 78 184204
Google Scholar
[8] Wang Y, Fan Z, Qian P, Caro M A, Ala-Nissila T 2023 Phys. Rev. B 107 054303
[9] Kittel C 1949 Phys. Rev. 75 972
Google Scholar
[10] Allen P B, Feldman J L 1989 Phys. Rev. Lett. 62 645
Google Scholar
[11] Zhu X, Shao C 2022 Phys. Rev. B 106 014305
[12] Qiu R, Zeng Q Y, Han J S, Chen K, Kang D D, Yu X X, Dai J Y 2025 Phys. Rev. B 111 064103
Google Scholar
[13] Luo T, Lloyd J R 2012 Adv. Funct. Mater. 22 2495
Google Scholar
[14] Li S H, Yu X X, Bao H, Yang N 2018 J. Phys. Chem. C 122 13140
Google Scholar
[15] Prasai K, Biswas P, Drabold D 2016 Semicond. Sci. Techn. 31 073002
Google Scholar
[16] 朱美芳 1996 45 499
Google Scholar
Zhu M F 1996 Acta Phys. Sin. 45 499
Google Scholar
[17] Mu X, Wu X, Zhang T, Go D B, Luo T 2014 Sci. Rep. 4 3909
Google Scholar
[18] 王学智, 汤雨婷, 车军伟, 令狐佳珺, 侯兆阳 2023 72 056101
Google Scholar
Wang X Z, Tang Y T, Che J W, Linghu J J, Hou Z Y 2023 Acta Physica Sinica 72 056101
Google Scholar
[19] Yang F H, Zeng Q Y, Chen B, Kang D D, Zhang S, Wu J H, Yu X X, Dai J Y 2022 Chin. Phys. Lett. 39 116301
Google Scholar
[20] 鲍华 2013 62 1
Google Scholar
Bao H 2013 Acta Phys. Sin. 62 1
Google Scholar
[21] Qiu R, Zeng Q Y, Wang H, Kang D D, Yu X X, Dai J Y 2023 Chin. Phys. Lett. 40 116301
Google Scholar
[22] Isaeva L, Barbalinardo G, Donadio D, Baroni S 2019 Nat. Commun. 10 3853
Google Scholar
[23] Simoncelli M, Marzari N, Mauri F 2019 Nat. Phys. 15 809
Google Scholar
[24] Harper A F, Iwanowski K, Witt W C, Payne M C, Simoncelli M 2024 Phys. Rev. Mater. 8 043601
Google Scholar
[25] Fiorentino A, Pegolo P, Baroni S 2023 npj Comput. Mater. 9 157
Google Scholar
[26] Barbalinardo G, Chen Z, Lundgren N W, Donadio D 2020 J. Appl. Phys. 128 135104
Google Scholar
[27] Fan Z Y, Wang Y Z, Ying P H, Song K K, Wang J J, Wang Y, Zeng Z Z, Xu K, Lindgren E, Rahm J M, Gabourie A J, Liu J H, Dong H K, Wu J Y, Chen Y, Zhong Z, Sun J, Erhart P, Su Y J, Ala-Nissila T 2022 J. Chem. Phys. 157 114801
Google Scholar
[28] Fan Z Y, Zeng Z Z, Zhang C Z, Wang Y Z, Song K K, Dong H K, Chen Y, Ala-Nissila T 2021 Phys. Rev. B 104 104309
Google Scholar
[29] Zhang H, Gu X, Fan Z, Bao H 2023 Phys. Rev. B 108 045422
Google Scholar
[30] Sivaraman G, Krishnamoorthy A N, Baur M, Holm C, Stan M, Csányi G, Benmore C, Vázquez-Mayagoitia Á 2020 npj Comput. Mater. 6 104
Google Scholar
[31] Plimpton S 1995 J. Comput. Phys. 117 1
Google Scholar
[32] Zeng Q Y, Yu X X, Yao Y P, Gao T Y, Chen B, Zhang S, Kang D D, Wang H, Dai J Y 2021 Phys. Rev. Res. 3 033116
Google Scholar
[33] Franzblau D 1991 Phys. Rev. B 44 4925
Google Scholar
[34] Le Roux S, Petkov V 2010 J. Appl. Crystallogr. 43 181
Google Scholar
[35] Xiang X, Fan H, Zhou Y G 2024 J. Appl. Phys. 135 125102
Google Scholar
[36] Zhang S L, Yi S L, Yang J Y, Liu J, Liu L H 2023 Int. J. Heat Mass Tran. 207 123971
Google Scholar
[37] Panzer M A, Shandalov M, Rowlette J A, Oshima Y, Chen Y W, McIntyre P C, Goodson K E 2009 IEEE Electron Dev. Lett. 30 1269
Google Scholar
[38] Lee S M, Cahill D G, Allen T H 1995 Phys. Rev. B 52 253
Google Scholar
[39] Chaubey G S, Yao Y, Makongo J P, Sahoo P, Misra D, Poudeu P F, Wiley J B 2012 RSC Adv. 2 9207
Google Scholar
[40] Tritt T M 2005 Thermal Conductivity: Theory, Properties, and Applications (Springer Science & Business Media
[41] Shenogin S, Bodapati A, Keblinski P, McGaughey A J 2009 J. Appl. Phys. 105 034906
Google Scholar
[42] Seyf H R, Henry A 2016 J. Appl. Phys. 120 025101
Google Scholar
DownLoad:
Metrics
- Abstract views: 45
- PDF Downloads: 6
- Cited By: 0
