Research on thermal transport mechanism of amorphous hafnia based on quasi-harmonic Green-Kubo theory combined with hydrodynamic extrapolation method

ZHU Xiongfei; SUN Jianshi; XIONG Yucheng; LI Shouhang; LIU Xiangjun

doi:10.7498/aps.74.20250350

Abstract

Amorphous hafnia (a-HfO₂) has attracted considerable attention due to its excellent dielectric properties and broad applicability in the electronic industry. Considering that the self-heating is becoming the bottleneck for the performance and reliability of microelectronic devices, it is necessary to clarify the thermal transport mechanism in a-HfO₂. The microstructures of a-HfO₂ can be significantly changed during the fabrication process, whose effects on thermal transport remain to be revealed. Here, we conduct a comprehensive investigation of thermal transport in a-HfO₂ based on the quasi-harmonic Green-Kubo (QHGK) theory combined with hydrodynamic extrapolation. The calculation scheme fully considers the contributions from low-frequency vibrational modes, overcoming the drawbacks of finite size in the single QHGK method and molecular dynamics simulation. It is found that the thermal conductivity (κ) of a-HfO₂ is weakly related to its degree of order. The amorphous structures with slower quenching speed and higher degree of order have higher thermal conductivities due to their slightly larger relaxation times. Modal analyses show that the mid- and low-frequency vibrational modes have significant contributions to thermal transport in a-HfO₂, which is the main reason for the underestimation of the κ in other methods. Based on the anharmonic dynamic structure factor, we further separate the contributions of two fundamental heat carriers in amorphous materials: propagons and diffusons. It is found that diffusons dominate the κ in all a-HfO₂ structures. Nevertheless, the contribution of the propagons is non-negligible, accounting for more than 20% and increasing with the degree of structural ordering. This study provides new insights into the microscopic mechanisms and guidance for manipulating thermal transport in a-HfO₂.

Keywords:

Authors and contacts

1.
Institute of Micro/Nano Electromechanical System and Integrated Circuit, College of Mechanical Engineering, Donghua University, Shanghai 201620, China
2.
Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay, 10 Boulevard Thomas Gobert, Palaiseau 91120, France

Corresponding author: LI Shouhang, shouhang.li@universite-paris-saclay.fr ; LIU Xiangjun, xjliu@dhu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12304039, 52150610495, 12374027), the Natural Science Foundation of Shanghai, China (Grant Nos. 22YF1400100, 21TS1401500), and the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant Nos. 2232022D-22, CUSF-DH-T-2024061).

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References

[1]	Wilk G D, Wallace R M, Anthony J 2001 J. Appl. Phys. 89 5243 Google Scholar
[2]	Chen J H, Liang M F, Song Y, Yuan J J, Zhang M Y, Luo Y M, Wang N N 2024 Chin. Phys. B 33 047503 Google Scholar
[3]	Wang Y, Zahid F, Wang J, Guo H 2012 Phys. Rev. B 85 224110 Google Scholar
[4]	董典萌, 汪成, 张清怡, 张涛, 杨永涛, 夏翰驰, 王月晖, 吴真平 2023 72 097302 Google Scholar Dong D M, Wang C, Zhang Q Y, Zhang T, Yang Y T, Xia H C, Wang Y H, Wu Z P 2023 Acta. Phys. Sin. 72 097302 Google Scholar
[5]	Gao R, Liu C, Shi B, Li Y, Luo B, Chen R, Ouyang W, Gao H, Hu S, Wang Y 2024 Chin. Phys. Lett. 41 087701 Google Scholar
[6]	Chen S, Chen M, Liu Y, Cao D, Chen G 2024 Chin. Phys. B 33 098701 Google Scholar
[7]	McKenna K, Shluger A, Iglesias V, Porti M, Nafría M, Lanza M, Bersuker G 2011 Microelectron. Eng. 88 1272 Google Scholar
[8]	袁国亮, 王琛皓, 唐文彬, 张睿, 陆旭兵 2023 72 097703 Google Scholar Yuan G L, Wang C H, Tang W B, Zhang R, Lu X B 2023 Acta. Phys. Sin. 72 097703 Google Scholar
[9]	Liu K, Liu K, Zhang X, Fang J, Jin F, Wu W, Ma C, Wang L 2024 Chin. Phys. Lett. 41 117701 Google Scholar
[10]	Scott E A, Gaskins J T, King S W, Hopkins P E 2018 APL Mater. 6 058302 Google Scholar
[11]	Lu S X, Cebe P 1996 Polymer 37 4857 Google Scholar
[12]	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
[13]	Wang S, Wang C, Li M, Huang L, Ott R, Kramer M, Sordelet D, Ho K 2008 Phys. Rev. B 78 184204 Google Scholar
[14]	Wang Y, Fan Z, Qian P, Caro M A, Ala-Nissila T 2023 Phys. Rev. B 107 054303 Google Scholar
[15]	林揆训, 林璇英, 梁厚蕴, 池凌飞, 余楚迎, 黄创君 2002 51 863 Google Scholar Lin K X, Lin X Y, Liang H Y, Chi L F, Yu C Y, Huang C J 2002 Acta. Phys. Sin. 51 863 Google Scholar
[16]	Kittel C 1949 Phys. Rev. 75 972 Google Scholar
[17]	Allen P B, Feldman J L 1989 Phys. Rev. Lett. 62 645 Google Scholar
[18]	Zhu X, Shao C 2022 Phys. Rev. B 106 014305 Google Scholar
[19]	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
[20]	Luo T, Lloyd J R 2012 Adv. Funct. Mater. 22 2495 Google Scholar
[21]	Li S H, Yu X X, Bao H, Yang N 2018 J. Phys. Chem. C 122 13140 Google Scholar
[22]	Xi Q, Zhong J, He J, Xu X, Nakayama T, Wang Y, Liu J, Zhou J, Li B 2020 Chin. Phys. Lett. 37 104401 Google Scholar
[23]	Prasai K, Biswas P, Drabold D 2016 Semicond. Sci. Techn. 31 073002 Google Scholar
[24]	朱美芳 1996 45 499 Google Scholar Zhu M F 1996 Acta Phys. Sin. 45 499 Google Scholar
[25]	Mu X, Wu X, Zhang T, Go D B, Luo T 2014 Sci. Rep. 4 3909 Google Scholar
[26]	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
[27]	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
[28]	鲍华 2013 62 1 Google Scholar Bao H 2013 Acta Phys. Sin. 62 1 Google Scholar
[29]	Qiu R, Zeng Q Y, Wang H, Kang D D, Yu X X, Dai J Y 2023 Chin. Phys. Lett. 40 116301 Google Scholar
[30]	Isaeva L, Barbalinardo G, Donadio D, Baroni S 2019 Nat. Commun. 10 3853 Google Scholar
[31]	Simoncelli M, Marzari N, Mauri F 2019 Nat. Phys. 15 809 Google Scholar
[32]	Harper A F, Iwanowski K, Witt W C, Payne M C, Simoncelli M 2024 Phys. Rev. Mater. 8 043601 Google Scholar
[33]	Fiorentino A, Pegolo P, Baroni S 2023 npj Comput. Mater. 9 157 Google Scholar
[34]	Barbalinardo G, Chen Z, Lundgren N W, Donadio D 2020 J. Appl. Phys. 128 135104 Google Scholar
[35]	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
[36]	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
[37]	Zhang H, Gu X, Fan Z, Bao H 2023 Phys. Rev. B 108 045422 Google Scholar
[38]	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
[39]	Plimpton S 1995 J. Comput. Phys. 117 1 Google Scholar
[40]	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
[41]	Franzblau D 1991 Phys. Rev. B 44 4925 Google Scholar
[42]	Le Roux S, Petkov V 2010 J. Appl. Crystallogr. 43 181 Google Scholar
[43]	Xiang X, Fan H, Zhou Y G 2024 J. Appl. Phys. 135 125102 Google Scholar
[44]	Zhang S L, Yi S L, Yang J Y, Liu J, Liu L H 2023 Int. J. Heat Mass Tran. 207 123971 Google Scholar
[45]	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
[46]	Lee S M, Cahill D G, Allen T H 1995 Phys. Rev. B 52 253 Google Scholar
[47]	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
[48]	Tritt T M 2005 Thermal Conductivity: Theory, Properties, and Applications (Springer Science & Business Media
[49]	Shenogin S, Bodapati A, Keblinski P, McGaughey A J 2009 J. Appl. Phys. 105 034906 Google Scholar
[50]	Seyf H R, Henry A 2016 J. Appl. Phys. 120 025101 Google Scholar

Cited By

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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, 图中图例的数值表示淬火速度, 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 values of the legend denote the quenching rate, error bar is standard deviations of thermal conductivity.

DownLoad: Full-Size Img PowerPoint

图 4 非晶HfO₂热导率随温度变化关系, 图中散点是Panzer等^[45]、Lee等^[46]、Scott等^[10]和Chaubey等^[47]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.^[45], Lee et al.^[46], Scott et al.^[10] and Chaubey et al.^[47].

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

map

[1]	Wilk G D, Wallace R M, Anthony J 2001 J. Appl. Phys. 89 5243 Google Scholar
[2]	Chen J H, Liang M F, Song Y, Yuan J J, Zhang M Y, Luo Y M, Wang N N 2024 Chin. Phys. B 33 047503 Google Scholar
[3]	Wang Y, Zahid F, Wang J, Guo H 2012 Phys. Rev. B 85 224110 Google Scholar
[4]	董典萌, 汪成, 张清怡, 张涛, 杨永涛, 夏翰驰, 王月晖, 吴真平 2023 72 097302 Google Scholar Dong D M, Wang C, Zhang Q Y, Zhang T, Yang Y T, Xia H C, Wang Y H, Wu Z P 2023 Acta. Phys. Sin. 72 097302 Google Scholar
[5]	Gao R, Liu C, Shi B, Li Y, Luo B, Chen R, Ouyang W, Gao H, Hu S, Wang Y 2024 Chin. Phys. Lett. 41 087701 Google Scholar
[6]	Chen S, Chen M, Liu Y, Cao D, Chen G 2024 Chin. Phys. B 33 098701 Google Scholar
[7]	McKenna K, Shluger A, Iglesias V, Porti M, Nafría M, Lanza M, Bersuker G 2011 Microelectron. Eng. 88 1272 Google Scholar
[8]	袁国亮, 王琛皓, 唐文彬, 张睿, 陆旭兵 2023 72 097703 Google Scholar Yuan G L, Wang C H, Tang W B, Zhang R, Lu X B 2023 Acta. Phys. Sin. 72 097703 Google Scholar
[9]	Liu K, Liu K, Zhang X, Fang J, Jin F, Wu W, Ma C, Wang L 2024 Chin. Phys. Lett. 41 117701 Google Scholar
[10]	Scott E A, Gaskins J T, King S W, Hopkins P E 2018 APL Mater. 6 058302 Google Scholar
[11]	Lu S X, Cebe P 1996 Polymer 37 4857 Google Scholar
[12]	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
[13]	Wang S, Wang C, Li M, Huang L, Ott R, Kramer M, Sordelet D, Ho K 2008 Phys. Rev. B 78 184204 Google Scholar
[14]	Wang Y, Fan Z, Qian P, Caro M A, Ala-Nissila T 2023 Phys. Rev. B 107 054303 Google Scholar
[15]	林揆训, 林璇英, 梁厚蕴, 池凌飞, 余楚迎, 黄创君 2002 51 863 Google Scholar Lin K X, Lin X Y, Liang H Y, Chi L F, Yu C Y, Huang C J 2002 Acta. Phys. Sin. 51 863 Google Scholar
[16]	Kittel C 1949 Phys. Rev. 75 972 Google Scholar
[17]	Allen P B, Feldman J L 1989 Phys. Rev. Lett. 62 645 Google Scholar
[18]	Zhu X, Shao C 2022 Phys. Rev. B 106 014305 Google Scholar
[19]	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
[20]	Luo T, Lloyd J R 2012 Adv. Funct. Mater. 22 2495 Google Scholar
[21]	Li S H, Yu X X, Bao H, Yang N 2018 J. Phys. Chem. C 122 13140 Google Scholar
[22]	Xi Q, Zhong J, He J, Xu X, Nakayama T, Wang Y, Liu J, Zhou J, Li B 2020 Chin. Phys. Lett. 37 104401 Google Scholar
[23]	Prasai K, Biswas P, Drabold D 2016 Semicond. Sci. Techn. 31 073002 Google Scholar
[24]	朱美芳 1996 45 499 Google Scholar Zhu M F 1996 Acta Phys. Sin. 45 499 Google Scholar
[25]	Mu X, Wu X, Zhang T, Go D B, Luo T 2014 Sci. Rep. 4 3909 Google Scholar
[26]	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
[27]	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
[28]	鲍华 2013 62 1 Google Scholar Bao H 2013 Acta Phys. Sin. 62 1 Google Scholar
[29]	Qiu R, Zeng Q Y, Wang H, Kang D D, Yu X X, Dai J Y 2023 Chin. Phys. Lett. 40 116301 Google Scholar
[30]	Isaeva L, Barbalinardo G, Donadio D, Baroni S 2019 Nat. Commun. 10 3853 Google Scholar
[31]	Simoncelli M, Marzari N, Mauri F 2019 Nat. Phys. 15 809 Google Scholar
[32]	Harper A F, Iwanowski K, Witt W C, Payne M C, Simoncelli M 2024 Phys. Rev. Mater. 8 043601 Google Scholar
[33]	Fiorentino A, Pegolo P, Baroni S 2023 npj Comput. Mater. 9 157 Google Scholar
[34]	Barbalinardo G, Chen Z, Lundgren N W, Donadio D 2020 J. Appl. Phys. 128 135104 Google Scholar
[35]	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
[36]	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
[37]	Zhang H, Gu X, Fan Z, Bao H 2023 Phys. Rev. B 108 045422 Google Scholar
[38]	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
[39]	Plimpton S 1995 J. Comput. Phys. 117 1 Google Scholar
[40]	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
[41]	Franzblau D 1991 Phys. Rev. B 44 4925 Google Scholar
[42]	Le Roux S, Petkov V 2010 J. Appl. Crystallogr. 43 181 Google Scholar
[43]	Xiang X, Fan H, Zhou Y G 2024 J. Appl. Phys. 135 125102 Google Scholar
[44]	Zhang S L, Yi S L, Yang J Y, Liu J, Liu L H 2023 Int. J. Heat Mass Tran. 207 123971 Google Scholar
[45]	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
[46]	Lee S M, Cahill D G, Allen T H 1995 Phys. Rev. B 52 253 Google Scholar
[47]	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
[48]	Tritt T M 2005 Thermal Conductivity: Theory, Properties, and Applications (Springer Science & Business Media
[49]	Shenogin S, Bodapati A, Keblinski P, McGaughey A J 2009 J. Appl. Phys. 105 034906 Google Scholar
[50]	Seyf H R, Henry A 2016 J. Appl. Phys. 120 025101 Google Scholar

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