合成石英玻璃粘度特征多尺度模拟研究进展

doi:10.16552/j.cnki.issn1001-1625.2025.1194

摘要/Abstract

摘要：

在集成电路制造过程中，热处理工艺是关键步骤之一，而石英炉管作为热处理设备的核心部件，其性能直接影响到集成电路的质量和生产效率。合成石英玻璃作为石英炉管的关键材料，其高温制备与成形过程的精准控制，深度依赖于粘度特征变化，这一变化涉及微观结构松弛与宏观流动行为的内在关联。因此，本文系统综述了合成石英玻璃粘度研究涉及的多尺度模拟策略及最新进展。在微观尺度，重点评述分子动力学模拟（MD）采用的关键势函数及其预测精度，总结常用的势函数在预测二氧化硅体系结构、扩散系数和粘度的准确性与局限性，综述通过分子动力学模拟研究碱金属离子、羟基等杂质对合成石英玻璃粘度和结构松弛的影响机理的相关成果。在宏观尺度，梳理了基于有限元方法（FEM）及计算流体动力学（CFD）的仿真研究，分析了将微观模拟或实验获得的粘度模型植入模拟软件进行热加工工艺模拟的现状。本文可为后续开展合成石英玻璃中杂质扩散规律及耐高温特性的研究提供参考，为合成石英玻璃材料的高温应用提供理论基础和技术支持。

关键词: 合成石英玻璃, 粘度, 多尺度模拟, 分子动力学, 有限元法, 计算流体动力学

Abstract:

In the manufacturing process of integrated circuits， thermal treatment process is one of the critical steps， and the quartz furnace tube， as a core component of thermal treatment equipment， its performance directly impacts the quality and production efficiency of integrated circuits. Synthetic quartz glass， as a key material for quartz furnace tubes， relies heavily on precise control of its high-temperature preparation and forming processes， which are intrinsically linked to viscosity characteristic changes involving the relaxation of microstructures and macroscopic flow behavior. Therefore， this paper systematically reviews multiscale simulation strategies and recent advancements in quartz glass viscosity research. At the microscopic scale， it focuses on evaluating key potential functions used in molecular dynamics （MD） simulations and their predictive accuracy， summarizing the accuracy and limitations of commonly used potential functions in predicting the structure， diffusion coefficients， and viscosity of the silican dioxide system， while reviewing the relevant achievements of influence mechanisms of impurities such as alkali metal ions and hydroxyl groups on synthetic quartz glass viscosity and structural relaxation through molecular dynamics simulations. At the macroscopic scale， it organizes simulation studies based on finite element method （FEM） and computational fluid dynamics （CFD）， analyzing the current status of incorporating viscosity models obtained from microscopic simulations or experiments into simulation software for thermal processing simulations. This paper provides a reference for future research on impurity diffusion laws and high-temperature resistance characteristics in synthetic quartz glass， and offers a theoretical foundation and technical support for high-temperature applications of quartz glass materials.

Key words: synthetic quartz glass, viscosity, multiscale simulation, molecular dynamics, finite element method, computational fluid dynamics

中图分类号:

TQ171.8

周建欣, 聂兰舰, 范江伟, 贾亚男, 刘瑞旺. 合成石英玻璃粘度特征多尺度模拟研究进展[J]. 硅酸盐通报, 2026, 45(3): 771-780.

ZHOU Jianxin, NIE Lanjian, FAN Jiangwei, JIA Yanan, LIU Ruiwang. Research Progress on Multiscale Simulation of Viscosity Characteristics of Synthetic Quartz Glass[J]. BULLETIN OF THE CHINESE CERAMIC SOCIETY, 2026, 45(3): 771-780.

图/表 6

图1 石英玻璃粘度与温度的关系曲线［8］

Fig.1 Relationship curves between viscosity and temperature of quartz glass［8］

图2 粘度-水含量关系［22］

Fig.2 Relationship between viscosity and H2O content ［22］

图3 以不同压力下组成为变量的过量摩尔体积函数［31］

Fig.3 Excess molar volume as a function of composition under different pressures［31］

图4 内表面和外表面冷却速度不同的玻璃管冷却几何形状［40］

Fig.4 Geometric shape of glass tube cooling with different cooling rates at inner and outer surfaces［40］

图5 内表面和外表面的虚拟温度比较［40］

Fig.5 Comparison of fictive temperatures between inner and outer surfaces［40］

图6 石英玻璃模压仿真结果［42］

Fig.6 Simulation results of quartz glass compression molding［42］

参考文献 46

[1]	章　谦. 新型国产8英寸半导体快速热处理设备［J］. 集成电路应用， 2004， 21（4）： 46-48.
	ZHANG Q. New domestic 8-inch semiconductor rapid heat treatment equipment［J］. Applications of IC， 2004， 21（4）： 46-48 （in Chinese）.
[2]	高　鹏，刘　阳，徐晋勇，等. 一种立式硅片扩散炉： CN206219721U［P］. 2017-06-06.
	GAO P， LIU Y， XU J Y， et al.A vertical silicon wafer diffusion furnace： CN206219721U［P］. 2017-06-06 （in Chinese）.
[3]	杨晓勇，孙　超，曹荆亚，等. 高纯石英的研究进展及发展趋势［J］. 地学前缘， 2022， 29（1）： 231-244.
	YANG X Y， SUN C， CAO J Y， et al. High purity quartz： research progress and perspective review［J］. Earth Science Frontiers， 2022， 29（1）： 231-244 （in Chinese）.
[4]	李雪娇.多尺度模拟方法研究固体电解质材料中质子的传输性质和机理［D］.上海大学， 2018.
	LI X J. Multi scale simulation method for studying the proton transport properties and mechanisms in solid electrolyte materials［D］. Shanghai University， 2018 （in Chinese）.
[5]	付健博，任　慧，刘晓晗，等. 微观尺度下黏结剂预聚物体系中硝酸酯的分解老化机制［J］. 装备环境工程， 2024， 21（10）： 16-25.
	FU J B， REN H， LIU X H， et al. Decomposition and aging mechanism of nitrate esters in binder prepolymer system at microscopic scale［J］. Equipment Environmental Engineering， 2024， 21（10）： 16-25 （in Chinese）.
[6]	王路生.基于分子动力学与有限元方法的金属材料变形及失效的多尺度模拟［D］. 重庆：重庆理工大学， 2018.
	WANG L S. Multi scale simulation of deformation and failure of metal materials based on molecular dynamics and finite element method［D］. Chongqing： Chongqing University of Technology， 2018 （in Chinese）.
[7]	陈忠海，谢美芬，陈家庆，等. 基于材料变粘度模型的摩擦液柱成形CFD数值模拟［J］. 电焊机， 2015， 45（7）： 132-139.
	CHEN Z H， XIE M F， CHEN J Q， et al. CFD numerical simulation of friction hydro pillar processing based on fluid model of varying viscosity［J］. Electric Welding Machine， 2015， 45（7）： 132-139 （in Chinese）.
[8]	王玉芬，刘连城. 石英玻璃［M］. 北京：化学工业出版社， 2007.
	WANG Y F， LIU L C. Quartz glass［M］. Beijing： Chemical Industry Press， 2007 （in Chinese）.
[9]	陈春雨，严惊涛，李　奥，等. 玻璃黏度理论模型的研究进展（续）［J］. 玻璃搪瓷与眼镜， 2021， 49（8）： 43-49.
	CHEN C Y， YAN J T， LI A， et al. Progress on glass viscosity theoretical models （contd.）［J］. Glass Enamel & Ophthalmic Optics， 2021， 49（8）： 43-49 （in Chinese）.
[10]	YU X M， DU X R， SONG X F， et al. A low-hydroxyl quartz glass prepared by using a plasma heat source as the flame and high-purity quartz sand as the raw material［J］. Applied Sciences， 2024， 14（19）： 9137.
[11]	MAURO J C， YUE Y Z， ELLISON A J， et al. Viscosity of glass-forming liquids［J］. Proceedings of the National Academy of Sciences of the United States of America， 2009， 106（47）： 19780-19784.
[12]	DOBLACK B N. The structure and properties of silica glass nanostructures using novel computational systems［D］.California： University of California， Merced， 2013.
[13]	LINDSEY R K， KROONBLAWD M P， FRIED L E， et al.Force matching approaches to extend density functional theory to large time and length scales［J］.Challenges and Advances in Computational Chemistry and Physics， 2019， 28： 71-93.
[14]	HORBACH J， KOB W. Static and dynamic properties of a viscous silica melt［J］. Physical Review B， 1999， 60（5）： 3169-3181.
[15]	ZHAO Y X， DU J C， CAO X， et al. A modified random network model for P₂O₅-Na₂O-Al₂O₃-SiO₂ glass studied by molecular dynamics simulations［J］. RSC Advances， 2021， 11（12）： 7025-7036.
[16]	MASSOBRIO C， DU J C， BERNASCONI M， et al. Molecular dynamics simulations of disordered materials： from network glasses to phase-change memory alloys［M］. Cham： Springer International Publishing， 2015.
[17]	ZHANG G H， CHOU K C， XUE Q G， et al. Modeling viscosities of CaO-MgO-FeO-MnO-SiO₂ molten slags［J］. Metallurgical and Materials Transactions B， 2012， 43（1）： 64-72.
[18]	MAHADEVAN T S， DU J C. Hydration and reaction mechanisms on sodium silicate glass surfaces from molecular dynamics simulations with reactive force fields［J］. Journal of the American Ceramic Society， 2020， 103（6）： 3676-3690.
[19]	MEI H， YANG Y J， VAN DUIN A C T， et al. Effects of water on the mechanical properties of silica glass using molecular dynamics［J］. Acta Materialia， 2019， 178： 36-44.
[20]	MARKUS P. Structure and dynamics of hydrous silicates as seen by molecular dynamics computer simulations and neutron scattering［D］. Munich： Technische Universität München，Technical University of Munich & University of Montpellier II， 2005.
[21]	NORITAKE F. Diffusion mechanism of network-forming elements in silicate liquids［J］. Journal of Non-Crystalline Solids， 2021， 553： 120512.
[22]	DUFILS T， SATOR N， GUILLOT B. A comprehensive molecular dynamics simulation study of hydrous magmatic liquids［J］. Chemical Geology， 2020， 533： 119300.
[23]	ZHOU W Y， HAO M， HRUBIAK R， et al. Migration and accumulation of hydrous mantle incipient melt in the Earth’s asthenosphere： constraints from in-situ falling sphere viscometry measurements［J］. Earth and Planetary Science Letters， 2024， 641： 118833.
[24]	NASYROV R S， BODUNOV B P， ARTEM’EV D A. Microgranular heterogeneity of quartz glass［J］. Glass and Ceramics， 2019， 75（11）： 471-474.
[25]	JIA Y J， WU X X， ZHU M K， et al. Relaxation mechanism analysis of synthetic fused quartz glass investigated by electrical impedance spectra［J］. Chinese Science Bulletin， 2014， 59（26）： 3271-3275.
[26]	ZHOU Y， LUO G H， HU Y X， et al. Interaction properties between molten metal and quartz by molecular dynamics simulation［J］. Journal of Molecular Liquids， 2021， 342： 117474.
[27]	CUI L， NI P Y， LV W， et al. Effect of BaO on viscosity and structure of B₂O₃-SiO₂-Al₂O₃-Na₂O-BaO glass lubricant［J］. Journal of the American Ceramic Society， 2025， 108（2）： e20181.
[28]	NORITAKE F， NAITO S. Mechanism of mixed alkali effect in silicate glass/liquid： pathway and network analysis［J］. Journal of Non-Crystalline Solids， 2023， 610： 122321.
[29]	ZHANG Q， WU S Y， ZHANG Z Y， et al. Theoretical investigations on the EPR parameters and local structures for V⁴⁺ in alkali niobium borate glasses［J］. Journal of Non-Crystalline Solids， 2019， 522： 119559.
[30]	NHAN N T， LIEN P T， KIEN P H， et al. Study of diffusion in sodium silicate glass using molecular dynamics simulation［J］. Silicon， 2024， 16（15）： 5571-5581.
[31]	LACKS D J， REAR D B， VAN ORMAN J A. Molecular dynamics investigation of viscosity， chemical diffusivities and partial molar volumes of liquids along the MgO-SiO₂join as functions of pressure［J］. Geochimica et Cosmochimica Acta， 2007， 71（5）： 1312-1323.
[32]	XING J T. Mixed finite element-computational fluid dynamics method for nonlinear fluid-solid interactions［M］//Fluid-Solid Interaction Dynamics. Amsterdam： Elsevier， 2019： 409-485.
[33]	TRABELSSI M， EBENDORFF-HEIDEPRIEM H， RICHARDSON K C， et al. Computational modeling of die swell of extruded glass preforms at high viscosity［J］. Journal of the American Ceramic Society， 2014， 97（5）： 1572-1581.
[34]	RYZHAKOV P B， GARCÍA J， OÑATE E. Lagrangian finite element model for the 3D simulation of glass forming processes［J］. Computers & Structures， 2016， 177： 126-140.
[35]	ZHANG M， CHEN D H， WANG X M. Theoretical derivation and verification of liquid viscosity and density measurements using quartz tuning fork sensor［C］//2019 13th Symposium on Piezoelectrcity， Acoustic Waves and Device Applications （SPAWDA）. January 11-14， 2019， Harbin， China. IEEE， 2019： 1-4.
[36]	ABBOUD A W， GUILLEN D P， POKORNY R. Effect of glass viscosity on foaming behavior and heat transfer in a laboratory-scale waste glass melter［Z］. 2018.
[37]	KIM H J， KIM J， PARK H J. Graph neural network modeling of free-surface flows in non-Newtonian power-law fluids［J］. Physics of Fluids， 2025， 37（12）： 123114.
[38]	JIANG C H， CHEN N Z. Graph neural networks （GNNs） based accelerated numerical simulation［J］. Engineering Applications of Artificial Intelligence， 2023， 123： 106370.
[39]	柏春光，徐东生，雷家峰，等.钛合金型材挤压玻璃润滑工艺的有限元模拟［J］.中国有色金属学报，2010，20（增刊1）：857-861.
	BAI C G， XU D S， LEI J F， et al. FEM simulation of glass lubrication during section extrusion of titanium alloy［J］. Chinese Journal of Nonferrous Metals. 2010， 20（supplement 1）： 857-861 （in Chinese）.
[40]	ZHANG Z， ZHANG R.Implementation of a viscoelastic material model to simulate relaxation in glass transition［Z］.Corning Incorporated， 2015.
[41]	许孔联，刘康华. 玻璃透镜模压成形三步退火的有限元仿真研究［J］. 机械工程师， 2014（8）： 69-72.
	XU K L， LIU K H. Simulation study of three-steps annealing in glass lens molding process［J］. Mechanical Engineer， 2014（8）： 69-72 （in Chinese）.
[42]	王启林，姚　鹏，王一帆，等. 非球面微柱面透镜阵列精密玻璃模压仿真研究［J］. 中国激光， 2024， 51（20）： 32-42.
	WANG Q L， YAO P， WANG Y F， et al. Simulation of precision glass molding for aspherical cylindrical microlens arrays［J］. Chinese Journal of Lasers， 2024， 51（20）： 32-42 （in Chinese）.
[43]	LI B Y， DOBOSZ K M， ZHANG H T， et al. Predicting the performance of pressure filtration processes by coupling computational fluid dynamics and discrete element methods［J］. Chemical Engineering Science， 2019， 208： 115162.
[44]	DE ROMA F， MARCHISIO D， BOCCARDO G， et al. Application of a multiscale approach for modeling the rheology of complex fluids in industrial mixing equipment［J］. Physics of Fluids， 2024， 36（2）： 023119.
[45]	JADHAO V， ROBBINS M O. Probing large viscosities in glass-formers with nonequilibrium simulations［J］. Proceedings of the National Academy of Sciences of the United States of America， 2017， 114（30）： 7952-7957.
[46]	MOSLEMZADEH H， MOHAMMADI S. An atomistic entropy based finite element multiscale method for modeling amorphous materials［J］. International Journal of Solids and Structures， 2022， 256： 111983.