Numerical Simulation of Stress Intensity Factor for Pore-Crack in Quartz Crucible under High Temperature Cyclic Loading

Abstract

Abstract: The inner wall of the quartz crucible for continuous Czocharlski will form more bubbles with the increase of Czocharlski times, and it is easy to generate dislocations in the crystal and the erosive silicon melt, which will cause the crucible to dissolve and corrode over time. In order to study the effect of the interaction of erosive silicon melt with bubbles on the crucible, in situ observations of the performance of quartz crucibles are expected. However, the extremely high temperature environment inside single crystal furnaces makes it difficult to investigate their interiors experimentally. In this paper, the pore-crack on the inner surface of the quartz crucible are taken as the research object, and the finite element simulation is used to obtain the stress intensity factor values of different pore shapes, crack shapes and crack inclination angles of the quartz crucible under high temperature cyclic loading at different Czocharlski stages. The results show that with the increase of the crack inclination angle, the K_Ι value shows a trend of gradually decreasing, the K_Ⅲ value shows a trend of first increasing and then decreasing, and the K_Ⅲ value is symmetrical distributed along 45°; furthermore, with the increase of the pore depth/diameter ratio, K_Ι value shows a decreasing trend, and the rate of reduction when the depth/diameter ratio is equal to 1 as the boundary has a significant increase, K_Ⅲ is much smaller than K_Ι value, indicating that the dominant form of cracking is type Ⅰ; the crack shape ratio has a significant impact on the value of K_Ι or K_Ⅲ, and the smaller the shape ratio, the greater the value of the stress intensity factor at the crack tip; when the inclination angle is 0°, the total stress intensity factor K value is the largest, which will make the crack most likely to expand and the most harmful to the quartz crucible. Finally, in the case of continuous Czocharlski, the total stress intensity factor of the crown growth process is always greater than that of the equal diameter growth, cone and cooling growth process. Simulation results bring certain theoretical guiding significance for production.

Key words: quartz crucible, pore, depth/diameter ratio, crack shape, stress intensity factor, finite element simulation

CLC Number:

O782
TB321

ZHAO Guoyan, QU Li, LI Jin, MA Run. Numerical Simulation of Stress Intensity Factor for Pore-Crack in Quartz Crucible under High Temperature Cyclic Loading[J]. Journal of Synthetic Crystals, 2023, 52(3): 493-500.

References

[1] HOU G F, SUN H H,JIANG Z Y, et al. Life cycle assessment of grid-connected photovoltaic power generation from crystalline silicon solar modules in China[J]. Applied Energy, 2016, 164: 882-890.
[2] PENG L H, QIN S, GU X B. Effects of melting parameters and quartz purity on silica glass crucible produced by arc method[J]. Engineering Research Express, 2020, 2(1): 015046.
[3] 孙占喜, 李涛陈, 官元. 一种石英坩埚生产工艺: CN104445886A[P]. 2014-11-24.
SONG Z X, LI T C, GUAN Y. Production process of quartz crucible: CN104445886-A[P]. 2014-11-24 (in Chinese).
[4] 张大虎, 田青越, 汪灵, 等. 单晶硅生长用石英坩埚的组成与结构特征[J]. 矿物岩石, 2016, 36(1): 12-16.
ZHANG D H, TIAN Q Y, WANG L, et al. Composition and structure of the quartz crucible for monocrystalline growth[J]. Journal of Mineralogy and Petrology, 2016, 36(1): 12-16 (in Chinese).
[5] PAULSEN O, RRVIK S, MUGGWRUD, et al. Bubble distribution in fused quartz crucibles studied by micro X-ray computational tomography. Comparing 2D and 3D analysis[J]. Journal of Crystal Growth, 2019, 520: 96-104.
[6] TOSHIRO M, SUSUMU M,MITSUO H, et al. In-situ observation of bubble formation at silicon melt-silica glass interface[J]. Journal of Crystal Growth, 2011, 318(1): 196-199.
[7] LIU X, GAO B, KOICHI K. Numerical investigation of carbon contamination during the melting process of Czochralski silicon crystal growth[J]. Journal of Crystal Growth, 2015, 417: 58-64.
[8] VOROB’EV A N, SID’KO A P, KALAEV V V. Advanced chemical model for analysis of Cz and DS Si-crystal growth[J]. Journal of Crystal Growth, 2014, 386: 226-234.
[9] CHEN C, CHIANG P Y, CHANG C H, et al. Three-dimensional numerical simulation of flow, thermal and oxygen distributions for a Czochralski silicon growth with in a transverse magnetic field[J]. Journal of Crystal Growth, 2014, 401: 813-819.
[10] VEGADA M, BHATT N M. Effect of location of zero Gauss plane on oxygen concentration at crystal melt interface during growth of magnetic silicon single crystal using czochralski technique[J]. Procedia Technology, 2016, 23: 480-487.
[11] LIU X, HIROFUMI H, YOSHIJI M, et al. Transient global modeling for the pulling process of Czochralski silicon crystal growth. II. Investigation on segregation of oxygen and carbon[J]. Journal of Crystal Growth, 2020, 532: 125404.
[12] ZHAO W H, LI J C, LIU L J. Control of oxygen impurities in a continuous-feeding Czochralski-silicon crystal growth by the double-crucible method[J]. Crystals, 2021, 11(3): 264.
[13] 罗晓斌, 张波, 辛玉龙. 直拉法硅单晶中石英坩埚析晶问题的探讨[J]. 河南科技, 2014(4): 64.
LUO X B, ZHANG B, XIN Y L. Discussion on crystallization of quartz crucible in Czochralski silicon single crystal[J]. Journal of Henan Science and Technology, 2014(4): 64 (in Chinese).
[14] HIRSCH A, TREMPA M, SCHULZE M, et al. Factors influencing the gas bubble evolution and the cristobalite formation in quartz glass Cz crucibles for Czochralski growth of silicon crystals[J]. Journal of Crystal Growth, 2021, 570: 126231.
[15] HUANG X M, HOSHIKAWA T, UDA S. Analysis of the reaction at the interface between Si melt and Ba-doped silica glass[J]. Journal of Crystal Growth, 2007, 306(2): 422-427.
[16] 石星宇. 连续拉晶下石英坩埚内气泡变化规律及晶棒的性能研究[D]. 银川: 宁夏大学, 2022.
SHI X Y. Study on the change law of bubbles in quartz crucible and the properties of crystal rod under continuous crystal pulling[D]. Yinchuan: Ningxia University, 2022 (in Chinese).
[17] 陶文铨. 传热学[M]. 5版. 北京: 高等教育出版社, 2019: 28-3.
TAO W Q, Heat transfer[M]. Version 5. Beijing: Higher Education Press, 2019:28-3 (in Chinese).
[18] 陈明祥. 弹塑性力学[M]. 北京: 科学出版社, 2007.
CHEN M X. Elastoplastic mechanics[M]. Beijing: Science Press, 2007 (in Chinese).
[19] LIN X B, SMITH R A. Finite element modelling of fatigue crack growth of surface cracked plates[J]. Engineering Fracture Mechanics, 1999, 63(5): 503-522.
[20] 宋德双, 周思柱, 曾云, 等. 轴向载荷下油管点蚀坑-裂纹应力强度因子研究[J]. 石油机械,2021, 49(6): 116-122.
SONG D S, ZHOU S Z, ZENG Y, et al. Study on stress intensity factor of pit-crack of tubing under axial load[J]. China Petroleum Machinery, 2021, 49(6): 116-122 (in Chinese).