Abstract
A transient global numerical simulation is adopted to develop a high quality multi-crystalline silicon (mc-Si) ingot using directional solidification (DS) furnace. The geometry of the simulation furnace is based on the G1 DS furnace. In this simulation, the modification is done on the side heaters wherein each heater group has different temperature profile. The thermal field is investigated during and after solidification process. The thermoelastic stress model is solved for the stress distribution in the mc-Si ingot. The modified heater system results in the reduction of thermal stress up to 8.3 × 103 Mpa and the reduction of dislocation up to 4.0 × 105 [1/m2]. Also, the melt crystal interface, temperature distribution and power profile are investigated. From the heater modification system will be reduce the thermal stress and dislocation density in the grown ingot.
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Data Availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author upon reasonable request.
References
Li L, Liu X, Liu Y, Zhang J (2014) **ong, heat transfer in an industrial directional solidification furnace with multi-heaters for silicon ingots. J Cryst Growth 385:9–15. https://doi.org/10.1016/j.jcrysgro.2013.01.053
Kesavan V, Srinivasan M, Ramasamy P (2019) Optimizing oxygen impurities using different heater design in the directional solidification of multi-crystalline silicon. Mater Res Express 6:106323. https://doi.org/10.1088/2053-1591/ab4154
Ma X, Zheng L, Zhang H, Zhao B, Wang C, Xu F (2011) Thermal system design and optimization of an industrial silicon directional solidification system. J Cryst Growth 318:288–292. https://doi.org/10.1016/j.jcrysgro.2010.10.102
Rao S, He L, Zhang F, Lei Q, Luo Y, **ong H, Hu Y, Huang X, Song B (2020) Numerical and experimental investigation of sectional heater for improving multi-crystalline silicon ingot quality for solar cells. J Cryst Growth 537:125606. https://doi.org/10.1016/j.jcrysgro.2020.125606
Gurusamy A, Thiyagarajan M, Srinivasan M, Ramasamy P (2023) Numerical investigation on modified bottom heater of DS furnace to improve mc-Si ingot. Silicon:1–12
Anbu G, Srinivasan M, Ramasamy P (2019) Modelling on modified heater design of DS system for improving the quality of mc-silicon ingot. Silicon 11:1393–1400. https://doi.org/10.1007/s12633-018-9944-7
Sanmugavel S, Srinivasan M, Aravinth K, Ramasamy P (2017) Effect of heater design on the melt crystal interface. In AIP conference proceedings (Vol. 1832, No. 1, p 120020). AIP Publishing LLC
Song B, Luo Y, Rao S et al (2020) Numerical simulation on Design of Temperature Control for side heater in directional solidification system of multi-crystalline silicon. Silicon 12:2179–2187. https://doi.org/10.1007/s12633-019-00310-6
Chen W, Wu Z, Zhong G, Ding J, Yu Y, Zhou X, Huang X (2016) Optimization of heat transfer by adjusting power ratios between top and side heaters for casting high-performance multi-crystalline silicon ingots. J Cryst Growth 451:155–160
Nguyen THT, Chen JC, Hu C, Chen CH, Huang YH, Lin HW, Yu A, Hsu B (2017) Numerical analysis of thermal stress and dislocation density distributions in large size multi-crystalline silicon ingots during the seeded growth process. J Cryst Growth 468:316–320
Fang HS, Wang S, Zhou L, Zhou NG, Lin MH (2012) Influence of furnace design on the thermal stress during directional solidification of multicrystalline silicon. J Cryst Growth 346(1):5–11
Yu Q, Liu L, Ma W, Zhong G, Huang X (2012) Local design of the hot-zone in an industrial seeded directional solidification furnace for quasi-single crystalline silicon ingots. J Cryst Growth 358:5–11
Sundaramahalingam S, Gurusamy A, Somi Ganesan N, Venkatachalam K, Perumalsamy R (2021) Simulation and experimental approach to investigate the annealing effect on mc-Si ingot grown by directional solidification process for PV application. Silicon 13:2569–2580. https://doi.org/10.1007/s12633-020-00604-0
Nagarajan SG, Sanmugavel S, Kesavan V, Aravindan G, Srinivasan M, Ramasamy P (2019) Influence of additional insulation block on multi-crystalline silicon ingot growth process for PV applications. J Cryst Growth 516:10–16. https://doi.org/10.1016/j.jcrysgro.2019.03.017
Hirth JP, Lothe J, Mura T (1983) Theory of Dislocations (2nd ed.), J Appl Mech 50(2):476–477
Smirnova OV, Mamedov VM, Kalaev VV (2014) Numerical modeling of stress and dislocations in Si ingots grown by seed-directional solidification and comparison to experimental data. Cryst Growth Des 14:5532–5536. https://doi.org/10.1021/cg500736j
Sugunraj S, Aravindan G, Srinivasan M, Ramasamy P (2023) Influence of argon gas flow rate on oxygen and carbon impurities concentration in multicrystalline silicon grown by directional solidification furnace: numerical and experimental investigation. Silicon 15(4):1701–1724
Wenjia S, Zuo R, Mazaev K, Kalaev V (2010) Optimization of crystal growth by changes of flow guide, radiation shield and sidewall insulation in Cz Si furnace. J Cryst Growth 312:495–501
Muthukumar R, Sanmugavel S, Aravinth K, Bhargav PB, Ramasamy P, Kesavan V (2023) Numerical simulation approach to investigate the effect of gas tube design on the impurities distribution and thermal properties of multi-crystalline silicon ingot grown by directional solidification process. J Cryst Growth 603:127001
Chen XJ, Nakano S, Liu LJ, Kakimoto K (2008) Study on thermal stress in a silicon ingot during a unidirectional solidification process. J Cryst Growth 310:4330–4335
Zhou N, Lin M, Wan M, Zhou L (2015) Lowering dislocation density of directionally grown multicrystalline silicon ingots for solar cells by simplifying their post-solidification processes—a simulation approach. J Therm Stresses 38:146–155. https://doi.org/10.1080/01495739.2014.985553
Acknowledgements
This work was supported by the Department of Science and Technology, Government.
of India. (Order No. DST/TMD / CERI /RES/ 2020/7(c) dated on 31/12/2020).
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All authors contributed to the study’s conception and design. Material preparation, data collection, and analysis were performed by Muthukumar R, Aravinth K*, Balaji Barghav P, Ramasamy P. The first draft of the manuscript was written by Muthukumar R, Aravinth K, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Muthukumar, R., Aravinth, K., Bhargav, P.B. et al. Numerical Investigation on Effect of Side Heater Modification on the Stress Distribution and Dislocation Density of Multi-Crystalline Silicon Ingot Grown by DS Process. Silicon 15, 7755–7764 (2023). https://doi.org/10.1007/s12633-023-02614-0
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DOI: https://doi.org/10.1007/s12633-023-02614-0