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1 This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier s archiving and manuscript policies are encouraged to visit:

2 Journal of Crystal Growth 385 (2014) 9 15 Contents lists available at ScienceDirect Journal of Crystal Growth journal homepage: Heat transfer in an industrial directional solidification furnace with multi-heaters for silicon ingots Zaoyang Li a, Lijun Liu a,n, Xin Liu a, Yunfeng Zhang b, Jingfeng Xiong b a Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi an Jiaotong University, Xi an, Shaanxi , China b Yingli Green Energy Holding Co., Ltd., Baoding, Hebei , China article info Available online 3 May 2013 Keywords: A1. Computer simulation A1. Heat transfer A1. Directional solidification B3. Solar cells abstract We carried out transient global simulations of melting, growing and annealing processes in an industrial directional solidification furnace with a top and side heater. The power distribution between the two heaters was set to 3:7, 5:5 and 7:3 to investigate its effect on global heat transfer and silicon crystal growth. Quantitative comparisons of temperature distributions are presented. Increasing the top heating power slightly increases the melting time and changes the melting sequence. In the crystal growth process, adjusting the power distribution from 3:7 to 7:3 can lead to an 8 12 K change in axial temperature difference in the silicon domain. Both the intensity and pattern of the silicon melt flow are influenced by the change in power distribution. The melt-crystal interface is less convex to the melt with an increase in top heating power, especially at the final stage of solidification. In the annealing process, the ingot temperature decreases to approximately 1600 K to reduce the thermal stress and dislocation density. Isotherm shapes are different at this stage and may lead to different thermal stress and dislocation density distributions in the silicon ingot. The numerical results provide a basic understanding of the heat transfer characteristics due to power distribution in an industrial multi-heater directional solidification furnace. & 2013 Elsevier B.V. All rights reserved. 1. Introduction Directional solidification (DS) is the main method for the manufacture of multi-crystalline silicon ingots for solar cells. The DS furnace is a highly coupled nonlinear thermal system with complex interactions among the silicon melt, argon gas and different solid components [1]. The thermal field in the furnace should be optimized, as it determines the ingot quality [2 4]. Heaters provide heating power and are thus the most important factor in controlling the thermal field. With an increase in ingot size, multiple heaters are preferred for better control of the thermal field in the furnace and in the silicon domain. In a multi-heater DS furnace, different heater positions and power distributions could influence the global temperature and flow fields as well as the melt-crystal interface shape [5]. Therefore, it is essential to investigate the characteristics of heat transfer resulting from heater settings in such a furnace to produce large size and high quality silicon ingot. The important roles of heater design and heating power control have been studied by some researchers for both Czochralski (CZ) and DS crystal growth. Müller and Friedrich [6] pointed out that it n Corresponding author. Tel./fax: addresses: ljliu@mail.xjtu.edu.cn, lijun_liu70@hotmail.com (L. Liu). is important to adjust the heater(s) power for high quality crystal growth. For the CZ furnace, Teng et al. [7] found that the amount of oxygen released from the silica crucible to the silicon melt could be lowered by adjusting the heater position to decrease the temperature on the crucible wall. Cao et al. [8] designed a new heater structure to increase the temperature gradient near the melt-crystal interface and thus the crystal could be grown at a faster rate. Rudolph et al. [9,10] even developed combined internal heater-magnet modules for the simultaneous generation of temperature and traveling magnetic fields. These heater designs are helpful in improving crystal quality and reducing production cost. For the DS furnace, Ma et al. [5] pointed out that maintaining a relatively flat growth interface throughout the entire growth process could be achieved by optimizing the top and side heating powers. Liu et al. [11] and Nakano et al. [12] tried to control crystal growth by adjusting the cooling rate, which is closely related to the heating power supply. As mentioned previously, multiple heaters are preferred in industrial DS furnaces to manufacture large size and high quality silicon ingots. However, few research have investigated these heaters' role so far. Heater settings can influence the melting, growing and annealing processes, yet few related research could be found in literatures. In this paper, an industrial multi-heater DS furnace with top and side heater that can produce 500 kg ingots was chosen for the numerical study. Transient simulations were carried out for the /$ - see front matter & 2013 Elsevier B.V. All rights reserved.

3 10 Z. Li et al. / Journal of Crystal Growth 385 (2014) 9 15 Temperature of TC1(K) melting of feedstock, crystal growth and ingot annealing. Based on the global modeling, we changed the power distribution between the two heaters to investigate its influence on the global thermal field, especially that in the silicon domain. Quantitative comparisons and analyses of temperature distributions for the different power ratios during the melting, growing and annealing processes are presented. The results are helpful in understanding the characteristics of heat transfer due to power setting in an industrial multi-heater DS furnace. 2. Model description mm TC TC1 13 The configuration, dimensions and computational grids of the multi-heater DS furnace for casting silicon ingots are shown in Fig. 1(a). A top and a side heater exist in the furnace. A quartz crucible is supported by graphite susceptors to avoid deformation at high temperature. The side length of the square crucible is 840 mm and the final solidified ingot is approximately 250 mm high. A thermocouple (TC1) installed near the upper surface of the top heater is used to control heating power by monitoring temperature. Another thermocouple (TC2) is installed in the upper center of the heat exchange block to monitor the temperature at the crucible base. The furnace is operated at a pressure of 600 mbar and the argon flow rate is 20 L/min. 3 4 TC Power Position 1:Melt 2:Crystal 3:Crucible 4:Susceptor 5:Heatexchangeblock 6-8:Insulations 9:Insulatedpad 10:Wall 11:Argontube 12:Cover 13:Heaters 14:Argondomain 15:Argoninlet 16:Argonoutlet Fig. 1. Model of an industrial multi-heater DS furnace: (a) configurations and computational grids; and (b) process parameters Power (kw) Insulation position (cm) The entire furnace is divided into a number of sub-domains for simulation and the structured/unstructured combined mesh scheme is applied to improve the computation efficiency. To describe the entire DS process accurately, transient global simulations including thermal conduction, thermal radiation, melt convection, gas flow as well as phase change are carried out. The algorithms for the global modeling of heat transfer in a DS furnace have been published elsewhere [13 15]. The enthalpy method on fixed grids is applied to track the solid liquid interface for both the melting and growing processes [16]. For the simulation of feedstock melting, it is assumed that both the feedstock volume and density are equal to those of the solidified ingot. During the DS process, silicon feedstock is loaded into the crucible and melted. Then the liquid silicon begins to crystallize from the crucible base and finally the hot silicon ingot is annealed and cooled to the ambient temperature. The control parameters corresponding to the above processes are shown in Fig. 1(b). The two thin solid vertical lines divided the curve sections into the melting, growing and annealing processes. The side insulation is closed through the entire melting process and the power increases sharply to heat the furnace initially. The temperature of TC1 reaches 1450 K at approximately 180 min and the power begins to be controlled by the preset temperature of TC1 until the end of solidification. At this moment, the process changes from power control to temperature control. The side insulation is opened and the temperature of TC1 is maintained almost constant when the crystal grows. The power increases accordingly to provide an appropriate heat flux through the silicon domain. When annealing, the side insulation is closed and temperature of TC1 decreases to reduce the temperature difference in the silicon ingot. Then, the side insulation is opened again and temperature of TC1 decreases to cool the furnace. The computation time needed for performing such a fully time-dependent simulation is about 50 h with a personal computer. The CPU of the computer is Intel (R) Core (TM) i GHz. The power distribution ratio between the top and side heaters is 5:5 in the industrial production process. Therefore, it is set to 3:7, 5:5 and 7:3 in the numerical simulations to remain within a practical application range. The total power applied in the melting process and the TC1 settings in the growing and annealing processes are the same as those in the experiment. Other process parameters, such as the side insulation moving velocity and the argon flow rate, are maintained the same for all three cases. The power distribution ratio is defined as the top to the side heating power. 3. Results and discussion 3.1. Validation of the heat transfer model We carried out transient global simulations of the melting, growing and annealing processes in an industrial multi-heater DS furnace. To validate the heat transfer model, we first compared the simulations with experimental data at a power distribution ratio of 5:5. In Fig. 2(a) and (b), we compare the temperature variation of TC2 between numerical simulations and experimental data for the melting, growing and annealing processes. Fig. 2(c) shows the evolutions of the solidification fraction when the crystal grows. The melt-crystal interface position is detected by using a quartz rod in the experiment. The numerical predictions agree satisfactorily with the experimental measurements. The transient heat transfer model can therefore reproduce the whole DS process in the multi-heater furnace.

4 Z. Li et al. / Journal of Crystal Growth 385 (2014) Temperature of TC2 (K) Experiment Calculation Temperature of TC2 (K) Experiment Calculation Solidification fraction Experiment Calculation Fig. 2. Comparison of simulations with experiment: (a) temperature evolutions of TC2 at melting stage; (b) temperature evolutions of TC2 at growing and annealing stages; and (c) evolutions of solidification fraction at growing stage Heat transfer in the melting process The total heating power is maintained the same in the melting processes for cases with different power distributions. Fig. 3 shows the temperature evolutions at the center of the silicon top surface. As shown in Fig. 3(a), there are two main stages in the melting processes: heating of the furnace and melting of the feedstock. The heating stage lasts from 0 to approximately 480 min and the furnace temperature increases rapidly. The temperature at the silicon top surface reaches the melting point of 1685 K at approximately 480 min and the feedstock begins to melt at the top. Then, the temperature increases relatively slowly as the feedstock absorbs heat when melting. There exists another turning point at approximately 730 min when the temperature begins to increase rapidly again after complete melting. Comparing the three cases in Fig. 3(a), it can be seen that the temperature at the silicon top surface is higher when the top heater shares more power. Fig. 3(b) shows the partial enlarged view of the zone indicated in Fig. 3(a). It is obvious that the time spent on melting of the feedstock is slightly longer when the top heater shares more power. As shown in Fig. 3(b), the time spent in melting feedstock is approximately 4 h. We therefore chose 5 time points, 480, 540, 600, 660 and 720 min, to analyze the phase change in the melting process. Evolutions of the solid liquid interface at these five time points for power distribution ratios of 3:7 and 7:3 are shown in Fig. 4. The feedstock melts first at the top corner, where it is in contact with the crucible. After the initial stage, the top layer of feedstock begins to melt from top to bottom, whereafter the side feedstock near the crucible wall and then that near the crucible bottom wall melts. By comparing the ten figures for the two cases, it is found that adjusting the power distribution slightly changes the feedstock melting sequence. With an increase in top heating power, the feedstock at the side and bottom regions melts slightly later. The early melting of the bottom feedstock indicates that the preservation of the seed crystals at the crucible bottom when casting quasi-single crystalline silicon ingots cannot be guaranteed in such a furnace by adjusting the power distribution [17] Heat transfer in the growing process The temperature variation of TC1 is preset to control the heating power in the growing process. The preset values are different for the three cases to maintain the same initial temperature at the base of the silicon melt, whereas the trends are the same to ensure comparability of the simulation results. Fig. 5 shows the temperature distribution (left hand side) and velocity

5 12 Z. Li et al. / Journal of Crystal Growth 385 (2014) Temperature at silicon top surface (K) :7 5:5 7:3 Temperature at silicon top surface (K) :7 5:5 7: Fig. 3. Evolutions of temperature at the center of silicon top surface: (a) whole melting process; and (b) partial enlarged view of (a). field (right hand side) in the silicon melt before the start of solidification. The side insulation is still closed at this moment and the bottom of the silicon melt is approximately 1687 K. The temperature differences along the axis for the three power distributions are 13.8, 17.9 and 21.9 K, and the corresponding temperature gradients are 0.58, 0.75 and 0.91 K/cm, respectively. Adjusting the power distribution from 3:7 to 7:3 can lead to an approximate 8.0 K change in axial temperature difference at this stage. The flow intensity increases while the side heater shares more power. This occurs because the side heating increases the radial temperature gradient, which induces melt convection in the crucible. The maximum difference in flow intensity is at the melt free surface. Apart from the flow intensity, the melt flow patterns are also different for the three cases. In Fig. 5(a), the silicon melt near the crucible side wall flows upwards as the side heater shares more power. For the power distribution ratio of 7:3, the side silicon melt flows downwards. Fig. 6 shows the thermal and flow fields as well as the meltcrystal interfaces when 50% of the silicon melt is solidified. The temperature differences along the crucible axis for the three cases are 116.3, 122.0, and K. The large difference results mainly from the upward movement of the side insulation and more heat is lost from the gap between the side and bottom insulations [2]. The axial temperature gradients in the silicon melt are 0.73, 0.96 and 1.17 K/cm, respectively. However, the gradients along the crystal axis for the three cases could be as high as 8.96, 9.21 and 9.43 K/cm. This is mainly due to the latent heat released at the melt-crystal interface. The isotherm of 1685 K is consistent with the melt-crystal interface, which is shown on the right hand side of the figures. The interface becomes less convex to the melt when the top heater shares more power, though the difference is minor. Silicon crystal growth takes approximately 20 h. The heating power keeps increasing during this process to guarantee an appropriate up-to-down heat flux through the silicon domain, as shown in Fig. 1(b). Fig. 7 shows the temperature distribution and melt-crystal interface shape at the end of solidification. The temperature differences along the ingot axis are as high as 181.0, and K for the three power distributions, respectively, corresponding to a temperature gradient along the ingot axis as 7.54, 7.80 and 8.05 K/cm, respectively. The change in temperature difference is approximately 12.0 K between the 3:7 and 7:3 ratios. Three factors are responsible for the large temperature gradient: the large amount of heat loss from the gap between the side and bottom insulations, the increasing heating power and the released latent heat. The right hand side of the figures shows that power distribution can influence the melt-crystal interface shape significantly at this stage of solidification Heat transfer in the annealing process After full solidification, the furnace temperature decreases gradually to anneal the hot silicon ingot. Fig. 8 shows the temperature distributions at different annealing stages for the three power distributions. The left and right boundaries of these figures are the ingot side wall and ingot axis, respectively. Figs. 8 (a1) (a3) shows the temperature distributions in the ingot after solidification and before annealing. The side insulation is still open at this moment. The temperature differences along the ingot axis are 158.5, and K for the three power ratios and the corresponding temperature gradients are 6.60, 7.02 and 7.43 K/cm, respectively. The values are smaller than those in Fig. 7, as there is no latent heat releasing any more. Figs. 8(b1) (b3) shows the temperature distributions during annealing. The temperature in the silicon ingot is approximately 1600 K, which is beneficial for the reduction in thermal stress and dislocation density [18]. The heating power decreases and the insulations are closed at this stage. Therefore, the temperature difference in the ingot decreases and the values along the axis for the three power distributions are 19.3, 26.7 and 34.4 K, respectively. The corresponding axial gradients are only 0.80, 1.11 and 1.42 K/cm, respectively. The isotherm shapes are different from one another in the three figures. These differences may lead to different thermal stress distributions and dislocation densities in the silicon ingot. After annealing, the furnace is cooled to ambient temperature to remove the silicon ingot. Figs. 8(c1) (c3) shows the temperature distributions in the ingots in such a process. The heating power decreases to zero and the insulation chamber is wide open at this time. Therefore, the silicon domain is the hottest in the furnace and heat is transferred from the ingot to its surroundings. Accordingly, annular isotherms are formed in the silicon ingot. The temperature difference in the ingot is approximately 50 K for the three cases.

6 Author's personal copy Z. Li et al. / Journal of Crystal Growth 385 (2014) Fig. 4. Melting processes in the multi-heater furnace for different power distributions: (a1 a5) 3:7; (b1 b5) 7:3. (a1) and (b1): 480 min; (a2) and (b2): 540 min; (a3) and (b3): 600 min; (a4) and (b4): 660 min; (a5) and (b5): 720 min. Fig. 5. Temperature distribution (left, 1 K between two isotherms) and velocity vector (right) in the melt just before solidification for different power distributions: (a) 3:7; (b) 5:5; and (c) 7:3. Fig. 6. Temperature distribution (left, 2 K between two isotherms), velocity vector and melt-crystal interface (right) in the silicon domain when half melt is solidified for different power distributions: (a) 3:7; (b) 5:5; and (c) 7:3.

7 14 Z. Li et al. / Journal of Crystal Growth 385 (2014) 9 15 Fig. 7. Temperature distribution (left, 5 K between two isotherms) and melt-crystal interface (right) in the silicon domain at the end of solidification for different power distributions: (a) 3:7; (b) 5:5; and (c) 7:3. Fig. 8. Temperature distribution in the annealing process for different power distributions (left: 3:7; middle: 5:5; right: 7:3): (a1 a3) before annealing, 5 K between two isotherms; (b1 b3) annealing, 2 K between two isotherms; (c1 c3) after annealing, 2 K between two isotherms. The left boundary is the ingot side wall; the right boundary is the ingot axis.

8 Z. Li et al. / Journal of Crystal Growth 385 (2014) Conclusions Heat transfer is the most important phenomenon for crystal growth. Therefore, we carried out transient global simulations of melting, growing and annealing processes in an industrial multiheater DS furnace to investigate the effect of power distribution on global heat transfer and silicon crystal growth. The power distribution can influence the temperature distribution in the silicon domain significantly and thus affect the whole DS process. Raising the top heating power can slightly increase the melting time and change the melting sequence, whereas it cannot prevent early melting of the feedstock at the crucible base. Adjusting the power distribution from 3:7 to 7:3 can lead to an 8 12 K change in axial temperature difference in the silicon domain when crystals grow. Changes in the thermal field influence the melt flow structure and melt-crystal interface shape simultaneously. Annealing of the hot silicon ingot reduces its temperature difference significantly. Isotherm distributions are different at this stage and may lead to different thermal stress distributions and dislocation densities in the silicon ingot. The numerical results provide a basic understanding of the heat transfer characteristics from power distribution in an industrial multi-heater DS furnace. Acknowledgments References [1] Z.Y. Li, L.J. Liu, X. Liu, Y.F. Zhang, J.F. Xiong, Journal of Crystal Growth 360 (2012) 87. [2] W.C. Ma, G.X. Zhong, L. Sun, Q.H. Yu, X.M. Huang, L.J. Liu, Solar Energy Materials and Solar Cells 100 (2012) 231. [3] M. M Hamdi, E.A. Meese, H. Laux, E.J. Øvrelid, Materials Science Forum 508 (2006) 597. [4] Y. Delannoy, F. Barvinschi, T. Duffar, Journal of Crystal Growth 303 (2007) 170. [5] X. Ma, L.L. Zheng, H. Zhang, B. Zhao, C. Wang, F.H. Xu, Journal of Crystal Growth 318 (2011) 288. [6] G. Müller, J. Friedrich, Selected Topics on Crystal Growth 1270 (2010) 255. [7] Y.Y. Teng, J.C. Chen, C.W. Lu, C.C. Huang, W.T. Wun, H.I. Chen, C.Y. Chen, W. C. Lan, International Journal of Photoenergy 2012 (2012) [8] J.W. Cao, Y. Gao, Y. Chen, G.H. Zhang, M.X. Qiu, Rare Metals 30 (2011) 155. [9] P. Rudolph, Journal of Crystal Growth 310 (2008) [10] P. Rudolph, M. Czupalla, B. Lux, F. Kirscht, C. Frank-Rotsch, W. Miller, M. Albrecht, Journal of Crystal Growth 318 (2011) 249. [11] L.J. Liu, S. Nakano, K. Kakimoto, Journal of Crystal Growth 310 (2008) [12] S. Nakano, X.J. Chen, B. Gao, K. Kakimoto, Journal of Crystal Growth 318 (2011) 280. [13] L.J. Liu, K. Kakimoto, International Journal of Heat and Mass Transfer 48 (2005) [14] Z.Y. Li, L.J. Liu, W.C. Ma, K. Kakimoto, Journal of Crystal Growth 318 (2011) 298. [15] L.J. Liu, S. Nakano, K. Kakimoto, Journal of Crystal Growth 303 (2007) 165. [16] V.R. Voller, A.D. Brent, C. Prakash, International Journal of Heat and Mass Transfer 32 (1989) [17] Q.H. Yu, L.J. Liu, W.C. Ma, G.X. Zhong, X.M. Huang, Journal of Crystal Growth 358 (2012) 5. [18] K. Hartman, M. Bertoni, J. Serdy, T. Buonassisi, Applied Physics Letters 93 (2008) This research was supported by the NSFC ( ), NCET and Fundamental Research Funds for the Central Universities of China.