Effect of Side Insulation on Stress and Dislocation in the Multi-crystalline Silicon Ingot during Cooling Process

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1 Journal of Materials Science and Engineering B 7 (5-6) (017) doi: /161-61/ D DAVID PUBLISHING Effect of Side Insulation on Stress and Dislocation in the Multi-crystalline Bing Zhou 1, Wenliang Chen, Hui Dong, Xucheng Zhou, Fengming Qi, Jianming Luo and Xinming Huang 1, 3 1. School of Materials Science and Engineering, Nanjing Tech University, Nanjing, Jiangsu 1009, China. Donghai JA Solar Technology Co., Ltd., Lianyungang, Jiangsu 300, China 3. JA Solar Holdings Co., Ltd., Feng Tai District, Being , China Abstract: Haasen-Alexander-Sumino model was applied to analyze the effects of the side insulation on thermal stress and dislocation density in silicon crystal during the cooling process. The simulation results showed that the side insulation being immobile initially and then rapidly moving up was the most favorable for the cooling process due to the low thermal stress and dislocation density were obtained. The optimized design was implemented in casting experiments, and the experimental results showed that the high-performance multi-crystalline silicon ingot had a lower dislocation agglomerates density. The average conversion efficiency of solar cells was about 0.05% higher with the optimized cooling process (18.43%) than with the original cooling process (18.38%). Key words: Computer simulation, thermal stresses, dislocations, industrial crystallization, solar cells. 1. Introduction Solar cells based on HP (high-performance) mc-si (multi-crystalline silicon) have been widely used in photovoltaic market due to well-balanced relatively high conversion efficiency and low casting cost. However, HP mc-si obtained using directional solidification contains many dislocations, an increase in dislocation density especially electrically active dislocation agglomerate density reduces the conversion efficiency of solar cells. As the inhomogeneous temperature distribution in the large-size crystal, the thermal stresses are inevitable. When the internal stress in the crystal is larger than the plastic yield stress, the amount of dislocations increases multiplicatively. It has been reported that dislocation density rapidly increased during the cooling process [1, ]. To reduce the dislocation density, it is very necessary to optimize the cooling process. Many researchers have investigated the evolutions Corresponding author: Bing Zhou, professor, research field: crystal growth. of thermal stress and dislocation density during the cooling process. Nakano et al. [3] investigated the effects of the cooling rate on dislocation density, and they found that the maximum dislocation density was decreased and that of residual stress was increased during a fast cooling process. Wang et al. [4] found that the dislocation-free regions and thermal stress were significantly affected by the bottom insulation motion, and deemed the sinusoidal motion of the bottom insulation is probably better for the improvement of the ingot quality. Zhou et al. [5, 6] proposed a modified cooling process with lower temperatures of both thermocouples 1 and, and they found that the final dislocation density could be reduced significantly with the modified cooling process. Wang et al. [7] investigated the effect of gas velocity on the thermal stress during the cooling process, and concluded that a fast gas inlet at the initial cooling changing a slow gas inlet at the later stage of cooling by a certain ramping-down rate is conducive to reduce the stress level. Some improved designs of cooling process were proposed by

2 90 numerical simulation in previous reports. However, there is a lack of casting experimental support to the simulation results. Furthermore, few detailed studies on the effects of the side insulationn on the thermal stress and dislocation density during the cooling process have been conducted. In this paper, four new designs based on existing cooling process were put forward to obtain a better cooling process for the HP mc-si industrial production. The HAS (Haasen-Alexander-Sumino) model was applied to analyze the effect of the position of side insulation on thermal stress and dislocation density in silicon crystal during the cooling process. The casting experiments were also carried out, the dislocation agglomerates density of silicon wafers and the conversion efficiency of solar cells were all evaluated.. Experimental and Numerical Methods.1 Model Description A JZ660 DS furnace was used in the experiments, as shown in Fig. 1. It consists of top and side graphite heaters, a quartz crucible, a graphite susceptor, a heat exchange block, a gas shield, insulations, thermocouples, and partition blocks. Specially processed quartz granules were first paved acrosss the entire bottom of crucible with a volume of 1,040 1, mmm 3, and then a Si 3 N 4 was coated on the inner wall of the crucible. About 810-kg Si feedstock was loaded into the prepared crucible to produce a silicon ingot with a height of 350 mm. The CGSim transient global model was used for the simulations presented in this paper, and it has been verified in our previous studies [8, 9]. In the numerical model, the furnace was axisymmetric based on the real DS system, and the model took into account thermal radiation, melt convection and gas flow. The melt was regarded as a Newtonian fluid, and the inert argon gas was treated assumed to be a -D the thermal conduction, as an ideal gas and incompressible, and all of the radiative surfaces weree assumed to be diffuse gray. Other descriptions of the model have been given in our previous publications, including the numerical mesh settings of each furnace part [8], the physical parameter settings of each material [8] and the algebraic turbulence model for melt convection [10]. The temperature at the crystallization interface was set to 1,685 K, a steady global simulation was first performed, and then an unsteady global simulation was performed. Unsteady computations were performed with taking into account the stress relaxation. Thermo-elastic stress model was used to analyze the thermal stresss Fig. 1 Configurations of the DS furnace.

3 91 distribution during the solidification process [11, 1]. The crystal was assumed as isotropic and the Von Mises stress was used to reflect the thermal stress. The process of dislocation formation related to plastic deformation was quantitatively described by the HAS model [13]. In the model, the total strain is assumed to be subdivided into components as follows: where e, T and e T c (1) are the elastic strain, thermal c strain and creep strain, respectively. Thermal strain is produced by isotropic thermal expansion: T T 1 3 T () 0 where is the Kronecker delta and is the crystal density depending of absolute temperature T. In this paper, T is set to 1,685 K. 0 The total strain is related to the displacement u and u of thermoelastic solid body as follows: i j 1 u u i j (3) x j xi In the HAS model, the effective stress eff is equal to the difference between applied stress a and internal stress int D N provided by forest m hardening effect of dislocation density increasing: D N ; in isotropic case, the equivalent eff a m shear stress J is used as applied stress, and it is proportional to the Von Mises stress with factor of 1 3 : von 3 J. The creep strain rate and the multiplication rate of the mobile dislocation density N m can be expressed as follows [3]: c d 3 1 bn m Sv (4) dt dn m dt pl von Q Nmv K D Nm Nm BT 0 exp (5) 3 L where K von S Eb D R 4 1 (6) 1 kk 3 k (7) von Q v k 0 D Nm exp (8) 3 kbt In Eqs. (4)-(8), b is the magnitude of the Burgers vector; S is the deviatoric stress; v is the average velocity of mobile dislocation; k 0, K, p and l are material constants; L is the average grain size; D and R are the strain hardening factor and relative strain hardening factor, respectively; E and are the Young s modulus and Poisson s ratio, respectively; is the stress tensor components; Q is the Peierls potential; k is Boltzmann s B constant. In cases where J D N 0, the creep p m strain rate and dislocation density rate are set equal to zero. The elastic strain e and total stress can be expressed by the momentum balance equations and Hook s law: 0 (9) x j j c (10) The initial dislocation density was set as 1 cm - to represent the multicrystalline silicon material, and the dislocation density on the interface was inherited. The volume expansion coefficient was used to obtain the crystal density, the vyolume thermal expansion and density T relate to each other by the following way: d / dt 1/ T (11) Assuming liner expression for T, one can formulate: T T T T T (1) j e. Side Insulation Design After the crystal growth process, the hot zone was

4 9 closed by descending the side insulation, and then annealing was begun. After the annealing, the cooling process was implemented. The side insulation would be open and the heater s power supply was turned off during the cooling process. Five cases were considered for the side insulation, as shown in Fig.. The total cooling time was 14 hours, and the final displacement of side insulation was 8 cm (the upward direction was defined as the positive direction). The displacement of the side insulation increased up to 8 cm at 8.5th hour and then kept still in Case 1 (the cooling process of industrial production); it increased up to 8 cm at 5.5th hour and then kept still in Case ; it increased uniformly up to 8 cm at 14th hour in Case 3, initially slow and then fast in Case 4; it was firstly maintained at 0 from 0 to 5.5th hour, and then increased up to 8 cm uniformly in Case 5. Besides the displacement of the side insulation, all other conditions were kept identical during the cooling process in all cases. 3. Results and Discussion 3.1 Simulation Results Fig. 3 shows the distribution of dislocation density at the end of cooling. The regions which arrow contained represented the dislocation density was larger than /cm. It could be found that the maximum dislocation density was in the central of silicon ingot. Comparing the region size which the dislocation density was larger than /cm, case 5 was the smallest. It meant that the dislocation density in case 5 was the lowest after the cooling process. The formation and multiplication of dislocation in a growing ingot are closely related to thermal stress. Fig. 4 shows the maximum von Mises stress with cooling time. As shown in Fig. 4, the maximum von Mises stress was lower at early stage of cooling for all cases. With the cooling time increased, it raised rapidly, and the maximum von Mises stress distribution is stabilized at last cooling stage. In the comparison, the maximum von Mises stress in the case 5 was almost the lowest during the full cooling time. It meant that the case 5 was the worst for the formation and multiplication of dislocation among the five cooling processes. Fig. 5 shows the maximum dislocation density evolution with the cooling time. It could be found that the maximum dislocation density Fig. Displacement of the side insulation (cm) Case 1 Case Case 3 Case 4 Case Cooling time (h) Displacement variation of the side insulation with the cooling time.

5 Effec ct of Side Insu ulation on Stress and Dislocation in th he Multi-crysttalline ot during Coo oling Process Silicon Ingo Fig. 3 Distriibution of disloocation densityy at the end of cooling. 933

6 94 Maximum von Mises stresses (MPa) Case 1 Case Case 3 Case 4 Case Cooling time (h) Fig. 4 Variation of maximum von Mises stress with cooling time. Dislocation density (10 8 /cm ) Cooling time (h) Case 1 Case Case 3 Case 4 Case 5 Fig. 5 Maximum dislocation density evolution with the cooling time.

7 Case 5 Case 1 Temperature (K) Cooling time (h) Fig. 6 Temperature profile of TC with cooling time. of cooling process was compared between case 1 and case 5, as shown in Fig. 6. At beginning of cooling process, the temperature reduction of TC in case 5 was much slower than case 1. But after 14 hours of cooling time, the difference of TC temperature was little, and it was only 15 C. It meant that the cooling time of case 5 was only a little longer than the case Experimental Results Fig. 7 Numbering of bricks from an ingot. gradually increased and then tendedd to be constant with increased cooling time for the both cases. In comparison with Case 1, the rate of propagation of the dislocation density for Case 5 was lowest among Cases -5, and the maximum dislocation density for Case 5 was lower than that of Case 1. This was agreed well with the distribution of von Mises stress. To summarize, the case 5 was the most appropriate cooling process among all the cases. As the side insulation was closed during the early stage of case 5, the ingot temperature may be higher after 14 hours of cooling time. Thus, the temperature of TC at the end The simulation results indicated that the Case 5 provided the most favorable experimental conditions for the cooling process of HP mc-si, because it achieved the lowest thermal stress and lowest dislocation density. Cases 1 and 5 weree selected as representative experiments to cast HP mc-si ingots. Each ingot was cut into 36 bricks, according to the number of contact surface between crucible and crystal, the bricks were marked as bricks A, B and C, and the corresponding numbers of contact surface between crucible and silicon crystal weree 3, and 1, respectively, as shown in Fig. 7. As the maximum dislocation agglomerates density appeared in the central of ingot, brick C15 was chosen

8 96 to test the dislocation agglomerates density. In the PL image of silicon wafers, the ratio of dark patterns area to the whole wafer area represents dislocation agglomerates density level [7], which could be used as evaluation criterion to track dislocation propagation trend along the growth direction. As shown in Fig. 8, Dislocation agglomerate area ratio (%) case 5 case Numbering of wafers from the bottom to the top Fig. 8 Dislocation agglomerates evolution along growth direction for the brick C15 from two kinds of ingot case1 case5 Percentage(%) Conversion efficiency (%) Fig. 9 Conversion efficiency of solar cells for the two cooling processes.

9 97 the ratio data of every PL image was collected in sequence from bottom to top for the brick of C15 from two kinds of ingots. In comparison with Case 1, the rate of propagation of the dislocation agglomerates was slower in Case 5, and the average density of dislocation agglomerates was lower, which agreed well with simulation of dislocation agglomerates density. These results were benefited from the low thermal stress. Fig. 9 shows the conversion efficiency of the p-type HP mc-si solar cells for the two process designs. The 7,00 silicon wafers with a width of 156 mm of each region for the two cases were used respectively to fabricate solar cells using the same manufacture technique. As shown in Fig. 8, the average conversion efficiencies of solar cells was 0.05% higher in absolute value with this optimized design. The experimental results showed that the Case 5 was beneficial for improving the conversion efficiency of the solar cells. 4. Conclusions Numerical simulations were applied to analyze the effects of the side insulation on thermal stresses and dislocation density in silicon crystal during the cooling process. The simulation results showed that initially closed side insulation and then rapidly moved up was most favorable for the cooling process as the low thermal stress and dislocation density were obtained. In order to validate the simulation results, case 1 and case 5 were all applied into an industrial scale DS furnace. The experimental results showed that the Case 5 was the optimal cooling process as a lower average dislocation agglomerates density of silicon wafers and a higher average conversion efficiency of solar cells were acquired. Acknowledgments This work was partly supported by the Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT) under grant no. IRT1146; a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD); a project funded by the Natural Science Foundation of the Jiangsu Higher Education Institutions under grant no. 13KJB430016; and a project funded by the Natural Science Foundation of the Jiangsu province under grant no. BK References [1] Franke, D., Rettelbach, T., Häßler. C., Koch, W., and Müller, A. 00. Silicon Ingot Casting: Process Development by Numerical Simulations. Solar Energy Materials and Solar Cells 7 (April): [] Mohammed, M., Arne, M. E., Harald, L., and Johannes, Ø. E Thermo-Mechanical Analysis Directional Crystallisation of Multi-crystalline Silicon Ingots. Materials Science Forum 508 (March): [3] Nakano, S., Chen, X. J., Gao, B., and Kakimoto, K Numerical Analysis of Cooling Rate Dependence on Dislocation Density in Multicrystalline Silicon for Solar Cells. Journal of Crystal Growth 318 (November): 80-. [4] Wang, S., Fang, H. S., Wei, G. H., Zhou, L., and Zhou, N Transient Analysis of the Cooling Process and Influence of Bottom Insulation on the Stress in the Multicrystalline Silicon Ingot. Crystal Research and Technology 48 (July): 454. [5] Zhou, N., Lin, M., Zhou, L., Hu, Q., Fang, H., and Wang, S A Modified Cooling Process in Directional Solidification of Multicrystalline Silicon. Journal of Crystal Growth 381 (July): -6. [6] Zhou, N., Lin, M., Wan, M., and Zhou, L Lowering Dislocation Density of Directionally Grown Multicrystalline Silicon Ingots for Solar Cells by Simplifying Their Post-Solidification Processes A Simulation Approach. Journal of Thermal Stresses 38 (February): 146. [7] Wang, S., Fang, H. S., Zhao, C. J., Zhang, Z., Zhang, M. J., and Xu, J. F Gas Flow Optimization during the Cooling of Multicrystalline Silicon Ingot. International Journal of Heat and Mass Transfer 84 (May): [8] Ding, C. L., Huang, M. L., Zhong, G. X., Ming, L., and Huang, X. M A Design of Crucible Susceptor for the Seeds Preservation during a Seeded Directional Solidification Process. Journal of Crystal Growth 387 (February): [9] Wu, Z. Y., Zhong, G. X., Zhang, Z. Y., Zhou, X. C., Wang, Z. X., and Huang, X. M Optimization of the High-Performance Multi-crystalline Silicon Solidification Process by Insulation Partition Design Using Transient Global Simulations. Journal of Crystal

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