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Effects of the hot zone design during the growth of large size multi-crystalline silicon ingots by the seeded directional solidification process
Journal of Crystal Growth ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Effects of the hot zone design during the growth of large size multi-crystalline silicon ingots by the seeded directional solidification process Thi Hoai Thu Nguyen a, Szu-Han Liao a, Jyh-Chen Chen a,n, Chun-Hung Chen b, Yen-Hao Huang b, Cheng-Jui Yang b, Huang-Wei Lin b, Huy Bich Nguyen c a b c
Department of Mechanical Engineering, National Central University, Jhongli 320, Taiwan, ROC Sino-American Silicon Products Inc., Taiwan, ROC Faculty of Engineering and Technology, Nong Lam University, Ho Chi Minh City, Vietnam
art ic l e i nf o
a b s t r a c t
Article history: Received 30 September 2015 Received in revised form 8 December 2015 Accepted 24 December 2015
In this study, the installation of insulation blocks in the hot zone is utilized to assist in the growth of multi-crystalline silicon ingots with 800 kg of silicon charge using the seeded directional solidification method. A transient global numerical simulation is carried out to investigate the heat and mass transport during growth process. At a higher solidification fraction, lower concavity of the crystal–melt interface near the crucible wall can be obtained as compared to the standard model. The lowest concavity and highest energy saving is achieved when insulation blocks are added to the side of a directional solidification block and to the low part of the side insulation. The simulation results for this design also show a reduction of the melt velocity. The average oxygen concentration is slightly higher along the crystal–melt interface, compared to the standard one. & 2016 Elsevier B.V. All rights reserved.
Keywords: A1. Computer simulation A1. Directional solidification A2. Seed crystals B3. Solar cells
1. Introduction Multi-crystalline silicon (mc-Si) solar cells have the highest market share in the photovoltaics (PV) market. To accomplish the goal of grid parity, the production cost of silicon solar cells must be reduced further and their efficiency has to be improved which is strongly dependent on wafer production and quality. Recently the growth of large size mc-Si ingots with high quality has become the main direction of development in wafer production. As the ingot weight goes up, however, the rate of increase in the height of the ingot becomes less than the rate of increase in the area. Martinuzzi et al. [1] has suggested that the height of large size mc-Si ingots produced from the casting process should not exceed 20 cm in order to avoid the production of extended defects, the expense of crucible use and the production of upgraded silicon waste. Seeded directional solidification (DS) systems have been developed capable of obtaining high quality large size mc-Si crystals. In this technology, the bottom of the quartz crucible is paved with crystalline silicon seed crystals which need to be preserved during the solidification process in order to prevent nucleation from the bottom crucible wall. Grain orientation is important because it n
Corresponding author. E-mail address: [email protected] (J.-C. Chen).
significantly affects the conversion efficiency of the solar cells. It is well-known that the crystal–melt (c–m) interface has a great influence on the orientation of the grain size and thermal stress during the growth process. A flat or slightly convex c–m interface is beneficial for an outward grain direction and lower thermal stress in the ingot. To obtain this favored interface, it is very important to reduce heat loss throughout crucible system, especially to control the radial heat flux. Different designs of insulation partitions for optimization of the DS process have been studied [2–6]. The modeling and experimental results have shown that using a partition block can reduce the total heat consumption and improve the shape of the solidification interface during the growth process. This design also has a significant effect on the temperature distribution and thermal stress in the silicon ingots. There is an optimal increase in velocity with a partition block which allows the fabrication of high quality wafers for high conversion efficiency mc-Si solar cells. Ding et al. [7] added an insulated crucible susceptor to the DS furnace to preserve seed crystals to produce a consistently flat or slightly convex seed–melt interface during the melting process, while Chen et al. [8] showed that large energy saving can be achieved with the current DS furnace design with only minor geometric modifications achieved by adding solid blocks to the lower corner of the side insulation. “Pivot surfaces” which were introduced to explain the decrease of total power, act by redirecting the radiation of the heat flux from the hot zone to
http://dx.doi.org/10.1016/j.jcrysgro.2015.12.045 0022-0248/& 2016 Elsevier B.V. All rights reserved.
Please cite this article as: T.H.T. Nguyen, et al., Journal of Crystal Growth (2016), http://dx.doi.org/10.1016/j.jcrysgro.2015.12.045i
T.H.T. Nguyen et al. / Journal of Crystal Growth ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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the bottom of the heat exchanger block in the cold zone. The effect of the addition of insulation blocks on the impurity distribution and the melt velocity, however, was not investigated in these studies. This modification of the DS furnace changes the temperature field near the crucible wall and affects convection in the silicon melt. The bottom corner of the crucible is the position where the heat flux becomes highest, therefore it is necessary to add insulation blocks in this region to reduce the heat loss. Teng et al. [9,10] added an insulation block to prevent heat loss from the heat exchanger block to the gap of the insulation cage, which resulted in an interface shape with lower deviation between the crystal edge and the center. They also investigated the thermal flow field and distribution of oxygen and carbon concentration in the silicon melt. A gas flow guidance device installed in a mc-Si crystal growth furnace enhanced the motion of argon gas flow near the free surface [11,12]. As a result, a greater amount of SiO gas is carried out of the furnace by the argon gas. In this study, a series of transient global numerical simulation are performed with 800 kg of total silicon charge. The effects of the addition of insulation blocks to the side of the DS block and/or to the low part of the side insulation, on the thermal field, the flow field and impurity transport during the growth process are investigated. Moreover, the enhancement of energy saving by these modifications is also discussed.
incompressible flow. Moreover, all of the solid surfaces are assumed to be gray surfaces. The differential equations governing the fluid flow and heat transfer are given below. In the fluid flow: ∂ρi ! þ ∇ U ρi u i ¼ 0 ð1Þ ∂t ! ∂ρi ui - þ ui U∇ ρi ui ¼ ∇pi þ ∇ U τi þ ρi ρi;0 U g ∂t ∂ρi C p;i T i ! þ ∇ U C p;i ρi ui T i ¼ ∇ Uðki ∇T i Þ ∂t ∂ ρi C p;j ! þ ∇ U ρi ui C j ¼ ∇ UðDj ∇C j Þ ∂t
ρg ¼
po M ; RT
A schematic illustration of the structure of the seeded industrial DS furnace used to grow 800 kg mc-Si ingots is shown in Fig. 1. The standard furnace is modified by the addition of insulation block A to the side of the DS block and insulation block B to the low part of the side insulation. During the growth process, the temperature at the furnace wall is kept constant at 300 K by a water-cooling system. The side insulation with block B moves upward independently. The melting process is controlled in the studied DS system, so as to preserve the 18mm high seed crystals at the crucible bottom. To save simulation time, the real configuration of a DS furnace with its square crucible is replaced by a 2D axially-symmetric model which is cylindrical in shape. This simplification has been widely used in the literature [2–12] and has been validated by experiments [2,5,7]. The silicon melt is considered to be a Newtonian fluid and the deformation of the free surface is neglected. Argon gas is regarded as an ideal gas with an
ð3Þ ð4Þ ð5Þ
where ρ, ρ0, Cp, u, τ, g, T, k, C, D, p0, M and R are density, reference density, specific heat, velocity, stress tensor, gravitational acceleration, temperature, thermal conductivity, concentration, diffusivity, pressure, molecular weight and universal gas constant, respectively. Subscript i represents argon gas (g) or liquid silicon (l), while subscript j stands for silicon monoxide (SiO) in the argon gas region or oxygen (O) in the melt. In the heater: _ ∇ðkh ∇T h Þ ¼ q;
2. Mathematical model
ð2Þ
ð6Þ
where q: is the heat generation from the heater. The thermal conditions on the interface between two opaque surfaces are ∂T ∂T k ¼ k ; ð7Þ ∂n 1 ∂n 2 T 1 ¼ T 2:
ð8Þ
The radiative heat transfer along the interface between the opaque surface and gas is as follows: ∂T ∂T k ¼ k þ σ s εT 4 qin ; ð9Þ ∂n opaque ∂n gas where σs is the Stefan–Boltzmann constant, ε is the thermal emissivity and qin is the incoming radiative heat flux. The heat fluxes at the c–m interface should satisfy the Stefan condition, and the temperature at this interface should be equal to
Fig. 1. Schematic diagram of the seeded industrial DSS furnace.
Please cite this article as: T.H.T. Nguyen, et al., Journal of Crystal Growth (2016), http://dx.doi.org/10.1016/j.jcrysgro.2015.12.045i
T.H.T. Nguyen et al. / Journal of Crystal Growth ∎ (∎∎∎∎) ∎∎∎–∎∎∎
the melting temperature: ∂T ∂T ρcryst un ΔH ¼ k þ k ; ∂n melt ∂n cryst T ¼ T melt ;
3. Results and discussion ð10Þ
ð11Þ
where ρcryst is the crystal density, un is the local crystalline rate normal to the c–m interface and ΔH is the latent heat. The normal velocity component at the solid walls and along the free surface are set to be zero while the tangential velocity component is equal to the solid wall velocity. In addition, the velocity in the tangential direction must satisfy the shear–stress condition:
μl
∂uτg ∂σ ∂uτl ¼ μg þ ∇τ T; ∂n ∂n ∂T
ð12Þ
where μ is the dynamic viscosity; n and τ are the normal and tangential directions to the free surface, respectively; σ is the surface tension of the silicon melt. The boundary condition for oxygen is the same as presented in our previous study [10]. The temperature at the crystallization front is considered to be the silicon melting temperature, 1685 K. It is assumed that sub-cooling does not occur at the c–m interface in this work. The governing equations for the heat and mass transport during seeded DS silicon crystal growth are solved numerically using the CGSim (Crystal Growth software) program package of STR based on the Finite Volume Method (FVM). The computational grid for a DS furnace for growing mc-Si ingots is shown in Fig. 2. It is found that the Rayleigh number of the silicon melt, based on the crucible radius, is about O(108). Obviously, the melt flow is in the transient regime because the order of the critical Rayleigh number is O(107) [13]. The Reynolds-averaged Navier-Stoke (RANS) equations with one equation model are used to calculate the transient regime in the melt flow that is owed to buoyancy. The Wolfshtein model is applied to catch the proper increase in the dissipation rate near the wall given the buoyancy flow in the transient regime. In the formulation of the turbulent kinetic viscosity, the constant Cμ is set to 0.09. The view factors used to determine the total radiative flux coming into a given surface are re-computed when the side insulation and the added solid block move upward. Thermocouple 1 (TC1) is positioned near the top heater while thermocouple 2 (TC2) is at the center of the bottom of the crucible support. TC1 is used as the target function for the unsteady computation to control the heater power output. During the process, the power will be adjusted using the well-known PID algorithm to reach the target temperature. The physical properties of the materials used in the present study are detailed in our previous papers [10,12]. The added solid blocks have the same thermal properties as the insulation.
Fig. 2. Grid distribution in DS crucible system.
3
In this study, a transient global model is used to investigate the effects of different modifications of the furnace structure on the thermal field, the flow field and the distribution of impurity during seeded DS process. As can be seen from Figs. 3 and 4, the simulated heating power consumption and the variation of TC2 agree with the experimental results. This good consistency demonstrates the applicability of the model for the simulation of the thermal conditions in a DS furnace. It is clear that the total heater power increases while TC2 is reduced with the growth time. A “W” shaped c–m interface always occurs during the DS growth process. The severe concavity of the c–m interface near the silica crucible wall causes a reduction of the yield and quality of the ingot. During growth, the side insulation moves up and the melt is solidified by heat extraction from the bottom and side wall of the crucible support. The occurrence of a concave c–m interface is due to heat removal from the side wall of the crucible support. It is obvious that to reduce the concavity of the c–m interface near the silica crucible wall, the heat flux in the positive radial direction at the c–m interface near the silica crucible wall should be reduced. To achieve this goal, three cases are considered in the present study. In Case 1, an insulation block (block A) is added to the side of the DS block. This block may have a significant effect on reducing the heat loss in the early stages. With a higher solidification fraction, however, it is difficult to control the heat flux using this design because the position of the c–m interface is far away from block A. Thus, heat loss through the crucible side wall becomes more significant, which leads to the addition of another insulation block to control radial heat flux at the later stages. In Case 2, therefore, block B is added at the low part of the side insulation. The reduction effect of heat extraction in the positive radial direction from this installation can be expected to become more significant as the side insulation moves further up (higher solidification fraction of silicon ingot). Finally, the effect of combining blocks A and B are investigated in Case 3. Fig. 5 shows a comparison of the interface shape between the modified cases (Cases 1, 2, 3) and standard case. A “W” shaped c– m interface is obtained during the process in all cases. The large size of the ingot and the growth conditions may result in this interface shape. As can be seen, these designs can produce significant improvement of the concavity of the c–m interface during the growth process. The best interface shape is obtained in the last case, combining block A and B. To clearly analyze the effect of these modifications, the shape of the c–m interface for one half
Fig. 3. Comparison of simulation and experimental total heater power.
Please cite this article as: T.H.T. Nguyen, et al., Journal of Crystal Growth (2016), http://dx.doi.org/10.1016/j.jcrysgro.2015.12.045i
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Fig. 4. Comparison of simulation and experimental TC2. Fig. 7. Convexity at the central region vs. different solidification fractions for the standard case and the modified cases.
Fig. 5. C–m interface shape at different solidification fractions for the standard case and the modified cases.
Fig. 8. Concavity near crucible wall vs. different solidification fractions for the standard case and the modified cases.
Fig. 6. Definition of D_center and D_wall of the c–m interface shape.
side is separated into two parts as indicated in Fig. 6. It can be seen that there is convexity in the central region and concavity near the crucible wall, where D_center is defined as the difference between the crystal center and the minimum point of the c–m interface, and D_wall is the difference between the highest position (which always appears at the side crucible wall) and the minimum point. Figs. 7 and 8 present the variation in the convexity and concavity of the crystallization front with different solidification fractions. When only block A (Case 1) is added to the side of the DS block, lower convexity of the c–m interface near the central region and concavity near the crucible wall are obtained. The addition of block A can lead to a significant decrease in heat loss from the side
Fig. 9. Heat loss presented by comparison of TC2 for the standard case and the modified cases.
region of DS block and the bottom of the graphite crucible support. In the only block B case (Case 2), however, escape of the radial heat flux from the side crucible wall is prevented. This means that there
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is a reduction in the loss of radial heat at the c–m interface near the crucible wall in the positive direction. The c–m interface becomes more convex in the central section and the concavity
5
near the crucible wall section is reduced more significantly in comparison with Case 1. It is clear that block A has greater influence on the convexity while block B has greater influence on the concavity of the c–m interface during the growth process. There is not much difference of convexity in the central region but there is a significant difference of concavity near the crucible wall in Case 3 as compared to Case 1. Moreover, a significant shift in the lowest position of the interface is obtained between the modified and standard model (Fig. 5). Fig. 9 shows a decrease in TC2 which represents heat loss through the crucible bottom. Heat flux moving out of the crucible system is prevented by the addition of insulation blocks so TC2 becomes lower in the modified models. A comparison of heating power consumption, plotted in Fig.10, is also made to estimate the energy saving of the modifications. The average reduction in total heater power for Case 1, Case 2, and Case 3 is 7.4%, 8.7%, and 13%, respectively, as compared to the standard case. The prevention of heat loss by adding insulation blocks to the side insulation or/and the side of a DS block lead to the decrease in heating power consumption. The greatest energy saving is obtained with the combination of block A and block B. Saving energy is an important goal for the optimization of crystal growth systems. The distribution of the oxygen concentration with SiO concentration and flow motion obtained with the standard model at
Fig. 10. Total heating power consumption vs. growth time for the standard case and the modified cases.
z 1500 1800 2400
2100
1 7.0
7.4
2
3
7.8
4
8.2
5
r
10%
z 200 500 800 2.4 2.8
2.0
2
4
r 50% Fig. 11. Distribution of oxygen and SiO concentration (left, ΔCO ¼0.2 ppma, ΔCSiO ¼ 100 ppma) and flow pattern (right) for the standard model.
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z 1800 2700
2100
2400
7.0
7.4 8.2
2+3
6.6
4
7.8
5
r
10%
z
500
200
6
800 2.8
2.4
2.0
2+3
3.2
4
r 50% Fig. 12. Distribution of oxygen and SiO concentration (left, ΔCO ¼ 0.2 ppma, ΔCSiO ¼100 ppma) and flow pattern (right) for Case 3.
10% and 50% silicon solidification is presented in Fig. 11. Heat is transferred to the melt through the crucible wall and radiated to the free melt surface. This results in the maximum temperature of the silicon melt appearing at the triple-junction point of the crucible-melt–gas phase. When 10% of the silicon melt is solidified, the flow pattern in the bulk silicon includes five vortexes. Since the temperature difference at the free surface near the center region is very small, the shear effect induced by the flow motion of the argon gas may be greater than the Marangoni effect in this region. Therefore, a very small clockwise vortex (1) appears near the free surface in the center region. Along the free surface, the temperature near the crucible side wall is higher than that near the center. The anti-clockwise vortices (2) and (3) are generated by both the buoyancy and thermocapillary forces. In contrast, in the bottom part of the melt region, the temperature near the crucible wall is lower than that near the center, since the c–m interface near the crucible wall is concave. Hence, vortex (4) induced by the buoyancy force is clockwise. The small cell (5) occurring near the c–m interface is due to the large size of the crucible. When the solidification fraction reaches 50%, vortices (1), (3) and (5) disappear. The decrease in the melt depth causes a significant reduction in the strength and size of cell (2). It then moves downward to partially cover the c–m interface while the other one (4) covers the free surface, as well as the rest of the region of the solidification interface. As shown in Fig. 11, the oxygen impurity
distribution is strongly dependent on the flow pattern. Fig. 12 displays the flow structure and the distribution of oxygen and SiO concentration for Case 3. The temperature at the side crucible wall is higher in Case 3 than that in the standard model because the addition of the insulation block prevents the loss of heat flux from the side crucible wall. A higher wall temperature results in a greater release of oxygen impurity from the silica crucible wall into the silicon melt. The effect of Maragoni convection becomes larger in Case 3, suppressing the shear stress effect induced by the argon gas flow, so vortex (1) does not occur in the center region near the free surface. Since there is a significant reduction in the concavity of the c–m interface in Case 3, in comparison with the standard one, the strength of buoyancy vortex (4) becomes weaker and vortices (2) and (3) get larger. This results in the merging of vortices (2) and (3), as shown in Fig. 12a. In Fig. 12b, a small vortex (6) appears at the free surface near the crucible wall due to the enhancement of the thermocapillary force by the higher radial temperature gradient. Fig. 13 presents a reduction in the melt velocity near the crucible side wall due to the decrease in the buoyancy force. The strength of the buoyancy cell is not enough to carry the oxygen atoms in the lower region of the silicon melt towards the free surface for evaporation. The slower flow motion also increases the evaporation of the oxygen atoms that have remained in the upper region near the crucible wall. There is clearly a higher SiO concentration above the free surface and a
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Fig. 15. Vcr/Gc parameter with different interface positions for the standard case and the modified cases.
higher oxygen level in the bulk melt for Case 3, as can be seen by comparing the distribution of the SiO and oxygen concentration in Fig. 11 and Fig. 12. Fig. 14 presents the average oxygen concentration along the c–m interface for the standard case and Case 3. The average oxygen content along the c–m interface decreases when the solidification fraction gets higher. It gets higher for Case 3. The Voronkov ratios Vcr/Gc, defined as the ratio of the crystallization rate to the crystal thermal gradient normal to the c–m interface, for the standard and modified model, are shown in Fig.15. It is well-known that the Vcr/Gc parameter stands for the formation of defects in silicon ingots. As can be seen, this parameter is reduced in the modified model as compared to the standard one. The lowest value is obtained for Case 3. For all cases, the Vcr/Gc parameter is higher than the critical value (Vcr/ Gc ¼0.12 mm2/min/K [14]). This means that vacancies will occur in the ingot but the formation of these defects is reduced in Case 1, Case 2 and Case 3. Fig. 13. Axial melt velocity at 10mm from the inner crucible wall immersed in the silicon melt for the standard case and Case 3.
4. Conclusions The hot zone inside a DS furnace used to grow mc-Si crystal with 800 kg total charge has been modified by adding insulation blocks to the side of the DS block or/and at the low part of the side insulation. The simulation results show that the addition of both insulation blocks can effectively improve the concavity of the c–m interface at a higher solidification fraction due to the significant decrease in heat loss through the side crucible wall. Moreover, this combination can obtain the highest energy saving in total heating power consumption. There is a slightly higher average oxygen concentration along the c–m interface due to the higher wall temperature and the lower melt velocity as compared to the standard one. The decrease of Vcr/Gc parameter for the modified models indicates the lower vacancy formation in the ingot.
Acknowledgments
Fig. 14. Comparison of average oxygen concentration with different solidification fractions for the standard case and Case 3.
The authors would like to thank the Ministry of Science and Technology of Taiwan, R.O.C, for their support for this study through Grant no. NSC-103-2221-E-008 -038 -MY3.
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[8] L. Chen, B. Dai, Optimization of power consumption on silicon directional solidification system by using numerical simulations, J. Cryst. Growth 354 (2012) 86–92. [9] Y.Y. Teng, J.C. Chen, C.W. Lu, C.Y. Chen, The carbon distribution in multicrystalline silicon ingots grown using the directional solidification process, J. Cryst. Growth 312 (2010) 1282–1290. [10] Y.Y. Teng, J.C. Chen, C.W. Lu, H.I. Chen, C. Hsu, C.Y. Chen, Effects of the furnace pressure on oxygen and silicon oxide distributions during the growth of multicrystalline silicon ingots by the directional solidification process, J. Cryst. Growth 318 (2011) 224–229. [11] Y.Y. Teng, J.C. Chen, C.W. Lu, C.Y. Chen, Numerical investigation of oxygen impurity distribution during multicrystalline silicon crystal growth using a gas flow guidance device, J. Cryst. Growth 360 (2012) 12–17. [12] Y.Y. Teng, J.C. Chen, B.S. Huang, C.H. Chang, Numerical simulation of impurity transport under the effect of a gas flow guidance device during the growth of multicrystalline silicon ingots by the directional solidification process, J. Cryst. Growth 385 (2014) (2014) 1–8. [13] A. Raufeisen, M. Breuer, T. Botsch, A. Delgado, DNS of rotating buoyancy and surface tension-driven flow, Int. J. Heat Mass Transf. 51 (2008) 6219. [14] V. Voronkov, R. Falster, Vacancy and self-interstitial concentration incorporated into growing silicon crystals, J. Appl. Phys. 56 (1999) 5975.
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Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Effects of the hot zone design during the growth of large size multi-crystalline silicon ingots by the seeded directional solidification process Thi Hoai Thu Nguyen a, Szu-Han Liao a, Jyh-Chen Chen a,n, Chun-Hung Chen b, Yen-Hao Huang b, Cheng-Jui Yang b, Huang-Wei Lin b, Huy Bich Nguyen c a b c
Department of Mechanical Engineering, National Central University, Jhongli 320, Taiwan, ROC Sino-American Silicon Products Inc., Taiwan, ROC Faculty of Engineering and Technology, Nong Lam University, Ho Chi Minh City, Vietnam
art ic l e i nf o
a b s t r a c t
Article history: Received 30 September 2015 Received in revised form 8 December 2015 Accepted 24 December 2015
In this study, the installation of insulation blocks in the hot zone is utilized to assist in the growth of multi-crystalline silicon ingots with 800 kg of silicon charge using the seeded directional solidification method. A transient global numerical simulation is carried out to investigate the heat and mass transport during growth process. At a higher solidification fraction, lower concavity of the crystal–melt interface near the crucible wall can be obtained as compared to the standard model. The lowest concavity and highest energy saving is achieved when insulation blocks are added to the side of a directional solidification block and to the low part of the side insulation. The simulation results for this design also show a reduction of the melt velocity. The average oxygen concentration is slightly higher along the crystal–melt interface, compared to the standard one. & 2016 Elsevier B.V. All rights reserved.
Keywords: A1. Computer simulation A1. Directional solidification A2. Seed crystals B3. Solar cells
1. Introduction Multi-crystalline silicon (mc-Si) solar cells have the highest market share in the photovoltaics (PV) market. To accomplish the goal of grid parity, the production cost of silicon solar cells must be reduced further and their efficiency has to be improved which is strongly dependent on wafer production and quality. Recently the growth of large size mc-Si ingots with high quality has become the main direction of development in wafer production. As the ingot weight goes up, however, the rate of increase in the height of the ingot becomes less than the rate of increase in the area. Martinuzzi et al. [1] has suggested that the height of large size mc-Si ingots produced from the casting process should not exceed 20 cm in order to avoid the production of extended defects, the expense of crucible use and the production of upgraded silicon waste. Seeded directional solidification (DS) systems have been developed capable of obtaining high quality large size mc-Si crystals. In this technology, the bottom of the quartz crucible is paved with crystalline silicon seed crystals which need to be preserved during the solidification process in order to prevent nucleation from the bottom crucible wall. Grain orientation is important because it n
Corresponding author. E-mail address: [email protected] (J.-C. Chen).
significantly affects the conversion efficiency of the solar cells. It is well-known that the crystal–melt (c–m) interface has a great influence on the orientation of the grain size and thermal stress during the growth process. A flat or slightly convex c–m interface is beneficial for an outward grain direction and lower thermal stress in the ingot. To obtain this favored interface, it is very important to reduce heat loss throughout crucible system, especially to control the radial heat flux. Different designs of insulation partitions for optimization of the DS process have been studied [2–6]. The modeling and experimental results have shown that using a partition block can reduce the total heat consumption and improve the shape of the solidification interface during the growth process. This design also has a significant effect on the temperature distribution and thermal stress in the silicon ingots. There is an optimal increase in velocity with a partition block which allows the fabrication of high quality wafers for high conversion efficiency mc-Si solar cells. Ding et al. [7] added an insulated crucible susceptor to the DS furnace to preserve seed crystals to produce a consistently flat or slightly convex seed–melt interface during the melting process, while Chen et al. [8] showed that large energy saving can be achieved with the current DS furnace design with only minor geometric modifications achieved by adding solid blocks to the lower corner of the side insulation. “Pivot surfaces” which were introduced to explain the decrease of total power, act by redirecting the radiation of the heat flux from the hot zone to
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the bottom of the heat exchanger block in the cold zone. The effect of the addition of insulation blocks on the impurity distribution and the melt velocity, however, was not investigated in these studies. This modification of the DS furnace changes the temperature field near the crucible wall and affects convection in the silicon melt. The bottom corner of the crucible is the position where the heat flux becomes highest, therefore it is necessary to add insulation blocks in this region to reduce the heat loss. Teng et al. [9,10] added an insulation block to prevent heat loss from the heat exchanger block to the gap of the insulation cage, which resulted in an interface shape with lower deviation between the crystal edge and the center. They also investigated the thermal flow field and distribution of oxygen and carbon concentration in the silicon melt. A gas flow guidance device installed in a mc-Si crystal growth furnace enhanced the motion of argon gas flow near the free surface [11,12]. As a result, a greater amount of SiO gas is carried out of the furnace by the argon gas. In this study, a series of transient global numerical simulation are performed with 800 kg of total silicon charge. The effects of the addition of insulation blocks to the side of the DS block and/or to the low part of the side insulation, on the thermal field, the flow field and impurity transport during the growth process are investigated. Moreover, the enhancement of energy saving by these modifications is also discussed.
incompressible flow. Moreover, all of the solid surfaces are assumed to be gray surfaces. The differential equations governing the fluid flow and heat transfer are given below. In the fluid flow: ∂ρi ! þ ∇ U ρi u i ¼ 0 ð1Þ ∂t ! ∂ρi ui - þ ui U∇ ρi ui ¼ ∇pi þ ∇ U τi þ ρi ρi;0 U g ∂t ∂ρi C p;i T i ! þ ∇ U C p;i ρi ui T i ¼ ∇ Uðki ∇T i Þ ∂t ∂ ρi C p;j ! þ ∇ U ρi ui C j ¼ ∇ UðDj ∇C j Þ ∂t
ρg ¼
po M ; RT
A schematic illustration of the structure of the seeded industrial DS furnace used to grow 800 kg mc-Si ingots is shown in Fig. 1. The standard furnace is modified by the addition of insulation block A to the side of the DS block and insulation block B to the low part of the side insulation. During the growth process, the temperature at the furnace wall is kept constant at 300 K by a water-cooling system. The side insulation with block B moves upward independently. The melting process is controlled in the studied DS system, so as to preserve the 18mm high seed crystals at the crucible bottom. To save simulation time, the real configuration of a DS furnace with its square crucible is replaced by a 2D axially-symmetric model which is cylindrical in shape. This simplification has been widely used in the literature [2–12] and has been validated by experiments [2,5,7]. The silicon melt is considered to be a Newtonian fluid and the deformation of the free surface is neglected. Argon gas is regarded as an ideal gas with an
ð3Þ ð4Þ ð5Þ
where ρ, ρ0, Cp, u, τ, g, T, k, C, D, p0, M and R are density, reference density, specific heat, velocity, stress tensor, gravitational acceleration, temperature, thermal conductivity, concentration, diffusivity, pressure, molecular weight and universal gas constant, respectively. Subscript i represents argon gas (g) or liquid silicon (l), while subscript j stands for silicon monoxide (SiO) in the argon gas region or oxygen (O) in the melt. In the heater: _ ∇ðkh ∇T h Þ ¼ q;
2. Mathematical model
ð2Þ
ð6Þ
where q: is the heat generation from the heater. The thermal conditions on the interface between two opaque surfaces are ∂T ∂T k ¼ k ; ð7Þ ∂n 1 ∂n 2 T 1 ¼ T 2:
ð8Þ
The radiative heat transfer along the interface between the opaque surface and gas is as follows: ∂T ∂T k ¼ k þ σ s εT 4 qin ; ð9Þ ∂n opaque ∂n gas where σs is the Stefan–Boltzmann constant, ε is the thermal emissivity and qin is the incoming radiative heat flux. The heat fluxes at the c–m interface should satisfy the Stefan condition, and the temperature at this interface should be equal to
Fig. 1. Schematic diagram of the seeded industrial DSS furnace.
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the melting temperature: ∂T ∂T ρcryst un ΔH ¼ k þ k ; ∂n melt ∂n cryst T ¼ T melt ;
3. Results and discussion ð10Þ
ð11Þ
where ρcryst is the crystal density, un is the local crystalline rate normal to the c–m interface and ΔH is the latent heat. The normal velocity component at the solid walls and along the free surface are set to be zero while the tangential velocity component is equal to the solid wall velocity. In addition, the velocity in the tangential direction must satisfy the shear–stress condition:
μl
∂uτg ∂σ ∂uτl ¼ μg þ ∇τ T; ∂n ∂n ∂T
ð12Þ
where μ is the dynamic viscosity; n and τ are the normal and tangential directions to the free surface, respectively; σ is the surface tension of the silicon melt. The boundary condition for oxygen is the same as presented in our previous study [10]. The temperature at the crystallization front is considered to be the silicon melting temperature, 1685 K. It is assumed that sub-cooling does not occur at the c–m interface in this work. The governing equations for the heat and mass transport during seeded DS silicon crystal growth are solved numerically using the CGSim (Crystal Growth software) program package of STR based on the Finite Volume Method (FVM). The computational grid for a DS furnace for growing mc-Si ingots is shown in Fig. 2. It is found that the Rayleigh number of the silicon melt, based on the crucible radius, is about O(108). Obviously, the melt flow is in the transient regime because the order of the critical Rayleigh number is O(107) [13]. The Reynolds-averaged Navier-Stoke (RANS) equations with one equation model are used to calculate the transient regime in the melt flow that is owed to buoyancy. The Wolfshtein model is applied to catch the proper increase in the dissipation rate near the wall given the buoyancy flow in the transient regime. In the formulation of the turbulent kinetic viscosity, the constant Cμ is set to 0.09. The view factors used to determine the total radiative flux coming into a given surface are re-computed when the side insulation and the added solid block move upward. Thermocouple 1 (TC1) is positioned near the top heater while thermocouple 2 (TC2) is at the center of the bottom of the crucible support. TC1 is used as the target function for the unsteady computation to control the heater power output. During the process, the power will be adjusted using the well-known PID algorithm to reach the target temperature. The physical properties of the materials used in the present study are detailed in our previous papers [10,12]. The added solid blocks have the same thermal properties as the insulation.
Fig. 2. Grid distribution in DS crucible system.
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In this study, a transient global model is used to investigate the effects of different modifications of the furnace structure on the thermal field, the flow field and the distribution of impurity during seeded DS process. As can be seen from Figs. 3 and 4, the simulated heating power consumption and the variation of TC2 agree with the experimental results. This good consistency demonstrates the applicability of the model for the simulation of the thermal conditions in a DS furnace. It is clear that the total heater power increases while TC2 is reduced with the growth time. A “W” shaped c–m interface always occurs during the DS growth process. The severe concavity of the c–m interface near the silica crucible wall causes a reduction of the yield and quality of the ingot. During growth, the side insulation moves up and the melt is solidified by heat extraction from the bottom and side wall of the crucible support. The occurrence of a concave c–m interface is due to heat removal from the side wall of the crucible support. It is obvious that to reduce the concavity of the c–m interface near the silica crucible wall, the heat flux in the positive radial direction at the c–m interface near the silica crucible wall should be reduced. To achieve this goal, three cases are considered in the present study. In Case 1, an insulation block (block A) is added to the side of the DS block. This block may have a significant effect on reducing the heat loss in the early stages. With a higher solidification fraction, however, it is difficult to control the heat flux using this design because the position of the c–m interface is far away from block A. Thus, heat loss through the crucible side wall becomes more significant, which leads to the addition of another insulation block to control radial heat flux at the later stages. In Case 2, therefore, block B is added at the low part of the side insulation. The reduction effect of heat extraction in the positive radial direction from this installation can be expected to become more significant as the side insulation moves further up (higher solidification fraction of silicon ingot). Finally, the effect of combining blocks A and B are investigated in Case 3. Fig. 5 shows a comparison of the interface shape between the modified cases (Cases 1, 2, 3) and standard case. A “W” shaped c– m interface is obtained during the process in all cases. The large size of the ingot and the growth conditions may result in this interface shape. As can be seen, these designs can produce significant improvement of the concavity of the c–m interface during the growth process. The best interface shape is obtained in the last case, combining block A and B. To clearly analyze the effect of these modifications, the shape of the c–m interface for one half
Fig. 3. Comparison of simulation and experimental total heater power.
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Fig. 4. Comparison of simulation and experimental TC2. Fig. 7. Convexity at the central region vs. different solidification fractions for the standard case and the modified cases.
Fig. 5. C–m interface shape at different solidification fractions for the standard case and the modified cases.
Fig. 8. Concavity near crucible wall vs. different solidification fractions for the standard case and the modified cases.
Fig. 6. Definition of D_center and D_wall of the c–m interface shape.
side is separated into two parts as indicated in Fig. 6. It can be seen that there is convexity in the central region and concavity near the crucible wall, where D_center is defined as the difference between the crystal center and the minimum point of the c–m interface, and D_wall is the difference between the highest position (which always appears at the side crucible wall) and the minimum point. Figs. 7 and 8 present the variation in the convexity and concavity of the crystallization front with different solidification fractions. When only block A (Case 1) is added to the side of the DS block, lower convexity of the c–m interface near the central region and concavity near the crucible wall are obtained. The addition of block A can lead to a significant decrease in heat loss from the side
Fig. 9. Heat loss presented by comparison of TC2 for the standard case and the modified cases.
region of DS block and the bottom of the graphite crucible support. In the only block B case (Case 2), however, escape of the radial heat flux from the side crucible wall is prevented. This means that there
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is a reduction in the loss of radial heat at the c–m interface near the crucible wall in the positive direction. The c–m interface becomes more convex in the central section and the concavity
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near the crucible wall section is reduced more significantly in comparison with Case 1. It is clear that block A has greater influence on the convexity while block B has greater influence on the concavity of the c–m interface during the growth process. There is not much difference of convexity in the central region but there is a significant difference of concavity near the crucible wall in Case 3 as compared to Case 1. Moreover, a significant shift in the lowest position of the interface is obtained between the modified and standard model (Fig. 5). Fig. 9 shows a decrease in TC2 which represents heat loss through the crucible bottom. Heat flux moving out of the crucible system is prevented by the addition of insulation blocks so TC2 becomes lower in the modified models. A comparison of heating power consumption, plotted in Fig.10, is also made to estimate the energy saving of the modifications. The average reduction in total heater power for Case 1, Case 2, and Case 3 is 7.4%, 8.7%, and 13%, respectively, as compared to the standard case. The prevention of heat loss by adding insulation blocks to the side insulation or/and the side of a DS block lead to the decrease in heating power consumption. The greatest energy saving is obtained with the combination of block A and block B. Saving energy is an important goal for the optimization of crystal growth systems. The distribution of the oxygen concentration with SiO concentration and flow motion obtained with the standard model at
Fig. 10. Total heating power consumption vs. growth time for the standard case and the modified cases.
z 1500 1800 2400
2100
1 7.0
7.4
2
3
7.8
4
8.2
5
r
10%
z 200 500 800 2.4 2.8
2.0
2
4
r 50% Fig. 11. Distribution of oxygen and SiO concentration (left, ΔCO ¼0.2 ppma, ΔCSiO ¼ 100 ppma) and flow pattern (right) for the standard model.
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z 1800 2700
2100
2400
7.0
7.4 8.2
2+3
6.6
4
7.8
5
r
10%
z
500
200
6
800 2.8
2.4
2.0
2+3
3.2
4
r 50% Fig. 12. Distribution of oxygen and SiO concentration (left, ΔCO ¼ 0.2 ppma, ΔCSiO ¼100 ppma) and flow pattern (right) for Case 3.
10% and 50% silicon solidification is presented in Fig. 11. Heat is transferred to the melt through the crucible wall and radiated to the free melt surface. This results in the maximum temperature of the silicon melt appearing at the triple-junction point of the crucible-melt–gas phase. When 10% of the silicon melt is solidified, the flow pattern in the bulk silicon includes five vortexes. Since the temperature difference at the free surface near the center region is very small, the shear effect induced by the flow motion of the argon gas may be greater than the Marangoni effect in this region. Therefore, a very small clockwise vortex (1) appears near the free surface in the center region. Along the free surface, the temperature near the crucible side wall is higher than that near the center. The anti-clockwise vortices (2) and (3) are generated by both the buoyancy and thermocapillary forces. In contrast, in the bottom part of the melt region, the temperature near the crucible wall is lower than that near the center, since the c–m interface near the crucible wall is concave. Hence, vortex (4) induced by the buoyancy force is clockwise. The small cell (5) occurring near the c–m interface is due to the large size of the crucible. When the solidification fraction reaches 50%, vortices (1), (3) and (5) disappear. The decrease in the melt depth causes a significant reduction in the strength and size of cell (2). It then moves downward to partially cover the c–m interface while the other one (4) covers the free surface, as well as the rest of the region of the solidification interface. As shown in Fig. 11, the oxygen impurity
distribution is strongly dependent on the flow pattern. Fig. 12 displays the flow structure and the distribution of oxygen and SiO concentration for Case 3. The temperature at the side crucible wall is higher in Case 3 than that in the standard model because the addition of the insulation block prevents the loss of heat flux from the side crucible wall. A higher wall temperature results in a greater release of oxygen impurity from the silica crucible wall into the silicon melt. The effect of Maragoni convection becomes larger in Case 3, suppressing the shear stress effect induced by the argon gas flow, so vortex (1) does not occur in the center region near the free surface. Since there is a significant reduction in the concavity of the c–m interface in Case 3, in comparison with the standard one, the strength of buoyancy vortex (4) becomes weaker and vortices (2) and (3) get larger. This results in the merging of vortices (2) and (3), as shown in Fig. 12a. In Fig. 12b, a small vortex (6) appears at the free surface near the crucible wall due to the enhancement of the thermocapillary force by the higher radial temperature gradient. Fig. 13 presents a reduction in the melt velocity near the crucible side wall due to the decrease in the buoyancy force. The strength of the buoyancy cell is not enough to carry the oxygen atoms in the lower region of the silicon melt towards the free surface for evaporation. The slower flow motion also increases the evaporation of the oxygen atoms that have remained in the upper region near the crucible wall. There is clearly a higher SiO concentration above the free surface and a
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Fig. 15. Vcr/Gc parameter with different interface positions for the standard case and the modified cases.
higher oxygen level in the bulk melt for Case 3, as can be seen by comparing the distribution of the SiO and oxygen concentration in Fig. 11 and Fig. 12. Fig. 14 presents the average oxygen concentration along the c–m interface for the standard case and Case 3. The average oxygen content along the c–m interface decreases when the solidification fraction gets higher. It gets higher for Case 3. The Voronkov ratios Vcr/Gc, defined as the ratio of the crystallization rate to the crystal thermal gradient normal to the c–m interface, for the standard and modified model, are shown in Fig.15. It is well-known that the Vcr/Gc parameter stands for the formation of defects in silicon ingots. As can be seen, this parameter is reduced in the modified model as compared to the standard one. The lowest value is obtained for Case 3. For all cases, the Vcr/Gc parameter is higher than the critical value (Vcr/ Gc ¼0.12 mm2/min/K [14]). This means that vacancies will occur in the ingot but the formation of these defects is reduced in Case 1, Case 2 and Case 3. Fig. 13. Axial melt velocity at 10mm from the inner crucible wall immersed in the silicon melt for the standard case and Case 3.
4. Conclusions The hot zone inside a DS furnace used to grow mc-Si crystal with 800 kg total charge has been modified by adding insulation blocks to the side of the DS block or/and at the low part of the side insulation. The simulation results show that the addition of both insulation blocks can effectively improve the concavity of the c–m interface at a higher solidification fraction due to the significant decrease in heat loss through the side crucible wall. Moreover, this combination can obtain the highest energy saving in total heating power consumption. There is a slightly higher average oxygen concentration along the c–m interface due to the higher wall temperature and the lower melt velocity as compared to the standard one. The decrease of Vcr/Gc parameter for the modified models indicates the lower vacancy formation in the ingot.
Acknowledgments
Fig. 14. Comparison of average oxygen concentration with different solidification fractions for the standard case and Case 3.
The authors would like to thank the Ministry of Science and Technology of Taiwan, R.O.C, for their support for this study through Grant no. NSC-103-2221-E-008 -038 -MY3.
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