- Email: [email protected]
Diffusion and mass transfer of boron in molten silicon during slag refining process of metallurgical grade silicon
Fluid Phase Equilibria 404 (2015) 70–74
Contents lists available at ScienceDirect
Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Diffusion and mass transfer of boron in molten silicon during slag refining process of metallurgical grade silicon Jijun Wua,b,* , Fanmao Wangb , Zhengjie Chenb , Wenhui Maa,b,* , Yanlong Lib , Bin Yanga , Yongnian Daia,b a State Key Laboratory of Complex Nonferrous Metal Resources Cleaning Utilization in Yunnan Province/The National Engineering Laboratory for Vacuum Metallurgy, Kunming University of Science and Technology, Kunming 650093, China b Engineering Research Center for Silicon Metallurgy and Silicon Materials of Yunnan Provincial Universities/Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, China
A R T I C L E I N F O
A B S T R A C T
Article history: Received 10 April 2015 Received in revised form 24 June 2015 Accepted 25 June 2015 Available online 2 July 2015
In this paper, the formulas of diffusion coefficient (D) and mass transfer coefficient (b) of boron in molten silicon were deduced. The diffusion coefficient of boron was determined to be 1.46 108 m2 s1 by the diffusion experiment at 1823 K in the resistance furnace. The mass transfer process of boron between silicon and slag was described using the two-film theory and the mass transfer coefficient (b) of boron was measured to be 1.7 104 m s1 while using the binary CaO–SiO2 slag refining at 1823 K. It was calculated by the relation between diffusion coefficient and mass transfer coefficient that the effective boundary layer thickness (d) close to molten silicon side was 0.086 mm. ã 2015 Elsevier B.V. All rights reserved.
Keywords: Solar-grade polysilicon Boron removal Kinetics Diffusion coefficient Mass transfer coefficient Boundary layer
1. Introduction The solar-grade polysilicon used as solar cell materials is mainly produced by the chemical methods including the Siemens process and the Fluidized Bed Reactor [1–3]. As a result of some disadvantages such as high cost and heavy environmental pollution, the chemical route is being substituted by some other techniques [4,5]. The metallurgical route for a low cost solar-grade polysilicon production has gradually become a hot topic of research. In this route, the slag refining can effectively remove impurity boron from metallurgical grade silicon and most of current researches have focused on the thermodynamics of boron removal by this method [6–9]. Wu et al. [10] found that boron in metallurgical grade silicon could be removed from 18 ppmw to 1.4 ppmw using a refining technique of high basic slag. Also, the thermodynamic relation between distribution coefficient of boron (LB) and slag activity parameter was established and confirmed. Li et al. [11] described that boron can be removed by increasing the
* Corresponding authors at: State Key Laboratory of Complex Nonferrous Metal Resources Cleaning Utilization in Yunnan Province/The National Engineering Laboratory for Vacuum Metallurgy, Kunming University of Science and Technology, Kunming 650093, China. Fax: +86 871 65161583. E-mail addresses: [email protected] (J. Wu), [email protected] (W. Ma). http://dx.doi.org/10.1016/j.fluid.2015.06.040 0378-3812/ ã 2015 Elsevier B.V. All rights reserved.
basicity and the oxygen potential of slag. Fang et al. [12] found that the boron concentration in silicon can be decreased from 10.6 ppmw to 0.65 ppmw by Na2O–SiO2 slag refining treatment and it is beneficial for boron removal while increasing refining time under the condition of a small mass ratio of slag to silicon. Some studies [13,14] show that the kinetic factors such as the diffusions of boron in molten silicon and borate in slag play the important roles to boron removal during the process of slag refining. The diffusion coefficient of boron in silicon melt was calculated to be 2.7 104 cm2 s1 by Tang et al. [15] and it was also experimentally determined to be (2.4 0.7) 104 cm2 s1 by Kodera [16]. Based on the work of Kodera [16], Garandet [17] propose new determinations of the diffusion coefficients of various dopants in liquid silicon, and a diffusion coefficient of 1.2 108 m2 s1 for boron in silicon melt was gotten. It has been reported that the rate controlling step of boron removal from metallurgical grade silicon is the mass transfer process of borate in slag. Nishimoto et al. [18] found that the boron removal rate was controlled by mass transport in the calcium silicate slag with a mass-transfer coefficient (kS) of 1.4 106 m/s. Krystad et al. [19] had also reported the larger values for the same slag and temperature in the range of 1.7 106–3.5106 m/s and a relatively larger value of 4.3 106 m/s has also been obtained using the CaO–MgO–SiO2 slag. Zhang et al. [20] calculated the total mass transfer coefficient of boron to be 6.85 104 cm/s for the 10% CaF2–10%Al2O3–20%CaO–60%SiO2 slag at 2073 K.
J. Wu et al. / Fluid Phase Equilibria 404 (2015) 70–74
In this paper, the diffusion coefficient of boron in molten silicon was determined by experiments. The mass transfer coefficient of boron removal using the binary CaO–SiO2 slag refining was also measured and calculated. The functional relationship between boron concentration in silicon and refining time was established and confirmed. Simultaneously, the effective boundary layer thickness close to silicon side was derived from the relationship between mass transfer coefficient and diffusion coefficient of boron.
The boron atoms will diffuse from solid boron toward liquid silicon when the solid boron and the liquid silicon are placed together. The concentration gradient of boron in molten silicon will be formed and distributed from the solid–liquid interface of B–Si with a high boron concentration to the molten silicon with a low boron concentration. Finally, the boron concentration in whole liquid silicon will be saturated. The schematic diagram of boron diffusion from B–Si interface to liquid silicon is shown in Fig. 1. According to Fick’s second law, the diffusion rate of boron in molten silicon can be described as Eq. (1). ! @c @2 c ¼D (1) @t @x2 The initial and boundary conditions of differential Eq. (1) are shown in Eqs. (2) and (3).
@cð0;tÞ ¼0 @x
(2)
(3)
where g and S are the total quantity and the sectional area of diffusible substance, respectively. dðxÞ is the Dirac function at x0 ¼ 0. The property of Dirac function dðxÞ can be expressed as Eqs. (4) and (5). dðx x0 Þ ¼ 0; x 6¼ x0 (4) þ1; x ¼ x0 Z
þ1 1
dðx x0 Þdx ¼ 1
(5)
Then, the integral result of Eq. (1) at the initial and boundary conditions for Eqs. (2) and (3) is shown in Eq. (6).
71
(6)
In the form of logarithm for Eqs. (6) and (7) can be gotten. g x2 lgcðx;tÞ ¼ lg pffiffiffiffiffiffiffiffiffiffi 2:3ð4D tÞ S pDt
(7)
By drawing to data, the curve of lgcðx;tÞ x2 and its slope (k) can be gotten and represented as Eq. (8). k¼
2. Theoretical formulations
g cðx;0Þ ¼ dðxÞ S
g x2 cðx;tÞ ¼ pffiffiffiffiffiffiffiffiffiffiexp 4Dt S pDt
1 9:2Dt
(8)
And lastly, the diffusion coefficient of boron in molten silicon (D) can be calculated and gotten according to Eq. (8). During the slag refining process of boron removal, there must be a silicon boundary layer (d) and a slag boundary layer (d0 ), respectively. According to the two-film theory, the oxidation and removal process of boron in silicon by the binary CaO–SiO2 slag refining can be shown in Fig. 2. According to the boundary-layer theory of convective mass transfer, the convective mass transfer rate is zero (uxc = 0) at the verticality of phase interface, where the characteristics of mass transfer is an unsteady state diffusion. So the mass transfer rate of boron can be explained as Eq. (9): @c V dc (9) ¼ J ¼ D @x x¼0 A dt Meanwhile, it can also be described as Eq. (10) J ¼ bðc c Þ
(10)
Then, Eq. (11) can be obtained by Eq. (9) = Eq. (10). dc A ¼ b ðc c Þ dt V
(11)
where b is the mass transfer coefficient of boron in molten silicon. A and V are the interface area of between silicon and slag and the volume of molten silicon, respectively. c and c* are the boron concentrations in the molten silicon and at the interface of siliconslag, respectively. The interface concentration (c*) can be replaced by the equilibrium concentration of boron in silicon (ce) for a very fast reaction rate of boron oxidation at the interface of silicon-slag. After substituting the molar concentration (c) with the weight percent concentration (w[B]), Eq. (12) can be obtained by integrating Eq. (11). The value of mass transfer coefficient (b) can be described as the slope of curve. w½B w½Be r A ¼ b m t ln Mm w½B0 w½Be
(12)
where w[B] is the mass concentration of boron in silicon after the refining time (t ). w[B]0 and w[B]e are the initial and the equilibrium mass concentrations of boron in molten silicon, respectively. rm and Mm are the density and the mass of molten silicon, respectively.
Fig. 1. Schematic diagram of boron diffusion in molten silicon.
Fig. 2. Schematic diagram of boron oxidation and removal by CaO–SiO2 slag.
72
J. Wu et al. / Fluid Phase Equilibria 404 (2015) 70–74
Fig. 3. Schematic diagram of diffusion experiment (a) and appearance picture of sampling (b).
3. Experimental The boron powder of 5 g with a purity of 4N was firstly pressed into a slice with a diameter of 20 mm and a thickness of 5 mm. The electronic grade silicon powder of 50 g with a purity of 9N was put into a high purity graphite crucible (F 40 mm 60 mm) and the upper surface of silicon powder was smoothed. Then the boron slice was placed on the surface of silicon powder. Subsequently, the graphite crucible was put into a resistance furnace and carried out for the diffusion experiment under the protection of argon gas. After it was kept at 1873 K for 180 min, the sample was cooled to room temperature and removed out from furnace. Finally, the sample was lengthways cut into half and the boron concentrations of different sampling positions at a distance of every 3 mm away from the B–Si interface were analyzed by the Inductively Coupled Plasma Atomic Emission Spectrometry (ICP-AES). The schematic diagram of diffusion experiment and the appearance picture of sampling are shown in Fig. 3. The raw material of refining experiment for boron removal was the metallurgical grade silicon with a boron concentration of 22 ppmw. The slag refining agent was composed of 50%CaO–50% SiO2. Firstly, the metallurgical grade silicon of 20 g and the calcium silicate slag of 20 g were loaded into a high purity graphite crucible with an inner diameter of 40 mm and a height of 60 mm. The slag was laid the upside of silicon. Then, the crucible was put into the heating zone of resistance furnace for refining at 1823 K with
different holding times of 30–180 min, respectively, under the protection of argon gas. The experimental sample is shown in Fig. 4. It can be seen that the Si–B interface obviously exist between molten silicon and molten slag. Lastly, the boron concentration in refined silicon was analyzed by the Inductively Coupled Plasma Mass Spectrometry (ICP-MS). 4. Results and discussion The B–Si interface between solid boron and molten silicon is considered as the initial position (“0” mm). The boron concentrations with 3 mm, 6 mm, 9 mm, 12 mm and 15 mm, respectively, away from the B–Si interface as shown in Fig. 3(b) are analyzed and the results were shown in Fig. 5. It is found that the boron concentration of sampling point gradually reduces with the increase of diffusion distance away from the B–Si interface. A non-linear decreasing trend displays that the boron diffusion in molten silicon is an unsteady state diffusion process, which confirms the deduced result ahead. According to the binary Si–B phase diagram, the maximal concentration of boron in liquid phase (on the liquidus) reaches 7.4% at 1823 K. On account of the use of a solid boron powder slice in the diffusion experiment, it is consequently considered that the dissolution of boron in molten silicon has reached a saturated state at the B–Si interface and the boron concentration at the B–Si interface can be replaced by the saturated solubility. Therefore, the
Fig. 4. Schematic (a) and appearance (b) diagrams of slag refining using the binary CaO–SiO2 slag.
J. Wu et al. / Fluid Phase Equilibria 404 (2015) 70–74
73
The mass distribution coefficient (LB) of boron between slag and silicon in equilibrium is represented in Eq. (14). LB ¼
wðBO1:5 Þe w½Be
(14)
Lastly, the boron concentration can be described as Eq. (15) when it reaches equilibrium. w½Be ¼
Fig. 5. Boron concentration of sampling point in silicon with different distance away from B–Si interface.
w½B0 MBO1:5 =MB LB Ms =Mm þ MBO1:5 =MB
(15)
where LB is the mass distribution coefficient of boron between slag and silicon in equilibrium. Ms and Mm are the mass of molten slag and molten silicon, respectively. MBO1:5 and MB are the molar mass of boron oxide and boron, respectively. It is calculated that the equilibrium boron concentration in molten silicon (w½Be ) is about 2.6 ppmw with a LB value of 1.8 by Eq. (15). Then, the equilibrium boron concentration is substituted into Eq. (14) and the relationship between refining time (t ) and Yln X is obtained and shown in Eq. (16). X and Y are represented by Eqs. (17) and (18). YlnX ¼ b t
X¼
Y¼
Fig. 6. Linear fitting results by experimental data.
linear fitting results for the diffusion coefficient of boron in molten silicon (D) at 1823 K are obtained and shown in Fig. 6 according to five sampling points by Eqs. (7) and (8). It is gotten as D = 1.46 108 m2 s1 and shown in Table 1. Due to the large diameter/height size of crucible and the experimental factor such as convection, the result is a little lower than the value of 2.7 104 cm2 s1 estimated by Tang et al. [15] using the Arrhenius equation but higher than the value of 1.2 108 m2 s1 posed d by Garandet [17]. The boron concentration in refined silicon using the binary CaO–SiO2 slag refining with different time of 30–180 min shown in Table 1. In the process of boron removal by slag refining, the mass conservation of boron between molten silicon and molten slag can be shown in Eq. (13). Mm Mm Ms w½B0 ¼ w½Be þ wðBO1:5 Þe MB MB MBO1:5
(13)
(16)
w½B w½Be w½B0 w½Be
(17)
Mm
(18)
rm A
Lastly, the curve derived by Eq. (16) is gotten in experiment and drawn in Fig. 7. Obviously, the slope of straight line is just the mass transfer coefficient (b) of boron in molten silicon and it is calculated to be 1.7 104 m s1. It exists a difference of fluidity between the immiscible molten silicon and molten slag at 1823 K. Therefore, a boundary layer between molten silicon and molten slag is generated. It is defined that the distance of intersection point between the tangent of boron concentration distribution curve at x = 0 and the extension line of concentration curve (c) away from silicon-slag interface is the effective boundary layer close to silicon side. The schematic diagram of boundary layer is described in Fig. 8. d can be calculated by Eq. (19).
d¼
c c ð@c=@xÞx¼0
(19)
where ð@c=@xÞx¼0 is the concentration gradient of boron nearby the interface of molten silicon and molten slag. c* is the boron concentration at the silicon-slag interface. In the meantime, Eq. (20) can be obtained by Eqs. (9) and (11), which displays the relationship between D and b. D¼bd
(20)
Finally, the effective boundary layer thickness (d) can be calculate. As it has been found by Nishimoto et al. [18] that the mass
Table 1 Experimental results of diffusion coefficient (D) and mass transfer coefficient (b). Sampling points
xi/mm
w[B]/%
1# 2# 3# 4# 5#
3 6 9 12 15
0.75 0.72 0.68 0.62 0.53
D 108/m2 s1
1.46
Refining time/min
w[B]/ppmw
b 104/m s1
30 60 120 180
22 14.8 9.5 4.7 3.7
1.7
74
J. Wu et al. / Fluid Phase Equilibria 404 (2015) 70–74
that the effective boundary layer thickness (d) close to molten silicon side was d = 0.086 mm. Acknowledgements The authors wish to acknowledge the financial support on this research from National Natural Science Foundation of China (51104080 and 51334002) and the Natural Science Foundation of Yunnan Province (2014FB124). References
Fig. 7. Relationship between Yln X and refining time (t ).
Fig. 8. Schematic diagram of boundary layer close to silicon side.
transport in the slag phase is the rate-controlling step, and hence the boundary layer thickness is 0.086 mm when this is the case. 5. Conclusions The diffusion coefficient (D) of boron in molten silicon at 1823 K was determined, D =1.46 108 m2 s1, by the diffusion experiment in the resistance furnace and the mass transfer coefficient (b) of boron was also measured and calculated b = 1.7 104 m s1 using the binary CaO–SiO2 slag refining. It was calculated by the relation between diffusion coefficient and mass transfer coefficient
[1] W.O. Filtvedt, A. Holt, P.A. Ramachandran, M.C. Melaaen, Chemical vapor deposition of silicon from silane: review of growth mechanisms and modeling/ scaleup of fluidized bed reactors, Solar Energy Mater. Solar Cells 107 (2012) 188–200. [2] S. Richter, M. Werner, M. Schley, F. Schaaff, H. Riemann, H.J. Rost, F. Zobel, R. Kunert, P. Dold, C. Hagendorf, Structural and chemical investigations of adapted Siemens feed rods for an optimized float zone process, Energy Procedia 38 (2013) 604–610. [3] H. Ni, S. Lu, C. Chen, Modeling and simulation of silicon epitaxial growth in Siemens CVD reactor, J. Cryst. Growth 404 (2014) 89–99. [4] H.A. Aulich, F.W. Schulze, Crystalline silicon feedstock for solar cell, Prog. Photovoltaics: Res. Appl. 10 (2002) 141–147. [5] L. Cai, X. Ren, B. Fan, J. Zheng, C. Chen, Effect of temperature on crystalline silicon solar cells processed from chemical and metallurgical route, Optik 125 (2014) 3918–3921. [6] Y. Li, J. Wu, W. Ma, Kinetics of boron removal from metallurgical grade silicon using a slag refining technique based on CaO–SiO2 binary system, Sep. Sci. Technol. 49 (2014) 1946–1952. [7] J. Wu, Y. Li, W. Ma, K. Wei, B. Yang, Y. Dai, Boron removal in purifying metallurgical grade silicon by a CaO–SiO2 slag refining, Trans. Nonferrous Met. Soc. China 24 (2014) 1231–1236. [8] K. Morita, T. Miki, Thermodynamics of solar-grade-silicon refining, Intermetallics 11 (2003) 1111–1117. [9] L.A.V. Teixeira, K. Morita, Removal of boron from molten silicon using CaO– SiO2 based slags, ISIJ Int. 49 (2009) 783–787. [10] J. Wu, M. Xu, K. Liu, W. Ma, B. Yang, Y. Dai, Removing boron from metallurgical grade silicon by a high basic slag refining technique, J. Min. Metall. B 50 (2014) 83–86. [11] M. Li, T. Utigard, M. Barati, Removal of boron and phosphorus from silicon using CaO–SiO2–Na2O–Al2O3 flux, Metall. Mater. Trans. B 45 (2014) 221–228. [12] M. Fang, C. Lu, L. Huang, H. Lai, J. Chen, X. Yang, J. Li, W. Ma, P. Xing, X. Luo, Multiple Slag operation on boron removal from metallurgical-grade silicon using Na2O–SiO2 Slags, Ind. Eng. Chem. Res. 53 (2014) 12054–12062. [13] J. Safarian, G. Tranell, M. Tangstad, Thermodynamic and kinetic behavior of B and Na through the contact of B-doped silicon with Na2O–SiO2 slags, Metall. Mater. Trans. B 44 (2013) 571–583. [14] J.F. White, D. Sichen, Mass transfer in slag refining of silicon with mechanical stirring: transient kinetics of Ca and B transfer, Metall. Mater. Trans. B 46 (2015) 135–144. [15] K. Tang, E.J. Øvrelid, G. Tranell, M. Tangstad, Critical assessment of the impurity diffusivities in solid and liquid silicon, JOM 61 (2009) 49–55. [16] H. Kodera, Diffusion coefficients of impurities in silicon melt, Jpn. J. Appl. Phys. 2 (1963) 212–219. [17] J.P. Garandet, New determinations of diffusion coefficients for various dopants in liquid silicon, Int. J. Thermophys. 28 (2007) 1285–1305. [18] H. Nishimoto, Y. Kang, T. Yoshikawa, K. Morita, The rate of boron removal from molten silicon by CaO–SiO2 slag and Cl2 treatment, High Temp. Mater. Processes 31 (2012) 471–477. [19] E. Krystad, S. Zhang, G. Tranell, The kinetics of boron removal during slag refining in the production of solar-grade silicon, in: L.F. Zhang, J.A. Pomykala, A. Ciftja (Eds.), EPD Congress 2012 (TMS), FL, USA, 2012, pp. 471–480. [20] L. Zhang, Y. Tan, J.Y. Li, Y. Liu, D.K. Wang, J.Y. Li, Study of boron removal from molten silicon by slag refining under atmosphere, Mater. Sci. Semicond. Process. 16 (2013) 1645–1649.
Contents lists available at ScienceDirect
Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Diffusion and mass transfer of boron in molten silicon during slag refining process of metallurgical grade silicon Jijun Wua,b,* , Fanmao Wangb , Zhengjie Chenb , Wenhui Maa,b,* , Yanlong Lib , Bin Yanga , Yongnian Daia,b a State Key Laboratory of Complex Nonferrous Metal Resources Cleaning Utilization in Yunnan Province/The National Engineering Laboratory for Vacuum Metallurgy, Kunming University of Science and Technology, Kunming 650093, China b Engineering Research Center for Silicon Metallurgy and Silicon Materials of Yunnan Provincial Universities/Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, China
A R T I C L E I N F O
A B S T R A C T
Article history: Received 10 April 2015 Received in revised form 24 June 2015 Accepted 25 June 2015 Available online 2 July 2015
In this paper, the formulas of diffusion coefficient (D) and mass transfer coefficient (b) of boron in molten silicon were deduced. The diffusion coefficient of boron was determined to be 1.46 108 m2 s1 by the diffusion experiment at 1823 K in the resistance furnace. The mass transfer process of boron between silicon and slag was described using the two-film theory and the mass transfer coefficient (b) of boron was measured to be 1.7 104 m s1 while using the binary CaO–SiO2 slag refining at 1823 K. It was calculated by the relation between diffusion coefficient and mass transfer coefficient that the effective boundary layer thickness (d) close to molten silicon side was 0.086 mm. ã 2015 Elsevier B.V. All rights reserved.
Keywords: Solar-grade polysilicon Boron removal Kinetics Diffusion coefficient Mass transfer coefficient Boundary layer
1. Introduction The solar-grade polysilicon used as solar cell materials is mainly produced by the chemical methods including the Siemens process and the Fluidized Bed Reactor [1–3]. As a result of some disadvantages such as high cost and heavy environmental pollution, the chemical route is being substituted by some other techniques [4,5]. The metallurgical route for a low cost solar-grade polysilicon production has gradually become a hot topic of research. In this route, the slag refining can effectively remove impurity boron from metallurgical grade silicon and most of current researches have focused on the thermodynamics of boron removal by this method [6–9]. Wu et al. [10] found that boron in metallurgical grade silicon could be removed from 18 ppmw to 1.4 ppmw using a refining technique of high basic slag. Also, the thermodynamic relation between distribution coefficient of boron (LB) and slag activity parameter was established and confirmed. Li et al. [11] described that boron can be removed by increasing the
* Corresponding authors at: State Key Laboratory of Complex Nonferrous Metal Resources Cleaning Utilization in Yunnan Province/The National Engineering Laboratory for Vacuum Metallurgy, Kunming University of Science and Technology, Kunming 650093, China. Fax: +86 871 65161583. E-mail addresses: [email protected] (J. Wu), [email protected] (W. Ma). http://dx.doi.org/10.1016/j.fluid.2015.06.040 0378-3812/ ã 2015 Elsevier B.V. All rights reserved.
basicity and the oxygen potential of slag. Fang et al. [12] found that the boron concentration in silicon can be decreased from 10.6 ppmw to 0.65 ppmw by Na2O–SiO2 slag refining treatment and it is beneficial for boron removal while increasing refining time under the condition of a small mass ratio of slag to silicon. Some studies [13,14] show that the kinetic factors such as the diffusions of boron in molten silicon and borate in slag play the important roles to boron removal during the process of slag refining. The diffusion coefficient of boron in silicon melt was calculated to be 2.7 104 cm2 s1 by Tang et al. [15] and it was also experimentally determined to be (2.4 0.7) 104 cm2 s1 by Kodera [16]. Based on the work of Kodera [16], Garandet [17] propose new determinations of the diffusion coefficients of various dopants in liquid silicon, and a diffusion coefficient of 1.2 108 m2 s1 for boron in silicon melt was gotten. It has been reported that the rate controlling step of boron removal from metallurgical grade silicon is the mass transfer process of borate in slag. Nishimoto et al. [18] found that the boron removal rate was controlled by mass transport in the calcium silicate slag with a mass-transfer coefficient (kS) of 1.4 106 m/s. Krystad et al. [19] had also reported the larger values for the same slag and temperature in the range of 1.7 106–3.5106 m/s and a relatively larger value of 4.3 106 m/s has also been obtained using the CaO–MgO–SiO2 slag. Zhang et al. [20] calculated the total mass transfer coefficient of boron to be 6.85 104 cm/s for the 10% CaF2–10%Al2O3–20%CaO–60%SiO2 slag at 2073 K.
J. Wu et al. / Fluid Phase Equilibria 404 (2015) 70–74
In this paper, the diffusion coefficient of boron in molten silicon was determined by experiments. The mass transfer coefficient of boron removal using the binary CaO–SiO2 slag refining was also measured and calculated. The functional relationship between boron concentration in silicon and refining time was established and confirmed. Simultaneously, the effective boundary layer thickness close to silicon side was derived from the relationship between mass transfer coefficient and diffusion coefficient of boron.
The boron atoms will diffuse from solid boron toward liquid silicon when the solid boron and the liquid silicon are placed together. The concentration gradient of boron in molten silicon will be formed and distributed from the solid–liquid interface of B–Si with a high boron concentration to the molten silicon with a low boron concentration. Finally, the boron concentration in whole liquid silicon will be saturated. The schematic diagram of boron diffusion from B–Si interface to liquid silicon is shown in Fig. 1. According to Fick’s second law, the diffusion rate of boron in molten silicon can be described as Eq. (1). ! @c @2 c ¼D (1) @t @x2 The initial and boundary conditions of differential Eq. (1) are shown in Eqs. (2) and (3).
@cð0;tÞ ¼0 @x
(2)
(3)
where g and S are the total quantity and the sectional area of diffusible substance, respectively. dðxÞ is the Dirac function at x0 ¼ 0. The property of Dirac function dðxÞ can be expressed as Eqs. (4) and (5). dðx x0 Þ ¼ 0; x 6¼ x0 (4) þ1; x ¼ x0 Z
þ1 1
dðx x0 Þdx ¼ 1
(5)
Then, the integral result of Eq. (1) at the initial and boundary conditions for Eqs. (2) and (3) is shown in Eq. (6).
71
(6)
In the form of logarithm for Eqs. (6) and (7) can be gotten. g x2 lgcðx;tÞ ¼ lg pffiffiffiffiffiffiffiffiffiffi 2:3ð4D tÞ S pDt
(7)
By drawing to data, the curve of lgcðx;tÞ x2 and its slope (k) can be gotten and represented as Eq. (8). k¼
2. Theoretical formulations
g cðx;0Þ ¼ dðxÞ S
g x2 cðx;tÞ ¼ pffiffiffiffiffiffiffiffiffiffiexp 4Dt S pDt
1 9:2Dt
(8)
And lastly, the diffusion coefficient of boron in molten silicon (D) can be calculated and gotten according to Eq. (8). During the slag refining process of boron removal, there must be a silicon boundary layer (d) and a slag boundary layer (d0 ), respectively. According to the two-film theory, the oxidation and removal process of boron in silicon by the binary CaO–SiO2 slag refining can be shown in Fig. 2. According to the boundary-layer theory of convective mass transfer, the convective mass transfer rate is zero (uxc = 0) at the verticality of phase interface, where the characteristics of mass transfer is an unsteady state diffusion. So the mass transfer rate of boron can be explained as Eq. (9): @c V dc (9) ¼ J ¼ D @x x¼0 A dt Meanwhile, it can also be described as Eq. (10) J ¼ bðc c Þ
(10)
Then, Eq. (11) can be obtained by Eq. (9) = Eq. (10). dc A ¼ b ðc c Þ dt V
(11)
where b is the mass transfer coefficient of boron in molten silicon. A and V are the interface area of between silicon and slag and the volume of molten silicon, respectively. c and c* are the boron concentrations in the molten silicon and at the interface of siliconslag, respectively. The interface concentration (c*) can be replaced by the equilibrium concentration of boron in silicon (ce) for a very fast reaction rate of boron oxidation at the interface of silicon-slag. After substituting the molar concentration (c) with the weight percent concentration (w[B]), Eq. (12) can be obtained by integrating Eq. (11). The value of mass transfer coefficient (b) can be described as the slope of curve. w½B w½Be r A ¼ b m t ln Mm w½B0 w½Be
(12)
where w[B] is the mass concentration of boron in silicon after the refining time (t ). w[B]0 and w[B]e are the initial and the equilibrium mass concentrations of boron in molten silicon, respectively. rm and Mm are the density and the mass of molten silicon, respectively.
Fig. 1. Schematic diagram of boron diffusion in molten silicon.
Fig. 2. Schematic diagram of boron oxidation and removal by CaO–SiO2 slag.
72
J. Wu et al. / Fluid Phase Equilibria 404 (2015) 70–74
Fig. 3. Schematic diagram of diffusion experiment (a) and appearance picture of sampling (b).
3. Experimental The boron powder of 5 g with a purity of 4N was firstly pressed into a slice with a diameter of 20 mm and a thickness of 5 mm. The electronic grade silicon powder of 50 g with a purity of 9N was put into a high purity graphite crucible (F 40 mm 60 mm) and the upper surface of silicon powder was smoothed. Then the boron slice was placed on the surface of silicon powder. Subsequently, the graphite crucible was put into a resistance furnace and carried out for the diffusion experiment under the protection of argon gas. After it was kept at 1873 K for 180 min, the sample was cooled to room temperature and removed out from furnace. Finally, the sample was lengthways cut into half and the boron concentrations of different sampling positions at a distance of every 3 mm away from the B–Si interface were analyzed by the Inductively Coupled Plasma Atomic Emission Spectrometry (ICP-AES). The schematic diagram of diffusion experiment and the appearance picture of sampling are shown in Fig. 3. The raw material of refining experiment for boron removal was the metallurgical grade silicon with a boron concentration of 22 ppmw. The slag refining agent was composed of 50%CaO–50% SiO2. Firstly, the metallurgical grade silicon of 20 g and the calcium silicate slag of 20 g were loaded into a high purity graphite crucible with an inner diameter of 40 mm and a height of 60 mm. The slag was laid the upside of silicon. Then, the crucible was put into the heating zone of resistance furnace for refining at 1823 K with
different holding times of 30–180 min, respectively, under the protection of argon gas. The experimental sample is shown in Fig. 4. It can be seen that the Si–B interface obviously exist between molten silicon and molten slag. Lastly, the boron concentration in refined silicon was analyzed by the Inductively Coupled Plasma Mass Spectrometry (ICP-MS). 4. Results and discussion The B–Si interface between solid boron and molten silicon is considered as the initial position (“0” mm). The boron concentrations with 3 mm, 6 mm, 9 mm, 12 mm and 15 mm, respectively, away from the B–Si interface as shown in Fig. 3(b) are analyzed and the results were shown in Fig. 5. It is found that the boron concentration of sampling point gradually reduces with the increase of diffusion distance away from the B–Si interface. A non-linear decreasing trend displays that the boron diffusion in molten silicon is an unsteady state diffusion process, which confirms the deduced result ahead. According to the binary Si–B phase diagram, the maximal concentration of boron in liquid phase (on the liquidus) reaches 7.4% at 1823 K. On account of the use of a solid boron powder slice in the diffusion experiment, it is consequently considered that the dissolution of boron in molten silicon has reached a saturated state at the B–Si interface and the boron concentration at the B–Si interface can be replaced by the saturated solubility. Therefore, the
Fig. 4. Schematic (a) and appearance (b) diagrams of slag refining using the binary CaO–SiO2 slag.
J. Wu et al. / Fluid Phase Equilibria 404 (2015) 70–74
73
The mass distribution coefficient (LB) of boron between slag and silicon in equilibrium is represented in Eq. (14). LB ¼
wðBO1:5 Þe w½Be
(14)
Lastly, the boron concentration can be described as Eq. (15) when it reaches equilibrium. w½Be ¼
Fig. 5. Boron concentration of sampling point in silicon with different distance away from B–Si interface.
w½B0 MBO1:5 =MB LB Ms =Mm þ MBO1:5 =MB
(15)
where LB is the mass distribution coefficient of boron between slag and silicon in equilibrium. Ms and Mm are the mass of molten slag and molten silicon, respectively. MBO1:5 and MB are the molar mass of boron oxide and boron, respectively. It is calculated that the equilibrium boron concentration in molten silicon (w½Be ) is about 2.6 ppmw with a LB value of 1.8 by Eq. (15). Then, the equilibrium boron concentration is substituted into Eq. (14) and the relationship between refining time (t ) and Yln X is obtained and shown in Eq. (16). X and Y are represented by Eqs. (17) and (18). YlnX ¼ b t
X¼
Y¼
Fig. 6. Linear fitting results by experimental data.
linear fitting results for the diffusion coefficient of boron in molten silicon (D) at 1823 K are obtained and shown in Fig. 6 according to five sampling points by Eqs. (7) and (8). It is gotten as D = 1.46 108 m2 s1 and shown in Table 1. Due to the large diameter/height size of crucible and the experimental factor such as convection, the result is a little lower than the value of 2.7 104 cm2 s1 estimated by Tang et al. [15] using the Arrhenius equation but higher than the value of 1.2 108 m2 s1 posed d by Garandet [17]. The boron concentration in refined silicon using the binary CaO–SiO2 slag refining with different time of 30–180 min shown in Table 1. In the process of boron removal by slag refining, the mass conservation of boron between molten silicon and molten slag can be shown in Eq. (13). Mm Mm Ms w½B0 ¼ w½Be þ wðBO1:5 Þe MB MB MBO1:5
(13)
(16)
w½B w½Be w½B0 w½Be
(17)
Mm
(18)
rm A
Lastly, the curve derived by Eq. (16) is gotten in experiment and drawn in Fig. 7. Obviously, the slope of straight line is just the mass transfer coefficient (b) of boron in molten silicon and it is calculated to be 1.7 104 m s1. It exists a difference of fluidity between the immiscible molten silicon and molten slag at 1823 K. Therefore, a boundary layer between molten silicon and molten slag is generated. It is defined that the distance of intersection point between the tangent of boron concentration distribution curve at x = 0 and the extension line of concentration curve (c) away from silicon-slag interface is the effective boundary layer close to silicon side. The schematic diagram of boundary layer is described in Fig. 8. d can be calculated by Eq. (19).
d¼
c c ð@c=@xÞx¼0
(19)
where ð@c=@xÞx¼0 is the concentration gradient of boron nearby the interface of molten silicon and molten slag. c* is the boron concentration at the silicon-slag interface. In the meantime, Eq. (20) can be obtained by Eqs. (9) and (11), which displays the relationship between D and b. D¼bd
(20)
Finally, the effective boundary layer thickness (d) can be calculate. As it has been found by Nishimoto et al. [18] that the mass
Table 1 Experimental results of diffusion coefficient (D) and mass transfer coefficient (b). Sampling points
xi/mm
w[B]/%
1# 2# 3# 4# 5#
3 6 9 12 15
0.75 0.72 0.68 0.62 0.53
D 108/m2 s1
1.46
Refining time/min
w[B]/ppmw
b 104/m s1
30 60 120 180
22 14.8 9.5 4.7 3.7
1.7
74
J. Wu et al. / Fluid Phase Equilibria 404 (2015) 70–74
that the effective boundary layer thickness (d) close to molten silicon side was d = 0.086 mm. Acknowledgements The authors wish to acknowledge the financial support on this research from National Natural Science Foundation of China (51104080 and 51334002) and the Natural Science Foundation of Yunnan Province (2014FB124). References
Fig. 7. Relationship between Yln X and refining time (t ).
Fig. 8. Schematic diagram of boundary layer close to silicon side.
transport in the slag phase is the rate-controlling step, and hence the boundary layer thickness is 0.086 mm when this is the case. 5. Conclusions The diffusion coefficient (D) of boron in molten silicon at 1823 K was determined, D =1.46 108 m2 s1, by the diffusion experiment in the resistance furnace and the mass transfer coefficient (b) of boron was also measured and calculated b = 1.7 104 m s1 using the binary CaO–SiO2 slag refining. It was calculated by the relation between diffusion coefficient and mass transfer coefficient
[1] W.O. Filtvedt, A. Holt, P.A. Ramachandran, M.C. Melaaen, Chemical vapor deposition of silicon from silane: review of growth mechanisms and modeling/ scaleup of fluidized bed reactors, Solar Energy Mater. Solar Cells 107 (2012) 188–200. [2] S. Richter, M. Werner, M. Schley, F. Schaaff, H. Riemann, H.J. Rost, F. Zobel, R. Kunert, P. Dold, C. Hagendorf, Structural and chemical investigations of adapted Siemens feed rods for an optimized float zone process, Energy Procedia 38 (2013) 604–610. [3] H. Ni, S. Lu, C. Chen, Modeling and simulation of silicon epitaxial growth in Siemens CVD reactor, J. Cryst. Growth 404 (2014) 89–99. [4] H.A. Aulich, F.W. Schulze, Crystalline silicon feedstock for solar cell, Prog. Photovoltaics: Res. Appl. 10 (2002) 141–147. [5] L. Cai, X. Ren, B. Fan, J. Zheng, C. Chen, Effect of temperature on crystalline silicon solar cells processed from chemical and metallurgical route, Optik 125 (2014) 3918–3921. [6] Y. Li, J. Wu, W. Ma, Kinetics of boron removal from metallurgical grade silicon using a slag refining technique based on CaO–SiO2 binary system, Sep. Sci. Technol. 49 (2014) 1946–1952. [7] J. Wu, Y. Li, W. Ma, K. Wei, B. Yang, Y. Dai, Boron removal in purifying metallurgical grade silicon by a CaO–SiO2 slag refining, Trans. Nonferrous Met. Soc. China 24 (2014) 1231–1236. [8] K. Morita, T. Miki, Thermodynamics of solar-grade-silicon refining, Intermetallics 11 (2003) 1111–1117. [9] L.A.V. Teixeira, K. Morita, Removal of boron from molten silicon using CaO– SiO2 based slags, ISIJ Int. 49 (2009) 783–787. [10] J. Wu, M. Xu, K. Liu, W. Ma, B. Yang, Y. Dai, Removing boron from metallurgical grade silicon by a high basic slag refining technique, J. Min. Metall. B 50 (2014) 83–86. [11] M. Li, T. Utigard, M. Barati, Removal of boron and phosphorus from silicon using CaO–SiO2–Na2O–Al2O3 flux, Metall. Mater. Trans. B 45 (2014) 221–228. [12] M. Fang, C. Lu, L. Huang, H. Lai, J. Chen, X. Yang, J. Li, W. Ma, P. Xing, X. Luo, Multiple Slag operation on boron removal from metallurgical-grade silicon using Na2O–SiO2 Slags, Ind. Eng. Chem. Res. 53 (2014) 12054–12062. [13] J. Safarian, G. Tranell, M. Tangstad, Thermodynamic and kinetic behavior of B and Na through the contact of B-doped silicon with Na2O–SiO2 slags, Metall. Mater. Trans. B 44 (2013) 571–583. [14] J.F. White, D. Sichen, Mass transfer in slag refining of silicon with mechanical stirring: transient kinetics of Ca and B transfer, Metall. Mater. Trans. B 46 (2015) 135–144. [15] K. Tang, E.J. Øvrelid, G. Tranell, M. Tangstad, Critical assessment of the impurity diffusivities in solid and liquid silicon, JOM 61 (2009) 49–55. [16] H. Kodera, Diffusion coefficients of impurities in silicon melt, Jpn. J. Appl. Phys. 2 (1963) 212–219. [17] J.P. Garandet, New determinations of diffusion coefficients for various dopants in liquid silicon, Int. J. Thermophys. 28 (2007) 1285–1305. [18] H. Nishimoto, Y. Kang, T. Yoshikawa, K. Morita, The rate of boron removal from molten silicon by CaO–SiO2 slag and Cl2 treatment, High Temp. Mater. Processes 31 (2012) 471–477. [19] E. Krystad, S. Zhang, G. Tranell, The kinetics of boron removal during slag refining in the production of solar-grade silicon, in: L.F. Zhang, J.A. Pomykala, A. Ciftja (Eds.), EPD Congress 2012 (TMS), FL, USA, 2012, pp. 471–480. [20] L. Zhang, Y. Tan, J.Y. Li, Y. Liu, D.K. Wang, J.Y. Li, Study of boron removal from molten silicon by slag refining under atmosphere, Mater. Sci. Semicond. Process. 16 (2013) 1645–1649.