- Email: [email protected]
Determination and controlling of crystal growth rate during silicon purification by directional solidification
Accepted Manuscript Determination and Controlling of Crystal Growth Rate during Silicon Purification by Directional Solidification Shutao Wen, Dachuan Jiang, Shuang Shi, Yi Tan, Pengting Li, Zheng Gu, Xiaofeng Zhang PII:
S0042-207X(15)30142-1
DOI:
10.1016/j.vacuum.2015.12.004
Reference:
VAC 6877
To appear in:
Vacuum
Received Date: 4 September 2015 Revised Date:
28 November 2015
Accepted Date: 5 December 2015
Please cite this article as: Wen S, Jiang D, Shi S, Tan Y, Li P, Gu Z, Zhang X, Determination and Controlling of Crystal Growth Rate during Silicon Purification by Directional Solidification, Vaccum (2016), doi: 10.1016/j.vacuum.2015.12.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Determination and Controlling of Crystal Growth Rate during Silicon Purification by Directional Solidification a, b
a, b
Shutao Wen , Dachuan Jiang , Shuang Shi a, b, Yi Tana, b*, Pengting Lia, b, Zheng Guc, Xiaofeng Zhangc School of Materials Science and Engineering, Dalian University of Technology, Dalian 116023, China
b
Key Laboratory for Solar Energy Photovoltaic System of Liaoning Province, Dalian 116023, China
c
Qingdao Longsun silicon technology Co., Ltd
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a
Corresponding author at: School of Materials Science and Engineering, Dalian University of
SC
Technology, No. 2 Linggong Road, Ganjingzi District, Dalian 116023, China.
M AN U
E-mail address: [email protected] (Yi Tan) Abstract
A theoretical model for investigating the crystal growth rate and the solidified height during silicon purification by directional solidification is proposed. The growth rate is not constant usually and it has
TE D
profound effects on the distribution of metal impurity in production process. The crystal growth rate and the solidified height, based on thermal equilibrium on the melt-crystal interface, were discussed. The relationship between the surface temperature of silicon melt (T1) and temperature of graphite
EP
heater (TC`1) was found. The result shows that the value of T1 has an approximate linear relationship
AC C
with the TC`1. The theoretical model can be used to design or predict the crystal growth rate by controlling the TC1 according to the different request. Then, the distribution of metal impurity during silicon purification by directional solidification can be calculated according to the crystal growth rate. Thus, the theoretical model can be used to design the growth rate and predict the distribution of impurity to the silicon purification process by directional solidification. The experiments proved that the calculation agreed well with the existing experimental results. Keywords: Purifying Silicon, Directional Solidification, Crystal Growth Rate
1
ACCEPTED MANUSCRIPT 1. Introduction With the rapid development of the photovoltaic industry, the demand for solar-grade silicon as a basic material for solar cells is greatly increasing [1-6]. However, the cost of solar electricity is high
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compared to traditional energy sources, due to the production cost of solar grade silicon (SOG-Si) is high and low efficiency of generate electricity. Reducing the production cost of SOG-Si and increasing the photoelectric conversion efficiency of solar cells have been seriously studied by scholars who are
SC
engaged in the field of photovoltaic. As is known, the photoelectric conversion efficiency of solar cells
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wills declines when the metal impurity content is higher than a specific critical concentration. Because of the metal impurity is detrimental to conversion efficiency of solar cells as recombination center of minority carriers. J.R. Davis [7] investigated the iron impurity content effects on the photoelectric conversion efficiency of solar cells and found that the photoelectric conversion efficiency of solar cells
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declines when the iron content is higher than 1 × 1014/cm3. However, studies [8] have indicated that the critical concentration of iron in silicon must be lower than 1 × 1014/cm3. J. W. Chen [9] investigated the titanium in silicon as a deep level impurity and found that titanium inserted in silicon by diffusion or
EP
during Czochralski ingot growth is electrically active to a concentration level of about 4×1014/cm3.
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Directional solidification is an indispensable link of SOG-Si manufacture. It is used for silicon purification as an effective way to remove metal impurity from silicon [10-12]. Metal impurity is segregated to the melt, thereby resulting in a pure solid. The growth rate of directional solidification is widely investigated by many researchers as an important parameter, which combines several factors, such as temperature gradient in molten silicon, heat transfer in the solidification process and the content of impurity. M.A. Martorano [10] and M. Trempa [12] investigated the distribution of metal impurity in silicon ingot with different crystal growth rates during directional solidification and found
2
ACCEPTED MANUSCRIPT that the purifying effect of directional solidification for metal impurity is mainly influenced by crystal growth rate. The reason is that crystal growth rate influences the segregation extent of impurity on the melt-crystal interface, which further determines solar conversion efficiency. However, the crystal
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growth rate can be obtained by measuring the height of silicon ingot every once in a while, but not all the time. It is important for investigating the impurity distribution during silicon purification by directional solidification when the crystal growth rate is clear at any moment in time.
SC
In this paper, a theoretical model to investigate the crystal growth rate during silicon purification by
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directional solidification is established. The crystal growth rate at any moment in time can be calculated during silicon purification by directional solidification, which sets up the basis on later research. Based on theoretical model, distribution of metal impurity during silicon purification by directional solidification can be designed or be predicted. In the meantime, the production processes of
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EP
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silicon purification by directional solidification can be designed with low energy consumption.
3
ACCEPTED MANUSCRIPT
Symbol
Property
T1
Surface temperature of silicon melt
K
T2
Bottom temperature of crucible
K
Tm
Melting temperature
TC1
Temperature of thermocouple controlling
Units
1687
K K
Temperature of graphite heater with the same horizontal plane
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TC`1
Value
of silicon melt surface
K
TC2
Bottom temperature of crucible
K
kl
Thermal conductivity of silicon melt
ks
Thermal conductivity of silicon solid
ke
Effective segregation coefficient
k0
Equilibrium segregation coefficient
x
Solidified height
L
Total solidification length
v
Growth rate
vi
Transient growth rate
f(time)
δ
Thickness of the stagnant liquid layer
0.005
66.5
W·m-1·K-1
f(T)
W·m-1·K-1
f(v)
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SC
8×10-6 m
0.299
m m·s-1 m·s-1 m 2 -1
Dl
Diffusivity of impurity in molten at 1687K
m ·s
ql
Heat flux in the silicon melt
W·m-2
qs
Heat flux in the silicon solid
W·m-2
Latent heat of crystallization
1.41×10
ρ
Density of silicon solid
2320
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Llatent
Constants related to the distance of crucible and graphite
b
heater
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a
4
6
J/kg kg·m-3
ACCEPTED MANUSCRIPT 2. Theoretical Models Figure 1 shows the sketch of the directional solidification process. The heat flux in the vertical
q = −k
dT dx .
(1)
Thus, heat flux in the silicon melt along vertical direction as follows:
kl (T1 − Tm ) , L−x
(2)
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ql =
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direction can be described by the Fourier heat equation as follows:
where kl is the thermal conductivity of silicon melt; T1 is the surface temperature of silicon melt; Tm is
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melting temperature; L is the total solidification length and x is the solidified height. Similarly, the heat flux of silicon solid in the vertical direction is
qs =
(Tm − T2 ) , x +R ks
(3)
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where ks is the thermal conductivity of silicon solid; T2 is the bottom temperature of crucible. Obviously, the value of T2 is equal to TC2. The R is the thermal resistance (TR) between the water
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cooling system and silicon ingot. Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow. Thermal resistance is the
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reciprocal of thermal conductance, which has great impact on the temperature field. The calculated temperature of silicon melt is lower than the actual temperature during directional solidification process, without considering the TR. Therefore, the temperature field can be more accurately calculated if the TR is considered. Previous research has indicated that there exists thermal resistance (TR) between the water cooling system and silicon ingot in production process [5]. The value of TR was obtained by Hertz’s theory combining with the characteristics of the material , which has an approximate Boltzmann equation relationship with the function of temperature as shown in Fig. 2 (Left) [5]. 5
ACCEPTED MANUSCRIPT The abscissa of Fig. 2 (Left) represents the temperature of contact surface at low temperature side, which can be approximated by TC2 in this paper. Thermal equilibrium on the melt-crystal interface can be decided in following equation:
dx , dt
(4)
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ql − qs = ρLlatent
where ρ is density of silicon solid; Llatent is the latent heat of crystallization in the solidification process; t is solidification time.
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By combining Eqs. (2), (3) and (4), the relationship among parameters is briefly given by Eq. (5) as
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follows:
x T −T T2 = Tm − + R 1 m − ρLlatent v , ks L − x k l
(5)
as follows:
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where v is crystal growth rate, the relationship between crystal growth rate and the solidified height is
t
x = ∫ vdt .
(6)
0
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Previous research by S. T. Wen has indicated that the growth rate is not usually constant and it has a
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profound effect on the distribution of impurity in production process [13]. Temperature of silicon melt at different locations as shown in Fig. 2 (Right). The points in the Fig. 2 (Right) are experimental measuring values, which are obtained by inserting a thermocouple (TC3) in the silicon melt at different locations. The line is fitted in the Fig. 2 (Right). Temperature gradient of silicon melt can be obtained according to the data in Fig. 2 (Right). The value of T1 is calculated by temperature trend extending method. Figure 3 shows the relationship between temperature of T1 and graphite heater. There is no obvious 6
ACCEPTED MANUSCRIPT regularity between T1 and TC1; however the value of T1 has an approximate linear relationship with the TC`1 as shown in Fig. 3. This means that the TC`1 directly reflects the surface temperature of silicon melt. The temperature of T1 can be controlled by TC`1. In the mean time, the crystal growth rate can
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also be controlled. The relationship between T1 and TC`1 is given by the following equation:
T1 = a ⋅ TC1` + b .
(7)
where a and b are constants, and are related to the distance of crucible and graphite heater; TC`1 is the
SC
temperature of graphite heater and the value of TC`1 in different time can be obtained according to
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temperature gradient of graphite heater. The point of TC`1 and surface of silicon melt are in the same horizontal plane. The relationship between T1 and TC`1 can be given by the following equation in this research:
T1 = 0.63 ⋅ TC1` + 485.5 .
(8)
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The Eq. (5) is not elementary function integral, and the integral equation of Eq. (5) can’t be given. In order to solve the integral of Eq. (5) or obtain the approximate solution, by discretizing the process of directional solidification is as follows:
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Assume that at a certain moment in the process of solidification, the value of proportion of
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solidification is x, the average crystal growth rate is vi in the next 60 seconds. The Eq. (5) can be written as follows:
k l (T1 − Tm ) (Tm − T2 ) = + ρLlatent vi , L − ( x + 60vi ) x + 60vi +R ks
(9)
where, n
x = ∑ 60vi (i=1, 2, 3…).
(10)
1
The approximate solution of Eq. (5) can be obtained by a MATLAB procedure. Thus, the crystal 7
ACCEPTED MANUSCRIPT growth rate and solidified height of silicon ingot in different time are obtained according to TC`1. 3. Experiment The experiments were carrying out by casting furnace (DPS-650). The configurations of the furnace
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were shown schematically in Fig. 4. The silicon melt is solidified by Vertical Bridgman method in this experimental system. The cooler plate accelerated heat loss along axial direction in favor of maintaining the direction of solidification in the process of solidification. The heater was used to
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provide heat and maintain the temperature field required by solidified stage. Three thermal couples
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were used in the experiments: TC1 was used to measure temperature of heater; TC2 was recorded the temperature of crucible bottom to evaluate the melting quantity of silicon in the melting process; TC3 was inserted in the silicon melt and recorded the temperature of silicon melt at solidified stage. The built-in data-logger of the control system can accomplish the functions of data acquisition and
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storage with computer. So, the data, such as the value of TC1, TC2 and pull-down distance of crucible, can be logged once per minute throughout the run.
The DS process involved three stages: melting stage, solidified stage and cooling stage. Fig. 5
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shows process parameters in the experiments, including the heater temperature and the pulling down
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height of crucible. In melting stage, solid silicon is melted under argon atmosphere. And the pull-down distance of crucible is zero, namely, the insulator was closed. Heater temperature increased gradually from room temperature to 1600
, and then maintained this temperature. The solid silicon is melted
completely once the temperature of TC2 increased abruptly. After holding time for 2~3h, heater temperature decreased to approximately 1525
, meanwhile, the furnace body vacuumize and the
crucible started pulling downwards to form a temperature gradient needed for directional solidification. When the bottom temperature decreased to melting point of silicon, the solidified stage occurred.
8
ACCEPTED MANUSCRIPT Solidification of silicon begins with time of 1381min in first experiment and with time of 1524min in the second experiment through measurements. The value of TC`1 is smaller than TC1 in the solidification process and the deviation value is gradually large as the crucible is drop-down. The TC`1
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can be considered as TC1 when the crucible and the graphite heater in the same relative location. The crystal growth rate and the solidified height were obtained by measuring the height of silicon ingot every once in a while. The solidified stage was considered completed with the same measured
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value for three times. Then enter into the cooling stage. Crucible didn’t pulling downwards
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continuatively, and heater temperature decreased gradually to room temperature under argon atmosphere. 4. Results and Discussion
The growth rate normally is considered as an average growth rate for the whole solidification process
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because it difficult to be accurately measured at every moment of the solidification process. So, previous studies on directional solidification with changing growth rate are limited. As it is known, the growth rate is not constant as one understands it usually, but it can changes over time in actual
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production. Thus, there exists a discrepancy between the actual distribution of metal impurity and the
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calculation when considering the growth rate as average. The fluctuation in crystal growth rate can have big influence on the distribution of metal impurity in the silicon ingot [10, 12]. Fig. 6 shows the influence of crystal growth rate on distribution of impurity in silicon ingot during silicon purification by directional solidification. Research results show that the purifying effect of directional solidification is mainly influenced by crystal growth rate. The crystal growth rate influences the segregation extent of impurity on the melt-crystal interface by the effective segregation coefficient, ke, which is given by the following equation [14]: 9
ACCEPTED MANUSCRIPT ke =
k0 k 0 + (1 − k 0 )e −δv / Dl .
(11)
where δ (m) is thickness of the stagnant liquid layer; Dl (m2·s-1) is the diffusion coefficient of impurity
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in molten silicon at melting point; v (m·s-1) is crystal growth rate; k0 is equilibrium segregation coefficient.
Impurity segregation effect on the melt-crystal interface in the solidification process can be expressed
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as [14]:
ρ s = ke ρl .
(12)
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The mass concentration of impurity in solid silicon can be given by Eq. (13):
ρ s = k e ρ l (1 − x) k
e −1
.
(13)
Figure 7 shows the comparisons between computational and experimental data of the crystal growth rate and the solidified height at different time. The growth rates fluctuate strongly with time for the
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entire directional solidification process as shown in Fig. 7. The growth rate and the solidified height of silicon ingot can be calculated by combining Eqs. (5) and (8) according to the TC`1 as shown in Fig. 5.
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The results show that the model is proposed in this paper can be a very good prediction and analysis of the growth rate and the solidified height during directional solidification process.
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In the first experiment, the maximum and minimum value of the crystal growth rate are 3.76×10-6(m·s-1) and 0 (m·s-1) respectively as shown in Fig. 7 (top). The corresponding ke are 5.7×10-2 and 8×10-6 respectively for iron impurity according to the Eq. (11), and the impurity segregation effects with ke=8×10-6 is much higher than that of ke=5.7×10-2 on the melt-crystal interface. There must be a big fluctuation of impurity distribution in the silicon ingot. Similarly, a big fluctuation of impurity distribution in the silicon ingot also exists in the second experiment as shown in Fig. 7 (bottom). Thus, it’s essential for controlling the crystal growth rate to obtain a satisfactory purifying effect of 10
ACCEPTED MANUSCRIPT directional solidification. 4. Conclusions A theoretical model for investigating the crystal growth rate and the solidified height during silicon
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purification by directional solidification is proposed. The crystal growth rate is not constant usually and it has profound effects on the distribution of metal impurity in production process. The relationship between the surface temperature of silicon melt (T1) and temperature of graphite heater (TC`1) was
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found. Namely, the value of T1 has an approximate linear relationship with the TC`1. The experiments
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proved that the calculation agreed well with the existing experimental results. Precisely, the theoretical model can be used to design or predict the growth rate by controlling the TC1 according to the different request. Therefore, the distribution of metal impurity during silicon purification by directional solidification can be more accurately calculated or predicted according to the calculation result. All
6. Acknowledgments
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these results have great significance in the purification of silicon by directional solidification.
The authors gratefully acknowledge financial support from the Natural Science Foundation of China
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(Grant No. U1137601, 51304033 and 51404053), and Specialized Research Fund for the Doctoral
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Program of Higher Education (Grant No. 20130041110004).
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ACCEPTED MANUSCRIPT References [1] K. Morita, T. Yoshikawa, Thermodynamic evaluation of new metallurgical refining processes for SOG-silicon production. Trans. Nonferrous Met. Soc., 2011, 21, 685-690.
Energy Mater. Sol. Cells, 2010, 94, 1528-1533.
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[2] S. Pizzini, Towards solar grade silicon: Challenges and benefits for low cost photovoltaics. Sol.
A review. Sol. Energy Mater. Sol. Cells, 2008, 92, 418-424.
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[3] A.F.B. Braga, S.P. Moreira, New processes for the production of solar-grade polycrystalline silicon:
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[4] X. Yang, W.H. Ma, G.Q. Lv, K.X. Wei, T. Luo, D.T. Chen, A modified vacuum directional solidification system of multicrystalline silicon based on optimizing for heat transfer. J. Cryst. Growth, 2014, 400, 7-14.
[5] S.T. Wen, Y. Tan, S. Shi, W. Dong, D.C. Jiang, J. Liao, Z. Zhu, Thermal contact resistance between
74, 37-43.
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the surfaces of silicon and copper crucible during electron beam melting. Int. J. Therm. Sci., 2013
[6] Y. Tan, S.T. Wen, S. Shi, D.C. Jiang, W. Dong, X.L. Guo, Numerical simulation for parameter
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optimization of silicon purification by electron beam melting. Vacuum, 2013, 95, 18-24.
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[7] J.R. Davis, A. Rohatgi, R.H. Hopkins, P.D. Blais, P. Raichoudhury, J.R. Mccormick, H.C. Mollenkopf. Impurities in Silicon Solar Cell. Ieee Transactions on Electron Devices, 1980; 27(4): 677-687.
[8] G. Coletti, R. Kvande, V.D. Mihailetchi, L.J. Geerligs, L. Arnberg, E.J. Ovrelid. Effect of iron in silicon feedstock on p- and n-type multicrystalline silicon solar cells[J]. Journal of Applied Physics, 2008; 104(10): 104913-11. [9] J.W. Chen, A.G. Milnes, A. Rohatgi, Titanium in Silicon as a Deep Level Impurity. Solid State
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ACCEPTED MANUSCRIPT Electron, 1979, 22, 801-808. [10] M.A. Martorano, J.B. Ferreira Neto, T.S. Oliveira, T.O. Tsubaki, Refining of metallurgical silicon by directional solidification. Materials Science and Engineering B, 2011, 176, 217-226
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[11] B. Ryningen, G. Stokkan, M. Kivambe, T. Ervik, O. Lohne, Growth of dislocation clusters during directional solidification of multicrystalline silicon ingots. Acta Mater., 2011, 59, 7703-7710.
[12] M. Trempa, C. Reimann, J. Friedrich, G. Muller, The influence of growth rate on the formation and
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silicon. J Cryst. Growth, 2010, 312, 1517-1524.
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avoidance of C and N related precipitates during directional solidification of multicrystalline
[13] S.T. Wen, D.C. Jiang, Y. Tan. A New Model to investigate Iron distribution during silicon purification by directional solidification. Crystal Growth & Design. Submitted to Journal. [14] W. Kurz, D.J. Fisher, Fundamentals of Solidification. Fourth Revised Edtion, Trails Tech
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EP
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Publications Ltd, 1998, 86-88.
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ACCEPTED MANUSCRIPT Figure captions Fig. 1. Sketch of the directional solidification process. Fig. 2. Thermal resistance and temperature of silicon melt using in model: (a). Thermal resistance between water cooling system and silicon ingot (Left) and temperature of silicon melt at different locations (Right). Fig. 3. Relationship between temperature of T1 and graphite heater. Fig. 5. Process parameters in the experiments.
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Fig. 4. Schematic of the DS furnace. Fig. 6. Distribution of impurity in silicon ingot during silicon purification by directional solidification with different growth rates.
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Fig. 7. Comparisons between computational and experimental data.
14
ACCEPTED MANUSCRIPT Figures
TC1 TC`1 Melt
Tm
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Latent Heat
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T1
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Figure 1
L
Solid
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R
x
T2
TC2
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Fig. 1. Sketch of the directional solidification process.
15
ACCEPTED MANUSCRIPT
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Figure 2
Fig. 2. Thermal resistance and temperature of silicon melt using in model: (a). Thermal resistance
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between water cooling system and silicon ingot (Left) and temperature of silicon melt at different
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locations (Right).
16
ACCEPTED MANUSCRIPT
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Figure 3
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Fig. 3. Relationship between temperature of T1 and graphite heater.
17
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Figure 4
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Fig. 4. Schematic of the DS furnace.
18
ACCEPTED MANUSCRIPT
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Figure 5
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Fig. 5. Process parameters in the experiments.
19
ACCEPTED MANUSCRIPT
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Figure 6
Fig. 6. Distribution of impurity in silicon ingot during silicon purification by directional solidification
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with different growth rates.
20
ACCEPTED MANUSCRIPT
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Figure 7
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Fig. 7. Comparisons between computational and experimental data.
21
ACCEPTED MANUSCRIPT Highlights
Crystal growth rate and solidified height Si purification by directional solidification is investigated. Relationship between temperature of melt surface and graphite heater was found.
Crystal growth rate can be designed or predicted by controlling temperature of graphite heater.
Distribution of impurity during silicon purification by directional solidification can be designed or
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AC C
EP
TE D
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predicted.
S0042-207X(15)30142-1
DOI:
10.1016/j.vacuum.2015.12.004
Reference:
VAC 6877
To appear in:
Vacuum
Received Date: 4 September 2015 Revised Date:
28 November 2015
Accepted Date: 5 December 2015
Please cite this article as: Wen S, Jiang D, Shi S, Tan Y, Li P, Gu Z, Zhang X, Determination and Controlling of Crystal Growth Rate during Silicon Purification by Directional Solidification, Vaccum (2016), doi: 10.1016/j.vacuum.2015.12.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Determination and Controlling of Crystal Growth Rate during Silicon Purification by Directional Solidification a, b
a, b
Shutao Wen , Dachuan Jiang , Shuang Shi a, b, Yi Tana, b*, Pengting Lia, b, Zheng Guc, Xiaofeng Zhangc School of Materials Science and Engineering, Dalian University of Technology, Dalian 116023, China
b
Key Laboratory for Solar Energy Photovoltaic System of Liaoning Province, Dalian 116023, China
c
Qingdao Longsun silicon technology Co., Ltd
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a
Corresponding author at: School of Materials Science and Engineering, Dalian University of
SC
Technology, No. 2 Linggong Road, Ganjingzi District, Dalian 116023, China.
M AN U
E-mail address: [email protected] (Yi Tan) Abstract
A theoretical model for investigating the crystal growth rate and the solidified height during silicon purification by directional solidification is proposed. The growth rate is not constant usually and it has
TE D
profound effects on the distribution of metal impurity in production process. The crystal growth rate and the solidified height, based on thermal equilibrium on the melt-crystal interface, were discussed. The relationship between the surface temperature of silicon melt (T1) and temperature of graphite
EP
heater (TC`1) was found. The result shows that the value of T1 has an approximate linear relationship
AC C
with the TC`1. The theoretical model can be used to design or predict the crystal growth rate by controlling the TC1 according to the different request. Then, the distribution of metal impurity during silicon purification by directional solidification can be calculated according to the crystal growth rate. Thus, the theoretical model can be used to design the growth rate and predict the distribution of impurity to the silicon purification process by directional solidification. The experiments proved that the calculation agreed well with the existing experimental results. Keywords: Purifying Silicon, Directional Solidification, Crystal Growth Rate
1
ACCEPTED MANUSCRIPT 1. Introduction With the rapid development of the photovoltaic industry, the demand for solar-grade silicon as a basic material for solar cells is greatly increasing [1-6]. However, the cost of solar electricity is high
RI PT
compared to traditional energy sources, due to the production cost of solar grade silicon (SOG-Si) is high and low efficiency of generate electricity. Reducing the production cost of SOG-Si and increasing the photoelectric conversion efficiency of solar cells have been seriously studied by scholars who are
SC
engaged in the field of photovoltaic. As is known, the photoelectric conversion efficiency of solar cells
M AN U
wills declines when the metal impurity content is higher than a specific critical concentration. Because of the metal impurity is detrimental to conversion efficiency of solar cells as recombination center of minority carriers. J.R. Davis [7] investigated the iron impurity content effects on the photoelectric conversion efficiency of solar cells and found that the photoelectric conversion efficiency of solar cells
TE D
declines when the iron content is higher than 1 × 1014/cm3. However, studies [8] have indicated that the critical concentration of iron in silicon must be lower than 1 × 1014/cm3. J. W. Chen [9] investigated the titanium in silicon as a deep level impurity and found that titanium inserted in silicon by diffusion or
EP
during Czochralski ingot growth is electrically active to a concentration level of about 4×1014/cm3.
AC C
Directional solidification is an indispensable link of SOG-Si manufacture. It is used for silicon purification as an effective way to remove metal impurity from silicon [10-12]. Metal impurity is segregated to the melt, thereby resulting in a pure solid. The growth rate of directional solidification is widely investigated by many researchers as an important parameter, which combines several factors, such as temperature gradient in molten silicon, heat transfer in the solidification process and the content of impurity. M.A. Martorano [10] and M. Trempa [12] investigated the distribution of metal impurity in silicon ingot with different crystal growth rates during directional solidification and found
2
ACCEPTED MANUSCRIPT that the purifying effect of directional solidification for metal impurity is mainly influenced by crystal growth rate. The reason is that crystal growth rate influences the segregation extent of impurity on the melt-crystal interface, which further determines solar conversion efficiency. However, the crystal
RI PT
growth rate can be obtained by measuring the height of silicon ingot every once in a while, but not all the time. It is important for investigating the impurity distribution during silicon purification by directional solidification when the crystal growth rate is clear at any moment in time.
SC
In this paper, a theoretical model to investigate the crystal growth rate during silicon purification by
M AN U
directional solidification is established. The crystal growth rate at any moment in time can be calculated during silicon purification by directional solidification, which sets up the basis on later research. Based on theoretical model, distribution of metal impurity during silicon purification by directional solidification can be designed or be predicted. In the meantime, the production processes of
AC C
EP
TE D
silicon purification by directional solidification can be designed with low energy consumption.
3
ACCEPTED MANUSCRIPT
Symbol
Property
T1
Surface temperature of silicon melt
K
T2
Bottom temperature of crucible
K
Tm
Melting temperature
TC1
Temperature of thermocouple controlling
Units
1687
K K
Temperature of graphite heater with the same horizontal plane
RI PT
TC`1
Value
of silicon melt surface
K
TC2
Bottom temperature of crucible
K
kl
Thermal conductivity of silicon melt
ks
Thermal conductivity of silicon solid
ke
Effective segregation coefficient
k0
Equilibrium segregation coefficient
x
Solidified height
L
Total solidification length
v
Growth rate
vi
Transient growth rate
f(time)
δ
Thickness of the stagnant liquid layer
0.005
66.5
W·m-1·K-1
f(T)
W·m-1·K-1
f(v)
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8×10-6 m
0.299
m m·s-1 m·s-1 m 2 -1
Dl
Diffusivity of impurity in molten at 1687K
m ·s
ql
Heat flux in the silicon melt
W·m-2
qs
Heat flux in the silicon solid
W·m-2
Latent heat of crystallization
1.41×10
ρ
Density of silicon solid
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Llatent
Constants related to the distance of crucible and graphite
b
heater
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a
4
6
J/kg kg·m-3
ACCEPTED MANUSCRIPT 2. Theoretical Models Figure 1 shows the sketch of the directional solidification process. The heat flux in the vertical
q = −k
dT dx .
(1)
Thus, heat flux in the silicon melt along vertical direction as follows:
kl (T1 − Tm ) , L−x
(2)
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ql =
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direction can be described by the Fourier heat equation as follows:
where kl is the thermal conductivity of silicon melt; T1 is the surface temperature of silicon melt; Tm is
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melting temperature; L is the total solidification length and x is the solidified height. Similarly, the heat flux of silicon solid in the vertical direction is
qs =
(Tm − T2 ) , x +R ks
(3)
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where ks is the thermal conductivity of silicon solid; T2 is the bottom temperature of crucible. Obviously, the value of T2 is equal to TC2. The R is the thermal resistance (TR) between the water
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cooling system and silicon ingot. Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow. Thermal resistance is the
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reciprocal of thermal conductance, which has great impact on the temperature field. The calculated temperature of silicon melt is lower than the actual temperature during directional solidification process, without considering the TR. Therefore, the temperature field can be more accurately calculated if the TR is considered. Previous research has indicated that there exists thermal resistance (TR) between the water cooling system and silicon ingot in production process [5]. The value of TR was obtained by Hertz’s theory combining with the characteristics of the material , which has an approximate Boltzmann equation relationship with the function of temperature as shown in Fig. 2 (Left) [5]. 5
ACCEPTED MANUSCRIPT The abscissa of Fig. 2 (Left) represents the temperature of contact surface at low temperature side, which can be approximated by TC2 in this paper. Thermal equilibrium on the melt-crystal interface can be decided in following equation:
dx , dt
(4)
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ql − qs = ρLlatent
where ρ is density of silicon solid; Llatent is the latent heat of crystallization in the solidification process; t is solidification time.
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By combining Eqs. (2), (3) and (4), the relationship among parameters is briefly given by Eq. (5) as
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follows:
x T −T T2 = Tm − + R 1 m − ρLlatent v , ks L − x k l
(5)
as follows:
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where v is crystal growth rate, the relationship between crystal growth rate and the solidified height is
t
x = ∫ vdt .
(6)
0
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Previous research by S. T. Wen has indicated that the growth rate is not usually constant and it has a
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profound effect on the distribution of impurity in production process [13]. Temperature of silicon melt at different locations as shown in Fig. 2 (Right). The points in the Fig. 2 (Right) are experimental measuring values, which are obtained by inserting a thermocouple (TC3) in the silicon melt at different locations. The line is fitted in the Fig. 2 (Right). Temperature gradient of silicon melt can be obtained according to the data in Fig. 2 (Right). The value of T1 is calculated by temperature trend extending method. Figure 3 shows the relationship between temperature of T1 and graphite heater. There is no obvious 6
ACCEPTED MANUSCRIPT regularity between T1 and TC1; however the value of T1 has an approximate linear relationship with the TC`1 as shown in Fig. 3. This means that the TC`1 directly reflects the surface temperature of silicon melt. The temperature of T1 can be controlled by TC`1. In the mean time, the crystal growth rate can
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also be controlled. The relationship between T1 and TC`1 is given by the following equation:
T1 = a ⋅ TC1` + b .
(7)
where a and b are constants, and are related to the distance of crucible and graphite heater; TC`1 is the
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temperature of graphite heater and the value of TC`1 in different time can be obtained according to
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temperature gradient of graphite heater. The point of TC`1 and surface of silicon melt are in the same horizontal plane. The relationship between T1 and TC`1 can be given by the following equation in this research:
T1 = 0.63 ⋅ TC1` + 485.5 .
(8)
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The Eq. (5) is not elementary function integral, and the integral equation of Eq. (5) can’t be given. In order to solve the integral of Eq. (5) or obtain the approximate solution, by discretizing the process of directional solidification is as follows:
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Assume that at a certain moment in the process of solidification, the value of proportion of
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solidification is x, the average crystal growth rate is vi in the next 60 seconds. The Eq. (5) can be written as follows:
k l (T1 − Tm ) (Tm − T2 ) = + ρLlatent vi , L − ( x + 60vi ) x + 60vi +R ks
(9)
where, n
x = ∑ 60vi (i=1, 2, 3…).
(10)
1
The approximate solution of Eq. (5) can be obtained by a MATLAB procedure. Thus, the crystal 7
ACCEPTED MANUSCRIPT growth rate and solidified height of silicon ingot in different time are obtained according to TC`1. 3. Experiment The experiments were carrying out by casting furnace (DPS-650). The configurations of the furnace
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were shown schematically in Fig. 4. The silicon melt is solidified by Vertical Bridgman method in this experimental system. The cooler plate accelerated heat loss along axial direction in favor of maintaining the direction of solidification in the process of solidification. The heater was used to
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provide heat and maintain the temperature field required by solidified stage. Three thermal couples
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were used in the experiments: TC1 was used to measure temperature of heater; TC2 was recorded the temperature of crucible bottom to evaluate the melting quantity of silicon in the melting process; TC3 was inserted in the silicon melt and recorded the temperature of silicon melt at solidified stage. The built-in data-logger of the control system can accomplish the functions of data acquisition and
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storage with computer. So, the data, such as the value of TC1, TC2 and pull-down distance of crucible, can be logged once per minute throughout the run.
The DS process involved three stages: melting stage, solidified stage and cooling stage. Fig. 5
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shows process parameters in the experiments, including the heater temperature and the pulling down
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height of crucible. In melting stage, solid silicon is melted under argon atmosphere. And the pull-down distance of crucible is zero, namely, the insulator was closed. Heater temperature increased gradually from room temperature to 1600
, and then maintained this temperature. The solid silicon is melted
completely once the temperature of TC2 increased abruptly. After holding time for 2~3h, heater temperature decreased to approximately 1525
, meanwhile, the furnace body vacuumize and the
crucible started pulling downwards to form a temperature gradient needed for directional solidification. When the bottom temperature decreased to melting point of silicon, the solidified stage occurred.
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ACCEPTED MANUSCRIPT Solidification of silicon begins with time of 1381min in first experiment and with time of 1524min in the second experiment through measurements. The value of TC`1 is smaller than TC1 in the solidification process and the deviation value is gradually large as the crucible is drop-down. The TC`1
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can be considered as TC1 when the crucible and the graphite heater in the same relative location. The crystal growth rate and the solidified height were obtained by measuring the height of silicon ingot every once in a while. The solidified stage was considered completed with the same measured
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value for three times. Then enter into the cooling stage. Crucible didn’t pulling downwards
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continuatively, and heater temperature decreased gradually to room temperature under argon atmosphere. 4. Results and Discussion
The growth rate normally is considered as an average growth rate for the whole solidification process
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because it difficult to be accurately measured at every moment of the solidification process. So, previous studies on directional solidification with changing growth rate are limited. As it is known, the growth rate is not constant as one understands it usually, but it can changes over time in actual
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production. Thus, there exists a discrepancy between the actual distribution of metal impurity and the
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calculation when considering the growth rate as average. The fluctuation in crystal growth rate can have big influence on the distribution of metal impurity in the silicon ingot [10, 12]. Fig. 6 shows the influence of crystal growth rate on distribution of impurity in silicon ingot during silicon purification by directional solidification. Research results show that the purifying effect of directional solidification is mainly influenced by crystal growth rate. The crystal growth rate influences the segregation extent of impurity on the melt-crystal interface by the effective segregation coefficient, ke, which is given by the following equation [14]: 9
ACCEPTED MANUSCRIPT ke =
k0 k 0 + (1 − k 0 )e −δv / Dl .
(11)
where δ (m) is thickness of the stagnant liquid layer; Dl (m2·s-1) is the diffusion coefficient of impurity
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in molten silicon at melting point; v (m·s-1) is crystal growth rate; k0 is equilibrium segregation coefficient.
Impurity segregation effect on the melt-crystal interface in the solidification process can be expressed
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as [14]:
ρ s = ke ρl .
(12)
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The mass concentration of impurity in solid silicon can be given by Eq. (13):
ρ s = k e ρ l (1 − x) k
e −1
.
(13)
Figure 7 shows the comparisons between computational and experimental data of the crystal growth rate and the solidified height at different time. The growth rates fluctuate strongly with time for the
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entire directional solidification process as shown in Fig. 7. The growth rate and the solidified height of silicon ingot can be calculated by combining Eqs. (5) and (8) according to the TC`1 as shown in Fig. 5.
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The results show that the model is proposed in this paper can be a very good prediction and analysis of the growth rate and the solidified height during directional solidification process.
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In the first experiment, the maximum and minimum value of the crystal growth rate are 3.76×10-6(m·s-1) and 0 (m·s-1) respectively as shown in Fig. 7 (top). The corresponding ke are 5.7×10-2 and 8×10-6 respectively for iron impurity according to the Eq. (11), and the impurity segregation effects with ke=8×10-6 is much higher than that of ke=5.7×10-2 on the melt-crystal interface. There must be a big fluctuation of impurity distribution in the silicon ingot. Similarly, a big fluctuation of impurity distribution in the silicon ingot also exists in the second experiment as shown in Fig. 7 (bottom). Thus, it’s essential for controlling the crystal growth rate to obtain a satisfactory purifying effect of 10
ACCEPTED MANUSCRIPT directional solidification. 4. Conclusions A theoretical model for investigating the crystal growth rate and the solidified height during silicon
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purification by directional solidification is proposed. The crystal growth rate is not constant usually and it has profound effects on the distribution of metal impurity in production process. The relationship between the surface temperature of silicon melt (T1) and temperature of graphite heater (TC`1) was
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found. Namely, the value of T1 has an approximate linear relationship with the TC`1. The experiments
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proved that the calculation agreed well with the existing experimental results. Precisely, the theoretical model can be used to design or predict the growth rate by controlling the TC1 according to the different request. Therefore, the distribution of metal impurity during silicon purification by directional solidification can be more accurately calculated or predicted according to the calculation result. All
6. Acknowledgments
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these results have great significance in the purification of silicon by directional solidification.
The authors gratefully acknowledge financial support from the Natural Science Foundation of China
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(Grant No. U1137601, 51304033 and 51404053), and Specialized Research Fund for the Doctoral
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Program of Higher Education (Grant No. 20130041110004).
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ACCEPTED MANUSCRIPT References [1] K. Morita, T. Yoshikawa, Thermodynamic evaluation of new metallurgical refining processes for SOG-silicon production. Trans. Nonferrous Met. Soc., 2011, 21, 685-690.
Energy Mater. Sol. Cells, 2010, 94, 1528-1533.
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[2] S. Pizzini, Towards solar grade silicon: Challenges and benefits for low cost photovoltaics. Sol.
A review. Sol. Energy Mater. Sol. Cells, 2008, 92, 418-424.
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[3] A.F.B. Braga, S.P. Moreira, New processes for the production of solar-grade polycrystalline silicon:
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[4] X. Yang, W.H. Ma, G.Q. Lv, K.X. Wei, T. Luo, D.T. Chen, A modified vacuum directional solidification system of multicrystalline silicon based on optimizing for heat transfer. J. Cryst. Growth, 2014, 400, 7-14.
[5] S.T. Wen, Y. Tan, S. Shi, W. Dong, D.C. Jiang, J. Liao, Z. Zhu, Thermal contact resistance between
74, 37-43.
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the surfaces of silicon and copper crucible during electron beam melting. Int. J. Therm. Sci., 2013
[6] Y. Tan, S.T. Wen, S. Shi, D.C. Jiang, W. Dong, X.L. Guo, Numerical simulation for parameter
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optimization of silicon purification by electron beam melting. Vacuum, 2013, 95, 18-24.
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[7] J.R. Davis, A. Rohatgi, R.H. Hopkins, P.D. Blais, P. Raichoudhury, J.R. Mccormick, H.C. Mollenkopf. Impurities in Silicon Solar Cell. Ieee Transactions on Electron Devices, 1980; 27(4): 677-687.
[8] G. Coletti, R. Kvande, V.D. Mihailetchi, L.J. Geerligs, L. Arnberg, E.J. Ovrelid. Effect of iron in silicon feedstock on p- and n-type multicrystalline silicon solar cells[J]. Journal of Applied Physics, 2008; 104(10): 104913-11. [9] J.W. Chen, A.G. Milnes, A. Rohatgi, Titanium in Silicon as a Deep Level Impurity. Solid State
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ACCEPTED MANUSCRIPT Electron, 1979, 22, 801-808. [10] M.A. Martorano, J.B. Ferreira Neto, T.S. Oliveira, T.O. Tsubaki, Refining of metallurgical silicon by directional solidification. Materials Science and Engineering B, 2011, 176, 217-226
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[11] B. Ryningen, G. Stokkan, M. Kivambe, T. Ervik, O. Lohne, Growth of dislocation clusters during directional solidification of multicrystalline silicon ingots. Acta Mater., 2011, 59, 7703-7710.
[12] M. Trempa, C. Reimann, J. Friedrich, G. Muller, The influence of growth rate on the formation and
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silicon. J Cryst. Growth, 2010, 312, 1517-1524.
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avoidance of C and N related precipitates during directional solidification of multicrystalline
[13] S.T. Wen, D.C. Jiang, Y. Tan. A New Model to investigate Iron distribution during silicon purification by directional solidification. Crystal Growth & Design. Submitted to Journal. [14] W. Kurz, D.J. Fisher, Fundamentals of Solidification. Fourth Revised Edtion, Trails Tech
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Publications Ltd, 1998, 86-88.
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ACCEPTED MANUSCRIPT Figure captions Fig. 1. Sketch of the directional solidification process. Fig. 2. Thermal resistance and temperature of silicon melt using in model: (a). Thermal resistance between water cooling system and silicon ingot (Left) and temperature of silicon melt at different locations (Right). Fig. 3. Relationship between temperature of T1 and graphite heater. Fig. 5. Process parameters in the experiments.
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Fig. 4. Schematic of the DS furnace. Fig. 6. Distribution of impurity in silicon ingot during silicon purification by directional solidification with different growth rates.
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Fig. 7. Comparisons between computational and experimental data.
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ACCEPTED MANUSCRIPT Figures
TC1 TC`1 Melt
Tm
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Latent Heat
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T1
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Figure 1
L
Solid
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R
x
T2
TC2
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Fig. 1. Sketch of the directional solidification process.
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Figure 2
Fig. 2. Thermal resistance and temperature of silicon melt using in model: (a). Thermal resistance
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between water cooling system and silicon ingot (Left) and temperature of silicon melt at different
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locations (Right).
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Figure 3
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Fig. 3. Relationship between temperature of T1 and graphite heater.
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Figure 4
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Fig. 4. Schematic of the DS furnace.
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Figure 5
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Fig. 5. Process parameters in the experiments.
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Figure 6
Fig. 6. Distribution of impurity in silicon ingot during silicon purification by directional solidification
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with different growth rates.
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Figure 7
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Fig. 7. Comparisons between computational and experimental data.
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ACCEPTED MANUSCRIPT Highlights
Crystal growth rate and solidified height Si purification by directional solidification is investigated. Relationship between temperature of melt surface and graphite heater was found.
Crystal growth rate can be designed or predicted by controlling temperature of graphite heater.
Distribution of impurity during silicon purification by directional solidification can be designed or
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predicted.