- Email: [email protected]
Effect of crucible rotation on oxygen concentration during unidirectional solidification process of multicrystalline silicon for solar cells
ARTICLE IN PRESS Journal of Crystal Growth 311 (2009) 1123–1128
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Effect of crucible rotation on oxygen concentration during unidirectional solidification process of multicrystalline silicon for solar cells Hitoshi Matsuo a,, R. Bairava Ganesh a,b, Satoshi Nakano c, Lijun Liu c,d, Koji Arafune e,f, Yoshio Ohshita e, Masafumi Yamaguchi e, Koichi Kakimoto a,c a
Graduate School of Engineering, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan Crystal Growth Centre, Anna University, Chennai 600025, India c Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan d National Engineering Research Center for Fluid Machinery and Compressors, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China e Toyota Technological Institute, 2-12-1 Hisakata, Tempaku-ku, Nagoya 468-8511, Japan f Department of Mechanical and System Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2280, Japan b
a r t i c l e in fo
abstract
Article history: Received 22 October 2008 Received in revised form 18 November 2008 Accepted 18 November 2008 Communicated by K.W. Benz Available online 24 November 2008
We studied the effects of crucible rotation on distribution of oxygen concentration in a crystal during the unidirectionally solidification process of multicrystalline silicon for solar cells. Oxygen concentration in the melt increased when crucible rotation rate was increased. Oxygen concentration in the silicon crystal was distributed inhomogeneously in the radial direction when crucible rotation rate was increased. This is due to suppression of oxygen transport. Consequently, less oxygen was transported from the crucible wall to the center of the melt. We found that oxygen concentration is small in the whole ingot and homogenized in the radial direction when crucible rotation rate during the solidification process is set to 1 rpm. & 2008 Elsevier B.V. All rights reserved.
PACS: 81.10.Fq Keywords: A1. Directional solidification A1. Impurities B2. Semiconducting silicon B3. Solar cells
1. Introduction
2. Oxygen transfer
The photovoltaic market has developed remarkably in recent years [1], and multicrystalline silicon now has a market share of more than 50% in all photovoltaic materials. Multicrystalline silicon is an important material for solar cells with the advantage of lowproduction cost. There are many impurities in a silicon crystal, such as oxygen, nitrogen, carbon and iron. The presence of oxygen causes SiO2 precipitation [2], dislocations [3] and stacking faults [4], which decrease the conversion efficiency of solar cells. Boron and oxygen in silicon have also been reported to form boron–oxygen complexes, which cause light-induced degradation in solar cells [5]. These defects reduce the conversion efficiency of solar cells because they act as recombination centers of photocarriers. Therefore, control of oxygen concentration in a silicon ingot is important for improving the conversion efficiency of a solar cell. In this study, we studied the effects of crucible rotation on distribution of oxygen concentration during the solidification process of multicrystalline silicon for solar cells.
It is well known that oxygen is dissolved from a quartz crucible into the silicon melt and that it is transported in silicon melt by convection and evaporates from the melt surface [6]. It has been reported that the concentration of oxygen in the melt can be controlled by modifying melt convection in the case of the Czochralski method [7,8]. Oxygen is mainly transported by both convection and diffusion in the melt. Convection in the melt plays a key role for the distribution of oxygen concentration in the melt and a crystal. It has been reported that convection in the melt can be suppressed by rotation of a crucible [9,10]. The phenomenon of suppression of melt flow was explained by using the momentum equation (the Navier–Stokes equation) [9] as follows:
Corresponding author.
E-mail address: [email protected] (H. Matsuo). 0022-0248/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2008.11.063
qu ¼ ur u 2ðO kÞ u qt ¼ ðO kÞ ðO kÞ r
1
r
rpþ
m Du þ g bðT T 0 Þ, r
(1)
where u, O, r and k represent vector of flow velocity, crucible rotation rate, position and unit vector along the growth direction,
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z
u3 u2
u1
θ r Ω Fig. 1. Cylindrical coordinates in the unidirectional solidification method.
respectively, as shown in Fig. 1. The symbols r, b, g, p, m and T are density, volume expansion coefficient of the silicon melt, vector of gravitational acceleration, pressure, viscosity of the fluid and temperature, respectively. Coriolis force is generated due to coupling of radial velocity and fluid rotation. The term 2(Ok) u in Eq. (1) represents a Coriolis force that is a cross product between vector of flow velocity and rotation. This term, which is called Coriolis acceleration vector, can be transformed: a ¼ 2ðO kÞ u ¼ 2Oðu1 j u2 iÞ,
(2)
where i and j represent unit vectors of the radial component and azimuthal component, respectively. The symbols u1, u2 and u3 are flow velocities in the radial direction, azimuthal direction and growth direction, respectively, as shown in Fig. 1. As a result, the radial component of the melt flow has a negative value and the azimuthal component has a positive value as in Eq. (2). Consequently, the radial velocity of the melt flow is decreased and azimuthal velocity is increased with increasing crucible rotation rate. Therefore, the radial velocity of the melt flow becomes small when crucible rotation is increased. The contribution of melt convection to transport of oxygen in the melt is larger than that of diffusion. Hence, the total amount of oxygen transferred by melt convection becomes small when melt velocity decreases. The distribution of oxygen concentration becomes inhomogeneous in the case of small velocity of the melt in the radial direction during solidification.
0.5 atm pressure in order to avoid impurity incorporation of SiO and CO into the melt during the solidification process [12]. After the heater had almost reached the top of the furnace, the temperature was lowered at a rate of 300 1C/h to room temperature. The grown ingot had a cylindrical shape with a diameter of 10 cm and height of 10 cm. The ingot was cut parallel to the growth direction into slices of 0.5 mm in thickness. Each sample was etched and polished before measurement by FTIR to remove the damaged layer formed by the cutting process. Sliced wafers were etched with a solution of hydrofluoric acid and nitric acid at the ratio of 1:13 for 10 min to remove the sawing damage. To obtain a mirror-like surface, the multicrystalline silicon wafers were polished with diamond particles of 0.5 and 0.3 mm in grain size, coordinated with water. Then the wafers were polished with alumina powder particles of 0.1 mm in grain size and deionized water. After polishing, the wafers were etched again using the same etchant as that described above for 3 min in order to remove the polishing damage. FTIR measurement was carried out using an MFT-2000 (JASCO) at room temperature in air. The length of the infrared beam was set to 50 mm with a square shape. The resolution and number of accumulation of the spectrum were set to 4 cm1 and 182 times, respectively. The absorbance of interstitial oxygen was measured at 1106 cm1 [3]. Oxygen concentration was calculated from the peak height of interstitial oxygen calibrated by pure Czochralski and floating zone silicon wafers with calibration factors of 3.03 1017 cm3 [13].
4. Experimental results Figs. 2(a)–(c) show distributions of oxygen concentration in the radial direction at heights 70, 50 and 20 mm from the bottom of the ingot, respectively. The abscissa shows the radius from the center of the ingot, and the ordinate shows the oxygen concentration. The concentrations of crystals with rotation rates 1 and 30 rpm are shown by open and closed circles in the figures. Oxygen concentration in the crystal at the crucible rotation rate 30 rpm showed an inhomogeneous distribution in the radial direction compared with that at the crucible rotation rate 1 rpm at 50 and 70 mm from the bottom of the ingot. At 20 mm from the bottom of the ingot, the concentrations in the two ingots were almost the same as shown in Fig. 2(c). Moreover, oxygen concentration near the top and middle of the ingot at the crucible rotation rate 30 rpm was larger than that at the crucible rotation rate 1 rpm.
3. Experimental procedure Oxygen concentration in multicrystalline silicon grown by the unidirectional solidification method was measured by Fourier transform infrared spectroscopy (FTIR). The multicrystalline silicon used in the present study was grown by the following method [11]. Off-grade silicon feedstock was used in the present experiment. Carrier concentration of a grown crystal with a dopant of gallium was approximately 1016 cm3. The crucible made of SiO2 had been coated with a liner made of Si3N4, which prevents the ingot from sticking to the crucible. The raw materials were heated up to 1550 1C to stabilize the temperature of the melt for 2 h. After melting, the heater power was decreased to keep the temperature at a center of heater at 1450 1C. Then heater power was kept constant for 1 h prior to the start of growth. The heater was pulled up at a rate of 30 mm/h to solidify the silicon melt from the bottom to the top. The crucible rotation rates were set to 1 and 30 rpm during the solidification process. Argon gas was introduced at the top of the melt at a flow rate of 0.8 l/min under
5. Numerical calculations In order to clarify the relationship between flow and oxygen concentration in the melt, we calculated oxygen concentration by using numerical calculations. The distribution of oxygen concentration was calculated using a global model [14]. Figs. 3(a) and (b) show the configuration and computation grid of a unidirectional solidification furnace and a zoomed-up view of the grid in the melt and crucible domains. Conductive heat transfer in all components and radiative heat exchange between all diffusive surfaces in the unidirectional solidification furnace were taken into account. Gas flow in the furnace was neglected. The value of 0.85 was used for the segregation coefficient of oxygen in these numerical calculations [6,15]. It was assumed that oxygen was dissolved from the crucible and evaporated at the melt surface. At the melt–crucible interfaces, the following equation, in which reaction between a liner made of Si3N4 and a crucible made of
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Fig. 3. (a) Configuration and computation grid of a unidirectional solidification furnace and (b) dynamic grid of the melt and the solid in a crucible.
Fig. 4. Oxygen concentration as a function of radius in the ingot estimated by numerical calculation at 50 mm from the bottom of the ingot.
where co represents oxygen concentration. On the melt surface, the oxygen evaporation was taken into account as follows [17]: D
Fig. 2. Oxygen concentration as a function of radius in the ingot measured by FTIR. Oxygen concentrations at 70 mm (a), 50 mm (b) and 20 mm (c) from the bottom of the ingot.
SiO2 was taken into account, was used as the boundary condition [16]: cO ¼ 0:5 1023
aO ðatoms=cm3 Þ, 1 aO
aO ¼ 1:32 expð7150=T 6:99Þ,
(3)
(4)
qc ¼ ðTÞc, qn
(5)
where c, D and e(T) are oxygen concentration, diffusion coefficient (D=5 108 m2/s) and evaporation velocity [17], respectively. Evaporation velocity is given by ! 4:1559 104 7 ðTÞ ¼ 5:9152 10 exp ðm=sÞ. (6) T Fig. 4 shows the calculated oxygen concentration in the radial direction in the silicon crystal. Height of the data corresponds to 50 mm from the bottom of the ingot. The concentrations of crystals with rotation rates 1 and 5 rpm are shown by solid and dashed lines, respectively, in the figures. Oxygen concentration in the radial direction at the crucible rotation rate 5 rpm showed an inhomogeneous distribution compared with that at the crucible rotation rate 1 rpm. Figs. 5(a)–(c) show the vectors of flow velocity at the crucible rotation rates 0, 1 and 5 rpm. The vortex near the melt surface becomes small with increase in the rate of crucible rotation. This
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means that flow velocity in the melt was suppressed by increasing the crucible rotation rate. Fig. 6 shows the average flow velocity in the radial direction as a function of crucible rotation rate. The results showed that averaged flow velocity was also decreased by increasing the crucible rotation rate.
Fig. 6. Averaged melt convection as a function of crucible rotation rate on the radial component during the solidification process.
Figs. 7(a)–(c) show temperature distributions of the melt at 0, 1 and 5 rpm crucible rotation rates. Figs. 8(a) and (b) show temperature distribution of the melt at melt surface as a function of radius and that at crucible wall as a function of height of the ingot, respectively. The result shows that the temperature distributions of the two cases are similar because temperature difference between 1 and 5 rpm is within 1 K as shown in Fig. 8.
6. Discussion
Fig. 5. Melt convection vector during solidification of the ingot. Crucible rotation rates of (a) 0 rpm, (b) 1 rpm and (c) 5 rpm.
Temperature distributions of the melt are modified by crucible rotation in the case of the Czochralski method [10]. Both equilibrium oxygen concentration at the melt–crucible interface expressed by Eq. (3) and evaporation velocity at melt surface expressed by Eq. (6) are increased with increasing temperature. However, in the case of unidirectional solidification process, temperature distributions in the system with crucible rotation rates 0, 1 and 5 rpm are similar as shown in Figs. 7 and 8. Therefore, the difference of oxygen distributions in the two cases shown in Fig. 4 is not attributed to the difference of temperature distributions in the system shown in Figs. 7 and 8. Oxygen concentrations in the radial direction at 20 mm from the bottom of the ingot are almost independent of crucible rotation rate. Since Rayleigh number of this system is as large as 106 at the beginning of the solidification process, the flow of the melt becomes time dependent or flow turbulent [18]. Due to the time dependent or turbulent flow, the melt was well mixed. Therefore, at 20 mm from the bottom of the ingot, the concentrations of oxygen in the two ingots become almost the same if crucible rotation rate is modified. Oxygen concentration at crucible rotation rate 30 rpm showed an inhomogeneous distribution compared with that at crucible rotation rate 1 rpm in the radial direction at 50 and 70 mm from the bottom of the ingot as shown in Figs. 2(a) and (b). Oxygen concentration in the condition of crucible rotation rate of 5 rpm obtained by numerical calculation was also distributed inhomogeneously in the radial direction as shown in Fig. 4. Flow velocity under these conditions deceased with increasing crucible rotation rate as shown in Figs. 5 and 6. We found the relationship between melt flow and distribution of oxygen concentration from these results of calculations. The centrifugal forces in the condition of crucible rotation rate between 5 and 30 rpm are different, however, the trend of inhomogeneous distributions of calculated oxygen concentration shown in Fig. 4 at the crucible rotation rate
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Fig. 8. Temperature distributions at melt surface as a function radius (a), and that at melt–crucible interface as a function of height. Temperature distribution of the melt with rotation rates of 1 and 5 rpm are shown by solid and dashed lines, respectively.
5 rpm is rather similar to that of the experimental distribution shown in Figs. 2(a) and (b) at the crucible rotation rate 30 rpm. It is thought that less oxygen incorporated from the quartz crucible was transported by melt flow due to suppression of natural convection. Therefore, oxygen concentration in the experiment for which results are presented in Figs. 2(a) and (b) at the crucible rotation rate 30 rpm showed an inhomogeneous distribution compared with that at the crucible rotation rate 1 rpm.
7. Summary
Fig. 7. Temperature distribution during solidification of the ingot. Crucible rotation rates of (a) 0 rpm, (b) 1 rpm and (c) 5 rpm.
We studied the effects of crucible rotation on distribution of oxygen concentration in a crystal during the unidirectional solidification process of multicrystalline silicon for solar cells. Oxygen concentration in the melt increased when crucible rotation rate was increased. Results of calculations and experimental results both showed that oxygen concentration near the top and middle of the crystal was distributed inhomogeneously in the radial direction when crucible rotation rate was increased. Less oxygen was transported from the crucible wall to the center of the melt. This is due to the suppression of oxygen transport. We found that oxygen concentration is minimized in the whole ingot and homogenized in the radial direction when crucible rotation rate is set to 1 rpm during the unidirectionally solidification process.
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Acknowledgement The authors would like to thank Associate prof. Kangawa in the Kyushu University for his help. References [1] A. Mu¨ller, M. Ghosh, R. Sonnenschein, P. Woditsch, Mater. Sci. Eng. B 134 (2006) 257. [2] H.J. Mo¨llar, L. Long, M. Werner, D. Yang, Phys. Status Solidi A 171 (1999) 175. [3] H.J. Mo¨ller, C. Funke, A. Lawerenz, S. Riedel, M. Werner, Sol. Energy Mater. Sol. Cells 72 (2002) 403. [4] V.V. Bolotov, M.D. Efremov, I. Babanskaya, K. Schmalz, Mater. Sci. Eng. B 21 (1993) 49. [5] T. Saitoh, X. Wang, H. Hashigami, T. Abe, T. Igarashi, S. Glunz, S. Rein, W. Wettling, I. Yamasaki, H. Sawai, H. Ohtuka, T. Warabisako, Sol. Energy Mater. Sol. Cells 65 (2001) 277. [6] K. Hoshikawa, X. Huang, Mater. Sci. Eng. B 72 (2000) 73. [7] A.E. Organ, N. Riley, J. Crystal Growth 82 (1987) 465.
[8] S. Kobayashi, J. Crystal Growth 85 (1987) 69. [9] K. Kakimoto, M. Watanabe, M. Eguchi, T. Hibiya, Int. J. Heat Mass Transfer 35 (1992) 2551. [10] S. Kobayashi, S. Miyahara, T. Fujiwara, T. Kubo, H. Fujiwara, J. Crystal Growth 109 (1991) 149. [11] K. Arafune, E. Ohishi, H. Sai, Y. Ohshita, M. Yamaguchi, J. Crystal Growth 308 (2007) 5. [12] D.E. Bornside, R.A. Brown, T. Fujiwara, H. Fujiwara, T. Kubo, J. Electrochem. Soc. 142 (1995) 2790. [13] T. Iizuka, S. Takasu, M. Tajima, T. Arai, T. Nozaki, N. Inoue, M. Watanabe, J. Electrochem. Soc. 132 (1985) 1707. [14] K. Kakimto, L. Liu, S. Nakano, Mater. Sci. Eng. B 134 (2006) 269. [15] K. Kakimoto, H. Ozoe, J. Electrochem. Soc. 145 (1998) 1692. [16] H. Matsuo, R. Bairava Ganesh, S. Nakano, L. Liu, Y. Kangawa, K. Arafune, Y. Ohshita, M. Yamaguchi, K. Kakimoto, J. Crystal Growth 310 (2008) 4666. [17] S. Togawa, X. Huang, K. Izunome, K. Terashima, S. Kimura, J. Crystal Growth 148 (1995) 70. [18] G. Mu¨ller, A. Ostrogorsky, Convection in melt growth, in: D.T.J. Hurle (Ed.), Handbook of Crystal Growth, North-Holland Publications, Amsterdam, 1994, p. 780.
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Effect of crucible rotation on oxygen concentration during unidirectional solidification process of multicrystalline silicon for solar cells Hitoshi Matsuo a,, R. Bairava Ganesh a,b, Satoshi Nakano c, Lijun Liu c,d, Koji Arafune e,f, Yoshio Ohshita e, Masafumi Yamaguchi e, Koichi Kakimoto a,c a
Graduate School of Engineering, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan Crystal Growth Centre, Anna University, Chennai 600025, India c Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan d National Engineering Research Center for Fluid Machinery and Compressors, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China e Toyota Technological Institute, 2-12-1 Hisakata, Tempaku-ku, Nagoya 468-8511, Japan f Department of Mechanical and System Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2280, Japan b
a r t i c l e in fo
abstract
Article history: Received 22 October 2008 Received in revised form 18 November 2008 Accepted 18 November 2008 Communicated by K.W. Benz Available online 24 November 2008
We studied the effects of crucible rotation on distribution of oxygen concentration in a crystal during the unidirectionally solidification process of multicrystalline silicon for solar cells. Oxygen concentration in the melt increased when crucible rotation rate was increased. Oxygen concentration in the silicon crystal was distributed inhomogeneously in the radial direction when crucible rotation rate was increased. This is due to suppression of oxygen transport. Consequently, less oxygen was transported from the crucible wall to the center of the melt. We found that oxygen concentration is small in the whole ingot and homogenized in the radial direction when crucible rotation rate during the solidification process is set to 1 rpm. & 2008 Elsevier B.V. All rights reserved.
PACS: 81.10.Fq Keywords: A1. Directional solidification A1. Impurities B2. Semiconducting silicon B3. Solar cells
1. Introduction
2. Oxygen transfer
The photovoltaic market has developed remarkably in recent years [1], and multicrystalline silicon now has a market share of more than 50% in all photovoltaic materials. Multicrystalline silicon is an important material for solar cells with the advantage of lowproduction cost. There are many impurities in a silicon crystal, such as oxygen, nitrogen, carbon and iron. The presence of oxygen causes SiO2 precipitation [2], dislocations [3] and stacking faults [4], which decrease the conversion efficiency of solar cells. Boron and oxygen in silicon have also been reported to form boron–oxygen complexes, which cause light-induced degradation in solar cells [5]. These defects reduce the conversion efficiency of solar cells because they act as recombination centers of photocarriers. Therefore, control of oxygen concentration in a silicon ingot is important for improving the conversion efficiency of a solar cell. In this study, we studied the effects of crucible rotation on distribution of oxygen concentration during the solidification process of multicrystalline silicon for solar cells.
It is well known that oxygen is dissolved from a quartz crucible into the silicon melt and that it is transported in silicon melt by convection and evaporates from the melt surface [6]. It has been reported that the concentration of oxygen in the melt can be controlled by modifying melt convection in the case of the Czochralski method [7,8]. Oxygen is mainly transported by both convection and diffusion in the melt. Convection in the melt plays a key role for the distribution of oxygen concentration in the melt and a crystal. It has been reported that convection in the melt can be suppressed by rotation of a crucible [9,10]. The phenomenon of suppression of melt flow was explained by using the momentum equation (the Navier–Stokes equation) [9] as follows:
Corresponding author.
E-mail address: [email protected] (H. Matsuo). 0022-0248/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2008.11.063
qu ¼ ur u 2ðO kÞ u qt ¼ ðO kÞ ðO kÞ r
1
r
rpþ
m Du þ g bðT T 0 Þ, r
(1)
where u, O, r and k represent vector of flow velocity, crucible rotation rate, position and unit vector along the growth direction,
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z
u3 u2
u1
θ r Ω Fig. 1. Cylindrical coordinates in the unidirectional solidification method.
respectively, as shown in Fig. 1. The symbols r, b, g, p, m and T are density, volume expansion coefficient of the silicon melt, vector of gravitational acceleration, pressure, viscosity of the fluid and temperature, respectively. Coriolis force is generated due to coupling of radial velocity and fluid rotation. The term 2(Ok) u in Eq. (1) represents a Coriolis force that is a cross product between vector of flow velocity and rotation. This term, which is called Coriolis acceleration vector, can be transformed: a ¼ 2ðO kÞ u ¼ 2Oðu1 j u2 iÞ,
(2)
where i and j represent unit vectors of the radial component and azimuthal component, respectively. The symbols u1, u2 and u3 are flow velocities in the radial direction, azimuthal direction and growth direction, respectively, as shown in Fig. 1. As a result, the radial component of the melt flow has a negative value and the azimuthal component has a positive value as in Eq. (2). Consequently, the radial velocity of the melt flow is decreased and azimuthal velocity is increased with increasing crucible rotation rate. Therefore, the radial velocity of the melt flow becomes small when crucible rotation is increased. The contribution of melt convection to transport of oxygen in the melt is larger than that of diffusion. Hence, the total amount of oxygen transferred by melt convection becomes small when melt velocity decreases. The distribution of oxygen concentration becomes inhomogeneous in the case of small velocity of the melt in the radial direction during solidification.
0.5 atm pressure in order to avoid impurity incorporation of SiO and CO into the melt during the solidification process [12]. After the heater had almost reached the top of the furnace, the temperature was lowered at a rate of 300 1C/h to room temperature. The grown ingot had a cylindrical shape with a diameter of 10 cm and height of 10 cm. The ingot was cut parallel to the growth direction into slices of 0.5 mm in thickness. Each sample was etched and polished before measurement by FTIR to remove the damaged layer formed by the cutting process. Sliced wafers were etched with a solution of hydrofluoric acid and nitric acid at the ratio of 1:13 for 10 min to remove the sawing damage. To obtain a mirror-like surface, the multicrystalline silicon wafers were polished with diamond particles of 0.5 and 0.3 mm in grain size, coordinated with water. Then the wafers were polished with alumina powder particles of 0.1 mm in grain size and deionized water. After polishing, the wafers were etched again using the same etchant as that described above for 3 min in order to remove the polishing damage. FTIR measurement was carried out using an MFT-2000 (JASCO) at room temperature in air. The length of the infrared beam was set to 50 mm with a square shape. The resolution and number of accumulation of the spectrum were set to 4 cm1 and 182 times, respectively. The absorbance of interstitial oxygen was measured at 1106 cm1 [3]. Oxygen concentration was calculated from the peak height of interstitial oxygen calibrated by pure Czochralski and floating zone silicon wafers with calibration factors of 3.03 1017 cm3 [13].
4. Experimental results Figs. 2(a)–(c) show distributions of oxygen concentration in the radial direction at heights 70, 50 and 20 mm from the bottom of the ingot, respectively. The abscissa shows the radius from the center of the ingot, and the ordinate shows the oxygen concentration. The concentrations of crystals with rotation rates 1 and 30 rpm are shown by open and closed circles in the figures. Oxygen concentration in the crystal at the crucible rotation rate 30 rpm showed an inhomogeneous distribution in the radial direction compared with that at the crucible rotation rate 1 rpm at 50 and 70 mm from the bottom of the ingot. At 20 mm from the bottom of the ingot, the concentrations in the two ingots were almost the same as shown in Fig. 2(c). Moreover, oxygen concentration near the top and middle of the ingot at the crucible rotation rate 30 rpm was larger than that at the crucible rotation rate 1 rpm.
3. Experimental procedure Oxygen concentration in multicrystalline silicon grown by the unidirectional solidification method was measured by Fourier transform infrared spectroscopy (FTIR). The multicrystalline silicon used in the present study was grown by the following method [11]. Off-grade silicon feedstock was used in the present experiment. Carrier concentration of a grown crystal with a dopant of gallium was approximately 1016 cm3. The crucible made of SiO2 had been coated with a liner made of Si3N4, which prevents the ingot from sticking to the crucible. The raw materials were heated up to 1550 1C to stabilize the temperature of the melt for 2 h. After melting, the heater power was decreased to keep the temperature at a center of heater at 1450 1C. Then heater power was kept constant for 1 h prior to the start of growth. The heater was pulled up at a rate of 30 mm/h to solidify the silicon melt from the bottom to the top. The crucible rotation rates were set to 1 and 30 rpm during the solidification process. Argon gas was introduced at the top of the melt at a flow rate of 0.8 l/min under
5. Numerical calculations In order to clarify the relationship between flow and oxygen concentration in the melt, we calculated oxygen concentration by using numerical calculations. The distribution of oxygen concentration was calculated using a global model [14]. Figs. 3(a) and (b) show the configuration and computation grid of a unidirectional solidification furnace and a zoomed-up view of the grid in the melt and crucible domains. Conductive heat transfer in all components and radiative heat exchange between all diffusive surfaces in the unidirectional solidification furnace were taken into account. Gas flow in the furnace was neglected. The value of 0.85 was used for the segregation coefficient of oxygen in these numerical calculations [6,15]. It was assumed that oxygen was dissolved from the crucible and evaporated at the melt surface. At the melt–crucible interfaces, the following equation, in which reaction between a liner made of Si3N4 and a crucible made of
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Fig. 3. (a) Configuration and computation grid of a unidirectional solidification furnace and (b) dynamic grid of the melt and the solid in a crucible.
Fig. 4. Oxygen concentration as a function of radius in the ingot estimated by numerical calculation at 50 mm from the bottom of the ingot.
where co represents oxygen concentration. On the melt surface, the oxygen evaporation was taken into account as follows [17]: D
Fig. 2. Oxygen concentration as a function of radius in the ingot measured by FTIR. Oxygen concentrations at 70 mm (a), 50 mm (b) and 20 mm (c) from the bottom of the ingot.
SiO2 was taken into account, was used as the boundary condition [16]: cO ¼ 0:5 1023
aO ðatoms=cm3 Þ, 1 aO
aO ¼ 1:32 expð7150=T 6:99Þ,
(3)
(4)
qc ¼ ðTÞc, qn
(5)
where c, D and e(T) are oxygen concentration, diffusion coefficient (D=5 108 m2/s) and evaporation velocity [17], respectively. Evaporation velocity is given by ! 4:1559 104 7 ðTÞ ¼ 5:9152 10 exp ðm=sÞ. (6) T Fig. 4 shows the calculated oxygen concentration in the radial direction in the silicon crystal. Height of the data corresponds to 50 mm from the bottom of the ingot. The concentrations of crystals with rotation rates 1 and 5 rpm are shown by solid and dashed lines, respectively, in the figures. Oxygen concentration in the radial direction at the crucible rotation rate 5 rpm showed an inhomogeneous distribution compared with that at the crucible rotation rate 1 rpm. Figs. 5(a)–(c) show the vectors of flow velocity at the crucible rotation rates 0, 1 and 5 rpm. The vortex near the melt surface becomes small with increase in the rate of crucible rotation. This
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means that flow velocity in the melt was suppressed by increasing the crucible rotation rate. Fig. 6 shows the average flow velocity in the radial direction as a function of crucible rotation rate. The results showed that averaged flow velocity was also decreased by increasing the crucible rotation rate.
Fig. 6. Averaged melt convection as a function of crucible rotation rate on the radial component during the solidification process.
Figs. 7(a)–(c) show temperature distributions of the melt at 0, 1 and 5 rpm crucible rotation rates. Figs. 8(a) and (b) show temperature distribution of the melt at melt surface as a function of radius and that at crucible wall as a function of height of the ingot, respectively. The result shows that the temperature distributions of the two cases are similar because temperature difference between 1 and 5 rpm is within 1 K as shown in Fig. 8.
6. Discussion
Fig. 5. Melt convection vector during solidification of the ingot. Crucible rotation rates of (a) 0 rpm, (b) 1 rpm and (c) 5 rpm.
Temperature distributions of the melt are modified by crucible rotation in the case of the Czochralski method [10]. Both equilibrium oxygen concentration at the melt–crucible interface expressed by Eq. (3) and evaporation velocity at melt surface expressed by Eq. (6) are increased with increasing temperature. However, in the case of unidirectional solidification process, temperature distributions in the system with crucible rotation rates 0, 1 and 5 rpm are similar as shown in Figs. 7 and 8. Therefore, the difference of oxygen distributions in the two cases shown in Fig. 4 is not attributed to the difference of temperature distributions in the system shown in Figs. 7 and 8. Oxygen concentrations in the radial direction at 20 mm from the bottom of the ingot are almost independent of crucible rotation rate. Since Rayleigh number of this system is as large as 106 at the beginning of the solidification process, the flow of the melt becomes time dependent or flow turbulent [18]. Due to the time dependent or turbulent flow, the melt was well mixed. Therefore, at 20 mm from the bottom of the ingot, the concentrations of oxygen in the two ingots become almost the same if crucible rotation rate is modified. Oxygen concentration at crucible rotation rate 30 rpm showed an inhomogeneous distribution compared with that at crucible rotation rate 1 rpm in the radial direction at 50 and 70 mm from the bottom of the ingot as shown in Figs. 2(a) and (b). Oxygen concentration in the condition of crucible rotation rate of 5 rpm obtained by numerical calculation was also distributed inhomogeneously in the radial direction as shown in Fig. 4. Flow velocity under these conditions deceased with increasing crucible rotation rate as shown in Figs. 5 and 6. We found the relationship between melt flow and distribution of oxygen concentration from these results of calculations. The centrifugal forces in the condition of crucible rotation rate between 5 and 30 rpm are different, however, the trend of inhomogeneous distributions of calculated oxygen concentration shown in Fig. 4 at the crucible rotation rate
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Fig. 8. Temperature distributions at melt surface as a function radius (a), and that at melt–crucible interface as a function of height. Temperature distribution of the melt with rotation rates of 1 and 5 rpm are shown by solid and dashed lines, respectively.
5 rpm is rather similar to that of the experimental distribution shown in Figs. 2(a) and (b) at the crucible rotation rate 30 rpm. It is thought that less oxygen incorporated from the quartz crucible was transported by melt flow due to suppression of natural convection. Therefore, oxygen concentration in the experiment for which results are presented in Figs. 2(a) and (b) at the crucible rotation rate 30 rpm showed an inhomogeneous distribution compared with that at the crucible rotation rate 1 rpm.
7. Summary
Fig. 7. Temperature distribution during solidification of the ingot. Crucible rotation rates of (a) 0 rpm, (b) 1 rpm and (c) 5 rpm.
We studied the effects of crucible rotation on distribution of oxygen concentration in a crystal during the unidirectional solidification process of multicrystalline silicon for solar cells. Oxygen concentration in the melt increased when crucible rotation rate was increased. Results of calculations and experimental results both showed that oxygen concentration near the top and middle of the crystal was distributed inhomogeneously in the radial direction when crucible rotation rate was increased. Less oxygen was transported from the crucible wall to the center of the melt. This is due to the suppression of oxygen transport. We found that oxygen concentration is minimized in the whole ingot and homogenized in the radial direction when crucible rotation rate is set to 1 rpm during the unidirectionally solidification process.
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