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Compensation effect of donor and acceptor impurities co-doping on the electrical properties of directionally solidified multicrystalline silicon ingots
ARTICLE IN PRESS Journal of Crystal Growth 311 (2009) 773–775
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Compensation effect of donor and acceptor impurities co-doping on the electrical properties of directionally solidified multicrystalline silicon ingots M. Dhamrin a,, T. Saitoh a, I. Yamaga b, K. Kamisako a a b
Department of Electronics and Information Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei, Tokyo 184-8588, Japan Dai-ichi-Kiden Co., Japan
a r t i c l e in fo
abstract
Available online 30 September 2008
This paper introduces a simple and attractive calculation technique to evaluate the directionally solidified ingot characteristics type when considerable donor and acceptor impurities exist simultaneously in a silicon melt. The threshold limit of boron concentration in n-type ingot is C0B ¼ 0.4375C0P and when the boron concentration is above the threshold value, the bottom of the ingot. The bottom of the ingot exhibits boron domination due to its higher effective segregation coefficient. The fractions where polarity changes from n-type to p-type and vice versa are calculated for different boron/phosphorus concentration ratios. In addition, calculations of the required counterdoping concentration to make use of heavily boron- or phosphorus-doped recycled silicon feedstock are made and simple examples are given. & 2008 Elsevier B.V. All rights reserved.
Keywords: A1. Solidification A3. Solar cells B1. Silicon
1. Introduction Multicrystalline silicon (Si) wafers share more than 60% of the photovoltaic market due to their cost advantage compared to monocrystalline Si wafers. Several solidification processes have been developed by industry, including casting [1,2], heat exchanger method [3] and electromagnetic casting [4]. These casting methods are very tolerant to virgin poly-Si and solar grade Si feedstock. However, the recent shortage of Si feedstock in the global market leads the photovoltaic industry to search for additional feedstock resources, including the use of recycled Si from semiconductor industry like the CZ ingot tops and tails. Multicrystalline Si ingot edges, bottom near the crucible surface and heavily contaminated top regions are cut and recycled to grow lower quality multicrystalline Si ingots. When such a feedstock is used, it is very difficult to predict the resistivity of the grown ingots or to grow ingots with the desired range of resistivity and maintain the ingot quality. In addition, the choice of the crucible and silicon nitride coating materials is a critical issue for growing high-quality multicrystalline Si ingots, especially when growing n-type multicrystalline Si, due to the heavy phosphorus contamination in industrial crucibles [5]. This paper introduces a simple and attractive calculation technique to evaluate the directionally solidified ingot characteristics type when considerable donor and acceptor impurities exist simultaneously in a Si melt. In addition, calculations of the
Corresponding author. Tel./fax: +81 423 887446.
E-mail address: [email protected] (M. Dhamrin). 0022-0248/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2008.09.094
counter-doping concentration required to make use of heavily boron- or phosphorus-doped recycled Si feedstock are made and simple examples are given.
2. The distribution of donor and acceptor impurities along the solidified height The distribution of donor and acceptor impurities along the solidified height can be expressed using the Scheil [6] law as C SD ¼ K eD C 0D ð1 f S ÞK eD 1
(1)
C SA ¼ K eA C 0A ð1 f S ÞK eA 1
(2)
where fs is the fraction solidified, C0D, C0A are the donor and acceptor concentrations in the Si melt, respectively, K0D, K0A are the effective segregation coefficients and CSD, CSA are the donor and acceptor concentrations in the solidified portion, respectively. For simplicity, the case of B-doped and P-doped co-doped ingots will be discussed. Therefore, here after, the boron and phosphorus symbols of B and P will be used instead of A and D, respectively.
2.1. n-Type multicrystalline ingots For P-doped multicrystalline Si ingots, if the boron content is large, boron atoms compensate phosphorus atoms and if the content of boron reaches the same value as that of phosphorus at the solidified portion, CSB ¼ CSP. Then, after some manipulations,
ARTICLE IN PRESS 774
M. Dhamrin et al. / Journal of Crystal Growth 311 (2009) 773–775
the fraction at which polarity changes from n-type to p-type is K eB C 0B 1=ðK eP K eB Þ fS ¼ 1 K eP C 0P
for f S 41
K eB C 0B K eP C 0P
1=ðK eP K eB Þ ;
n-type
(6)
(3) 2.2. p-Type multicrystalline silicon ingots
for boron concentration with K eP C 0P C 0B 4 K eB
(4)
By considering the effective segregation coefficients of phosphorus and boron to be 0.35 and 0.8, respectively, the threshold limit of boron concentrations in n-type ingot is C0B ¼ 0.4375C0P. At boron concentrations above the threshold value, the bottom of the ingot exhibits boron domination due to its higher effective segregation coefficient and therefore a fraction of the bottom will be p-type Si before it changes again into n-type, as can be seen in Fig. 1. The polarity and total effective dopant concentrations will then be given by
C S;Total ¼ C SB C SP
C S;Total ¼ C SP C SB
for f S o1
K eB C 0B K eP C 0P
1=ðK eP K eB Þ ;
p-type
(5)
Similarly, for the case of p-type, the fraction at which polarity changes from p-type to n-type is K eP C 0P 1=ðK eB K eP Þ (7) fS ¼ 1 K eB C 0B for a phosphorus concentration of K eB C 0P o C 0B K eP
(8)
The polarity and total effective dopant concentrations are given by K eP C 0P 1=ðK eB K eP Þ C S;Total ¼ C SB C SP for f S o1 ; p-type (9) K eB C 0B C S;Total ¼ C SB C SP
for f S 41
K eP C 0P K eB C 0B
1=ðK eB K eP Þ ;
n-type (10)
Fraction of p-type Fraction of n-type
n-type ingot
Ingot height [%]
100 80 60
Growing multicrystalline ingots with total p-type polarity over the solidified fraction of 0.98 requires very low phosphorus contaminations in the melt of C0Po0.39C0B. At higher phosphorous content, polarity of p-type ingot changes into n-type, as can be seen in Fig. 2.
3. Application of counter-doping engineering to heavily doped recycled ingots
40 20 0 0.1
0.2
0.3
0.4
0.5 0.6 C0B/C0P
0.7
0.8
0.9
1.0
Fig. 1. Height of the p-type polarity fraction in the n-type ingot as a function of increasing counter-doped boron concentration.
By considering the use of recycled top regions of multicrystalline Si ingots grown with a target resistivity of 1 O cm at the bottom of the ingot, the excluded top region of the ingot will have a resistivity of less than 0.3 O cm. Only two easy options are available to make use of such wasted Si, the first one is to mix it with high-quality virgin poly-Si, which is considered as an expensive solution. The other option is to co-dope the recycled silicon with phosphorus to reach the desired resistivity range and optimize it with the total desired mono-polarity of the ingot.
p-type Fraction of p-type Fraction of n-type
p-type ingot
Resistivity [Ω⋅cm]
Ingot height [%]
100 80 60 40
Compensated with phosphorus conc. of 7.5×1016 [cm-3]
1
Boron Conc. in melt
20
7.5×1016 [cm-3]
0 0.1
0.2
0.3
0.4
0.5 0.6 C0P/C0B
0.7
0.8
0.9
1.0
Fig. 2. Height of the n-type polarity fraction in the p-type ingot as a function of increasing counter-doped phosphorus concentration.
0.1 0.0
0.2
0.4 0.6 Fraction solidified
0.8
1.0
Fig. 3. Effect of counter-doping phosphorus concentration on resistivity of the ptype, boron-doped ingot.
ARTICLE IN PRESS M. Dhamrin et al. / Journal of Crystal Growth 311 (2009) 773–775
10
n-type
775
120
Measured Fit
Compensated with boron conc. of 2.3×1016 [cm-3]
Resistivity [Ω.⋅cm]
Resistivity [Ω⋅cm]
100
1
0.1
Phosphorus Conc. in melt 5.4×1016 [cm-3]
Fitting Parameters:
80 60
Phosphorus Conc.
1.92E+15
Fraction of Boron
0.412
Boron Conc.
7.91E+14
40 20 0
0.0
0.2
0.4 0.6 Fraction solidified
0.8
1.0
Fig. 4. Effect of counter-doping boron concentration on resistivity of the n-type, phosphorus-doped ingot.
Higher phosphorus content rises the target resistivity but on account of the total ingot polarity. As can be seen in Fig. 3, the optimization of phosphorus content increases the resistivity of the ingot from 0.3 to about 0.5 O cm at the bottom of the ingot. In addition, when going toward the top, resistivity increases further for the total solidified fraction of the ingot of 0.82 before the phosphorus content becomes a dominant impurity and changes the ingot polarity into n-type ingot, which will, therefore, increase the carrier lifetime at the top region, a feature that is seldom found in normal mono-doped ingots. In n-type ingots, the low segregation coefficient of phosphorus in silicon resulted in large resistivity variation. Co-doping the ingot with boron makes the resistivity variation even stronger. Fig. 4 shows the calculated amount of boron concentration required to increase the resistivity of n-type ingot from 0.3 to about 8 O cm at the bottom of the ingot, utilizing more than 80% of the ingot with resistivities higher than 0.3 O cm. An example of such ingots co-doped with phosphorus and boron is illustrated in Fig. 5, where the total resistivity of the ingot was fitted very well by the co-doping calculation considering both segregation mechanisms of boron and phosphorus in silicon during the solidification process.
0.0
0.2
0.4
0.6
0.8
1.0
Fraction solidified Fig. 5. Exact fitting to the four-point-probe-measured resistivity of directionally solidified multicrystalline ingot co-doped with phosphorus and boron impurities.
4. Conclusion A simple and attractive calculation technique to evaluate the directionally solidified ingot characteristics type when donor and acceptor impurities exist simultaneously in a Si melt was introduced. The threshold limit of boron concentration in n-type ingot was calculated. At boron concentration above the threshold value C0B ¼ 0.4375C0P, the bottom of the ingot exhibits boron domination due to its higher effective segregation coefficient.
References [1] I.A. Dorrity, B.J. Garrard, D.A. Nukin, in: Proceedings of the 10th E.C. Photovoltaic Solar Energy Conference, Lisbon, Portugal, 1991, p. 317. [2] C.P. Khattak, F. Schmid, in: Proceedings of the 13th IEEE Photovoltaic Specialists Conference, 1978, p. 137. [3] T.F. Ciszek, J. Electrochem. Soc. 132 (1985) 963. [4] K. Kaneko, R. Kawamura, H. Mizumoto, T. Misawa, in: Proceedings of the 11th European Photovoltaic Solar Energy Conference, 1992, p. 1070. [5] M. Dhamrin, A. Uzum, T. Saitoh, K. Kamisako, K. Yamada, H. Suzuki, N. Araki, I. Yamaga, in: Proceedings of the 17th Photovoltaic Science and Engineering Conference, December 2007, pp. 587–588. [6] E. Scheil, Z. Metallkd. 34 (1942) 70–72.
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Compensation effect of donor and acceptor impurities co-doping on the electrical properties of directionally solidified multicrystalline silicon ingots M. Dhamrin a,, T. Saitoh a, I. Yamaga b, K. Kamisako a a b
Department of Electronics and Information Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei, Tokyo 184-8588, Japan Dai-ichi-Kiden Co., Japan
a r t i c l e in fo
abstract
Available online 30 September 2008
This paper introduces a simple and attractive calculation technique to evaluate the directionally solidified ingot characteristics type when considerable donor and acceptor impurities exist simultaneously in a silicon melt. The threshold limit of boron concentration in n-type ingot is C0B ¼ 0.4375C0P and when the boron concentration is above the threshold value, the bottom of the ingot. The bottom of the ingot exhibits boron domination due to its higher effective segregation coefficient. The fractions where polarity changes from n-type to p-type and vice versa are calculated for different boron/phosphorus concentration ratios. In addition, calculations of the required counterdoping concentration to make use of heavily boron- or phosphorus-doped recycled silicon feedstock are made and simple examples are given. & 2008 Elsevier B.V. All rights reserved.
Keywords: A1. Solidification A3. Solar cells B1. Silicon
1. Introduction Multicrystalline silicon (Si) wafers share more than 60% of the photovoltaic market due to their cost advantage compared to monocrystalline Si wafers. Several solidification processes have been developed by industry, including casting [1,2], heat exchanger method [3] and electromagnetic casting [4]. These casting methods are very tolerant to virgin poly-Si and solar grade Si feedstock. However, the recent shortage of Si feedstock in the global market leads the photovoltaic industry to search for additional feedstock resources, including the use of recycled Si from semiconductor industry like the CZ ingot tops and tails. Multicrystalline Si ingot edges, bottom near the crucible surface and heavily contaminated top regions are cut and recycled to grow lower quality multicrystalline Si ingots. When such a feedstock is used, it is very difficult to predict the resistivity of the grown ingots or to grow ingots with the desired range of resistivity and maintain the ingot quality. In addition, the choice of the crucible and silicon nitride coating materials is a critical issue for growing high-quality multicrystalline Si ingots, especially when growing n-type multicrystalline Si, due to the heavy phosphorus contamination in industrial crucibles [5]. This paper introduces a simple and attractive calculation technique to evaluate the directionally solidified ingot characteristics type when considerable donor and acceptor impurities exist simultaneously in a Si melt. In addition, calculations of the
Corresponding author. Tel./fax: +81 423 887446.
E-mail address: [email protected] (M. Dhamrin). 0022-0248/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2008.09.094
counter-doping concentration required to make use of heavily boron- or phosphorus-doped recycled Si feedstock are made and simple examples are given.
2. The distribution of donor and acceptor impurities along the solidified height The distribution of donor and acceptor impurities along the solidified height can be expressed using the Scheil [6] law as C SD ¼ K eD C 0D ð1 f S ÞK eD 1
(1)
C SA ¼ K eA C 0A ð1 f S ÞK eA 1
(2)
where fs is the fraction solidified, C0D, C0A are the donor and acceptor concentrations in the Si melt, respectively, K0D, K0A are the effective segregation coefficients and CSD, CSA are the donor and acceptor concentrations in the solidified portion, respectively. For simplicity, the case of B-doped and P-doped co-doped ingots will be discussed. Therefore, here after, the boron and phosphorus symbols of B and P will be used instead of A and D, respectively.
2.1. n-Type multicrystalline ingots For P-doped multicrystalline Si ingots, if the boron content is large, boron atoms compensate phosphorus atoms and if the content of boron reaches the same value as that of phosphorus at the solidified portion, CSB ¼ CSP. Then, after some manipulations,
ARTICLE IN PRESS 774
M. Dhamrin et al. / Journal of Crystal Growth 311 (2009) 773–775
the fraction at which polarity changes from n-type to p-type is K eB C 0B 1=ðK eP K eB Þ fS ¼ 1 K eP C 0P
for f S 41
K eB C 0B K eP C 0P
1=ðK eP K eB Þ ;
n-type
(6)
(3) 2.2. p-Type multicrystalline silicon ingots
for boron concentration with K eP C 0P C 0B 4 K eB
(4)
By considering the effective segregation coefficients of phosphorus and boron to be 0.35 and 0.8, respectively, the threshold limit of boron concentrations in n-type ingot is C0B ¼ 0.4375C0P. At boron concentrations above the threshold value, the bottom of the ingot exhibits boron domination due to its higher effective segregation coefficient and therefore a fraction of the bottom will be p-type Si before it changes again into n-type, as can be seen in Fig. 1. The polarity and total effective dopant concentrations will then be given by
C S;Total ¼ C SB C SP
C S;Total ¼ C SP C SB
for f S o1
K eB C 0B K eP C 0P
1=ðK eP K eB Þ ;
p-type
(5)
Similarly, for the case of p-type, the fraction at which polarity changes from p-type to n-type is K eP C 0P 1=ðK eB K eP Þ (7) fS ¼ 1 K eB C 0B for a phosphorus concentration of K eB C 0P o C 0B K eP
(8)
The polarity and total effective dopant concentrations are given by K eP C 0P 1=ðK eB K eP Þ C S;Total ¼ C SB C SP for f S o1 ; p-type (9) K eB C 0B C S;Total ¼ C SB C SP
for f S 41
K eP C 0P K eB C 0B
1=ðK eB K eP Þ ;
n-type (10)
Fraction of p-type Fraction of n-type
n-type ingot
Ingot height [%]
100 80 60
Growing multicrystalline ingots with total p-type polarity over the solidified fraction of 0.98 requires very low phosphorus contaminations in the melt of C0Po0.39C0B. At higher phosphorous content, polarity of p-type ingot changes into n-type, as can be seen in Fig. 2.
3. Application of counter-doping engineering to heavily doped recycled ingots
40 20 0 0.1
0.2
0.3
0.4
0.5 0.6 C0B/C0P
0.7
0.8
0.9
1.0
Fig. 1. Height of the p-type polarity fraction in the n-type ingot as a function of increasing counter-doped boron concentration.
By considering the use of recycled top regions of multicrystalline Si ingots grown with a target resistivity of 1 O cm at the bottom of the ingot, the excluded top region of the ingot will have a resistivity of less than 0.3 O cm. Only two easy options are available to make use of such wasted Si, the first one is to mix it with high-quality virgin poly-Si, which is considered as an expensive solution. The other option is to co-dope the recycled silicon with phosphorus to reach the desired resistivity range and optimize it with the total desired mono-polarity of the ingot.
p-type Fraction of p-type Fraction of n-type
p-type ingot
Resistivity [Ω⋅cm]
Ingot height [%]
100 80 60 40
Compensated with phosphorus conc. of 7.5×1016 [cm-3]
1
Boron Conc. in melt
20
7.5×1016 [cm-3]
0 0.1
0.2
0.3
0.4
0.5 0.6 C0P/C0B
0.7
0.8
0.9
1.0
Fig. 2. Height of the n-type polarity fraction in the p-type ingot as a function of increasing counter-doped phosphorus concentration.
0.1 0.0
0.2
0.4 0.6 Fraction solidified
0.8
1.0
Fig. 3. Effect of counter-doping phosphorus concentration on resistivity of the ptype, boron-doped ingot.
ARTICLE IN PRESS M. Dhamrin et al. / Journal of Crystal Growth 311 (2009) 773–775
10
n-type
775
120
Measured Fit
Compensated with boron conc. of 2.3×1016 [cm-3]
Resistivity [Ω.⋅cm]
Resistivity [Ω⋅cm]
100
1
0.1
Phosphorus Conc. in melt 5.4×1016 [cm-3]
Fitting Parameters:
80 60
Phosphorus Conc.
1.92E+15
Fraction of Boron
0.412
Boron Conc.
7.91E+14
40 20 0
0.0
0.2
0.4 0.6 Fraction solidified
0.8
1.0
Fig. 4. Effect of counter-doping boron concentration on resistivity of the n-type, phosphorus-doped ingot.
Higher phosphorus content rises the target resistivity but on account of the total ingot polarity. As can be seen in Fig. 3, the optimization of phosphorus content increases the resistivity of the ingot from 0.3 to about 0.5 O cm at the bottom of the ingot. In addition, when going toward the top, resistivity increases further for the total solidified fraction of the ingot of 0.82 before the phosphorus content becomes a dominant impurity and changes the ingot polarity into n-type ingot, which will, therefore, increase the carrier lifetime at the top region, a feature that is seldom found in normal mono-doped ingots. In n-type ingots, the low segregation coefficient of phosphorus in silicon resulted in large resistivity variation. Co-doping the ingot with boron makes the resistivity variation even stronger. Fig. 4 shows the calculated amount of boron concentration required to increase the resistivity of n-type ingot from 0.3 to about 8 O cm at the bottom of the ingot, utilizing more than 80% of the ingot with resistivities higher than 0.3 O cm. An example of such ingots co-doped with phosphorus and boron is illustrated in Fig. 5, where the total resistivity of the ingot was fitted very well by the co-doping calculation considering both segregation mechanisms of boron and phosphorus in silicon during the solidification process.
0.0
0.2
0.4
0.6
0.8
1.0
Fraction solidified Fig. 5. Exact fitting to the four-point-probe-measured resistivity of directionally solidified multicrystalline ingot co-doped with phosphorus and boron impurities.
4. Conclusion A simple and attractive calculation technique to evaluate the directionally solidified ingot characteristics type when donor and acceptor impurities exist simultaneously in a Si melt was introduced. The threshold limit of boron concentration in n-type ingot was calculated. At boron concentration above the threshold value C0B ¼ 0.4375C0P, the bottom of the ingot exhibits boron domination due to its higher effective segregation coefficient.
References [1] I.A. Dorrity, B.J. Garrard, D.A. Nukin, in: Proceedings of the 10th E.C. Photovoltaic Solar Energy Conference, Lisbon, Portugal, 1991, p. 317. [2] C.P. Khattak, F. Schmid, in: Proceedings of the 13th IEEE Photovoltaic Specialists Conference, 1978, p. 137. [3] T.F. Ciszek, J. Electrochem. Soc. 132 (1985) 963. [4] K. Kaneko, R. Kawamura, H. Mizumoto, T. Misawa, in: Proceedings of the 11th European Photovoltaic Solar Energy Conference, 1992, p. 1070. [5] M. Dhamrin, A. Uzum, T. Saitoh, K. Kamisako, K. Yamada, H. Suzuki, N. Araki, I. Yamaga, in: Proceedings of the 17th Photovoltaic Science and Engineering Conference, December 2007, pp. 587–588. [6] E. Scheil, Z. Metallkd. 34 (1942) 70–72.