Influence of Back-Diffusion of Iron Impurity on Lifetime Distribution

Dec 5, 2011 - Bing Gao,* Satoshi Nakano, and Koichi Kakimoto. Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka 816-8580, ...
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Influence of Back-Diffusion of Iron Impurity on Lifetime Distribution near the Seed-Crystal Interface in Seed Cast-Grown Monocrystalline Silicon by Numerical Modeling Bing Gao,* Satoshi Nakano, and Koichi Kakimoto

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Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka 816-8580, Japan ABSTRACT: The distribution of minority carrier lifetime near the seed−crystal interface found in seed cast-grown monocrystalline silicon was clarified in this work. The distribution of lifetime first decreases and then increases from a seed to a crystal. Modeling of the temperature- and time-dependent iron diffusion and segregation during crystal growth showed a concentration distribution of an increase followed by a decrease from a seed to a crystal. The consistency between lifetime and iron distribution near the seed− crystal interface indicates that the back-diffusion of iron impurity from silicon melt into the seed at the duration stage before crystal growth is one of the main reasons for lifetime variation near the seed−crystal interface. Therefore, it is essential to reduce the duration time before crystal growth to obtain good-quality monocrystalline silicon.

1. INTRODUCTION The casting technique for producing monocrystalline silicon has recently become popular due to its cost-efficiency, high throughput, and large-scale processes. The quality of monocrystalline silicon produced by this technique depends on the characteristics of the seed−crystal interface, such as seed−crystal interface shape and seed−crystal interface structure. Some research reports1−3 of Czochralski methods have shown that the characteristics of the seed−crystal interface have an essential influence on the crystal quality. The study of the relationship between crystal quality and the seed−crystal interface is helpful to optimize and improve the casting process during monocrystalline silicon production. Since monocrystalline silicon is mainly used to produce solar cells, minority carrier lifetime is an essential parameter for measuring crystal quality. Thus, the quality of the grown crystal at the interface can effectively be indicated by the distribution of the minority carrier lifetime across the seed−crystal interface. Witting et al. measured the distribution of minority carrier lifetime across the seed−crystal interface4 in cast-grown monocrystalline silicon. They found that the lifetime has a minimal value near the seed−crystal interface and gradually increases toward the seed and toward the interior of the grown crystal. From the seed to the grown crystal, the lifetime exhibits a high−low−high distribution within a narrow area. Salo et al.3 also found a similar phenomenon by measuring the structural characteristics of the seed−crystal interface of rapidly grown KDP crystals using the X-ray diffraction method. They found a transitional zone of more than 12 mm in width near the seed− crystal interface, with an increased concentration of defects and nonmonotonic variation of the crystal lattice parameter. Experiments have shown that a large scale defect type was observed near the seed−crystal interface.4 These defects are © 2011 American Chemical Society

small angle grain boundaries with a high density of dislocations along them.4 They have high recombination activity and disrupt the crystallinity of the ingot.4 It is essential to determine their cause to grow high-quality monocrystalline silicon by a casting process. In the present monocrystalline silicon, there is no possibility that the lifetime is affected by large grain size, since the large grain size is much larger than the minority carrier diffusion length.5 Thus, the defects and impurities might play an important role in deterioration of the performance of monocrystalline silicon. Experimental data4 showed that the lifetime in the seed gradually decreases from the interior of the seed to the seed−crystal interface, indicating that impurity contamination is the most probable reason for this kind of progressive variation. Salo et al. also pointed out that impurity contamination is a main reason for growth defects of the structure near the seed−crystal interface.3 Therefore, it is the impurity that causes that kind of nonmonotonic variation of crystal quality near the seed−crystal interface. Three main impurities, carbon, oxygen, and iron, can possibly affect the minority carrier lifetime in cast-grown monocrystalline silicon. Nevertheless, the diffusion coefficients of carbon and oxygen in solid silicon are extremely small compared to that of iron.5 Thus, the carbon and oxygen impurities might have little contribution to the lifetime distribution at the seed− crystal interface. Iron impurity is most likely to affect the lifetime distribution near the seed−crystal interface, since iron has a high diffusivity in solid silicon,6 and it can easily diffuse into the seed within the duration time before crystal growth. Received: November 8, 2011 Revised: December 4, 2011 Published: December 5, 2011 522

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1015 [atoms/cm3].8 The system is assumed to be axisymmetric; and therefore, a zero-gradient condition is applied along the symmetry axis line. Zero flux is used at the normal direction of the free surface. The equilibrium segregation coefficient of iron, kFe, is taken to be 8.0 × 10−6.8 The diffusivities of iron in the melt and in the solid are 1.0 × 10−3 cm2/s and exp[−(3.028 + 3286/T) ln 10] cm2/s, respectively.8 T is the temperature in kelvin. The equilibrium value of iron between the crucible and solid silicon is taken to be the same value as that between the crucible and liquid silicon. The boundary condition at the solid−liquid interface can be automatically satisfied by using the law of mass conservation within a united solver for both the solid region and the liquid region.

The above explanation of the particular distribution of lifetime near the seed−crystal interface needs to be validated. An effective method is to obtain the iron distribution near the seed−crystal interface and to compare the iron distribution with the lifetime distribution. If their distributions exhibit good consistency, the present explanation is logically acceptable. Nevertheless, it is very difficult to determine the original iron concentration because processes such as slicing, cutting, heating, and cooling can change the original distribution of the iron concentration due to the large diffusivity of iron. Therefore, numerical simulation is a good alternative to obtain the iron distribution and to validate the present explanation.

2. NUMERICAL EXPERIMENTAL SECTION Iron impurity transfer and segregation during the casting process of monocrystalline silicon are simulated by numerical modeling. An enthalpy method based on the fixed-grid method has been used to track the complex interface morphology.7 Similar to the derivation of enthalpy formulation on fixed grids for interface-tracking, a governing equation for impurity transfer and segregation can be derived according to the law of mass conservation. Because the melt interface is not considered explicitly during impurity segregation, the efficiency of the calculation is high. This can help us to rapidly track the tendency of impurity distribution and variation within a short time. The furnace used in this work is not exhibited here, and the configurations of the silica crucible are shown in Figure 1. The

3. RESULTS AND DISCUSSION 3.1. Duration Stage. Before crystal growth, a 1 h duration is intentionally set to effectively diffuse iron impurity into the seed. The initial iron concentration in the seed is set to zero, and a uniform concentration field CFe* is given in the melt and at the wall. The iron concentration in the seed after diffusion for 1 h is shown in Figure 2. It can be seen that the iron

Figure 2. Iron concentration distribution in the seed after 1 h of diffusion.

impurity obviously diffuses into the seed from the melt and from the bottom of the crucible. To compare the diffusion depths from the top and from the bottom, a distribution profile along the central axis line inside the seed is shown in Figure 3. Figure 3 shows an almost

Figure 1. Configurations inside a crucible.

materials in the present furnace are similar to those in a directional solidification system (DSS). One layer of liner Si3N4 is used along the inner wall of the crucible to reduce iron impurity concentration inside the melt. A silicon seed is placed on the bottom of the crucible. The silica crucible is a main source of iron impurity due to its dissolution at high temperature. The iron impurity can be transported into the melt by convection and diffusion. The concentrations of iron impurity at the bottom and at the side of the crucible are taken as equilibrium value CFe* = 2.0 ×

Figure 3. Distribution profile of iron concentration inside the seed along the central axis line after 1 h of diffusion. 523

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Figure 4. Distributions of iron concentration at different solidification times.

symmetric distribution along the central axis. It can be seen that a strong diffusion flux occurs at the duration stage. There are two possible reasons for the strong diffusion flux. One is that there is a strong gradient of iron concentration from the melt to the seed and from the wall to the seed, since the initial iron concentration in the seed is zero. The other possible reason is that the crystal does not grow at this stage and there is no inverse segregation flux from the crystal to the melt to counterbalance the diffusion flux from the melt to the crystal. Therefore, a strong diffusion flux of iron always occurs at this stage. 3.2. Crystal Growth Stage. After the 1 h duration, the crystal begins to grow. To clearly observe the interface evolution and iron diffusion during crystal growth, iron distributions inside the crystal at different times are shown in Figure 4. The time interval is 5500 s. When the crystal surface grows as a function of time, diffusion toward the seed and diffusion toward the crystal occur simultaneously, and the width of the high concentration region gradually increases. It is obvious that the diffusion velocity of iron in the crystal is much less than the growth velocity of the crystal surface. Thus, at the final stage in Figure 4f, the high concentration band is not wide. The widths of the high concentration region at different solidification times can be measured by the calculated concentration profiles along the central axis line. Figure 5 shows the concentration profiles near the high concentration band at different times. It can be seen that all of the concentration profiles exhibit a distribution of an increase followed by a decrease. This distribution shows consistency with the minority carrier lifetime measured in experiments.3,4 The width of the high concentration band gradually increases, and the maximum concentration gradually decreases. If the high concentration band is defined as a region that has a concentration of more than 2.0 × 1013 atoms/cm3, the width of the high concentration region at the final stage of solidification in Figure 4f is 10 mm, which is very close to experimental data.3 Therefore, iron impurity is the most likely reason for the high−low−high nonmonotonic distribution of minority carrier lifetime near the seed−crystal interface. 3.3. Other Discussion. Since the iron impurity most probably causes a nonmonotonic distribution of minority carrier lifetime near the seed-crystal interface, a good method to

Figure 5. Distribution profile of iron concentration along the central axis line near the high concentration region after solidification obtained by numerical simulation.

improve the quality of the seed−crystal interface would be to reduce the iron concentration by reducing the duration time before crystal growth. The duration before crystal growth is necessary for practical industrial crystal growth, and it is determined by the characteristics of furnace response to heater power. However, the duration time can be effectively reduced by using a fast cooling technique such as crucible movement or large thermal conductivity of a pedestal. It is important to observe the final distribution of iron impurity after solidification. Until now, experimental data has not been available in our laboratory. Thus, numerical results are shown here. Figure 6 shows a distribution profile along the central axis line obtained by numerical simulation. From the bottom to the top, a W-shaped distribution is observed. The middle peak is not desirable, since it diffuses into two sides. Therefore, it is better to reduce the duration time to reduce that peak value of iron. Figure 7 shows a concentration distribution of iron impurity focusing on the low concentration 524

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located in the as-grown crystal. The difference between numerical results and experiments might be due to the assumed curved seed interface and the smaller thermal shock at the beginning of crystal growth in the present study.

4. CONCLUSIONS The high−low−high nonmonotonic distribution of minority carrier lifetime near the seed−crystal interface found in the castgrown monocrystalline silicon is possibly caused by iron impurity. Modeling of the temperature- and time-dependent iron diffusion and segregation during crystal growth shows a concentration distribution of low−high−low variation from seed to crystal. The consistency between lifetime and iron distribution near the seed−crystal interface indicates that the back-diffusion of iron impurity from silicon melt into the seed at the duration stage before crystal growth is the main reason for the lifetime variation near the seed−crystal interface. Therefore, it is essential to reduce the duration time before crystal growth to obtain good-quality monocrystalline silicon.

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AUTHOR INFORMATION Corresponding Author *Telephone: +81-92-583-7744. Fax: +81-92-583-7743. E-mail: [email protected].

Figure 6. Distribution profile of iron concentration along the central axis line after solidification obtained by numerical simulation.

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ACKNOWLEDGMENTS This work was partly supported by the New Energy and Industrial Technology Development Organization (NEDO) under the Ministry of Economy, Trade and Industry (METI).

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REFERENCES

(1) Taishi, T.; Ohno, Y.; Yonenaga, I.; Hoshikaw, K. Physica B 2007, 401−402, 560−563. (2) Bliss, D. F.; Zhao, J. Y.; Bryant, G.; Lancto, R.; Dudley, M.; Prasad, V. 11th Int. Conf. Indium Phosphide Relat. Mater. 1999, 163− 166. (3) Salo, V. I.; Tkachenko, V. F.; Kolybayeva, M. I. Proc. SPIE 1999, 3578, 519. (4) Witting, I.; Stoddard, N.; Rozgonyi, G. Proc. 18th Workshop Cryst. Silicon Sol. Cells Modules 2008, 155−158. (5) Ohshita, Y.; Arafune, K.; Sasaki, T.; Tachibana, M.; Terada, Y.; Tanaka, S.; Yamaguchi, M. IEEE Photovoltaic Spec. Conf., 31st 2005, 1269−1272. (6) Kvande, R.; Geerligs, L. J.; Coletti, G.; Arnberg, L.; Sabatino, M. Di; Øvrelid, E. J.; Swanson, C. C. J. Appl. Phys. 2008, 104, 064905. (7) Voller, V. R.; Cross, M.; Markatos, N. C. Int. J. Numer. Methods Eng. 1987, 24, 271−284. (8) Liu, L. J.; Nakano, S.; Kakimoto, K. J. Cryst. Growth 2006, 292, 515−518.

Figure 7. Region of low concentration ranging from1.0 × 1010 atoms/ cm3 to 1.0 × 1012 atoms/cm3 after solidification obtained by numerical simulation.

region after solidification obtained by numerical simulation. The low concentration region is defined as 1.0 × 1010 atoms/ cm3 to 1.0 × 1012 atoms/cm3. It can be seen that the low concentration region is located inside the crystal surrounded by a high concentration region near the crucible wall and the seed surface. Therefore, from the point of view of increasing the area of low concentration, it is desirable to use a small seed, since the seed used in the present calculation occupied a large ratio of volume inside the crucible. There are some other factors that might affect the quality of the seed−crystal interface, such as the thermal shock produced by this special furnace setting. A large thermal shock might introduce some defects and dislocations. However, the influence of the thermal shock might not be so large compared to the influence of iron impurity. It is our next target to minimize this kind of influence by designing some smooth starting processes. Concerning industrial applications, it is feasible to reutilize the seed after one growth. However, the Fe concentration at the crystal−melt interface due to another back-diffusion of Fe might be larger than the previous case. More defects can form and march into the inside of the crystal. Therefore, it is necessary to melt the surface part of the seed more at the new melting process to provide a good starting condition. In our paper, the low lifetime coincides with the high iron area. In experimental data,4 the low lifetime region is more 525

dx.doi.org/10.1021/cg201465t | Cryst. Growth Des. 2012, 12, 522−525