- Email: [email protected]
In situ observation of twin boundary formation at grain-boundary groove during directional solidification of Si
Scripta Materialia 133 (2017) 65–69
Contents lists available at ScienceDirect
Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Regular article
In situ observation of twin boundary formation at grain-boundary groove during directional solidification of Si Kozo Fujiwara ⁎, Ryoichi Maeda, Kensaku Maeda, Haruhiko Morito Institute for Materials Research (IMR), Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan
a r t i c l e
i n f o
Article history: Received 5 October 2016 Received in revised form 15 February 2017 Accepted 18 February 2017 Available online xxxx
a b s t r a c t Twin boundary formation at grain boundaries in multicrystalline Si during directional solidification was investigated by in situ observation of the crystal/melt interface. It was clearly shown that a twin boundary was formed on the {111} facet of grain-boundary groove at the crystal/melt interface. The large amount of undercooling in the melt at grain-boundary grooves promoted rapid crystallization and twin boundary formation. © 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Crystal/melt interface Grain boundary Twin boundary
Multicrystalline Si (mc-Si) ingots grown by directional solidification for use in solar cells always exhibit twin boundaries [1–12]. Structural analysis of mc-Si ingots and wafers thereof has revealed that Σ3 twins with a {111} boundary plane were often generated at grain boundaries. However, it is not well understood when or why this occurs. It has been argued that one reason might be to reduce the free energy at the crystal/ melt interface [2]. If the grain boundary energy is large, defects such as dislocations, twins, or a new crystal grain may be generated to reduce the energy. On the other hand, Duffar and Nadri argued that, theoretically, twins would be expected to appear on facets at grain boundarysolid-liquid triple junctions (that is, at grain-boundary grooves) [13]. Recently, Tsoutsouva et al. directly observed twin boundary generation at a grain-boundary groove at the crystal/melt interface during directional solidification from a Si{110} seed crystal by using in situ X-ray imaging [14]. They showed that the twin boundary was generated when the melt at the grain boundary groove crystallized. However, such direct evidence for the formation of twin boundaries remains very limited, owing to the difficulties in observing the Si crystal/melt interface due to the high melting temperature (1687 K). Therefore, the details of this process have not been clarified yet. We previously reported the formation of grain-boundary grooves [15] and impurity accumulation [16] at the Si crystal/melt interface using in situ observations. Reflection optical digital microscopy could be performed in our system, allowing the surface structure of the sample to be clearly observed. In the present study, we attempted to obtain experimental evidence for the generation of {111} Σ3 twin boundaries at grain boundaries during the directional growth of mc-Si. In particular, we focused on twin ⁎ Corresponding author. E-mail address: [email protected] (K. Fujiwara).
http://dx.doi.org/10.1016/j.scriptamat.2017.02.028 1359-6462/© 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
boundary formation at grain-boundary grooves, which has been reported by Tsoutsouva et al. [14]. The crystal/melt interface of a mc-Si sample with grain boundaries was observed during the directional solidification process by using an in situ observation system that consisted of a furnace and a microscope [15,16]. The Si raw materials, placed in a silica crucible, were melted completely in the furnace. Then, directional growth was promoted by cooling one side of the crucible. A high-speed camera with a light source was used to obtain a reflected image of the sample surface, allowing us to clearly identify grain boundaries and twin boundaries in the growing crystal. The crystal growth process was recorded as a video at 250 frames/s. After crystallization, a crystallographic orientation analysis was performed to determine the Σ values of the observed grain boundaries by the electron backscattering diffraction pattern (EBSP) method. Fig. 1 shows a mc-Si crystal/melt interface in motion. The recording was started at t = 0 s, at which time we could observe two grain boundaries that formed grooves at the crystal/melt interface. It is known that {111} facets appear on the growth surface at the grain boundary. Thus, the groove was formed by two {111} facets [13,15]. Another groove started to appear at the crystal/melt interface at t = 5.7 s in the area indicated by the red circle (clearer in the magnified image in the red square). Let us focus on the morphological changes occurring in the vicinity of this groove. The depth of the groove increased with crystal growth until around t = 30 s. Then, the melt in this deep groove rapidly crystallized, filling the groove, as shown in the images for t = 35–60 s. Fig. 2 shows a frame taken at t = 60 s and its schematic. The remnant of a deep groove is clearly visible in the crystal. We note that a new line, indicating the formation of a new boundary, extends from under the {111} facet that formed a deep groove, while there is no boundary extending from the upper {111} plane. These results strongly indicate
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Fig. 1. Crystal/melt interface during unidirectional growth of mc-Si. The recording was started at time t = 0 s.
that a {111}Σ3 twin boundary was formed upon rapid growth at the deep groove. EBSP analysis was performed to identify the grain boundary characteristics and grain orientations. Fig. 3 shows (a) a scanning electron microscopy (SEM) image, (b) an image quality (IQ) map with colored grain boundaries, and (c) an orientation map for the TD direction
(crystal growth direction). We can easily identify the observation area shown in Fig. 1 because the remnant of the deep groove is visible in the SEM image, as shown in Fig. 3(a). Thus, the orientation analysis was performed around this area. Analysis of the grain boundary characteristics (Fig. 3(b)) confirmed that the new boundary, which was generated upon rapid crystallization at the deep groove, was a Σ3 twin
Fig. 2. Image of crystal/melt interface at t = 60 s and its schematic. The remnant of a deep groove is clearly visible in the crystal.
K. Fujiwara et al. / Scripta Materialia 133 (2017) 65–69
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Fig. 3. (a) SEM image of the sample. (b) IQ map with colored grain boundaries. A {111} Σ3 twin boundary and Σ27 grain boundary are colored red and yellow, respectively. (c) Orientation map for TD direction (crystal growth direction). (d) Schematic of twin boundary formation at grain boundary. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
boundary. In Fig. 3(c), the 3D octahedron lattice bounded by {111} planes of each grain were shown. The direction of each lattice reflects the orientation of each grain. It was confirmed that the boundary plane of newly formed Σ3 twin boundary was {111} plane, as indicated by red triangles in the 3D lattice images. The growth orientation of the upper grain was found to be 〈18 8 19〉, which will be important to estimate the undercooling at the interface later. Also, from Fig. 3(b) and (c), we can explain what happened during crystal growth, as illustrated in Fig. 3(d). As seen in the left panel in Fig. 3(d), at the beginning of growth (t = 0–4 s in Fig. 1), there were three grain boundaries in the observation area of the crystal, and only two grain boundary grooves were observed at the crystal/melt interface because the {111} Σ3 twin boundary did not form a groove, as we have reported previously [15]. It should be noted that a new crystal grain was formed at this {111}Σ3 twin boundary between t = 4 and 5.7 s, as seen in the orientation map in Fig. 3(c) (indicated by yellow), although the reason why the nucleation occurred at this position was not clarified. Thus, a random grain boundary formed which led to the formation of a grain boundary groove in this region of the crystal/melt interface (second figure from the left in Fig. 3(d)). This new groove deepened until rapid growth occurred (third figure from the left in Fig. 3(d)). When the melt in the deep groove
crystallized, a new {111}Σ3 twin boundary was formed on the {111} facet of the deep groove (right figure in Fig. 3(d)). Clearly, twin boundary generation was triggered by the formation of the grain boundary groove, in agreement with a theoretical prediction [13] and an experimental result [14]. Now, we consider how the crystal growth occurred at this groove. When the atoms in the melt at the groove crystallized on the {111} planes, there are two ways energetically, as schematically shown in the red box in Fig. 3(d). The one is that the atoms attach on the {111} plane with epitaxial configuration, which leads to the formation of no boundary, as shown in the left figure. The other one is that the atoms attach on the {111} plane with twin relationship (right figure), because the formation energy of Si {111} twin boundary is quite low, such as 30 mJ/m2 [17]. It seems that the twin boundary is easy to form at the crystal/melt interface when the crystal/melt interface has a {111} plane and there exists some amounts of driving force. Next, we discuss the conditions for twin boundary formation at the grain boundary groove. It was observed that the twin boundary was formed when rapid growth occurred at the deep grain boundary groove. This suggested that a large driving force (undercooling, ΔT) for crystallization assisted twin boundary formation. Thus, we will estimate the undercooling at the twin boundary formation. It was thought that
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growth on the {111} facet plane proceeded by two-dimensional (2D) nucleation [18]. On the other hand, Buta et al. suggested that the stepflow growth mode is stable at {111} facets at low undercooling, ΔT b 40 K, by non-equilibrium molecular dynamics simulations [19]. In our experiments, it seems that the undercooling at the growth was not so high, and thus, we will estimate the undercooling under the step-growth mode. An expression for the growth velocity (V) of stepgrowth mode is written as V¼
h vs l
ð1Þ
where h is the step height, l is the distance between two steps (a terrace length), and vs is the velocity of step described as vs = βsΔT. βs is the step kinetic constant. From the classical Wilson-Frenkel theory, the step kinetic constant βs is obtained as βs = 0.02 [m/(sK)] [19]. However,
Chernov [20] suggested that the value of βs obtained from WilsonFrenkel theory was much smaller than the experimental results of Voronkov [21], and Buta et al. also showed the value of βs was more than an order larger than 0.02 [m/(sK)] by molecular dynamic simulations [19]. In their simulations, it was shown that the step kinetic coefficient βs was strongly dependent on the distance between the steps (l), and βs reached to a plateau at a value of 0.7–0.8 [m/(sK)] for l N 50 Å. Fig. 4 shows traces of the moving crystal/melt interface and a plot of interface position versus time (x-t plot). Fig. 4(a) is a trace of the interface around the deep groove during rapid crystallization. We traced the interface at 0.1-s intervals (from t = 31.0 to 31.5 s). From Fig. 3(c), it was confirmed that the crystal/melt interface forming the groove was {111} plane. Here, we need to measure the growth velocity along the normal to the {111} plane, thus, the x-t plot was obtained along the dotted line in the trace figure. The growth velocity was estimated to be V ≈ 5.85 × 10−5 m/s by linear regression. Using Eq. (1) to estimate
Fig. 4. Traces of moving crystal/melt interface and plot of interface position versus time (x-t plot). (a) Trace around deep groove during rapid crystallization; (b) trace of entire observation area.
K. Fujiwara et al. / Scripta Materialia 133 (2017) 65–69
the undercooling, we obtained ΔT ≈ 1.3 × 10−3 K. For the estimation, h = 3.13 × 10−10 m [17], l = 5 × 10−9 m, and βs = 0.7 [m/(sK)] were used. Fig. 4(b) is the trace of the whole observation area, and the x-t plot was obtained by measuring the position of the interface along the dotted line in the trace figure. The growth velocity at this position was estimated to be V ≈ 9.5 × 10−6 m/s. From Fig. 3(c), it was found that the growth orientation at this position was 〈18 8 19〉. This plane is not the facet plane, therefore, a normal growth mode for a rough crystal/melt interface, which is expressed as V = βroughΔT: where βrough is a kinetic coefficient for the rough plane, might be considered. There were reports that the value of βrough was around 0.10 m/(sK) for Si {100} rough plane [17,19,22], although there is no date for {18 8 19} plane. Using the value of 0.10 m/(sK) to estimate the undercooling, we obtained ΔT ≈ 9.5 × 10− 5 K. If a step-growth mode was adapted for this plane, the undercooling would be estimated as ΔT ≈ 2.2 × 10− 4 K. The real value of undercooling might be 9.5 × 10−5 K b ΔT b 2.2 × 10−4 K. In this way, it was shown that the amount of undercooling in the melt at the deep groove was larger than that at the planar interface. In general, during the growth of mc-Si ingots, the temperature gradient is positive in the growth direction, as in the present study. Under these conditions, as the grain boundary groove deepens, the local undercooling at the groove increases, as estimated here. As the undercooling, i.e., the driving force for crystallization, increases, so does the probability of twin boundary formation. Indeed, the grain boundary groove that became the source of the twin boundary was also relatively deep in the study by Tsoutsouva et al. [14]. Thus, we conclude that the formation of the grain boundary groove is one of the main causes of twin boundary formation from grain boundaries during the growth of mc-Si ingots for solar cells. In summary, we observed twin boundary formation in a grain boundary groove at the crystal/melt interface during directional solidification of mc-Si. The grain boundary groove at the crystal/melt interface becomes the source of the {111} Σ3 twin boundary, because the grain boundary groove is formed by {111} facet planes. It was also shown that the local undercooling at the deep groove increases, which promotes twin boundary formation at the grain boundary groove.
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Acknowledgements This work was supported by a Kakenhi Grant-in-Aid (No. 26246016) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. References [1] J. Chen, T. Sekiguchi, D. Yang, F. Yin, K. Kido, S. Tsurekawa, J. Appl. Phys. 96 (2004) 5490. [2] M. Kitamura, N. Usami, T. Sugawara, K. Kutsukake, K. Fujiwara, Y. Nose, T. Shishido, K. Nakajima, J. Cryst. Growth 280 (2005) 419. [3] K. Nakajima, K. Morishita, R. Murai, K. Kutsukake, J. Cryst. Growth 355 (2012) 38. [4] C.W. Lan, W.C. Lan, T.F. Lee, A. Yu, Y.M. Yang, W.C. Hsu, B. Hsu, A. Yang, J. Cryst. Growth 360 (2012) 68. [5] X. Tang, L.A. Francis, L. Gong, F. Wang, J.-P. Raskin, D. Flandre, S. Zhang, D. You, L. Wu, B. Dai, Sol. Energy Mater. Sol. Cells 117 (2013) 225. [6] G. Stokkan, J. Cryst. Growth 384 (2013) 107. [7] T. Duffar, C.T. Nwosu, I.M. Asuo, J. Muzy, N.D.Q. Chau, Y. Du Terrail-Couvat, F. Robaut, J. Cryst. Growth 401 (2014) 404. [8] A. Nadri, Y. Duterrail-Couvat, T. Duffar, J. Cryst. Growth 385 (2014) 16. [9] Y.M. Yang, A. Yu, B. Hsu, W.C. Hsu, A. Yang, C.W. Lan, Prog. Photovolt. Res. Appl. 23 (2015) 340. [10] T. Riberi-Béridot, N. Mangelinck-Noël, A. Tandjaoui, G. Reinhart, B. Billia, T. Lafford, J. Baruchel, L. Barrallier, J. Cryst. Growth 418 (2015) 38. [11] R.R. Prakash, K. Jiptner, J. Chen, Y. Miyamura, H. Harada, T. Sekiguchi, Appl. Phys. Express 8 (2015) 035502. [12] K.E. Ekstrøm, G. Stokkan, A. Autruffe, R. Søndenå, H. Dalaker, L. Arnberg, J. Cryst. Growth 441 (2016) 95. [13] T. Duffar, A. Nadri, Scr. Mater. 62 (2010) 955. [14] M.G. Tsoutsouva, T. Riberi-Béridot, G. Regula, G. Reinhart, J. Baruchel, F. Guittonneau, L. Barrallier, N. Mangelinck-Noël, Acta Mater. 115 (2016) 210. [15] K. Fujiwara, M. Ishii, K. Maeda, H. Koizumi, J. Nozawa, S. Uda, Scr. Mater. 69 (2013) 266. [16] M. Mokhtari, K. Fujiwara, H. Koizumi, J. Nozawa, S. Uda, Scr. Mater. 117 (2016) 73. [17] M. Kohyama, R. Yamamoto, M. Doyama, Phys. Status Solidi B 138 (1986) 387. [18] K.M. Beatty, K.A. Jackson, J. Cryst. Growth 211 (2000) 13. [19] D. Buta, M. Asta, J.J. Hoyt, J. Chem. Phys. 127 (2007) 074703. [20] A.A. Chernov, J. Cryst. Growth 264 (2004) 499. [21] V.V. Voronkov, Crystals 9 (1983) 74. [22] M.D. Kluge, J.R. Ray, Phys. Rev. B 39 (1989) 1738.
Contents lists available at ScienceDirect
Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Regular article
In situ observation of twin boundary formation at grain-boundary groove during directional solidification of Si Kozo Fujiwara ⁎, Ryoichi Maeda, Kensaku Maeda, Haruhiko Morito Institute for Materials Research (IMR), Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan
a r t i c l e
i n f o
Article history: Received 5 October 2016 Received in revised form 15 February 2017 Accepted 18 February 2017 Available online xxxx
a b s t r a c t Twin boundary formation at grain boundaries in multicrystalline Si during directional solidification was investigated by in situ observation of the crystal/melt interface. It was clearly shown that a twin boundary was formed on the {111} facet of grain-boundary groove at the crystal/melt interface. The large amount of undercooling in the melt at grain-boundary grooves promoted rapid crystallization and twin boundary formation. © 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Crystal/melt interface Grain boundary Twin boundary
Multicrystalline Si (mc-Si) ingots grown by directional solidification for use in solar cells always exhibit twin boundaries [1–12]. Structural analysis of mc-Si ingots and wafers thereof has revealed that Σ3 twins with a {111} boundary plane were often generated at grain boundaries. However, it is not well understood when or why this occurs. It has been argued that one reason might be to reduce the free energy at the crystal/ melt interface [2]. If the grain boundary energy is large, defects such as dislocations, twins, or a new crystal grain may be generated to reduce the energy. On the other hand, Duffar and Nadri argued that, theoretically, twins would be expected to appear on facets at grain boundarysolid-liquid triple junctions (that is, at grain-boundary grooves) [13]. Recently, Tsoutsouva et al. directly observed twin boundary generation at a grain-boundary groove at the crystal/melt interface during directional solidification from a Si{110} seed crystal by using in situ X-ray imaging [14]. They showed that the twin boundary was generated when the melt at the grain boundary groove crystallized. However, such direct evidence for the formation of twin boundaries remains very limited, owing to the difficulties in observing the Si crystal/melt interface due to the high melting temperature (1687 K). Therefore, the details of this process have not been clarified yet. We previously reported the formation of grain-boundary grooves [15] and impurity accumulation [16] at the Si crystal/melt interface using in situ observations. Reflection optical digital microscopy could be performed in our system, allowing the surface structure of the sample to be clearly observed. In the present study, we attempted to obtain experimental evidence for the generation of {111} Σ3 twin boundaries at grain boundaries during the directional growth of mc-Si. In particular, we focused on twin ⁎ Corresponding author. E-mail address: [email protected] (K. Fujiwara).
http://dx.doi.org/10.1016/j.scriptamat.2017.02.028 1359-6462/© 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
boundary formation at grain-boundary grooves, which has been reported by Tsoutsouva et al. [14]. The crystal/melt interface of a mc-Si sample with grain boundaries was observed during the directional solidification process by using an in situ observation system that consisted of a furnace and a microscope [15,16]. The Si raw materials, placed in a silica crucible, were melted completely in the furnace. Then, directional growth was promoted by cooling one side of the crucible. A high-speed camera with a light source was used to obtain a reflected image of the sample surface, allowing us to clearly identify grain boundaries and twin boundaries in the growing crystal. The crystal growth process was recorded as a video at 250 frames/s. After crystallization, a crystallographic orientation analysis was performed to determine the Σ values of the observed grain boundaries by the electron backscattering diffraction pattern (EBSP) method. Fig. 1 shows a mc-Si crystal/melt interface in motion. The recording was started at t = 0 s, at which time we could observe two grain boundaries that formed grooves at the crystal/melt interface. It is known that {111} facets appear on the growth surface at the grain boundary. Thus, the groove was formed by two {111} facets [13,15]. Another groove started to appear at the crystal/melt interface at t = 5.7 s in the area indicated by the red circle (clearer in the magnified image in the red square). Let us focus on the morphological changes occurring in the vicinity of this groove. The depth of the groove increased with crystal growth until around t = 30 s. Then, the melt in this deep groove rapidly crystallized, filling the groove, as shown in the images for t = 35–60 s. Fig. 2 shows a frame taken at t = 60 s and its schematic. The remnant of a deep groove is clearly visible in the crystal. We note that a new line, indicating the formation of a new boundary, extends from under the {111} facet that formed a deep groove, while there is no boundary extending from the upper {111} plane. These results strongly indicate
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Fig. 1. Crystal/melt interface during unidirectional growth of mc-Si. The recording was started at time t = 0 s.
that a {111}Σ3 twin boundary was formed upon rapid growth at the deep groove. EBSP analysis was performed to identify the grain boundary characteristics and grain orientations. Fig. 3 shows (a) a scanning electron microscopy (SEM) image, (b) an image quality (IQ) map with colored grain boundaries, and (c) an orientation map for the TD direction
(crystal growth direction). We can easily identify the observation area shown in Fig. 1 because the remnant of the deep groove is visible in the SEM image, as shown in Fig. 3(a). Thus, the orientation analysis was performed around this area. Analysis of the grain boundary characteristics (Fig. 3(b)) confirmed that the new boundary, which was generated upon rapid crystallization at the deep groove, was a Σ3 twin
Fig. 2. Image of crystal/melt interface at t = 60 s and its schematic. The remnant of a deep groove is clearly visible in the crystal.
K. Fujiwara et al. / Scripta Materialia 133 (2017) 65–69
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Fig. 3. (a) SEM image of the sample. (b) IQ map with colored grain boundaries. A {111} Σ3 twin boundary and Σ27 grain boundary are colored red and yellow, respectively. (c) Orientation map for TD direction (crystal growth direction). (d) Schematic of twin boundary formation at grain boundary. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
boundary. In Fig. 3(c), the 3D octahedron lattice bounded by {111} planes of each grain were shown. The direction of each lattice reflects the orientation of each grain. It was confirmed that the boundary plane of newly formed Σ3 twin boundary was {111} plane, as indicated by red triangles in the 3D lattice images. The growth orientation of the upper grain was found to be 〈18 8 19〉, which will be important to estimate the undercooling at the interface later. Also, from Fig. 3(b) and (c), we can explain what happened during crystal growth, as illustrated in Fig. 3(d). As seen in the left panel in Fig. 3(d), at the beginning of growth (t = 0–4 s in Fig. 1), there were three grain boundaries in the observation area of the crystal, and only two grain boundary grooves were observed at the crystal/melt interface because the {111} Σ3 twin boundary did not form a groove, as we have reported previously [15]. It should be noted that a new crystal grain was formed at this {111}Σ3 twin boundary between t = 4 and 5.7 s, as seen in the orientation map in Fig. 3(c) (indicated by yellow), although the reason why the nucleation occurred at this position was not clarified. Thus, a random grain boundary formed which led to the formation of a grain boundary groove in this region of the crystal/melt interface (second figure from the left in Fig. 3(d)). This new groove deepened until rapid growth occurred (third figure from the left in Fig. 3(d)). When the melt in the deep groove
crystallized, a new {111}Σ3 twin boundary was formed on the {111} facet of the deep groove (right figure in Fig. 3(d)). Clearly, twin boundary generation was triggered by the formation of the grain boundary groove, in agreement with a theoretical prediction [13] and an experimental result [14]. Now, we consider how the crystal growth occurred at this groove. When the atoms in the melt at the groove crystallized on the {111} planes, there are two ways energetically, as schematically shown in the red box in Fig. 3(d). The one is that the atoms attach on the {111} plane with epitaxial configuration, which leads to the formation of no boundary, as shown in the left figure. The other one is that the atoms attach on the {111} plane with twin relationship (right figure), because the formation energy of Si {111} twin boundary is quite low, such as 30 mJ/m2 [17]. It seems that the twin boundary is easy to form at the crystal/melt interface when the crystal/melt interface has a {111} plane and there exists some amounts of driving force. Next, we discuss the conditions for twin boundary formation at the grain boundary groove. It was observed that the twin boundary was formed when rapid growth occurred at the deep grain boundary groove. This suggested that a large driving force (undercooling, ΔT) for crystallization assisted twin boundary formation. Thus, we will estimate the undercooling at the twin boundary formation. It was thought that
68
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growth on the {111} facet plane proceeded by two-dimensional (2D) nucleation [18]. On the other hand, Buta et al. suggested that the stepflow growth mode is stable at {111} facets at low undercooling, ΔT b 40 K, by non-equilibrium molecular dynamics simulations [19]. In our experiments, it seems that the undercooling at the growth was not so high, and thus, we will estimate the undercooling under the step-growth mode. An expression for the growth velocity (V) of stepgrowth mode is written as V¼
h vs l
ð1Þ
where h is the step height, l is the distance between two steps (a terrace length), and vs is the velocity of step described as vs = βsΔT. βs is the step kinetic constant. From the classical Wilson-Frenkel theory, the step kinetic constant βs is obtained as βs = 0.02 [m/(sK)] [19]. However,
Chernov [20] suggested that the value of βs obtained from WilsonFrenkel theory was much smaller than the experimental results of Voronkov [21], and Buta et al. also showed the value of βs was more than an order larger than 0.02 [m/(sK)] by molecular dynamic simulations [19]. In their simulations, it was shown that the step kinetic coefficient βs was strongly dependent on the distance between the steps (l), and βs reached to a plateau at a value of 0.7–0.8 [m/(sK)] for l N 50 Å. Fig. 4 shows traces of the moving crystal/melt interface and a plot of interface position versus time (x-t plot). Fig. 4(a) is a trace of the interface around the deep groove during rapid crystallization. We traced the interface at 0.1-s intervals (from t = 31.0 to 31.5 s). From Fig. 3(c), it was confirmed that the crystal/melt interface forming the groove was {111} plane. Here, we need to measure the growth velocity along the normal to the {111} plane, thus, the x-t plot was obtained along the dotted line in the trace figure. The growth velocity was estimated to be V ≈ 5.85 × 10−5 m/s by linear regression. Using Eq. (1) to estimate
Fig. 4. Traces of moving crystal/melt interface and plot of interface position versus time (x-t plot). (a) Trace around deep groove during rapid crystallization; (b) trace of entire observation area.
K. Fujiwara et al. / Scripta Materialia 133 (2017) 65–69
the undercooling, we obtained ΔT ≈ 1.3 × 10−3 K. For the estimation, h = 3.13 × 10−10 m [17], l = 5 × 10−9 m, and βs = 0.7 [m/(sK)] were used. Fig. 4(b) is the trace of the whole observation area, and the x-t plot was obtained by measuring the position of the interface along the dotted line in the trace figure. The growth velocity at this position was estimated to be V ≈ 9.5 × 10−6 m/s. From Fig. 3(c), it was found that the growth orientation at this position was 〈18 8 19〉. This plane is not the facet plane, therefore, a normal growth mode for a rough crystal/melt interface, which is expressed as V = βroughΔT: where βrough is a kinetic coefficient for the rough plane, might be considered. There were reports that the value of βrough was around 0.10 m/(sK) for Si {100} rough plane [17,19,22], although there is no date for {18 8 19} plane. Using the value of 0.10 m/(sK) to estimate the undercooling, we obtained ΔT ≈ 9.5 × 10− 5 K. If a step-growth mode was adapted for this plane, the undercooling would be estimated as ΔT ≈ 2.2 × 10− 4 K. The real value of undercooling might be 9.5 × 10−5 K b ΔT b 2.2 × 10−4 K. In this way, it was shown that the amount of undercooling in the melt at the deep groove was larger than that at the planar interface. In general, during the growth of mc-Si ingots, the temperature gradient is positive in the growth direction, as in the present study. Under these conditions, as the grain boundary groove deepens, the local undercooling at the groove increases, as estimated here. As the undercooling, i.e., the driving force for crystallization, increases, so does the probability of twin boundary formation. Indeed, the grain boundary groove that became the source of the twin boundary was also relatively deep in the study by Tsoutsouva et al. [14]. Thus, we conclude that the formation of the grain boundary groove is one of the main causes of twin boundary formation from grain boundaries during the growth of mc-Si ingots for solar cells. In summary, we observed twin boundary formation in a grain boundary groove at the crystal/melt interface during directional solidification of mc-Si. The grain boundary groove at the crystal/melt interface becomes the source of the {111} Σ3 twin boundary, because the grain boundary groove is formed by {111} facet planes. It was also shown that the local undercooling at the deep groove increases, which promotes twin boundary formation at the grain boundary groove.
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