3D visualization of growth interfaces in cast Si ingot using inclusions distribution

Journal of Crystal Growth 535 (2020) 125535

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Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro

3D visualization of growth interfaces in cast Si ingot using inclusions distribution

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Soichiro Kamibeppua, , Patricia Krenckelb, Theresa Trötschlerb, Adam Hessb, Stephan Riepeb, Noritaka Usamia a b

Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Japan Fraunhofer Institute for Solar Energy Systems ISE, Heidenhofstrasse 2, D-79110 Freiburg, Germany

A R T I C LE I N FO

A B S T R A C T

Communicated by Pierre Müller

We propose a method of three-dimensional (3D) visualization of growth interfaces in crystalline ingots prepared by directional solidification and apply the method to cast silicon ingot for solar cells. The method consists of dispersing inclusions along with the growth interface by insertion of a quartz rod followed by measuring inclusions distribution by an infrared brick inspection system. Then, inclusions distribution can be visualized in 3D, which allows extracting growth interfaces as planes. By fitting the plane with a simple polynomial expression, its macroscopic shape and local gradient can be estimated. The method yields us the local changes in growth interfaces and thus contributes to the development of the crystal growth method for high-quality ingots.

Keywords: A1. Characterization A1. Interfaces A2. Growth from melt A2. Industrial crystallization B2. Semiconducting silicon B3. Solar cells

1. Introduction The shape of growth interfaces during directional solidification depends on temperature distribution and velocity of solidification [1]. A flat growth interface is generally suitable to obtain a homogeneous ingot to produce wafers with controlled properties by slicing the ingot perpendicular to the solidification direction. In addition, a flat growth interface has less stress to multiply dislocations. On the other hand, some scientists argue that convex growth interfaces are preferable to obtain high-quality ingots because some grain boundaries propagate perpendicularly with the growth surface [2]. Hence, in any case, controlling the shape of growth interfaces during crystal growth is of crucial importance to improve the quality of the crystalline ingot, and visualization of growth interfaces will help to realize better control of the growth process. Striation patterns, which can be intentionally introduced during growth by delta doping of impurities, are widely used to visualize growth interfaces. X-ray topography technique or lateral photovoltage scanning measurement is used to get growth interfaces of crystalline ingots with striation patterns [3–6]. This method requires cutting of the ingots followed by etching to obtain striation patterns, and only twodimensional (2D) visualization has been achieved. For better control of the growth interface, three-dimensional (3D) visualization with simplified sample preparation is desired so that we could acquire a detailed shape of the growth interface. ⁎

In this paper, we report on our attempt for 3D visualization of the growth interface in a cast silicon ingot grown by directional solidification. We chose a casted Si ingot due to a great demand in the photovoltaic market [7,8] to improve crystalline quality while keeping lower manufacturing cost than Czochralski silicon. We combine dispersion of inclusions along with the growth interface and inspection of their distribution, and show that a detailed 3D shape of the growth interfaces can be obtained from bricks with 156 mm edge length. 2. Method 2.1. Approach In cast Si ingots, there are many inclusions such as Si3N4 and SiC. Si3N4 inclusions are caused by silicon nitride layers that were coated on the crucibles to avoid sticking of the silica crucibles with the cast Si ingots, and SiC inclusions are caused by the reaction of liquid silicon and CO gas which occurs in a furnace by the reaction of O2 from the crucible with the graphite parts of the furnace [9–13]. These inclusions can be dispersed along with the growth interface by inserting a quartz rod into the liquid silicon also used to check the progress of crystal growth. The quartz rod was inserted at certain time steps. Since this process results in changing the heat transport of liquid silicon, the temperature gradients in the melt and the convection were also changed, which led to a change in growth velocity. Therefore,

Corresponding author. E-mail address: [email protected] (S. Kamibeppu).

https://doi.org/10.1016/j.jcrysgro.2020.125535 Received 20 December 2019; Received in revised form 21 January 2020; Accepted 28 January 2020 Available online 30 January 2020 0022-0248/ © 2020 Elsevier B.V. All rights reserved.

Journal of Crystal Growth 535 (2020) 125535

S. Kamibeppu, et al.

Fig. 1. Standard IR cross-section images of contiguous 4 bricks in an mc-Si ingot. On the top left, there are strange contrasts, which are not polished parts on the brick surface.

be output as 3D coordinates in the mc-Si bricks.

inclusions get caught by the growing interface and freeze in the layers. Hence, it is thought that the layers are along with growth interfaces and measuring inclusions distribution makes it possible to know the shape of interfaces. Fig. 1 shows cross-sectional images in contiguous four mcSi bricks measured by the Intego Orion HighRes IR brick inspection system [14]. This image is a standard IR image and spatial resolution is ~90 μm. Black parts reflect the distribution of inclusions. It is seen that inclusions in the cross-section are distributed into lines that are roughly perpendicular to the expected growth direction. This means that inclusions are distributed into layers in the cast Si ingot in 3D.

2.3. 3D visualization Based on a large quantity of data from the HighRes IR measurement, growth interfaces were visualized in 3D as described in the following. First of all, the positions of high-density inclusions were extracted from the data and plotted in 3D. The position of high-density inclusions was defined as the point where the distance between neighboring inclusions is within 54 μm. This is because the amount of data was too big and inclusions distribution was most clearly observed at threshold 54 μm. Secondly, the plots of bricks were connected according to Fig. 2. Then, as plots were distributed into planes, the planes were extracted by a 2D polynomial fit with the polynomial of the fifth degree described in (1) [15]. We optimized the degree of the fitting equation to avoid overlearning at a higher degree. In fact, by fitting with the polynomial of the sixth or seventh degree, we observed non smooth plane at some parts, which does not obviously represent inclusions distribution. Ci, i = 1,2, 14, are coefficients Finally, gradients of the planes were calculated as described in (2). ∇z is the gradient for the z-axis of the position (x,y,z) on the plane.

2.2. Measuring inclusions distribution A G6 size high-performance (HP) mc-Si ingot (936 mm×936mm×290 mm) was used for inspection. The ingot was divided into 36 bricks (156 mm × 156 mm × 290 mm) and named as shown in Fig. 2. HighRes IR was used for measuring inclusions distribution in the brick. The spatial resolution of the measurement is ~18 μm. The inclusions distribution in brick was measured with changing the focus plane of the infrared camera from front to back of the brick resulting in 45 images. In addition, a brick was measured from two directions, front to back and left to right. Then, from IR images measured by this process, the inclusions are detected using an image processing algorithm that checks for sharp contrast changes. By this inspection system, inclusions can be identified and their positions can

z (x , y ) = C0 + C1 x + C2 y + C3 xy + C4 x 2 + C5 y 2 + C6 x 2y + C7 xy 2 + C8 x 3 + C9 y 3 + C10 x 4 + C11 xy 3 + C12 x 2y 2 + C13 xy 3 + C14 y 4 2

2

|∇z| =

(1)

⎛ ∂z ⎞ + ⎛ ∂z ⎞ ⎝ ∂x ⎠ ⎝ ∂y ⎠ ⎜

⎟

(2)

A1

A2

A3

A4

A5

A6

B1

B2

B3

B4

B5

B6

C1

C2

C3

C4

C5

C6

D1

D2

D3

D4

D5

D6

All these calculations were performed on a laptop computer equipped with a CPU: Intel Core i5–5200U 2.20 GHz, RAM: 8 GB, GPU: Intel HD Graphics 5500 (onboard graphics), OS: Windows 10 Home. In this laptop, Anaconda3 (open source distribution of the Python programing language) and Matplotlib 3.1.1 (library for visualizing depiction of the graph) were installed for using Python and visualization, respectively.

E1

E2

E3

E4

E5

E6

3. Results and discussion

F1

F2

F3

F4

F5

F6

Fig. 3 shows the distribution of inclusions for four continuous bricks that are connected from C4 to F4. Also in Fig. 3, we can see that inclusions are distributed into layers and the layers are connected from C4 to F4. The layers would correspond to growth interfaces. Since planes around 170 mm and 200 mm height were seen clearly in

Fig. 2. Nomenclature of bricks cut from a G6-sized mc-Si ingot. Bricks C4 to F4 were used in this evaluation. 2

Journal of Crystal Growth 535 (2020) 125535

S. Kamibeppu, et al.

Fig. 3. Inclusions distribution of contiguous 4 bricks that are connected from C4 to F4 (a) views from oblique above, (b) view from the side. The mass of the plots goes vertically between bricks are not the actual inclusions, but the edge effect. The contrast of inclusions distribution is due to the number of plots (inclusions).

Fig. 4. Extracting the planes from the plots of inclusions distribution by using curved surface fitting. The height of red parts is relatively higher and the height of blue parts is relatively lower on the planes. The interfaces are asymmetric because these are parts of an ingot as shown in Fig. 2.

particular, those planes were fitted in Fig. 4 and extracted in Fig. 5. In Figs. 4 and 5, the height of red parts is relatively higher and the height of blue parts is relatively lower in relation to the mean value. It is seen that the shape of the upper plane and the shape of the lower plane are

not the same. This means that the shape of the growth interface has changed during crystal growth. Finally, the gradient of the planes was calculated and is shown in Fig. 6. Red parts have relatively high gradient and blue parts have relatively low gradient. This means that red 3

Journal of Crystal Growth 535 (2020) 125535

S. Kamibeppu, et al.

Fig. 5. Planes that visualize the growth interface at two points in time viewed from two directions.

parts were heavily stressed because high stress is applied to the parts where have a high gradient, and dislocations are easy to occur there. This figure should be emphasized that local changes in growth interfaces, which cannot be seen in 2D, can be visualized. It is useful to know local temperature distribution during crystal growth, and the local shape of growth interfaces would be controlled by controlling the temperature in a crucible. As shown above, we succeeded in extracting approximate planes of inclusions distribution. The interface was extracted at the height at which it is easy to observe that inclusions are distributed into a plane. In principle, the interface can be extracted at any height by the fitting range if it is a region where a large number of inclusions are present. It should be discussed how accurately the plane corresponds to the growth interface. First of all, we could not detect inclusions smaller than ~18 μm due to the spatial resolution of the inspection system. However, there are many smaller inclusions in mc-Si ingot, which can be seen only under an IR-microscope. Hence, it is difficult to measure them on a macro-scale and to get the growth interface on a micro-scale now. Then, we used a polynomial of the fifth degree to extract planes. Although this is also useful to obtain macroscopic shape, it might smooth out sharp local changes, which cannot be fitted by the equation. Other equations might be better applied depending on the shape of planes. It is also noted that the amount of the temperature drops by inserting the quartz rod would be different depending on the position of

Fig. 6. The gradient of the planes in Fig. 6. Red parts have relatively high gradient and blue parts have relatively low gradient. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Journal of Crystal Growth 535 (2020) 125535

S. Kamibeppu, et al.

interests or personal relationships that could have appeared to influence the work reported in this paper.

the interface and amount of the melt. This might result in anomalous growth to lead to uncontrolled inclusions distribution. Fortunately, this did not happen in our case as evident by inclusions distribution along the plane in the whole ingot and it is assumed that changes in growth velocity at all regions. In spite of these facts, we could conclude that we succeed in 3D visualization of the growth interfaces in cast Si ingot prepared by directional solidification as planes with dispersed inclusions. These planes yield information about the local changes of growth interfaces, which could play an important role in getting temperature distributions during crystal growth as well as the stress applied to the cast Si ingot, and could also contribute to improving the precision of simulations such as CGSim [16,17]. Furthermore, fundamental understanding in generation mechanisms of crystal defects could be accelerated by combing them with 3D visualization of dislocation clusters [18] and analysis of grain structure evolution [19,20]. This method to visualize growth interfaces in 3D will enable the development of the crystal growth method of high-quality crystals by controlling growth interfaces.

Acknowledgments This work was supported by Japan Science and Technology Agency (JST), CREST, Grant Number JPMJCR17J1, and by the German Federal Ministry for Economic Affairs and Energy (FKZ 0325823 and 0324034). The authors sincerely acknowledge Mr. Tetsuro Muramatsu, Dr. Tetsuya Matsumoto, Dr. Kentaro Kutsukake, Dr. Takuto Kojima and Dr. Hiroaki Kudo for the fruitful discussion. References [1] H. Miyazawa, L. Liu, S. Hisamatsua, K. Kakimoto, J. Cryst. Growth 310 (2008) 1034–1039. [2] F.M. Kiessling, Freiberger Silicon Days, Freiberg, Germany, June 15-17, 2011. [3] K. Kakimoto, M. Eguchi, H. Watanabe, T. Hibiya, J. Cryst. Growth 91 (1988) 509–514. [4] N.V. Abrosimov, A. Ludge, H. Riemann, W. Schröder, J. Cryst. Growth 237–239 (2002) 356–360. [5] A. Tandjaoui, N. Mangelinck-Noël, G. Reinhart, J.-J. Furter, B. Billia, T. Lafford, J. Baruchel, X. Guichard, Energ. Proc. 27 (2012) 82–87. [6] F.-M. Kiessling, F. Büllesfeld, N. Dropka, Ch. Frank-Rotsch, M. Müller, P. Rudolph, J. Cryst. Growth 360 (2012) 81–86. [7] C.W. Lan, C.F. Yang, A. Lan, M. Yang, A. Yu, H.P. Hsu, B. Hsu, C. Hsu, Cryst. Eng. Comm. 18 (2016) 1474. [8] R.N. Andrews, S.J. Clarson, Silicon 7 (2015) 303. [9] A. Lotnyk, J. Bauer, O. Breitenstein, H. Blumtritt, Sol. Energ. Mat. Sol. C. 92 (2008) 1236. [10] D. Camel, B. Drevet, V. Brizé, F. Disdier, E. Cierniak, N. Eustathopoulos, Acta Mater. 129 (2017) 415–427. [11] G. Dua, L. Zhou, P. Rossetto, Y. Wan, Sol. Energ. Mat. Sol. C 91 (2007) 1743–1748. [12] K. Jiptner, H. Harada, Y. Miyamura, M. Fukuzawa, T. Sekiguchi, Mater. Sci. Forum 725 (2012) 247. [13] H.J. Möller, T. Kaden, S. Scholz, S. Würzner, Appl. Phys. A Mater. Sci. Process. 96 (2009) 207. [14] A. Hess, P. Krenckel, T. Trötschler, T. Fehrenbach, S. Riepe, EU PVSEC 35, Brussels, Belguim, Septmber 24–28, 2018. [15] X. Zhang, H. Li, Z. Cheng, ASIAGRAPH 2008, Tokyo, Japan, October 23-26, 2008. [16] V.V. Kalaeva, D.P. Lukanina, V.A. Zabelina, Yu.N. Makarovb, J. Virbulisc, E. Dornbergerc, W. von Ammonc, Mat. Sci. Semicon. Proc. 5 (2003) 369–373. [17] A. Boucetta, K. Kutsukake, T. Kojima, H. Kudo, T. Matsumoto, N. Usami, Appl. Phys. Exp. 12 (2019) 12. [18] Y. Hayama, T. Matsumoto, T. Muramatsu, K. Kutsukake, H. Kudo, N. Usami, Solar Energy Mat. Solar Cells 189 (2019) 239–246. [19] T. Strauch, M. Demant, P. Krenckel, S. Riepe, S. Rein, J. Cryst. Growth 454 (2016) 147–155. [20] T. Strauch, M. Demant, P. Krenckel, S. Riepe, S. Rein, Solar Energy Mat. Solar Cells 182 (2018) 105–112.

4. Conclusion We proposed a method of visualizing growth interfaces in 3D by using inclusions distribution and applied the method to a cast Si ingot. By using infrared brick inspection system to measure inclusions distribution and fitting to extract planes, growth interfaces could be visualized successfully in 3D, which allows us to acquire local changes in growth interfaces. This 3D visualization of the growth interface could contribute to the development of the growth method of high-quality crystals with various materials. CRediT authorship contribution statement Soichiro Kamibeppu: Software, Formal analysis, Writing - original draft, Visualization. Patricia Krenckel: Writing - review & editing, Project administration. Theresa Trötschler: Software, Writing - review & editing. Adam Hess: Investigation, Resources, Writing - review & editing, Project administration. Stephan Riepe: Conceptualization, Writing - review & editing, Supervision. Noritaka Usami: Writing review & editing, Supervision, Funding acquisition. Declaration of Competing Interest The authors declare that they have no known competing financial

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