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The five parameter grain boundary character distribution of polycrystalline silicon

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Abstract

The purpose of this paper is to describe the five-parameter grain boundary character distribution (GBCD) of polycrystalline silicon and compare it to distributions measured in metals and ceramics. The GBCD was determined from the stereological analysis of electron backscatter diffraction maps. The distribution of grain boundary disorientations is non-random and has peaks at 36°, 39°, 45°, 51°, and 60°. The axis-angle distribution reveals that most of the grain boundaries have misorientations around the [111], [110], and [100] axes. The most common grain boundary type (30 % number fraction) has a 60° misorientation around [111] and of these boundaries, the majority are twist boundaries. For other common boundaries, symmetric tilt configurations are preferred. The grain boundary character distribution of Si is distinct from those previously observed for metals and ceramics. The measured grain boundary populations are inversely correlated to calculated grain boundary energies available in the literature.

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References

  1. Bahrami A, Mohammadnejad S, Soleimaninezhad S (2013) Photovoltaic cells technology: principles and recent developments. Opt Quant Electron 45:161–197. doi:10.1007/s11082-012-9613-9

    Article  Google Scholar 

  2. Saga T (2010) Advances in crystalline silicon solar cell technology for industrial mass production. NPG Asia Mat 2:96–102. doi:10.1038/asiamat.2010.82

    Article  Google Scholar 

  3. Shah A, Torres P, Tscharner R, Wyrsch N, Keppner H (1999) Photovoltaic technology: the case for thin-film solar cells. Science 285:692–698. doi:10.1126/science.285.5428.692

    Article  Google Scholar 

  4. M Tanaka (2013) Recent progress in crystalline silicon solar cells. IEICE Electronics Express 10:1–12. doi:10.1587/elex.10.20132006

  5. J Chen, T Sekiguchi (2007) Carrier recombination activity and structural properties of small-angle grain boundaries in multicrystalline silicon.Jpn J Appl Phys Part 1 46:6489–6497. doi:10.1143/jjap.46.6489

    Google Scholar 

  6. Tsurekawa S, Kido K, Watanabe T (2007) Interfacial state and potential barrier height associated with grain boundaries in polycrystalline silicon. Mater Sci Eng A 462:61–67. doi:10.1016/j.msea.2006.02.471

    Article  Google Scholar 

  7. Wang ZJ, Tsurekawa S, Ikeda K, Sekiguchi T, Watanabe T (1999) Relationship between electrical activity and grain boundary structural configuration in polycrystalline silicon. Interface Sci 7:197–205. doi:10.1023/a:1008796005240

    Article  Google Scholar 

  8. B Chen, J Chen, T Sekiguchi, M Saito, K Kimoto (2009) Structural characterization and iron detection at Sigma 3 grain boundaries in multicrystalline silicon. J Appl Phys 105:113502. doi:10.1063/1.3129583

    Google Scholar 

  9. Chen J, Sekiguchi T, Yang D, Yin F, Kido K, Tsurekawa S (2004) Electron-beam-induced current study of grain boundaries in multicrystalline silicon.J Appl Phys 96:5490–5495. doi:10.1063/1.1797548

    Article  Google Scholar 

  10. Rohrer GS, Saylor DM, El Dasher B, Adams BL, Rollett AD, Wynblatt P (2004) The distribution of internal interfaces in polycrystals. Zeitschrift Fur Metallkunde 95:197–214

    Article  Google Scholar 

  11. Saylor DM, El-Dasher BS, Adams BL, Rohrer GS (2004) Measuring the five-parameter grain-boundary distribution from observations of planar sections. Metall Mater Trans A-Phys Metall Mat Sci 35:1981–1989

    Article  Google Scholar 

  12. Rohrer GS (2011) Measuring and interpreting the structure of grain-boundary networks. J Am Ceram Soc 94:633–646. doi:10.1111/j.1551-2916.2011.04384.x

    Article  Google Scholar 

  13. Kim CS, Hu Y, Rohrer GS, Randle V (2005) Five-parameter grain boundary distribution in grain boundary engineered brass. Scripta Mater 52:633–637. doi:10.1016/j.scriptamat.2004.11.025

    Article  Google Scholar 

  14. Li J, Dillon SJ, Rohrer GS (2009) Relative grain boundary area and energy distributions in nickel. Acta Mater 57:4304–4311. doi:10.1016/j.actamat.2009.06.004

    Article  Google Scholar 

  15. Rohrer GS, Holm EA, Rollett AD, Foiles SM, Li J, Olmsted DL (2010) Comparing calculated and measured grain boundary energies in nickel. Acta Mater 58:5063–5069. doi:10.1016/j.actamat.2010.05.042

    Article  Google Scholar 

  16. Rohrer GS, Randle V, Kim CS, Hu Y (2006) Changes in the five-parameter grain boundary character distribution in alpha-brass brought about by iterative thermomechanical processing. Acta Mater 54:4489–4502. doi:10.1016/j.actamat.2006.05.035

    Article  Google Scholar 

  17. Saylor DM, El Dasher BS, Rollett AD, Rohrer GS (2004) Distribution of grain boundaries in aluminum as a function of five macroscopic parameters. Acta Mater 52:3649–3655. doi:10.1016/j.actamat.2004.04.018

    Article  Google Scholar 

  18. Beladi H, Rohrer GS (2013) The relative grain boundary area and energy distributions in a ferritic steel determined from three-dimensional electron backscatter diffraction maps. Acta Mater 61:1404–1412. doi:10.1016/j.actamat.2012.11.017

    Article  Google Scholar 

  19. Liu X, Choi D, Beladi H, Nuhfer NT, Rohrer GS, Barmak K (2013) The five-parameter grain boundary character distribution of nanocrystalline tungsten. Scripta Mater 69:413–416. doi:10.1016/j.scriptamat.2013.05.046

    Article  Google Scholar 

  20. Kim CS, Massa TR, Rohrer GS (2008) Interface character distributions in WC-Co composites. J Am Ceram Soc 91:996–1001. doi:10.1111/j.1551-2916.2007.02226.x

    Article  Google Scholar 

  21. Randle V, Rohrer GS, Hu Y (2008) Five-parameter grain boundary analysis of a titanium alloy before and after low-temperature annealing. Scripta Mater 58:183–186. doi:10.1016/j.scriptamat.2007.09.044

    Article  Google Scholar 

  22. Dillon SJ, Helmick L, Miller HM et al (2011) The orientation distributions of lines, surfaces, and interfaces around three-phase boundaries in solid oxide fuel cell cathodes. J Am Ceram Soc 94:4045–4051. doi:10.1111/j.1551-2916.2011.04673.x

    Article  Google Scholar 

  23. Dillon SJ, Rohrer GS (2009) Characterization of the grain-boundary character and energy distributions of Yttria using automated serial sectioning and EBSD in the FIB. J Am Ceram Soc 92:1580–1585. doi:10.1111/j.1551-2916.2009.03064.x

    Article  Google Scholar 

  24. Saylor DM, Morawiec A, Adams BL, Rohrer GS (2000) Misorientation dependence of the grain boundary energy in magnesia. Interface Sci 8:131–140

    Article  Google Scholar 

  25. Saylor DM, Morawiec A, Rohrer GS (2002) Distribution and energies of grain boundaries in magnesia as a function of five degrees of freedom. J Am Ceram Soc 85:3081–3083

    Article  Google Scholar 

  26. Saylor DM, Morawiec A, Rohrer GS (2003) Distribution of grain boundaries in magnesia as a function of five macroscopic parameters. Acta Mater 51:3663–3674. doi:10.1016/S1359-6454(03)00181-2

    Article  Google Scholar 

  27. Rohrer G (2011) Grain boundary energy anisotropy: a review. J Mater Sci 46:5881–5895. doi:10.1007/s10853-011-5677-3

    Article  Google Scholar 

  28. HJ Ryu, DB Fortner, GS Rohrer, MR Bockstaller (2012) Measuring relative grain-boundary energies in block-copolymer microstructures. Phys Rev Lett 108:107801. doi:10.1103/PhysRevLett.108.107801

    Google Scholar 

  29. Wright SI, Larsen RJ (2002) Extracting twins from orientation imaging microscopy scan data. J Microsc-Oxf 205:245–252. doi:10.1046/j.1365-2818.2002.00992.x

    Article  Google Scholar 

  30. Brandon DG (1966) Structure of high-angle grain boundaries. Acta Metall 14:1479–1484

    Article  Google Scholar 

  31. Miyazawa K, Iwasaki Y, Ito K, Ishida Y (1996) Combination rule of Sigma values at triple junctions in cubic polycrystals. Acta Cryst A 52:787–796. doi:10.1107/s0108767396005934

    Article  Google Scholar 

  32. Randle V, Rohrer GS, Miller HM, Coleman M, Owen GT (2008) Five-parameter grain boundary distribution of commercially grain boundary engineered nickel and copper. Acta Mater 56:2363–2373. doi:10.1016/j.actamat.2008.01.039

    Article  Google Scholar 

  33. Rohrer GS, Li J, Lee S, Rollett AD, Groeber M, Uchic MD (2010) Deriving grain boundary character distributions and relative grain boundary energies from three-dimensional EBSD data. Mater Sci Technol 26:661–669. doi:10.1179/026708309X12468927349370

    Article  Google Scholar 

  34. Kohyama M, Yamamoto R, Doyama M (1986) Reconstructed structures of symmetrical (011) tilt grain-boundaries in silicon. Phys Status Solidi B 138:387–397. doi:10.1002/pssb.2221380202

    Article  Google Scholar 

  35. Paxton AT, Sutton AP (1988) A simple theoretical approach to grain-boundaries in silicon. J Phys C 21:L481–L488. doi:10.1088/0022-3719/21/15/001

    Article  Google Scholar 

  36. Paxton AT, Sutton AP (1989) A tight-binding study of grain boundaries in silicon. Acta Metall 37:1693–1715. doi:10.1016/0001-6160(89)90056-4

    Article  Google Scholar 

  37. S von Alfthan, PD Haynes, K Kaski, AP Sutton (2006) Are the structures of twist grain boundaries in silicon ordered at 0 K?. Phys Rev Lett 96:055505. doi:10.1103/PhysRevLett.96.055505

  38. Dillon SJ, Rohrer GS (2009) Mechanism for the development of anisotropic grain boundary character distributions during normal grain growth. Acta Mater 57:1–7. doi:10.1016/j.actamat.2008.08.062

    Article  Google Scholar 

  39. Gruber J, George DC, Kuprat AP, Rohrer GS, Rollett AD (2005) Effect of anisotropic grain boundary properties on grain boundary plane distributions during grain growth. Scripta Mater 53:351–355. doi:10.1016/j.scriptamat.2005.04.004

    Article  Google Scholar 

  40. Fujiwara K, Tsumura S, Tokairin M et al (2009) Growth behavior of faceted Si crystals at grain boundary formation. J Cryst Growth 312:19–23. doi:10.1016/j.jcrysgro.2009.09.055

    Article  Google Scholar 

  41. Tandjaoui A, Mangelinck-Noel N, Reinhart G, Billia B, Guichard X (2013) Twinning occurrence and grain competition in multi-crystalline silicon during solidification. CR Phys 14:141–148. doi:10.1016/j.crhy.2012.12.001

    Article  Google Scholar 

  42. Kohyama M (2002) Computational studies of grain boundaries in covalent materials. Modell Simul Mater Sci Eng 10:R31–R39. doi:10.1088/0965-0393/10/3/202

    Article  Google Scholar 

  43. Kohyama M, Yamamoto R, Doyama M (1986) Structures and energies of symmetrical 011 tilt grain boundaries in silicon. Phys Status Solidi B-Basic Res 137:11–20. doi:10.1002/pssb.2221370102

    Article  Google Scholar 

  44. Phillpot SR, Wolf D (1989) Structure-energy correlation for grain boundaries in silicon. Philos Mag A-Phys Condens Matter Struct Defects Mech Prop 60:545–553

    Google Scholar 

  45. Kohyama M (1987) Structures and energies of symmetical <001> tilt grain-boudaries in silicon. Phys Status Solidi B 141:71–83. doi:10.1002/pssb.2221410106

    Article  Google Scholar 

  46. Kohyama M, Yamamoto R, Doyama M (1986) Energies and structures of (111) coinciendence twist boudnaries in 3C-SiC, diamond, and silicon. Phys Status Solidi B 136:31–36. doi:10.1002/pssb.2221360103

    Article  Google Scholar 

  47. Kohyama M, Yamamoto R (1994) Tight-binding study of grain-boundaries in Si – energies and atomic structure of twist grain-boundies. Phys Rev B 49:17102–17117. doi:10.1103/PhysRevB.49.17102

    Article  Google Scholar 

  48. Cleri F (2001) Atomic and electronic structure of high-energy grain boundaries in silicon and carbon. Comput Mater Sci 20:351–362. doi:10.1016/s0927-0256(00)00194-4

    Article  Google Scholar 

  49. Cleri F, Keblinski P, Colombo L, Phillpot SR, Wolf D (1998) Correlation between atomic structure and localized gap states in silicon grain boundaries. Phys Rev B 57:6247–6250. doi:10.1103/PhysRevB.57.6247

    Article  Google Scholar 

  50. Keblinski P, Phillpot SR, Wolf D, Gleiter H (1996) Thermodynamic criterion for the stability of amorphous intergranular films in covalent materials. Phys Rev Lett 77:2965–2968. doi:10.1103/PhysRevLett.77.2965

    Article  Google Scholar 

  51. Keblinski P, Phillpot SR, Wolf D, Gleiter H (1997) On the thermodynamic stability of amorphous intergranular films in covalent materials. J Am Ceram Soc 80:717–732

    Article  Google Scholar 

  52. Keblinski P, Wolf D, Phillpot SR, Gleiter H (1998) Role of bonding and coordination in the atomic structure and energy of diamond and silicon grain boundaries. J Mater Res 13:2077–2099. doi:10.1557/jmr.1998.0292

    Article  Google Scholar 

  53. S Von Alfthan, K Kaski, AP Sutton (2007) Molecular dynamics simulations of temperature-induced structural transitions at twist boundaries in silicon..Phys Rev B 76:245317. doi:10.1103/PhysRevB.76.245317

  54. Tarnow E, Dallot P, Bristowe PD, Joannopoulos JD, Francis GP, Payne MC (1990) Structural complexity in grain-boudaries with covalent bounding. Phys Rev B 42:3644–3657. doi:10.1103/PhysRevB.42.3644

    Article  Google Scholar 

  55. Cantwell PR, Tang M, Dillon SJ, Luo J, Rohrer GS, Harmer MP (2014) Grain boundary complexions. Acta Mater 62:1–48. doi:10.1016/j.actamat.2013.07.037

    Article  Google Scholar 

  56. Mattheiss LF, Patel JR (1981) Electronic stacking-fault states in silicon. Phys Rev B 23:5384–5396. doi:10.1103/PhysRevB.23.5384

    Article  Google Scholar 

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Acknowledgements

The work at Carnegie Mellon was supported by the MRSEC program of the National Science Foundation under Award Number DMR-0520425. S.R. Acknowledges the Higher Educational Strategic Scholarship for Frontier Research Network from The Commission on Higher Education, Thailand. All of the authors acknowledge the assistance of Prof. George Rozgonyi of NCSU.

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Author notes

  1. Yohan Yoon

    Present address: National Institute of Standards and Technology, 100 Bureau Dr., Gaithersburg, MD, 20899, USA

  2. Sutatch Ratanaphan

    Present address: Department of Tool and Materials Engineering, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd, Thung Khru, Bangkok, 10140, Thailand

Authors and Affiliations

  1. Department of Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213, USA

    Sutatch Ratanaphan & Gregory S. Rohrer

  2. Department of Materials Science and Engineering, North Carolina State University, 911 Partners Way, Raleigh, NC, 27695, USA

    Yohan Yoon

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  1. Sutatch Ratanaphan
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Correspondence to Gregory S. Rohrer.

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Ratanaphan, S., Yoon, Y. & Rohrer, G.S. The five parameter grain boundary character distribution of polycrystalline silicon. J Mater Sci 49, 4938–4945 (2014). https://doi.org/10.1007/s10853-014-8195-2

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