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Dislocation-controlled microscopic mechanical phenomena in single crystal silicon under bending stress at room temperature

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Abstract

Silicon is widely used within energy, electro-mechanical, environmental devices by nanostructural control. As silicon parts constitute structural components whose size is ever decreasing, it is critical to understand the mechanical properties of single crystal silicon from precise measurements of load and displacement using microscopic sample in sub-micron and macroscopic scales. Here, the mechanical properties of single crystal silicon were precisely evaluated by bending tests at room temperature using microcantilever beam specimens having a several micron size. The microcantilever beam specimens were prepared using a focused ion beam technique, followed by loading the tip of the specimens. The smaller specimens deformed nonlinearly and then fractured. The unloaded specimen after nonlinear deformation showed permanent strain and many dislocations close to the region where high tensile stress was applied. This means that the nonlinear stress–strain relationship in the very high bending stress is determined by plastic deformation controlled by dislocation despite occurring at room temperature. The bending strength increased with a decrease in specimen size, and the smallest specimens had close to ideal strength. The size of the region where the dislocations accumulated in high density corresponded to the flaw size estimated from the fracture mechanics. This means that the bending strength of the microcantilever beam specimens of silicon is dominated by newly generated defects resulting from dislocations; in other words, the size effect of bending strength of silicon at the micrometer scale is controlled by the accumulation of newly formed dislocations because the dense dislocation region should be lower in a smaller-sized specimen.

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References

  1. Chen W, Liu Y, Wu J, Chen Q, Zhao Y, Wang Y, Du X (2019) High-efficient solar cells textured by Cu/Ag-cocatalyzed chemical etching on diamond wire sawing multicrystalline silicon. ACS Appl Mater Interfaces 11:10052–10058

    CAS  Google Scholar 

  2. Xu ZL, Liu X, Luo Y, Zhou L, Kim JK (2017) Nanosilicon anodes for high performance rechargeable batteries. Prog Mater Sci 90:1–44

    Google Scholar 

  3. Harpak N, Davidi G, Schneier D, Menkin S, Mados E, Golodnitsky D, Peled E, Patolsky F (2019) Large-scale self-catalyzed spongelike silicon nano-network-based 3D anodes for high-capacity lithium-ion batteries. Nano Lett 19:1944–1954

    CAS  Google Scholar 

  4. Pandolfi S, Lecuna CR, Godec YL, Baptiste B, Menguy N, Lazzeri M, Gervais C, Spektor K, Crichton WA, Kurakevych OO (2018) Nature of hexagonal silicon forming via high-pressure synthesis: nanostructured hexagonal 4H polytype. Nano Lett 18:5989–5995

    CAS  Google Scholar 

  5. Asano K, Tang H, Chen CY, Nagoshi T, Chang TFM, Yamane D, Konishi T, Machida K, Masu K, Sone M (2018) Promoted bending strength in micro-cantilevers composed of nanograined gold toward MEMS applications. Microel Eng 196:20–24

    CAS  Google Scholar 

  6. Tang H, Hashigata K, Chang TFM, Chen CY, Nagoshi T, Yamane D, Konishi T, Machida K, Masu K, Sone M (2018) Sample size effect on micro-mechanical properties of gold electroplated with dense carbon dioxide. Surf Coat Technol 350:1065–1070

    CAS  Google Scholar 

  7. Dehm G, Jaya BN, Raghavan R, Kirchlechner C (2018) Overview on micro- and nanomechanical testing: new insights in interface plasticity and fracture at small length scales. Acta Mater 142:248–282

    CAS  Google Scholar 

  8. Ramezany A, Pourkamali S (2018) Ultrahigh frequency nanomechanical piezoresistive amplifiers for direct channel-selective receiver front-ends. Nano Lett 18:2551–2556

    CAS  Google Scholar 

  9. Lu YW, Shieh J, Tsai FY (2016) Induction of ferroelectricity in nanoscale ZrO2/HfO2 bilayer thin films on Pt/Ti/SiO2/Si substrates. Acta Mater 115:68–75

    CAS  Google Scholar 

  10. Schlich FF, Spolenak R (2016) Size- and phase-dependent mechanical properties of ultrathin Si films on polyimide substrates. Acta Mater 110:122–130

    CAS  Google Scholar 

  11. Cook RF (2006) Strength and sharp contact fracture of silicon. J Mater Sci 41:841–872. https://doi.org/10.1007/s10853-006-6567-y

    Article  CAS  Google Scholar 

  12. Jadaan OM, Nemeth NN, Bagdahn J, Sharpe WN Jr (2003) Probabilistic Weibull behavior and mechanical properties of MEMS brittle materials. J Mater Sci 38:4087–4113. https://doi.org/10.1023/A:1026317303377

    Article  CAS  Google Scholar 

  13. Hauch JA, Holland D, Marder MP, Swinney HL (1999) Dynamic fracture in single crystal silicon. Phys Rev Lett 82(19):2823–2826

    Google Scholar 

  14. Lawn B (1975) Fracture in brittle solids. Cambridge University Press, Cambridge

    Google Scholar 

  15. Mier JGMV, Vliet MRAV (2003) Influence of microstructure of concrete on size/scale effects in tensile fracture. Eng Fract Mech 70:2281–2306

    Google Scholar 

  16. Östlund F, Malyska KR, Leifer K, Hale L, Tang Y, Ballarini R, Gerberich W, Michler J (2009) Brittle-to-ductile transition in uniaxial compression of silicon pillars at room temperature. Adv Funct Mater 19:2439–2444

    Google Scholar 

  17. Wang YC, Zhang W, Wang LY, Zhuang Z, Ma E, Li J, Shan ZW (2016) In situ TEM study of deformation-induced crystalline-to-amorphous transition in silicon. NPG Asia Mater 8:e291

    CAS  Google Scholar 

  18. Wessel K, Alexsander H (1977) On the mobility of partial dislocations in silicon. Philos Mag 35(6):1523–1536

    CAS  Google Scholar 

  19. Nishino Y, Saka H, Imura T (1984) Temperature dependence of friction force acting on dislocations in silicon crystals. J Mater Sci 19:245–253. https://doi.org/10.1007/BF02403131

    Article  CAS  Google Scholar 

  20. Izumi S, Ohta H, Takahashi C, Suzuki T, Saka H (2010) Shuffle-set dislocation nucleation in semiconductor silicon device. Philos Mag Lett 90(10):707–714

    CAS  Google Scholar 

  21. Castaing J, Veyssiere P, Kubin L, Rabier J (1981) The plastic deformation of silicon between 300 and 600 °C. Philos Mag 44(6):1407–1413

    CAS  Google Scholar 

  22. Okuno T, Saka H (2013) Electron microscope study of dislocations introduced by deformation in a Si between 77 and 873 K. J Mater Sci 48:115–124. https://doi.org/10.1007/s10853-012-6860-x

    Article  CAS  Google Scholar 

  23. Asaoka K, Umeda T, Arai S, Saka H (2005) Direct evidence for shuffle dislocations in Si activated by indentations at 77K. Mater Sci Eng A 400–401:93–96

    Google Scholar 

  24. Ray I, Cockayne D (1971) The dissociation of dislocations in silicon. Proc R Soc A 325:543–554

    CAS  Google Scholar 

  25. Rabier J (2007) High-stress plasticity and the core structures of dislocations in silicon. Phys Stat Sol 204(7):2248–2255

    CAS  Google Scholar 

  26. Saka H, Yamamoto Y, Arai S, Kuroda K (2006) In-situ TEM observation of transformation of dislocations from shuffle to glide sets in Si under supersaturation of interstitials. Philos Mag 86:4841–4850

    CAS  Google Scholar 

  27. William WG, Douglas DS, Aaron RB, Natalia IT (2011) A brittleness transition in silicon due to scale. J Mater Res 27(3):552–561

    Google Scholar 

  28. Elhebeary M, Saif MTA (2018) A novel MEMS stage for in situ thermomechanical testing of single crystal silicon microbeams under bending. Extreme Mech Lett 23:1–8

    Google Scholar 

  29. Balila NJ, Jeffrey MW, Juri W, James PB, Rafael S, Johann M, Christoph K, Gerhard D (2016) Microscale fracture behavior of single crystal silicon beams at elevated temperatures. Nano Lett 16:7597–7603

    Google Scholar 

  30. Wang B, Zhang Z, Chang K, Cui J, Rosenkranz A, Yu J, Lin CT, Chen G, Zang K, Luo J, Jiang N, Guo D (2018) New deformation-induced nanostructure in silicon. Nano Lett 18:4611–4617

    CAS  Google Scholar 

  31. Tsuchiya T, Hemmi T, Suzuki J, Hirai Y, Tabata O (2018) Tensile strength of silicon nanowires batch-fabricated into electrostatic MEMS testing device. Appl Sci 8:880

    Google Scholar 

  32. Fugii T, Sudoh K, Inoue S, Namazu T (2016) Design and development of electrostatically driven uniaxial tensile test device for silicon nanowires. Sens Mater 28(2):89–102

    Google Scholar 

  33. Sundararajan S, Bhushan B (2002) Devlopment of AFM-based technique to measure mechanical properties of nanoscale structures. Sens Actuat A 101:338–351

    CAS  Google Scholar 

  34. Sundararajan S, Bhushan B, Namazu T, Isono Y (2002) Mechanical property measurements of nanoscale structures using an atomic force microscope. Sens Actuat A 91:111–118

    CAS  Google Scholar 

  35. Fujii T, Sudoh K, Sakakihara S, Naito M, Inoue S, Namazu T (2013) Nano-scale tensile testing and sample preparation techniques for silicon nanowires. Jpn J Appl Phys 52:110118

    Google Scholar 

  36. Kang W, Saif MTA (2013) In situ study of size and temperature dependent brittle-to-ductile transition in single crystal silicon. Adv Funct Mater 23:713–719

    CAS  Google Scholar 

  37. Tsuchiya T, Hemmi T, Suzuki J, Hirai Y, Tabata O (2016) Tensile fracture of integrated single-crystal silicon nanowire using MEMS electrostatic testing device. Proc Struct Integr 2:1405–1412

    Google Scholar 

  38. Goel S, Kovalchenko A, Stukowski A, Cross G (2016) Influence of microstructure on the cutting behaviour of silicon. Acta Mater 105:464–478

    CAS  Google Scholar 

  39. Tang DM, Ren CL, Wang MS, Wei X, Kawamoto N, Liu C, Bando Y, Mitome M, Fukata N, Golberg D (2012) Mechanical properties of Si nanowires as revealed by in situ transmission electron microscopy and molecular dynamics simulations. Nano Lett 12:1898–1904

    CAS  Google Scholar 

  40. Wang L, Zheng K, Zhang Z, Han X (2011) Direct atomic-scale imaging about the mechanisms of ultralarge bent straining in Si nanowires. Nano Lett 11:2382–2385

    CAS  Google Scholar 

  41. Uesugi A, Hirai Y, Tsuchiya T, Tabata O (2016) Effect of crystallographic orientations on fractures and slip occurrences at 500 °C of (110) single crystal silicon microstructures. Proc Struct Integr 2:1413–1420

    Google Scholar 

  42. Fujita S, Tatami J, Yahagi T, Takahashi T, Iijima M (2017) Degradation evaluation of Si3N4 ceramic surface layer in contact with molten Al using microcantilever beam specimens. J Eur Ceram Soc 37:4351–4356

    CAS  Google Scholar 

  43. Tatami J, Katayama M, Ohnishi M, Yahagi T, Takahashi T, Horiuchi T, Yokouchi M, Yasuda K, Kim DK, Wakihara T, Komeya K (2015) Local fracture toughness of Si3N4 ceramics measured using single-edge notched microcantilever beam specimens. J Am Ceram Soc 98(3):965–971

    CAS  Google Scholar 

  44. Camposivan E, Anglada M (2016) Size and plasticity effects in zirconia micropillars compression. Acta Mater 103:882–892

    Google Scholar 

  45. Wheeler JM, Ranghavan R, Wehrs J, Zhang Y, Erni R, Michler J (2016) Approaching the limits of strength: measuring the uniaxial compressive strength of diamond at small scales. Nano Lett 16:812–816

    CAS  Google Scholar 

  46. Lu Y, Shu X, Liao X (2018) Size effect for achieving high mechanical performance body-centered cubic metals and alloys. Sci China Mater 61(12):1495–1516

    CAS  Google Scholar 

  47. Yamaguchi H, Tatami J, Iijima M (2019) Measurement of mechanical properties of BaTiO3 layer in multilayered ceramic capacitor using a microcantilever beam specimen. J Ceram Soc Jpn 127(6):335–338

    CAS  Google Scholar 

  48. Colas G, Serles P, Saulot A, Filleter T (2019) Strength measurement and rupture mechnisms of a micron thick nanocrystalline MoS2 coating using AFM based micro-bending test. J Mech Phys Solids 128:151–161

    CAS  Google Scholar 

  49. Yoshida K, Nishiyama N, Sone M, Wakai F (2017) Strength and toughness of nanocrystalline SiO2 stishovite toughened by fracture-induced amorphization. Acta Mater 124:316–324

    CAS  Google Scholar 

  50. Ronan H, Thierry B, Thierry D, Armel DM, Isabelle ZA, Jean MG, Cyril L, Sylvain M (2019) Local fracture toughness measurements in polycrystalline cubic zirconia using micro-cantilever bending tests. Mech Mater 136:103086

    Google Scholar 

  51. Brantley WA (1973) Calculated elastic constants for stress problems associated with semiconductor devices. J Appl Phys 44(1):534–535

    CAS  Google Scholar 

  52. Saka H (2017) Classical theory of crystal dislocations: from iron to gallium nitride. World Scientific, Singapore

    Google Scholar 

  53. Han XD, Zhang YF, Zheng K, Zhang XN, Zhang Z, Hao YJ, Guo XY, Yuan J, Wang ZL (2007) Low-temperature in situ large strain plasticity of ceramic SiC nanowires and its atomic-scale mechanism. Nano Lett 7(2):452–457

    CAS  Google Scholar 

  54. Rabier J, Renault PO, Eyidi D, Demenet JL, Chen J, Couvy H, Wang L (2007) Low-temperature in situ large strain plasticity of ceramic SiC nanowires and its atomic-scale mechanism. Phys Stat Sol C 4:3110

    CAS  Google Scholar 

  55. Dubois SMM, Rignanese GM, Pardoen T, Charlier JC (2006) Ideal strength of silicon: an ab initio study. Phys Rev B 74:235203

    Google Scholar 

  56. Sumigawa T, Ashida S, Tanaka S, Sanada K, Kitamura T (2015) Fracture toughness of silicon in nanometer-scale singular stress field. Eng Fract Mech 150:161–167

    Google Scholar 

  57. Gallo P, Yan Y, Sumigawa T, Kitamura T (2018) Fracture behavior of nanoscale notched silicon beams investigated by the theory of critical distances. Adv Theory Simul 1:1700006

    Google Scholar 

  58. Gallo P, Sumigawa T, Kitamura T (2019) Experimental characterization at nanoscale of single crystal silicon fracture toughness. Frattura ed Integrità Strutturale 47:408–415

    Google Scholar 

  59. Kunio H, Shinji T, Yasunori O, Tomozo N (1991) Fracture toughness of single crystal silicon. J Soc Mater Sci Jpn 40(451):405–410

    Google Scholar 

  60. Balila NJ, Christoph K, Gerhard D (2014) Can microscale fracture tests provide reliable fracture toughness values? A case study in silicon. J Mater Res 30(5):686–698

    Google Scholar 

  61. Ando T, Li X, Nakano S, Kasai T, Tanaka H, Shikida M, Sato K (2005) Fracture toughness measurement of thin film silicon. Fatigue Fract Eng Mater Struct 28:687–694

    CAS  Google Scholar 

  62. Motz C, Schöberl T, Pippan R (2005) Mechanical properties of micro-sized copper bending beams machined by the focused ion beam technique. Acta Mater 53:4269–4279

    CAS  Google Scholar 

  63. Jiang BC, Zhao DW, Wang BQ, Zhao HJ, Liu YH, Lu XC (2019) Flatness maintenance and roughness reduction of silicon mirror in chemical mechanical polishing process. Sci China Technol Sci. https://doi.org/10.1007/s11431-018-9414-6

    Article  Google Scholar 

  64. Johannes W (1996) Dislocation based fracture mechanics. World Scientific, Singapore

    Google Scholar 

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Acknowledgements

This work was partly supported by JSPS KAKENHI Grant Numbers 17H01319.

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Correspondence to Junichi Tatami.

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Yamaguchi, H., Tatami, J., Yahagi, T. et al. Dislocation-controlled microscopic mechanical phenomena in single crystal silicon under bending stress at room temperature. J Mater Sci 55, 7359–7372 (2020). https://doi.org/10.1007/s10853-020-04528-3

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