Fluctuation Microscopy in the STEM

  • Paul M. Voyles
  • Stephanie Bogle
  • John R. Abelson


Fluctuation electron microscopy is a technique for measuring nanoscale order in amorphous materials. Implementing fluctuation microscopy using electron nanodiffraction in a STEM has significant advantages, including improved coherence and a high degree of flexibility in the probe forming optics. Here we review the fluctuation microscopy technique in the STEM, including theory, practice, and example applications.


Amorphous Silicon Bulk Metallic Glass Probe Size Chromatic Aberration Bragg Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors thank Jian-Min Zuo, Bong-Sub Lee, and Feng Yi for helpful discussions, and gratefully acknowledge the support of the U.S. National Science Foundation (DMR-0605890).


  1. G. Adam, J.H. Gibbs, On the temperature dependence of cooperative relaxation properties in glass-forming liquids. J. Chem. Phys. 43, 139–146 (1965).CrossRefGoogle Scholar
  2. A.S. Argon, Plastic deformation in metallic glasses. Acta Metall. 27, 47–58 (1979).CrossRefGoogle Scholar
  3. U. Bengtzelius, W. Goetze, et al., Dynamics of supercooled liquids and the glass transition. J. Phys. C: Solid State Physics 17, 5915–5934 (1984).CrossRefGoogle Scholar
  4. J.D. Bernal, The Bakerian lecture, 1962: the structure of liquids. Proc. Roy. Soc. Lond. A 280(1382), 299–322 (1964).CrossRefGoogle Scholar
  5. P. Biswas, R. Atta-Fynn, et al., Reverse Monte Carlo modeling of amorphous silicon. Phys. Rev. B 69, 195207 (2004a).Google Scholar
  6. P. Biswas, D.N. Tagen, et al., The inclusion of experimental information in first principles modelling of materials. J. Phys. Condens. Matter 16, S5173–S5182 (2004b).CrossRefGoogle Scholar
  7. S.N. Bogle, Quantifying Nanoscale Order in Amorphous Materials via Fluctuation Electron Microscopy. Materials Science and Engineering (University of Illinois, Champaign-Urbana, IL, 2009).Google Scholar
  8. S.N. Bogle, L.N. Nittala, et al., Size analysis of nanoscale order in amorphous materials by variable-resolution fluctuation electron microscopy. Ultramicroscopy 110, 1273–1278 (2010).CrossRefGoogle Scholar
  9. S.N. Bogle, P.M. Voyles, et al., Quantifying nanoscale order in amorphous materials: simulating fluctuation electron microscopy of amorphous silicon. J. Phys. Cond. Mat. 19, 455204 (2007).CrossRefGoogle Scholar
  10. D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, Oxford, 1987).Google Scholar
  11. X. Chen, J.P. Sullivan, et al., Fluctuation microscopy studies of medium-range ordering in amorphous diamond-like carbon films. Appl. Phys. Lett. 84, 2823–2825 (2004).CrossRefGoogle Scholar
  12. J.-Y. Cheng, J.M. Gibson, et al., Quantitative analysis of annealing-induced structure disordering in ion-implanted amorphous silicon. J. Vac. Sci. Tech. A 20(6), 1855–1859 (2002).CrossRefGoogle Scholar
  13. J.-Y. Cheng, J.M. Gibson, et al., Observation of structural order in ion-implanted amorphous silicon. J. Mat. Res. 16, 3030–3033 (2001).CrossRefGoogle Scholar
  14. D.J.H. Cockayne, The study of nanovolumes of amorphous materials using electron scattering. Ann. Rev. Mater. Res. 37, 159–187 (2007).CrossRefGoogle Scholar
  15. D.J.H. Cockayne, D.R. McKenzie, Electron diffraction analysis of polycrystalline and amorphous thin films. Acta Cryst. A44, 870–878 (1988).Google Scholar
  16. J.M. Cowley, STEM imaging with a thin annular detector. J. Electron Microsc. 50, 147–155 (2001).CrossRefGoogle Scholar
  17. J.M. Cowley, Electron nanodiffraction methods for measuring medium-range order. Ultramicroscopy 90(2–3), 197–206 (2002).CrossRefGoogle Scholar
  18. N. Cusack, The Physics of Structurally Disordered Matter (A. Hilger, 1987).Google Scholar
  19. R.K. Dash, P.M. Voyles, et al., A quantitative measure of medium-range order in amorphous materials from transmission electron micrographs. J. Phys Condens Matter 15(31), S2425–S2435 (2003).CrossRefGoogle Scholar
  20. C. Dwyer, A.I. Kirkland, et al., Electron nanodiffraction using sharply focused parallel probes. Appl. Phys. Lett. 90, 151104 (2007).CrossRefGoogle Scholar
  21. S.R. Elliot, The structure of amorphous hydrogenated silicon and its alloys: A review. Adv. Phys. 38, 1–88 (1989).CrossRefGoogle Scholar
  22. L. Fan, I. McNulty, et al., Fluctuation microscopy – a tool for examining medium-range order in noncrystalline systems. Nucl. Instr. Meth. Phys. Res. B 238(1–4), 196–199 (2005).CrossRefGoogle Scholar
  23. L. Fan, D. Paterson, et al., Fluctuation X-ray microscopy: a novel approach for the structural study of disordered materials. J. Microsc. 225(1), 41–48 (2007).CrossRefGoogle Scholar
  24. H.E. Fischer, A.C. Barnes, et al., Neutron and x-ray diffraction studies of liquids and glasses. Rep. Prog. Phys. 69, 233–299 (2006).CrossRefGoogle Scholar
  25. J.C. Foley, D.R. Allen, et al., Analysis of nanocrystal development in Al-Y-Fe and Al-Sm glasses. Scripta Mat. 35, 655–660 (1996).CrossRefGoogle Scholar
  26. L.A. Freeman, A. Howie, et al., Bright field and hollow cone dark field electron microscopy of palladium catalysts. J. Microsc. 111, 165–178 (1977).CrossRefGoogle Scholar
  27. J.E. Gerbi, P.M. Voyles, et al., Control of medium-range order in amorphous silicon via ion and neutral bombardment. Appl. Phys. Lett. 82(21), 3665–3667 (2003).CrossRefGoogle Scholar
  28. J.E. Gerbi, P.M. Voyles, et al., Increasing medium-range order in amorphous silicon with low-energy ion bombardment. Appl. Phys. Lett. 82(21), 3665–3667 (2003).CrossRefGoogle Scholar
  29. P.C. Gibbons, Y.T. Shen, et al., Intermediate-range order in amorphous metal alloys. Phil. Mag. 86(3–5), 293–298 (2006).CrossRefGoogle Scholar
  30. J.M. Gibson, M.M.J. Treacy, Diminished medium-range order observed in annealed amorphous germanium. Phys. Rev. Lett. 78, 1074–1077 (1997).CrossRefGoogle Scholar
  31. J.M. Gibson, M.M.J. Treacy, et al., Atom pair persistence in disordered materials from fluctuation microscopy. Ultramicroscopy 83(3–4), 169–178 (2000).CrossRefGoogle Scholar
  32. J.M. Gibson, M.M.J. Treacy, et al., Structural disorder induced in hydrogenated amorphous silicon by light soaking. Applied Physics Letters 73(21), 3093–3095 (1998).CrossRefGoogle Scholar
  33. M. Haider, S. Uhlemann, et al., Electron microscopy image enhanced. Nature 392, 768–769 (1998).CrossRefGoogle Scholar
  34. A. Hirata, Y. Hirotsu, et al., Direct imaging of local atomic ordering in a Pd–Ni–P bulk metallic glass using Cs-corrected transmission electron microscopy. Ultramicroscopy 107, 116–123 (2007).CrossRefGoogle Scholar
  35. M.Y. Ho, H. Gong, et al., Morphology and crystallization kinetics in HfO2 thin films grown by atomic layer deposition. J. Appl. Phys. 93(3), 1477–1481 (2003).CrossRefGoogle Scholar
  36. A. Howie, O.L. Krivanek, et al., Interpretation of electron micrographs and diffraction patterns of amorphous materials. Philosophical Magazine 27(1), 235–255 (1973).CrossRefGoogle Scholar
  37. S.O. Hruszkewycz, T. Fujita, et al., Selected area nanodiffraction fluctuation electron microscopy for studying structural order in amorphous solids. Scripta Mat. 58, 303–306 (2008).CrossRefGoogle Scholar
  38. T.C. Hufnagel, C. Fan, et al., Controlling shear band behavior in metallic glass through microstructural design. Intermetallics 10, 1163–1166 (2002).CrossRefGoogle Scholar
  39. J. Hwang, H. Cao, et al., in Nanometer-Scale Structure of a Zr-Based Bulk Metallic Glass. Bulk Metallic Glasses, eds. by J. Schoers, R. Busch, N. Nishiyama, M. Li (Fall Materials Research Society Meeting, Boston, MA, 2007).Google Scholar
  40. J.A. Johnson, J.B. Woodford, et al., Insights into “near-frictionless carbon films”. J. Appl. Phys. 95, 7765–7771 (2004).CrossRefGoogle Scholar
  41. S.V. Khare, S.M. Nakhmanson, et al., Evidence from atomistic simulations of fluctuation electron microscopy for preferred local orientations in amorphous silicon. Appl. Phys. Lett. 85(5), 745–747 (2004).CrossRefGoogle Scholar
  42. E.J. Kirkland, in Advanced Computing in Electron Microscopy (Plenum Press, New York, NY, 1998).Google Scholar
  43. M. Kisa, T.K. Minton, et al., Homogeneous silica formed by the oxidation of Si(100) in hyperthermal atomic oxygen. J. Spacecraft Rockets 43, 431–435 (2006).CrossRefGoogle Scholar
  44. D. Kivelson, S.A. Kivelson, et al., A thermodynamic theory of supercooled liquids. Physica A 219(1–2), 27–38 (1995).CrossRefGoogle Scholar
  45. O.L. Krivanek, P.H. Gaskell, et al., Seeing order in ‘amorphous’ materials. Nature 262, 454–457 (1976).CrossRefGoogle Scholar
  46. M.H. Kwon, B.S. Lee, et al., Nanometer-scale order in amorphous Ge2Sb2Te5 analyzed by fluctuation electron microscopy. Appl. Phys. Lett. 90(2) (2007).Google Scholar
  47. B. Lee, in Optical and Electronic Properties, Nanoscale Structural Order, and Transformation Kinetics of Phase Change Materials (University of Illinois at Urbana-Champaign, 2006).Google Scholar
  48. B.S. Lee, G.W. Burr, et al., Observation of the role of subcritical nuclei in crystallization of a glassy solid. Science 326, 980–984 (2009).CrossRefGoogle Scholar
  49. E. Leutheusser, Dynamical model of the liquid-glass transition. Phys. Rev. A 29, 2765–2773 (1984).CrossRefGoogle Scholar
  50. J. Li, X. Gu, et al., Using fluctuation microscopy to characterize structural order in metallic glass. Microsc. Microanal. 9, 509–515 (2003).CrossRefGoogle Scholar
  51. R.L. McGreevy, Reverse Monte Carlo modelling. J. Phys. Condens. Matter 13, R877–R913 (2001).CrossRefGoogle Scholar
  52. D.B. Miracle, On the universal model for medium-range order in amorphous metal structures. J. Non-Cryst. Sol. 317, 40–44 (2003).CrossRefGoogle Scholar
  53. S.M. Nakhmanson, P.M. Voyles, et al., Realistic models of paracrystalline silicon. Phys. Rev. B 63(23), 235207 (2001).CrossRefGoogle Scholar
  54. Y. Pan, F. Inam, et al., Atomistic origin of Urbach tails in amorphous silicon. Phys. Rev. Lett. 1000, 206403 (2008).CrossRefGoogle Scholar
  55. C.R. Perrey, S. Thompson, et al., Observation of Si nanocrystals in a/nc-Si: H films by spherical-aberration corrected transmission electron microscopy. J. Non-Cryst. Solids 343(1–3), 78–84 (2004).CrossRefGoogle Scholar
  56. J.M. Rodenburg, in Measurement of Higher-Order Correlation Functions in Amorphous Materials Via Coherent Microdiffraction. EMAG99 Proceedings (Institute of Physics Conference Serials, 1999).Google Scholar
  57. J.M. Rodenburg, I.A. Rauf, in A Cross-Correlation Measure of Order in ‘Amorphous’ Indium Oxide. EMAG-MICRO 89 (Institute of Physics, London, UK, 1990).Google Scholar
  58. M.L. Rudee, A. Howie, Structure of amorphous Si and Ge. Philos. Mag. 25(4), 1001–1007 (1972).CrossRefGoogle Scholar
  59. J.V. Ryan, C.G. Pantano, Medium-range order in silicon oxycarbide glass by fluctuation electron microscopy. J. Phys. Cond. Mat. 19, 455205 (2007).CrossRefGoogle Scholar
  60. C.A. Schuh, T.C. Hufnagel, et al., Mechanical behavior of amorphous alloys. Acta Mat. 55, 4067–4100 (2007).CrossRefGoogle Scholar
  61. H.W. Sheng, W.K. Lou, et al., Atomic packing and short-to-medium-range order in metallic glasses. Nature 439, 419–425 (2006).CrossRefGoogle Scholar
  62. A.P. Sokolov, A.P. Shebanin, Structural order and optical properties of amorphous silicon. Sov. Phys. Semicon.: 720. REPLACE WITH: A.P. Sokolov, A.P. Shebanin, O.A. Golikova, M.M. Mezdrogina (1991) Structural order in amorphous silicon and its alloys: Raman spectra and optical gap J. Non-Cryst. Sol. 137138, 99–102 (1990).Google Scholar
  63. W.G. Stratton, J. Hamann, et al., Aluminum nanoscale order in amorphous Al92Sm8 measured by fluctuation electron microscopy. Appl. Phys. Lett. 86, 141910 (2005).CrossRefGoogle Scholar
  64. W.G. Stratton, J. Hamann, et al., Electron beam induced crystallization of amorphous Al-based alloys in the TEM. Intermetallics 14, 1061–1065 (2006).CrossRefGoogle Scholar
  65. W.G. Stratton, P.M. Voyles, Comparison of fluctuation electron microscopy theories and experimental methods. J. Phys. Cond. Mat. 19, 455203 (2007).CrossRefGoogle Scholar
  66. W.G. Stratton, P.M. Voyles, A phenomenological model of fluctuation electron microscopy for a nanocrystal/amorphous composite. Ultramicroscopy 108, 727–736 (2008).CrossRefGoogle Scholar
  67. M.M.J. Treacy, J.M. Gibson, Coherence and multiple scattering in “Z-contrast” images. Ultramicroscopy 52(1), 31–53 (1993).CrossRefGoogle Scholar
  68. M.M.J. Treacy, J.M. Gibson, Variable coherence microscopy: a rich source of structural information from disordered systems. Acta Cryst. A 52(2), 212–220 (1996).Google Scholar
  69. M.M.J. Treacy, J.M. Gibson, et al., Fluctuation microscopy: a probe of medium range order. Rep. Prog. Phys. 68, 2899–2944 (2005).CrossRefGoogle Scholar
  70. M.M.J. Treacy, J.M. Gibson, et al., Paracrystallites found in evaporated amorphous tetrahedral semiconductors. J. Non-Cryst. Sol. 231(1–2), 99–110 (1998).CrossRefGoogle Scholar
  71. M.M.J. Treacy, P.M. Voyles, et al., Schläfli cluster topological analysis of medium range order in paracrystalline amorphous semiconductor models. J. Non-Cryst. Sol. 266, 150–155 (2000).CrossRefGoogle Scholar
  72. D.V. Tsu, B.S. Chao, et al., Effect of hydrogen dilution on the structure of amorphous silicon alloys. Appl. Phys. Lett. 71, 1317–1319 (1997).CrossRefGoogle Scholar
  73. D. Van Dyck, S. Van Aert, et al., Is atomic resolution transmission electron microscopy able to resolve and refine amorphous structures? Ultramicroscopy 98, 27–42 (2003).CrossRefGoogle Scholar
  74. P.M. Voyles, Fluctuation electron microscopy of medium-range order in amorphous silicon. Physics. Urbana-Champaign, IL, University of Illinois (2001).Google Scholar
  75. P.M. Voyles, J.R. Abelson, Medium-range order in amorphous silicon measured by fluctuation electron microscopy. Solar Energy Mater. Solar Cells 78(1–4), 85–113 (2003).CrossRefGoogle Scholar
  76. P.M. Voyles, J.E. Gerbi, et al., Absence of an abrupt phase change from polycrystalline to amorphous in silicon with deposition temperature. Phys. Rev. Lett. 86(24), 5514–5517 (2001).CrossRefGoogle Scholar
  77. P.M. Voyles, J.M. Gibson, et al., Fluctuation microscopy: a probe of atomic correlations in disordered materials. J. Electron Microsc. 49(2), 259–266 (2000).CrossRefGoogle Scholar
  78. P.M. Voyles, D.A. Muller, Fluctuation microscopy in the STEM. Ultramicroscopy 93(2), 147–159 (2002).CrossRefGoogle Scholar
  79. P.M. Voyles, M.M.J. Treacy, et al., in Experimental Procedures and Data Analysis for Fluctuation Microcopy. Advances in Materials Problem Solving with the Electron Microscope. (Materials Research Society, Boston, MA, 1999).Google Scholar
  80. P.M. Voyles, M.M.J. Treacy, et al., in Comparative Fluctuation Microscopy Study of Medium-Range Order in Hydrogenated Amorphous Silicon Deposited by Various Methods. Amorphous and Heterogeneous Silicon Thin Films 2000. (Materials Research Society, San Francisco, CA, 2000).Google Scholar
  81. P.M. Voyles, N. Zotov, et al., Structure and physical properties of paracrystalline atomistic models of amorphous silicon. J. Appl. Phys. 90(9), 4437–4451 (2001).CrossRefGoogle Scholar
  82. R.J. Walters, G.I. Bourianoff, et al., Field-effect electroluminescence in silicon nanocrystals. Nature Materials 4(2), 143–146 (2005).CrossRefGoogle Scholar
  83. J. Wen, Y.Q. Cheng, et al., Distinguishing medium-range order in metallic glasses using fluctuation electron microscopy: A theoretical study using atomic models. J. Appl. Phys. 105, 043519 (2009).CrossRefGoogle Scholar
  84. J. Wen, H.W. Yang, et al., Fluctuation electron microscopy of Al-based metallic glasses: effects of minor alloying addition and structural relaxation on medium-range structural homogeneity. J. Phys. Condens. Matter 19, 455211 (2007).CrossRefGoogle Scholar
  85. F. Wooten, K. Winer, et al., Computer-generation of structural models of amorphous Si and Ge. Phys. Rev. Lett. 54(13), 1392–1395 (1985).CrossRefGoogle Scholar
  86. W.H. Zachariasen, The atomic arrangement in glass. J. Am. Chem. Soc. 54, 3841–3851 (1932).CrossRefGoogle Scholar
  87. G. Zhao, P.R. Buseck, et al., Medium-range order in molecular materials: fluctuation electron microscopy for detecting fullerenes in disordered carbons. Ultramicroscopy 109, 177–188 (2009).CrossRefGoogle Scholar
  88. J.M. Zuo, Electron detection characteristics of slow-scan CCD camera. Ultramicroscopy 66, 21–33 (1996).CrossRefGoogle Scholar
  89. J.M. Zuo, M. Gao, et al., Coherent nano-area electron diffraction. Microsc. Res. Tech. 64, 347–355 (2004).CrossRefGoogle Scholar
  90. J.M. Zuo, I. Vartanyants, et al., Atomic resolution imaging of a carbon nanotube from diffraction intensities. Science 300, 1419–1421 (2003).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Paul M. Voyles
    • 1
  • Stephanie Bogle
    • 2
  • John R. Abelson
    • 2
  1. 1.Department of Materials Science and EngineeringUniversity of WisconsinMadisonUSA
  2. 2.Department of Materials Science and EngineeringUniversity of IllinoisUrbana-ChampaignUSA

Personalised recommendations