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Speckle Suppression by Decoherence in Fluctuation Electron Microscopy

Published online by Cambridge University Press:  18 September 2015

Aram Rezikyan ,
Zechariah J. Jibben ,
Bryan A. Rock ,
Gongpu Zhao ,
Franz A.M. Koeck ,
Robert F. Nemanich  and
Michael M.J. Treacy
Aram Rezikyan*
Affiliation:
Department of Physics, Arizona State University, Tempe, AZ 85287, USA
Zechariah J. Jibben
Affiliation:
Ira A. Fulton School of Engineering, Arizona State University, Tempe, AZ 85287, USA
Bryan A. Rock
Affiliation:
Department of Physics, Arizona State University, Tempe, AZ 85287, USA
Gongpu Zhao
Affiliation:
Department of Structural Biology, University of Pittsburgh School of Medicine, Pittsburgh, PA 15260, USA
Franz A.M. Koeck
Affiliation:
Department of Physics, Arizona State University, Tempe, AZ 85287, USA
Robert F. Nemanich
Affiliation:
Department of Physics, Arizona State University, Tempe, AZ 85287, USA
Michael M.J. Treacy
Affiliation:
Department of Physics, Arizona State University, Tempe, AZ 85287, USA
*
*Corresponding author.arezikya@hotmail.com
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Abstract

We compare experimental fluctuation electron microscopy (FEM) speckle data with electron diffraction simulations for thin amorphous carbon and silicon samples. We find that the experimental speckle intensity variance is generally more than an order of magnitude lower than kinematical scattering theory predicts for spatially coherent illumination.

We hypothesize that decoherence, which randomizes the phase relationship between scattered waves, is responsible for the anomaly. Specifically, displacement decoherence can contribute strongly to speckle suppression, particularly at higher beam energies. Displacement decoherence arises when the local structure is rearranged significantly by interactions with the beam during the exposure. Such motions cause diffraction speckle to twinkle, some of it at observable time scales.

We also find that the continuous random network model of amorphous silicon can explain the experimental variance data if displacement decoherence and multiple scattering is included in the modeling. This may resolve the longstanding discrepancy between X-ray and electron diffraction studies of radial distribution functions, and conclusions reached from previous FEM studies.

Decoherence likely affects all quantitative electron imaging and diffraction studies. It likely contributes to the so-called Stobbs factor, where high-resolution atomic-column image intensities are anomalously lower than predicted by a similar factor to that observed here.

Keywords

Fluctuation electron microscopydecoherencecontinuous random networkmedium-range orderamorphous materials
Type
Materials Applications and Techniques
Information
Microscopy and Microanalysis , Volume 21 , Issue 6 , December 2015 , pp. 1455 - 1474
Copyright
© Microscopy Society of America 2015 

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References

Abramowitz, M. & Stegun, I.A. (Eds.) 1965). Handbook of Mathematical Functions. Dover Publications: Mineola, New York.Google Scholar
Barkema, G.T. & Mousseau, N. (2000). High-quality continuous random networks. Phys Rev B 62(8), 4985–4990.CrossRefGoogle Scholar
Biswas, P., Tafen, D. & Drabold, D.A. (2005). Experimentally constrained molecular relaxation: The case of GeSe2 . Phys Rev B 71, 054204.CrossRefGoogle Scholar
Bogle, S.N., Voyles, P.M., Khare, S.V. & Abelson, J.R. (2007). Quantifying nanoscale order in amorphous materials: Simulating fluctuation electron microscopy of amorphous silicon. J Phys Condens Matter 19(45), 455204.CrossRefGoogle Scholar
Boothroyd, C.B. (1998). Why don’t high-resolution simulations and images match? J Microsc 190(1–2), 99–108.CrossRefGoogle Scholar
Borisenko, K.B., Haberl, B., Chen, Y., Li, G., Liu, A., Williams, J.S., Bradby, J.E., Cockayne, D.J.H. & Treacy, M.M.J. (2012). Medium-range order in amorphous silicon investigated by constrained structural relaxation of two-body and four-body electron diffraction data. Acta Mater 60(1), 359–375.CrossRefGoogle Scholar
Chen, L., Cheng, S., Yu, C., Su, P., Lin, H. & Chi, K. (2002). Structural evolution in amorphous silicon and germanium thin films. Microsc Microanal 8, 268–273.CrossRefGoogle ScholarPubMed
Chen, X., Sullivan, J.P., Friedmann, T.A. & Gibson, J.M. (2004). Fluctuation microscopy studies of medium-range ordering in amorphous diamond-like carbon films. Appl Phys Lett 84, 2823–2825.CrossRefGoogle Scholar
Cheng, J.-Y., Treacy, M.M.J., Keblinski, P.J. & Gibson, J.M. (2004). Diffraction microscopy for disordered tetrahedral networks. J Appl Phys 95, 7779–7784.CrossRefGoogle Scholar
Cheng, S.L., Lin, H.H., He, J.H., Chiang, T.F., Yu, C.H., Chen, L.J., Yang, C.K., Wu, D.Y., Chien, S.C. & Chen, W.C. (2002). Evolution of structural order in germanium ion-implanted amorphous Si layers. J Appl Phys 92, 910–913.CrossRefGoogle Scholar
Cockayne, D.J.H. (2007). The study of nanovolumes of amorphous materials using electron scattering. Annu Rev Mater Res 37, 159–187.CrossRefGoogle Scholar
Dainty, J.C. (1975). Stellar speckle interferometry. In Laser Speckle and Related Phenomena, Dainty, J.C. (Ed.), pp. 255–280). New York, NY: Springer-Verlag.Google Scholar
Doyle, P.A. & Turner, P.S. (1968). Relativistic Hartree-Fock X-ray and electron scattering factors. Acta Crystallogr A 24, 390–397.CrossRefGoogle Scholar
Fan, G.Y. & Cowley, J.M. (1985). Autocorrelation analysis of high-resolution electron-micrographs of near-amorphous thin-films. Ultramicroscopy 17, 345–355.CrossRefGoogle Scholar
Fan, G.Y. & Cowley, J.M. (1988). Assessing the information-content of HREM images. Ultramicroscopy 24, 49–60.CrossRefGoogle Scholar
Forbes, B., D’Alfonso, A., Findlay, S., Van Dyck, D., LeBeau, J., Stemmer, S. & Allen, L. (2011). Thermal diffuse scattering in transmission electron microscopy. Ultramicroscopy 111(12), 1670–1680.CrossRefGoogle ScholarPubMed
Gibbs, J.W. (1902). Elementary Principles in Statistical Mechanics. Mineola, New York: Dover Publications.Google Scholar
Gibson, J.M. (1978). Investigations of Amorphous Structures. PhD Thesis. Cambridge University, Cambridge, UK.Google Scholar
Gibson, J.M. & Howie, A. (1978). Investigation of local structure and composition in amorphous solids by high resolution electron microscopy. Chem Scr 14, 109–116.Google Scholar
Gibson, J.M. & Treacy, M.M.J. (1997). Diminished medium-range order observed in annealed amorphous germanium. Phys Rev Lett 78, 1074–1077.CrossRefGoogle Scholar
Gibson, J.M., Treacy, M.M.J., Sun, T. & Zaluzec, N.J. (2010). Substantial crystalline topology in amorphous silicon. Phys Rev Lett 105(12), 125504.CrossRefGoogle ScholarPubMed
Gibson, J.M., Treacy, M.M.J., Voyles, P.M., Jin, H.-C. & Abelson, J.R. (1998). Structural disorder induced in hydrogenated amorphous silicon by light soaking. Appl Phys Lett 73, 3093–3096.CrossRefGoogle Scholar
Goodman, J. (1975 a). Probability density function of the sum of n partially correlated speckle patterns. Opt Commun 13(3), 244–247.CrossRefGoogle Scholar
Goodman, J.W. (1975 b). Some fundamental properties of speckle. In Laser Speckle and Related Phenomena, Dainty, J.C. (Ed.), pp. 60–68). New York, NY: Springer-Verlag.Google Scholar
Hirsch, P., Howie, A., Nicholson, R., Pashley, D.W. & Whelan, M.J. (1977). Electron Microscopy of Thin Crystals. Malabar, FL: Krieger Publishing.Google Scholar
Howie, A. (1978). High resolution electron microscopy of amorphous thin films. J Non Cryst Solids 31, 41–45.CrossRefGoogle Scholar
Howie, A. (2011). Mechanisms of decoherence in electron microscopy. Ultramicroscopy 111(7), 761–767.CrossRefGoogle ScholarPubMed
Howie, A., Krivanek, O.L. & Rudee, M.L. (1973). Interpretation of electron micrographs and diffraction patterns of amorphous materials. Philos Mag 27, 235–255.CrossRefGoogle Scholar
Howie, A., McGill, C.A. & Rodenburg, J.M. (1985). Intensity correlations in microdiffraction from amorphous materials. J Phys Colloques 46, C9-59–C9-62.CrossRefGoogle Scholar
Humphry, M.J., Kraus, B., Hurst, A.C., Maiden, M. & Rodenburg, J.M. (2012). Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging. Nat Commun 3, 730.CrossRefGoogle ScholarPubMed
Hwang, J., Clausen, A.M., Cao, H. & Voyles, P.M. (2009). Reverse monte carlo structural model for a zirconium-based metallic glass incorporating fluctuation microscopy medium-range order data. J Mater Res 24(10), 3121–3129.CrossRefGoogle Scholar
Hÿtch, M. & Stobbs, W. (1994). Quantitative comparison of high resolution TEM images with image simulations. Ultramicroscopy 53(3), 191–203.CrossRefGoogle Scholar
Jaynes, E.T. (1957). Information theory and statistical mechanics. Phys Rev 106, 620–630.CrossRefGoogle Scholar
Kamimura, O., Dobashi, T., Kawahara, K., Abe, T. & Gohara, K. (2010). 10-kv diffractive imaging using newly developed electron diffraction microscope. Ultramicroscopy 110(2), 130–133.CrossRefGoogle ScholarPubMed
Kapur, J.N. (1989). Maximum-Entropy Models in Science and Engineering. New Delhi, India: New Age International Publishers.Google Scholar
Keblinski, P., Phillpot, S., Wolf, D. & Gleiter, H. (1997). Amorphous structure of grain boundaries and grain junctions in nanocrystalline silicon by molecular-dynamics simulation. Acta Mater 45(3), 987–998.CrossRefGoogle Scholar
Kirkland, E.J. (1998). Advanced Computing in Electron Microscopy. New York, NY and London: Plenum Press.CrossRefGoogle Scholar
Laaziri, K., Kycia, S., Roorda, S., Chicoine, M., Robertson, J.L., Wang, J. & Moss, S.C. (1999). High-energy x-ray diffraction study of pure amorphous silicon. Phys Rev B 60(19), 13520–13533.CrossRefGoogle Scholar
Lee, B.-S., Bishop, S.G. & Abelson, J.R. (2010). Fluctuation transmission electron microscopy: Detecting nanoscale order in disordered structures. Chemphyschem 11, 2311–2317.CrossRefGoogle ScholarPubMed
Li, J., Gu, X. & Hufnagel, T.C. (2001). Medium-range order in metallic glasses studied by fluctuation microscopy. Microsc Microanal 7(Suppl 2), 1260–1261.CrossRefGoogle Scholar
Li, J., Gu, X. & Hufnagel, T.C. (2003). Using fluctuation microscopy to characterize structural order in metallic glass. Microsc Microanal 9, 509–515.CrossRefGoogle Scholar
Li, T.T., Bogle, S.N. & Abelson, J.R. (2014). Quantitative fluctuation electron microscopy in the stem: Methods to identify, avoid, and correct for artifacts. Microsc Microanal 20, 1605–1618.CrossRefGoogle ScholarPubMed
Li, T.T., Darmawikarta, K. & Abelson, J.R. (2013). Quantifying nanoscale order in amorphous materials via scattering covariance in fluctuation electron microscopy. Ultramicroscopy 133, 95–100.CrossRefGoogle ScholarPubMed
Liu, A.C.Y., Arenal, R., Miller, D.J., Chen, X., Johnson, J.A., Eryilmaz, O.L., Erdemir, A. & Woodford, J.B. (2007). Structural order in near-frictionless hydrogenated diamond like carbon films probed at three length scales via transmission electron microscopy. Phys Rev B 75, 205402.CrossRefGoogle Scholar
McBride, W. & Cockayne, D.J.H. (2003). The structure of nanovolumes of amorphous materials. J Non Cryst Solids 318, 233–238.CrossRefGoogle Scholar
Press, W.H., Teukolsky, S.A., Vetterling, W.T. & Flannery, B.P. (1992). Numerical Recipes in C; the Art of Scientific Computing, 2nd ed Cambridge, UK: Cambridge University Press.Google Scholar
Rodenburg, J.M. (1988). Properties of electron microdiffraction patterns from amorphous materials. Ultramicroscopy 25, 329–344.CrossRefGoogle Scholar
Rodenburg, J.M. (2008). Ptychography and related diffracted imaging methods. In Advances in Imaging and Electron Physics (vol. 150 Hawkes, P.W. (Ed.), pp. 87–184). Amsterdam, Netherlands: Elsevier.Google Scholar
Stratton, W.G., Hamann, J., Perepezko, J.H., Voyles, P.M., Khare, S.V. & Mao, X. (2005). Aluminum nanoscale order in amorphous Al92Sm8 measured by fluctuation electron microscopy. Appl Phys Lett 86, 141910.CrossRefGoogle Scholar
Stratton, W.G. & Voyles, P.M. (2008). A phenomenological model of fluctuation electron microscopy for a nanocrystal/amorphous composite. Ultramicroscopy 108(8), 727–736.CrossRefGoogle ScholarPubMed
Sun, T., Koeck, F.A.M., Rezikyan, A., Treacy, M.M.J. & Nemanich, R.J. (2014). Thermally enhanced photoinduced electron emission from nitrogen-doped diamond films on silicon substrates. Phys Rev B 90, 121302.CrossRefGoogle Scholar
Treacy, M. & Gibson, J. (2012). Examination of a polycrystalline thin-film model to explore the relation between probe size and structural correlation length in fluctuation electron microscopy. Microsc Microanal 18, 241–253.CrossRefGoogle ScholarPubMed
Treacy, M.M.J. (2005). What is fluctuation microscopy? Micros Today 13(5), 20–21.CrossRefGoogle Scholar
Treacy, M.M.J. (2012). Speckles in images and diffraction patterns. In Handbook of Nanoscopy (chapter 12 van Tendeloo, G., van Dyck, D. & Pennycook, S.J. (Eds.), pp. 405–435). Hoboken, New Jersey, USA: John Wiley and Sons.CrossRefGoogle Scholar
Treacy, M.M.J. & Borisenko, K.B. (2012 a). The local structure of amorphous silicon. Science 335(6071), 950–953.CrossRefGoogle ScholarPubMed
Treacy, M.M.J. & Borisenko, K.B. (2012 b). Response to comment on local structure of amorphous silicon. Science 338(6114), 1539.CrossRefGoogle Scholar
Treacy, M.M.J. & Gibson, J.M. (1993). Coherence and multiple scattering in “Z”-contrast images. Ultramicroscopy 52, 31.CrossRefGoogle Scholar
Treacy, M.M.J. & Gibson, J.M. (1996). Variable coherence microscopy: A rich source of structural information from disordered materials. Acta Cryst A 52, 212–220.CrossRefGoogle Scholar
Treacy, M.M.J., Gibson, J.M., Fan, L., Paterson, D.J. & McNulty, I. (2005). Fluctuation microscopy: A probe of medium range order. Rep Prog Phys 68(12), 2899–2944.CrossRefGoogle Scholar
Treacy, M.M.J., Gibson, J.M. & Keblinski, P.J. (1998). Paracrystallites found in evaporated amorphous tetrahedral semiconductors. J Non Cryst Solids 231, 99–110.CrossRefGoogle Scholar
Voyles, P.M. & Abelson, J.R. (2003). Medium-range order in amorphous silicon measured by fluctuation electron microscopy. Sol Energy Mater Sol Cells 78, 85–113.CrossRefGoogle Scholar
Voyles, P.M., Gerbi, J.E., Treacy, M.M.J., Gibson, J.M. & Abelson, J.R. (2001). Increased medium-range order in amorphous silicon with increased substrate temperature. Phys Rev Lett 86, 5514–5518.CrossRefGoogle Scholar
Wen, J., Cheng, Y.Q., Wang, J.Q. & Ma, E. (2009). Distinguishing medium-range order in metallic glasses using fluctuation electron microscopy: A theoretical study using atomic models. J Appl Phys 105, 043519.CrossRefGoogle Scholar
Wooten, F., Winer, K. & Weaire, D. (1985). Computer-generation of structural models of amorphous Si and Ge. Phys Rev Lett 54, 1392–1395.CrossRefGoogle ScholarPubMed
Xie, R., Long, G.G., Weigand, S.J., Moss, S.C., Carvalho, T., Roorda, S., Hejna, M., Torquato, S. & Steinhardt, P.J. (2013). Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor. Proc Natl Acad Sci USA 110, 13250–13254.CrossRefGoogle ScholarPubMed
Zhao, G., Buseck, P.R., Rougée, A. & Treacy, M.M.J. (2009). Medium-range order in molecular materials: Fluctuation electron microscopy for detecting fullerenes in disordered carbons. Ultramicroscopy 109, 177–188.CrossRefGoogle ScholarPubMed
Zhao, G., Treacy, M.M.J. & Buseck, P.R. (2010). Fluctuation electron microscopy of medium-range order in ion-irradiated zircon. Philos Mag 90(35), 4661–4677.CrossRefGoogle Scholar