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Strain Measurements and Mapping

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Abstract

The concepts of strain and stress were introduced in Chap. 15. Direct measurements of strain and stress always rely on the measurement of deformation in a structure.

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References

  • Armigliato A, Balboni R, Carnevale GP, Pavia G, Piccolo D, Frabboni S, Benedetti A, Cullis AG (2003) Application of convergent beam electron diffraction to two-dimensional strain mapping in silicon devices. Appl Phys Lett 82:2172–2174

    Article  Google Scholar 

  • Armigliato A, Balboni R, Frabboni S (2005) Improving spatial resolution of convergent beam electron diffraction strain mapping in silicon microstructures. Appl Phys Lett 86:063508

    Article  Google Scholar 

  • Armigliato A, Frabboni S, Gazzadi GC (2008) Electron diffraction with ten nanometer beam size for strain analysis of nanodevices. Appl Phys Lett 93:161906

    Article  Google Scholar 

  • Barna A, Pecz B, Menyhard M (1998) Amorphisation and surface morphology development at low-energy ion milling. Ultramicroscopy 70:161–171

    Article  Google Scholar 

  • Baumann FH (2014) High precision two-dimensional strain mapping in semiconductor devices using nanobeam electron diffraction in the transmission electron microscope. Appl Phys Lett 104:262102

    Article  Google Scholar 

  • Beche A, Rouviere JL, Clement L, Hartmann JM (2009) Improved precision in strain measurement using nanobeam electron diffraction. Appl Phys Lett 95:123114

    Article  Google Scholar 

  • Beche A, Rouviere JL, Barnes JP, Cooper D (2011) Dark field electron holography for strain measurement. Ultramicroscopy 111:227–238

    Article  Google Scholar 

  • Beche A, Rouviere JL, Barnes JP, Cooper D (2013) Strain measurement at the nanoscale: Comparison between convergent beam electron diffraction, nano-beam electron diffraction, high resolution imaging and dark field electron holography. Ultramicroscopy 131:10–23

    Article  Google Scholar 

  • Braidy N, Le Bouar Y, Lazar S, Ricolleau C (2012) Correcting scanning instabilities from images of periodic structures. Ultramicroscopy 118:67–76

    Article  Google Scholar 

  • Buxton BF (1976) Bloch waves and higher-order Laue zone effects in high-energy electron-diffraction. P Roy Soc Lond A 350:335–361

    Article  Google Scholar 

  • Carpenter RW, Spence JCH (1982) Three-dimensional strain-field information in convergent-beam electron diffraction patterns. Acta Cryst A38:55–61

    Article  Google Scholar 

  • Chuvilin A, Kaiser U (2005) On the peculiarities of CBED pattern formation revealed by multislice simulation. Ultramicroscopy 104:73–82

    Article  Google Scholar 

  • Clement L, Pantel R, Kwakman LFT, Rouviere JL (2004) Strain measurements by convergent-beam electron diffraction: The importance of stress relaxation in lamella preparations. Appl Phys Lett 85:651–653

    Article  Google Scholar 

  • Denneulin T, Cooper D, Rouviere JL (2014) Practical aspects of strain measurement in thin SiGe layers by (004) dark-field electron holography in Lorentz mode. Micron 62:52–65

    Article  Google Scholar 

  • Diercks DR, Kaufman MJ, Irwin RB, Jain A, Robertson L, Weijtmans JW, Wise R (2010) Using a <670> zone axis for convergent beam electron diffraction measurements of lattice strain in strained silicon. J Microsc 239:154–158

    Google Scholar 

  • Dingley D (2004) Progressive steps in the development of electron backscatter diffraction and orientation imaging microscopy. J Microsc 213:214–224

    Article  Google Scholar 

  • Du K, Rau Y, Jin-Phillipp NY, Phillipp F (2002) Lattice distortion analysis directly from high resolution transmission electron microscopy images—the LADIA program package. J Mater Sci Technol 18:135–138

    Google Scholar 

  • Fienup JR (1982) Phase retrieval algorithms—a comparison. Appl Opt 21:2758–2769

    Article  Google Scholar 

  • Galindo PL, Kret S, Sanchez AM, Laval JY, Yanez A, Pizarro J, Guerrero E, Ben T, Molina SI (2007) The peak pairs algorithm for strain mapping from hrtem images. Ultramicroscopy 107:1186–1193

    Article  Google Scholar 

  • Gerchberg RW, Saxton WO (1972) A practical algorithm for the determination of the phase from image and diffraction plane pictures. Optik 35, 237

    Google Scholar 

  • Gibson JM, Treacy Michael Matthew John (1984) The effect of elastic relaxation on the local structure of lattice-modulated thin films. Ultramicroscopy 14:345–349

    Article  Google Scholar 

  • Glowacki E, Le Royer C, Morand Y, Pedini JM, Denneulin T, Cooper D, Barnes JP, Nguyen P, Rouchon D, Hartmann JM, Gourhant O, Baylac E, Campidelli Y, Barge D, Bonnin O, Schwarzenbach W (2014) Ultrathin (5 nm) SiGe-on-insulator with high compressive strain (−2 GPa): from fabrication (Ge enrichment process) to in-depth characterizations. Solid-State Electron 97:82–87

    Article  Google Scholar 

  • Guckel H, Randazzo T, Burns DW (1985) A simple technique for the determination of mechanical strain in thin-films with applications to polysilicon. J Appl Phys 57:1671–1675

    Article  Google Scholar 

  • Harscher A, Lichte H (1996) Experimental study of amplitude and phase detection limits in electron holography. Ultramicroscopy 64:57–66

    Article  Google Scholar 

  • Hirsch P, Howie A, Nicolson RB, Pashley DW, Whelan MJ (1977) Electron microscopy of thin crystals. Robert E Krieger Publishing Company, Malabar

    Google Scholar 

  • Houdellier F, Roucau C, Clement L, Rouviere JL, Casanove MJ (2006) Quantitative analysis of HOLZ line splitting in CBED patterns of epitaxially strained layers. Ultramicroscopy 106:951–959

    Article  Google Scholar 

  • Hytch MJ, Snoeck E, Kilaas R (1998) Quantitative measurement of displacement and strain fields from HREM micrographs. Ultramicroscopy 74:131–146

    Article  Google Scholar 

  • Hytch MJ, Putaux JL, Penisson JM (2003) Measurement of the displacement field of dislocations to 0.03 angstrom by electron microscopy. Nature 423:270–273

    Article  Google Scholar 

  • Hytch MJ, Putaux JL, Thibault J (2006) Stress and strain around grain-boundary dislocations measured by high-resolution electron microscopy. Philos Mag 86:4641–4656

    Article  Google Scholar 

  • Hytch M, Houdellier F, Hue F, Snoeck E (2008) Nanoscale holographic interferometry for strain measurements in electronic devices. Nature 453:1086

    Google Scholar 

  • Hytch MJ, Houdellier F, Huee F, Snoeck E (2011) Dark-field electron holography for the measurement of geometric phase. Ultramicroscopy 111:1328–1337

    Article  Google Scholar 

  • Jacob D, Lefebvre A (2003) Interpretation of unexpected rocking curve asymmetry in lacbed patterns of semiconductors. Ultramicroscopy 96:1–9

    Article  Google Scholar 

  • Jacob D, Zuo JM, Lefebvre A, Cordier Y (2008) Composition analysis of semiconductor quantum wells by energy filtered convergent-beam electron diffraction. Ultramicroscopy 108:358–366

    Article  Google Scholar 

  • Janssens KGF, Vanderbiest O, Vanhellemont J, Maes HE, Hull R, Bean JC (1995) Localized strain characterization in semiconductor structures using electron-diffraction contrast imaging. Mater Sci Tech 11:66–71

    Article  Google Scholar 

  • Jones PM, Rackham GM, Steeds JW (1977) Higher-order Laue zone effects in electron-diffraction and their use in lattice-parameter determination. P Roy Soc Lond A 354:197

    Article  Google Scholar 

  • Kasama T, Dunin-Borkowski RE, Beleggia M (2011) In: Ramírez FAM (ed) Electron holography of magnetic materials. Holography—different fields of application. InTech

    Google Scholar 

  • Kaufman MJ, Pearson DD, Fraser HL (1986) The use of convergent-beam electron-diffraction to determine local lattice-distortions in nickel-base superalloys. Philos Mag A 54:79–92

    Article  Google Scholar 

  • Keckes J, Bartosik M, Daniel R, Mitterer C, Maier G, Ecker W, Vila-Comamala J, David C, Schoeder S, Burghammer M (2012) X-ray nanodiffraction reveals strain and microstructure evolution in nanocrystalline thin films. Scripta Mater 67:748–751

    Article  Google Scholar 

  • Kim M, Zuo JM, Park GS (2004) High-resolution strain measurement in shallow trench isolation structures using dynamic electron diffraction. Appl Phys Lett 84:2181–2183

    Article  Google Scholar 

  • Kimoto K, Asaka T, Yu XZ, Nagai T, Matsui Y, Ishizuka K (2010) Local crystal structure analysis with several picometer precision using scanning transmission electron microscopy. Ultramicroscopy 110:778–782

    Article  Google Scholar 

  • Kramer S, Mayer J, Witt C, Weickenmeier A, Ruhle M (2000) Analysis of local strain in aluminium interconnects by energy filtered CBED. Ultramicroscopy 81:245–262

    Article  Google Scholar 

  • LeBeau JM, Findlay SD, Allen LJ, Stemmer S (2008) Quantitative atomic resolution scanning transmission electron microscopy. Phys Rev Lett 100:206101

    Article  Google Scholar 

  • LeBeau JM, Findlay SD, Allen LJ, Stemmer S (2010) Standardless atom counting in scanning transmission electron microscopy. Nano Lett 10:4405–4408

    Article  Google Scholar 

  • Lichte H (1995) In: Tonomura A, Allard LF, Pozzi G, Joy DC, Ono YA (eds) Electron holography

    Google Scholar 

  • Lichte H (2008) Performance limits of electron holography. Ultramicroscopy 108:256–262

    Article  Google Scholar 

  • Lin YP, Bird DM, Vincent R (1989) Errors and correction term for HOLZ line simulations. Ultramicroscopy 27:233–240

    Article  Google Scholar 

  • Martin Y, Zuo JM, Favre-Nicolin V, Rouviere JL (2016) Measuring lattice parameters and local rotation using convergent beam electron diffraction: one step further. Ultramicroscopy 160:64–73

    Google Scholar 

  • Matteucci G, Missiroli F, Pozzi G (1998) Electron holography of long-range electrostatic fields. Adv Imag Elect Phys 99:178–240

    Google Scholar 

  • Mayer J, Giannuzzi LA, Kamino T, Michael J (2007) TEM sample preparation and FIB-induced damage. MRS Bull 32:400–407

    Article  Google Scholar 

  • Midgley PA (2001) An introduction to off-axis electron holography. Micron 32:167–184

    Article  Google Scholar 

  • Nakanishi N, Yamazaki T, Recnik A, Ceh M, Kawasaki M, Watanabe K, Shiojiri M (2002) Retrieval process of high-resolution HAADF-STEM images. J Electron Microsc 51:383–390

    Article  Google Scholar 

  • Nix WD (1989) Mechanical-properties of thin-films. Metall Trans A 20:2217–2245

    Article  Google Scholar 

  • Ophus C, Ciston J, Nelson CT (2016) Correcting nonlinear drift distortion of scanning probe and scanning transmission electron microscopies from image pairs with orthogonal scan directions. Ultramicroscopy 162:1–9

    Article  Google Scholar 

  • Rose H (1995) In: Reimer L (ed) Energy-filtering transmission electron microscopy. Springer, Berlin

    Google Scholar 

  • Rouviere JL, Sarigiannidou E (2005) Theoretical discussions on the geometrical phase analysis. Ultramicroscopy 106:1–17

    Article  Google Scholar 

  • Rouviere JL, Beche A, Martin Y, Denneulin T, Cooper D (2013) Improved strain precision with high spatial resolution using nanobeam precession electron diffraction. Appl Phys Lett 103:241913

    Article  Google Scholar 

  • Rouvière JL, Mouti A, Stadelmann P (2011) Measuring strain on HR-STEM images: Application to threading dislocations in Al0.8In0.2N. J Phys: Conf Ser 326:012022

    Google Scholar 

  • Rozeveld SJ, Howe JM (1993) Determination of multiple lattice-parameters from convergent-beam electron-diffraction patterns. Ultramicroscopy 50:41–56

    Article  Google Scholar 

  • Sang XH, LeBeau JM (2014) Revolving scanning transmission electron microscopy: correcting sample drift distortion without prior knowledge. Ultramicroscopy 138:28–35

    Article  Google Scholar 

  • Senez V, Armigliato A, De Wolf I, Carnevale G, Balboni R, Frabboni S, Benedetti A (2003) Strain determination in silicon microstructures by combined convergent beam electron diffraction, process simulation, and micro-raman spectroscopy. J Appl Phys 94:5574–5583

    Article  Google Scholar 

  • Spence JCH (2013) High resolution electron microscopy, 4th edn. Oxford University Press, Oxford

    Book  Google Scholar 

  • Spence JCH, Weierstall U, Howells M (2002) Phase recovery and lensless imaging by iterative methods in optical, x-ray and electron diffraction. Philos T Roy Soc A 360:875–895

    Article  Google Scholar 

  • Spessot A, Frabboni S, Balboni R, Armigliato A (2007) Method for determination of the displacement field in patterned nanostructures by TEM/CBED analysis of split high-order Laue zone line profiles. J Microsc 226:140–155

    Article  Google Scholar 

  • Stoney GG (1909) The tension of metallic films deposited by electrolysis. Proc Royal Soc Lond A 82:172–175

    Article  Google Scholar 

  • Tao J, Niebieskikwiat D, Varela M, Luo W, Schofield MA, Zhu Y, Salamon MB, Zuo JM, Pantelides ST, Pennycook SJ (2009) Direct imaging of nanoscale phase separation in La0.55Ca0.45MnO3: relationship to colossal magnetoresistance. Phys Rev Lett 103:097202

    Article  Google Scholar 

  • Twigg ME, Chu SNG, Joy DC, Maher DM, Macrander AT, Chin AK (1987) Relative lattice-parameter measurement of submicron quaternary (InGaAsP) device structures grown on inp substrates. J Appl Phys 62:3156–3160

    Article  Google Scholar 

  • Uesugi F, Hokazono A, Takeno S (2011) Evaluation of two-dimensional strain distribution by STEM/NBD. Ultramicroscopy 111:995–998

    Article  Google Scholar 

  • Van Aert S, Verbeeck J, Erni R, Bals S, Luysberg M, Van Dyck D, Van Tendeloo G (2009) Quantitative atomic resolution mapping using high-angle annular dark field scanning transmission electron microscopy. Ultramicroscopy 109:1236–1244

    Article  Google Scholar 

  • Vaudin MD, Gerbig YB, Stranick SJ, Cook RF (2008) Comparison of nanoscale measurements of strain and stress using electron back scattered diffraction and confocal raman microscopy. Appl Phys Lett 93:193116

    Article  Google Scholar 

  • Verbeeck J, Bertoni G, Lichte H (2011) A holographic biprism as a perfect energy filter? Ultramicroscopy 111:887–893

    Article  Google Scholar 

  • Villert S, Maurice C, Wyon C, Fortunier R (2009) Accuracy assessment of elastic strain measurement by EBSD. J Microsc 233:290–301

    Article  Google Scholar 

  • Vincent R, Walsh TD, Pozzi M (1999) Iterative phase retrieval from kinematic rocking curves in CBED patterns. Ultramicroscopy 76:125–137

    Article  Google Scholar 

  • Wilkinson AJ, Meaden G, Dingley DJ (2006a) High resolution mapping of strains and rotations using electron backscatter diffraction. Mater Sci Technol 22:1271–1278

    Article  Google Scholar 

  • Wilkinson AJ, Meaden G, Dingley DJ (2006b) High-resolution elastic strain measurement from electron backscatter diffraction patterns: new levels of sensitivity. Ultramicroscopy 106:307–313

    Article  Google Scholar 

  • Zhang P, Istratov AA, Weber ER, Kisielowski C, He H, Nelson C, Spence JC (2006) Direct strain measurement in a 65 nm node strained silicon transistor by convergent-beam electron diffraction. Appl Phys Lett 89:161907

    Article  Google Scholar 

  • Zuo JM (1992) Automated lattice-parameter measurement from HOLZ lines and their use for the measurement of oxygen-content in YBa2Cu3O7-Δ from nanometer-sized region. Ultramicroscopy 41:211–223

    Article  Google Scholar 

  • Zuo JM, Spence JCH (1993) Coherent electron nanodiffraction from perfect and imperfect crystals. Philos Mag A 68:1055–1078

    Article  Google Scholar 

  • Zuo JM, Tao J (2011) Scanning electron nanodiffraction and diffraction imaging. In: Pennycook S, Nellist P (eds) Scanning transmission electron microscopy. Springer, New York

    Google Scholar 

  • Zuo JM, Kim M, Holmestad R (1998) A new approach to lattice parameter measurements using dynamic electron diffraction and pattern matching. J Electron Microsc 47:121–127

    Article  Google Scholar 

  • Zuo JM, Gao M, Tao J, Li BQ, Twesten R, Petrov I (2004) Coherent nano-area electron diffraction. Microsc Res Tech 64:347–355

    Article  Google Scholar 

  • Zuo J-M, Shah AB, Kim H, Meng Y, Gao W, Rouviére J-L (2014) Lattice and strain analysis of atomic resolution Z-contrast images based on template matching. Ultramicroscopy 136:50–60

    Article  Google Scholar 

  • Zuo JM, Zhang J, Rouviere J-L (2016) Transistor strain measurement using electron beam techniques. In: ZMADG Seiler (ed) Characterization and metrology for nanoelectronics and nanostructures. Pan Stanford Publishing Pte Ltd (in print)

    Google Scholar 

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Correspondence to Jian Min Zuo or John C. H. Spence .

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Zuo, J.M., Spence, J.C.H. (2017). Strain Measurements and Mapping. In: Advanced Transmission Electron Microscopy. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6607-3_16

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