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Critical Conditions of Dislocation Generation in Core-Shell Nanowires: A Review
Authors
A.M. Smirnov 1 , S.A. Krasnitckii 1, 2 , S.S. Rochas 1 , M.Yu. Gutkin 1, 2, 31 School of Photonics, ITMO University, Kronverkskiy pr. 49, St. Petersburg, 197101, Russia
2 Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bolshoj 61, Vasil. Ostrov, St. Petersburg 199178, Russia
3 Higher School of Mechanics and Control Processes, Peter the Great St. Petersburg Polytechnic University, Polytekhnicheskaya 29, St. Petersburg 195251, Russia
Rev. Adv. Mater. Technol., 2020, vol. 2, no. 3, pp. 19–43
Foundings
Ministry of Science and Higher Education of the Russian Federation: project No. 2019-1442.
- Y. Chong, A Brief Review on the Recent Progress of Superconducting Nanowire Single Photon Detectors, Prog. Supercond. Cryog., 2017, vol. 19, no. 4, pp. 22–25.
- J.-W. Min, D. Priante, M. Tangi, G. Liu, C.H. Kang, A. Prabaswara, C. Zhao, L. Al-Maghrabi, Y. Alaskar, A.M. Albadri, A.Y. Alyamani, T.K. Ng and B.S. Ooi, Unleashing the Potential of Molecular Beam Epitaxy Grown AlGaN-Based Ultraviolet-Spectrum Nanowires Devices, J. Nanophotonics, 2018, vol. 12, no. 4, art. 043511.
- A. Sajid, M.J. Ford and J.R. Reimers, Single-Photon Emitters in Hexagonal Boron Nitride: a Review of Progress, Reports Prog. Phys., 2020, vol. 83, no. 4, art. 044501.
- J.S. Marsland, On the Effect of Ionization Dead Spaces on Avalanche Multiplication and Noise for Uniform Electric Fields, J. Appl. Phys., 1990, vol. 67, no. 4, pp. 1929–1933.
- C. Hu, K.A. Anselm, B.G. Streetman and J.C. Campbell, Noise Characteristics of Thin Multiplication Region GaAs Avalanche Photodiodes, Appl. Phys. Lett., 1996, vol. 69, no. 24, pp. 3734–3736.
- K. Kim and K. Hess, Simulations of Electron Impact Ionization Rate in GaAs in Nonuniform Electric Fields, J. Appl. Phys., 1986, vol. 60, no. 7, pp. 2626–2629.
- G. Bulgarini, M.E. Reimer, M. Hocevar, E.P.A.M. Bakkers, L.P. Kouwenhoven and V. Zwiller, Avalanche Amplification of a Single Exciton in a Semiconductor Nanowire, Nat. Photonics, 2012, vol. 6, no. 7, pp. 455–458.
- A.C. Farrell, P. Senanayake, C.-H. Hung, G. El-Howayek, A. Rajagopal, M. Currie, M.M. Hayat and D.L. Huffaker, Plasmonic Field Confinement for Separate Absorption-multiplication in InGaAs Nanopillar Avalanche Photodiodes, Sci. Rep., 2015, vol. 5, no. 1, art. 17580.
- V. Jain, M. Heurlin, E. Barrigon, L. Bosco, A. Nowzari, S. Shroff, V. Boix, M. Karimi, R.J. Jam, A. Berg, L. Samuelson, M.T. Borgström, F. Capasso and H. Pettersson, InP/InAsP Nanowire-Based Spatially Separate Absorption and Multiplication Avalanche Photodetectors, ACS Photonics, 2017, vol. 4, no. 11, pp. 2693–2698.
- A.C. Farrell, X. Meng, D. Ren, H. Kim, P. Senanayake, N.Y. Hsieh, Z. Rong, T.-Y. Chang, K.M. Azizur-Rahman and D.L. Huffaker, InGaAs–GaAs Nanowire Avalanche Photodiodes Toward Single-Photon Detection in Free-Running Mode, Nano Lett., 2019, vol. 19, no. 1, pp. 582–590.
- S. Giaremis, P. Komninou, I. Belabbas, J. Chen and J. Kioseoglou, Structural and Electronic Properties of a Edge Dislocations Along ⟨1-100⟩ in GaN, J. Appl. Phys., 2018, vol. 123, no. 24, art. 244301.
- I. Goldthorpe, A.F. Marshall and P.C. Mcintyre, Synthesis and Strain Relaxation of Ge-Core / Si-Shell Nanowire Arrays, Nano Lett., 2008, vol. 8, no. 11, pp. 4081–4086.
- K.L. Kavanagh, I. Saveliev, M. Blumin, G. Swadener and H.E. Ruda, Faster Radial Strain Relaxation in InAs–GaAs Core–Shell Heterowires, J. Appl. Phys., 2012, vol. 111, no. 4, art. 044301.
- G. Perillat-Merceroz, R. Thierry, P.-H. Jouneau, P. Ferret and G. Feuillet, Strain Relaxation by Dislocation Glide in ZnO/ZnMgO Core-Shell Nanowires, Appl. Phys. Lett., 2012, vol. 100, no. 17, art. 173102.
- S. Lee, A. Vaid, J. Im, B. Kim, A. Prakash, J. Guénolé, D. Kiener, E. Bitzek and S.H. Oh, In-situ Observation of the Initiation of Plasticity by Nucleation of Prismatic Dislocation Loops, Nat. Commun., 2020, vol. 11, no. 1, art. 2367.
- E. Ertekin, P.A. Greaney, D.C. Chrzan and T.D. Sands, Equilibrium Limits of Coherency in Strained Nanowire Heterostructures, J. Appl. Phys., 2005, vol. 97, no. 11, art. 114325.
- F. Glas, Critical Dimensions for the Plastic Relaxation of Strained Axial Heterostructures in Free-Standing Nanowires, Phys. Rev. B., 2006, vol. 74, no. 12, art. 121302.
- A. Arumbakkam, E. Davidson and A. Strachan, Heteroepitaxial Integration of Metallic Nanowires: Transition from Coherent to Defective Interfaces via Molecular Dynamics, Nanotechnology, 2007, vol. 18, no. 34, art. 345705.
- M. de la Mata, C. Magén, P. Caroff and J. Arbiol, Atomic Scale Strain Relaxation in Axial Semiconductor III–V Nanowire Heterostructures, Nano Lett., 2014, vol. 14, no. 11, pp. 6614–6620.
- H. Ye and Z. Yu, Plastic Relaxation of Mixed Dislocation in Axial Nanowire Heterostructures Using Peach-Koehler Approach, Phys. Status Solidi – Rapid Res. Lett., 2014, vol. 8, no. 5, pp. 445–448.
- F. Glas, Strain in Nanowires and Nanowire Heterostructures, In: Semicond. Nanowires I Growth Theory, Semicond. Semimetals, ed. by A.F.I. Morral, S.A. Dayeh and C. Jagadish (Elsevier Inc., 2015), pp. 79–123.
- X. Kong, S. Albert, A. Bengoechea-Encabo, M.A. Sanchez-Garcia, E. Calleja and A. Trampert, Lattice Pulling Effect and Strain Relaxation in Axial (In,Ga)N/GaN Nanowire Heterostructures Grown on GaN-Buffered Si(111) Substrate, Phys. Status Solidi., 2015, vol. 212, no. 4, pp. 736–739.
- M.Yu. Gutkin, I.A. Ovid’ko and A.G. Sheinerman, Misfit Dislocations in Wire Composite Solids, J. Phys. Condens. Matter., 2000, vol. 12, no. 25, pp. 5391–5401.
- A.G. Sheinerman and M.Yu. Gutkin, Misfit Disclinations and Dislocation Walls in a Two-Phase Cylindrical Composite, Phys. Status Solidi., 2001, vol. 184, no. 2, pp. 485–505.
- H.-M. Lin, Y.-L. Chen, J. Yang, Y.-C. Liu, K.-M. Yin, J.-J. Kai, F.-R. Chen, L.-C. Chen, Y.-F. Chen and C.-C. Chen, Synthesis and Characterization of Core−Shell GaP@GaN and GaN@GaP Nanowires, Nano Lett.,. 2003, vol. 3, no. 4, pp. 537–541.
- I.A. Ovid’ko and A.G. Sheinerman, Misfit Dislocation Loops in Composite Nanowires, Philos. Mag., 2004, vol. 84, pp. 2103–2118.
- S. Raychaudhuri and E.T. Yu, Critical Dimensions in Coherently Strained Coaxial Nanowire Heterostructures, J. Appl. Phys., 2006, vol. 99, no. 11, art. 114308.
- I.A. Ovid’ko and A.G. Sheinerman, Misfit Dislocations in Nanocomposites with Quantum Dots, Nanowires and their Ensembles, Adv. Phys., 2006, vol. 55, no. 7–8, pp. 627–689.
- K.E. Aifantis, A.L. Kolesnikova and A.E. Romanov, Nucleation of Misfit Dislocations and Plastic Deformation in Core/Shell Nanowires, Philos. Mag., 2007, vol. 87, no. 30, pp. 4731–4757.
- I.A. Goldthorpe, A.F. Marshall and P.C. McIntyre, Inhibiting Strain-Induced Surface Roughening: Dislocation-Free Ge/Si and Ge/SiGe Core−Shell Nanowires, Nano Lett., 2009, vol. 9, no. 11, pp. 3715–3719.
- J. Colin, Prismatic Dislocation Loops in Strained Core-Shell Nanowire Heterostructures, Phys. Rev. B - Condens. Matter Mater. Phys., 2010, vol. 82, no. 5, art. 054118.
- X. Wang, E. Pan and P.W. Chung, Misfit Dislocation Dipoles in Wire Composite Solids, Int. J. Plast., 2010, vol. 26, no. 9, pp. 1415–1420.
- H.J. Chu, J. Wang, C.Z. Zhou and I.J. Beyerlein, Self-Energy of Elliptical Dislocation Loops in Anisotropic Crystals and its Application for Defect-Free Core/Shell Nanowires, Acta Mater., 2011, vol. 59, no. 18, pp. 7114–7124.
- M.Yu. Gutkin, K.V. Kuzmin and A.G. Sheinerman, Misfit Stresses and Relaxation Mechanisms in a Nanowire Containing a Coaxial Cylindrical Inclusion of Finite Height, Phys. Status Solidi., 2011, vol. 248, no. 7, pp. 1651–1657.
- K.L. Kavanagh, J. Salfi, I. Savelyev, M. Blumin and H.E. Ruda, Transport and Strain Relaxation in Wurtzite InAs–GaAs Core-Shell Heterowires, Appl. Phys. Lett., 2011, vol. 98, no. 15, art. 152103.
- R. Popovitz-Biro, A. Kretinin, P. Von Huth and H. Shtrikman, InAs/GaAs Core–Shell Nanowires, Cryst. Growth Des., 2011, vol. 11, no. 9, pp. 3858–3865.
- C.M. Haapamaki, J. Baugh and R.R. LaPierre, Critical Shell Thickness for InAs-AlxIn1−xAs(P) Core-Shell Nanowires, J. Appl. Phys., 2012, vol. 112, no. 12, art. 124305.
- S.G. Ghalamestani, M. Heurlin, L.-E. Wernersson, S. Lehmann and K.A. Dick, Growth of InAs/InP Core–Shell Nanowires with Various Pure Crystal Structures, Nanotechnology, 2012, vol. 23, no. 28, art. 285601.
- A. Nie, J. Liu, Q. Li, Y. Cheng, C. Dong, W. Zhou, P. Wang, Q. Wang, Y. Yang, Y. Zhu, Y. Zeng and H. Wang, Epitaxial TiO2/SnO2 Core-Shell Heterostructure by Atomic Layer Deposition, J. Mater. Chem., 2012, vol. 22, no. 21, pp. 10665–10671.
- A. Biermanns, T. Rieger, G. Bussone, U. Pietsch, D. Grützmacher and M.I. Lepsa, Axial Strain in GaAs/InAs Core-Shell Nanowires, Appl. Phys. Lett., 2013, vol. 102, no. 4, art. 043109.
- B.T. Sneed, C.N. Brodsky, C.H. Kuo, L.K. Lamontagne, Y. Jiang, Y. Wang, F. Tao, W. Huang and C.K. Tsung, Nanoscale-Phase-Separated Pd-Rh Boxes Synthesized via Metal Migration: An Archetype for Studying Lattice Strain and Composition Effects in Electrocatalysis, J. Am. Chem. Soc., 2013, vol. 135, no. 39, pp. 14691–14700.
- S.A. Dayeh, W. Tang, F. Boioli, K.L. Kavanagh, H. Zheng, J. Wang, N.H. Mack, G. Swadener, J.Y. Huang, L. Miglio, K.-N. Tu and S.T. Picraux, Direct Measurement of Coherency Limits for Strain Relaxation in Heteroepitaxial Core/Shell Nanowires, Nano Lett., 2013, vol. 13, no. 5, pp. 1869–1876.
- O. Salehzadeh, K.L. Kavanagh and S.P. Watkins, Growth and Strain Relaxation of GaAs and GaP Nanowires with GaSb Shells, J. Appl. Phys., 2013, vol. 113, no. 13, art. 134309.
- O. Salehzadeh, K.L. Kavanagh and S.P. Watkins, Geometric Limits of Coherent III-V Core/Shell Nanowires, J. Appl. Phys., 2013, vol. 114, no. 5, art. 054301.
- Y.X. Zhao, Q.H. Fang and Y.W. Liu, Edge Misfit Dislocations in Core–Shell Nanowire with Surface/Interface Effects and Different Elastic Constants, Int. J. Mech. Sci., 2013, vol. 74, pp. 173–184.
- M.Yu. Gutkin and A.M. Smirnov, Initial Stages of Misfit Stress Relaxation by Rectangular Prismatic Dislocation Loops in Composite Nanostructures, J. Phys. Conf. Ser., 2014, vol. 541, no. 1, art. 012007.
- M.Yu. Gutkin, S.A. Krasnitckii, A.M. Smirnov, A.L. Kolesnikova and A.E. Romanov, Dislocation Loops in Solid and Hollow Semiconductor and Metal Nanoheterostructures, Phys. Solid State., 2015, vol. 57, no. 6, pp. 1177-1182.
- M.Yu. Gutkin AND A.M. Smirnov, Initial Stages of Misfit Stress Relaxation in Composite Nanostructures through Generation of Rectangular Prismatic Dislocation Loops, Acta Mater., 2015, vol. 88, pp. 91–101.
- C. Enzevaee, M.Y. Gutkin and H.M. Shodja, Surface/Interface Effects on the Formation of Misfit Dislocation in a Core–Shell Nanowire, Philos. Mag., 2014, vol. 94, no. 5, pp. 492–519.
- J. Colin, Circular Dislocation Loop in a Three-Layer Nanowire, Int. J. Solids Struct., 2015, vol. 63, pp. 114–120.
- B.M. Nguyen, B. Swartzentruber, Y.G. Ro and S.A. Dayeh, Facet-Selective Nucleation and Conformal Epitaxy of Ge Shells on Si Nanowires, Nano Lett., 2015, vol. 15, no. 11, pp. 7258–7264.
- M.B. Katz, M.E. Twigg and S.M. Prokes, Formation and Stability of Crystalline and Amorphous Al2O3 Layers Deposited on Ga2O3 Nanowires by Atomic Layer Epitaxy, J. Appl. Phys., 2016, vol. 120, no. 12, art. 124311.
- S.A. Krasnitckii, A.M. Smirnov and M.Yu. Gutkin, Misfit Stresses in a Core-Shell Nanowire with Core in the Form of Long Parallelepiped, J. Phys. Conf. Ser., 2016, vol. 690, art. 012022.
- M.Yu. Gutkin and A.M. Smirnov, Initial Stages of Misfit Stress Relaxation through the Formation of Prismatic Dislocation Loops in GaN–Ga2O3 Composite Nanostructures, Phys. Solid State, 2016, vol. 58, no. 8, pp. 1611–1621.
- S.A. Krasnitckii, D.R. Kolomoetc, A.M. Smirnov and M.Yu. Gutkin, Misfit Stresses in a Composite Core-Shell Nanowire with an Eccentric Parallelepipedal Core Subjected to One-Dimensional Cross Dilatation Eigenstrain, J. Phys. Conf. Ser., 2017, vol. 816, art. 012043.
- R.B. Lewis, L. Nicolai, H. Küpers, M. Ramsteiner, A. Trampert and L. Geelhaar, Anomalous Strain Relaxation in Core–Shell Nanowire Heterostructures via Simultaneous Coherent and Incoherent Growth, Nano Lett., 2017, vol. 17, no. 1, pp. 136–142.
- Y.C. Lin, D. Kim, Z. Li, B.M. Nguyen, N. Li, S. Zhang and J. Yoo, Strain-Induced Structural Defects and their Effects on the Electrochemical Performances of Silicon Core/Germanium Shell Nanowire Heterostructures, Nanoscale, 2017, vol. 9, no. 3, pp. 1213–1220.
- S.A. Krasnitckii, D.R. Kolomoetc, A.M. Smirnov and M.Yu. Gutkin, Misfit Stress Relaxation in Composite Core-Shell Nanowires with parallelepiped Cores Using Rectangular Prismatic Dislocation Loops, J. Phys. Conf. Ser., 2018, vol. 993, no. 1, art. 012021.
- A.M. Smirnov, E.C. Young, V.E. Bougrov, J.S. Speck and A.E. Romanov, Stress Relaxation in Semipolar and Nonpolar III-Nitride Heterostructures by Formation of Misfit Dislocations of Various Origin, J. Appl. Phys., 2019, vol. 126, art. 245104.
- S.A. Krasnitckii, A.M. Smirnov and M.Yu. Gutkin, Axial Misfit Stress Relaxation in Core–Shell Nanowires with Polyhedral Cores through the Nucleation of Misfit Prismatic Dislocation Loops, J. Mater. Sci., 2020, vol. 55, no. 22, pp. 9198–9210.
- A.M. Smirnov, S.A. Krasnitckii and M.Yu. Gutkin, Generation of Misfit Dislocations in a Core-Shell Nanowire near the Edge of Prismatic Core, Acta Mater., 2020, vol. 186, pp. 494–510.
- S.A. Krasnitckii, A.M. Smirnov and M.Yu. Gutkin, Pair Interaction of Coaxial Circular Prismatic Dislocation Loops in Elastic Solids with Spherical Surfaces, Mater. Phys. Mech., 2020, vol. 44, no. 1, pp. 116–124.
- A.P. Chernakov, A.L. Kolesnikova, M.Yu. Gutkina and A.E. Romanov, Periodic Array of Misfit Dislocation Loops and Stress Relaxation in Core-Shell Nanowires, Int. J. Eng. Sci., 2020, vol. 156, art. 103367.
- F.C. Frank and J.H. Van der Merwe, One-Dimensional Dislocations. I. Static Theory, Proc. Roy. Soc. London A, 1949, vol. 198, pp. 205–225.
- J.W. Matthews, Defects Associated with the Accommodation of Misfit between Crystals, J. Vac. Sci. Technol., 1975, vol. 12, no. 1, pp. 126–133.
- V.I. Vladimirov, M.Yu. Gutkin and A.E. Romanov, Influence of Free Surface on Equiponderant Stress State in Heteroepitaxial Systems, Poverkhnost'. Fizika, khimiya, mekhanika (USSR), 1988, no. 6, pp. 46–51, In Russian.
- M.Yu. Gutkin and A.E. Romanov, States of the Interfacial Defect Structures in Thin-Film Heterosystems, Sov. Phys. – Solid State (USA), 1990, vol. 32, no. 5, pp. 751–753.
- J.R. Willis, S.C. Jain and R. Bullough, The Energy of an Array of Dislocations: Implications for Strain Relaxation in Semiconductor Heterostructures, Philos. Mag. A, 1990, vol. 62, no. 1, pp. 115–129.
- A. Rocket and C.J. Kiely, Energetics of Misfit- and Threading-Dislocation Arrays in Heteroepitaxial Films, Phys. Rev. B, 1991, vol. 44, no. 3, pp. 1154–1162.
- A. Atkinson and S.C. Jain, The Energy of Systems of Misfit Dislocations in Epitaxial Strained Layers, Thin Solid Films, 1992, vol. 222, no. 1-2, pp. 161–165.
- A. Atkinson and S.C. Jain, The Energy of Finite Systems of Misfit Dislocations in Epitaxial Strained Layers, J. Appl. Phys., 1992, vol. 72, no. 6, pp. 2242–2248.
- T.J. Gosling, S.C. Jain, J.R. Willis, A. Atkinson and R. Bullough, Stable Configurations in Strained Epitaxial Layers, Philos. Mag. A, 1992, vol. 66, no. 1, pp. 119–132.
- M.Yu. Gutkin and A.E. Romanov, Misfit Dislocations in a Thin Two-Phase Heteroepitaxial Plate, Phys. Stat. Sol. A, 1992, vol. 129, no. 2, pp. 117–126.
- S.C. Jain, T.J. Gosling, J.R. Willis, R. Bullough and P. Balk, Theoretical Comparison of the Stability Characteristics of Capped and Uncapped GexSi1–x Strained Epilayers, Solid-State Electronics, 1992, vol. 35, no. 8, pp. 1073–1079.
- S.C. Jain, T.J. Gosling, J.R. Willis, D.H.J. Totterdell and R. Bullough, A New Study of Critical Layer Thickness, Stability and Strain Relaxation in Pseudomorphic GexSi1–x Strained Epilayers, Philos. Mag. A, 1992, vol. 65, no. 5, pp. 1151–1167.
- T.J. Gosling, R. Bullough, S.C. Jain and J.R. Willis, Misfit Dislocation Distributions in Capped (Buried) Strained Semiconductor Layers, J. Appl. Phys., 1993, vol. 73, no. 12, pp. 8267–8268.
- M.Yu. Gutkin, A.L. Kolesnikova and A.E. Romanov, Misfit Dislocations and Other Defects in Thin Films, Mater. Sci. Eng. A, 1993, vol. 164, no. 1-2, pp. 433–437.
- U. Jain, S.C. Jain, J. Nijs, J.R. Willis, R. Bullough, R.P. Mertens and R. Van Oversraeten, Calculation of Critical-Layer-Thickness and Strain Relaxation in GexSi1–x Strained Layers with Interacting 60 and 90º Dislocations, Solid State Electronics, 1993, vol. 36, no. 3, pp. 331–337.
- T.J. Gosling and J.R. Willis, The Energy of Arrays of Dislocations in an Anisotropic Half-Space, Philos. Mag. A, 1994, vol. 69, no. 1, pp. 5–50.
- F. Bailly, M. Barbé and G. Cohen-Solal, Setting up of Misfit Dislocations in Heteroepitaxial Growth and Critical Thicknesses, J. Cryst. Growth, 1995, vol. 153, no. 3-4, pp. 115–122.
- M.Yu. Gutkin, K.N. Mikaelyan and I.A. Ovid'ko, Equilibrium Configurations of Partial Misfit Dislocations in Thin-Film Heterosystems, Phys. Solid State, 1998, vol. 40, no. 11, pp. 1864–1869.
- Yu.A. Tkhorik and L.S. Khazan, Plastic Deformation and Misfit Dislocations in Heteroepitaxial Systems (Naukova Dumka, Kiev, 1983), In Russian.
- L.B. Freund and S. Suresh, Thin Film Materials. Stress. Defect Formation and Surface Evolution (Cambridge University Press, Cambridge, UK, 2003).
- M.Yu. Gutkin and I.A. Ovid'ko, Physical Mechanics of Deformed Nanostructures. Vol. II. Nanolayered Structures (Yanus, Saint-Petersburg, 2005), In Russian.
- M.Yu. Gutkin, Strength and Plasticity of Nanocomposites: Textbook (Izdatel’stvo Politekhnicheskogo universiteta, 2011), In Russian.
- H.M. Shodja, C. Enzevaee and M.Yu. Gutkin, Interface Effect on the Formation of a Dipole of Screw Misfit Dislocations in an Embedded Nanowire with Uniform Shear Eigenstrain Field, European Journal of Mechanics – A /Solids, 2015, vol. 51, no. 1, pp. 154-159.
- J.W. Gibbs, The Scientific Papers of J. Willard Gibbs, Vol. 1 (Longmans Green, London, 1906).
- R. Shuttleworth, The Surface Tension of Solids, Proc. Phys. Soc. A, 1950, vol. 63, pp. 445–458.
- M.E. Gurtin and A.I. Murdoch, A Continuum Theory of Elastic Material Surfaces, Arch. Rational Mech. Anal., 1975, vol. 57, pp. 291–323.
- M.E. Gurtin and A.I. Murdoch, Surface Stress in Solids, Int. J. Solids Struct, 1978, vol. 14, pp. 431–440.
- R.C. Cammarata, Surface and Interface Stress Effects in Thin Film, Prog. Surf. Sci., 1994, vol. 46, pp. 1–38.
- M.E. Gurtin, J. Weissmuller and F. Larché, A General Theory of Curved Deformable Interfaces in Solids at Equilibrium, Phil. Mag. A, 1998, vol. 78, pp. 1093–1109.
- H. Altenbach, V.A. Eremeyev and N.F. Morozov, On Equations of the Linear Theory of Shells with Surface Stresses Taken into Account, Mechanics of Solids, 2010, vol. 45, pp. 331–342.
- R.V. Goldstein, V.A. Gorodtsov and K.B. Ustinov, Effect of Residual Surface Stress and Surface Elasticity on Deformation of Nanometer Spherical Inclusions in an Elastic Matrix, Phys. Mesomech., 2010, vol. 13, pp. 318–328.
- M.A. Grekov and T.S. Sergeeva, Interaction of Edge Dislocation Array with Biomaterial Interface Incorporating Interface Elasticity, Int. J. Engng. Sci., 2020, vol. 149, pp. 103233(1)–103233(17).
- P. Sharma and S. Ganti, Size-Dependent Eshelby’s Tensor for Embedded Nano-Inclusions Incorporating Surface/Interface Energies, J. Appl. Mech., 2004, vol. 71, pp. 663–671.
- P. Sharma, S. Ganti and N. Bhate, Effect of Surfaces on Size-Dependent Elastic State of Nanoinhomogeneities, Appl. Phys. Lett., 2003, vol. 82, pp. 535–537.
- L. Tian and R.K.N.D. Rajapakse, Elastic Field of an Isotropic Matrix with a Nanoscale Elliptical Inhomogeneity, Int. J. Solids Struct., 2007, vol. 44, pp. 7988–8005.
- S. Timoshenko and J.N. Goodier, Theory of Elasticity (McGraw-Hill Book Co., New York / Toronto / London, 1951).
- I.A. Ovid’ko and A.G. Sheinerman, Mechanics of Nanowires and Nanostructured Films ( Exlibris-Nord, Saint-Petersburg, 2011), In Russian.
- A.L. Kolesnikova and A.E. Romanov, Dislocation and Disclination Loops in the Virtual-Defect Method, Phys. Solid State, 2003, vol. 45, no. 9, pp. 1706–1718.
- A.L. Kolesnikova and A.E. Romanov, Virtual Circular Dislocation-Disclination Loop Technique in Boundary Value Problems in the Theory of Defects, J. Appl. Mech., 2004, vol. 71, no. 3, pp. 409–417.
- M.Yu. Gutkin, M. Militzer, A.E. Romanov and V.I. Vladimirov, Equilibrium Position of Misfit Dislocations, Phys. Stat. Sol. (a), 1989, vol. 113, no. 2, pp. 337–344.
- M.Yu. Gutkin and A.E. Romanov, Misfit Dislocations in a Thin Two-Phase Heteroepitaxial Plate, Phys. Stat. Sol. (a), 1992, vol. 129, no. 2, pp. 117–126.
- M.Yu. Gutkin and A.E. Romanov, On the Stand-off Positions of Misfit Dislocations, Phys. Stat. Sol. (a), 1994, vol. 144, no. 1, pp. 39–57.
- A.I. Lurie, Spatial Problems of Theory of Elasticity (State Publishing House of Scientific and Technical Literature , Moscow, 1955), In Russian.
- M.Y. Gutkin, I.A. Ovid’ko and A.G. Sheinerman, Misfit Dislocations in Composites with Nanowires, J. Physics – Condensed Matter., 2003, vol. 15, no. 21, pp. 3539–3554.
- M.Yu. Gutkin, Misfit Stress Relaxation in Composite Nanoparticles, Intern. J. Eng. Sci., 2012, vol. 61 (Special Issue), pp. 59–74.
- M.Yu. Gutkin, A.L. Kolesnikova, S.A. Krasnitckii and A.E. Romanov, Misfit Dislocation Loops in Composite Core-Shell Nanoparticles, Phys. Solid State, 2014, vol. 56, no. 4, pp. 723–730.
- M.Yu. Gutkin, A.L. Kolesnikova, S.A. Krasnitckii, A.E. Romanov and A.G. Shalkovskii, Misfit Dislocation Loops in Hollow Core-Shell Nanoparticles, Scripta Materialia, 2014, vol. 83, no. 1, pp. 1–4.
- M.Yu. Krauchanka, S.A. Krasnitckii, M.Yu. Gutkin, A.L. Kolesnikova and A.E. Romanov, Circular Loops of Misfit Dislocations in Decahedral Core-Shell Nanoparticles, Scripta Materialia, 2019, vol. 167, pp. 81-85.
- M.Yu. Gutkin and A.M. Smirnov, Generation of Rectangular Prismatic Dislocation Loops in Shells and Cores of Composite Nanoparticles, Phys. Solid State, 2014, vol. 56, no. 4, pp. 731–738.
- I.A. Ovid’ko and A.G. Sheinerman, Perfect, Partial, and Split Dislocations in Quantum Dots, Phys. Rev. B, 2002, vol. 66, art. 245309.
Volume 2, No 3
pages 19-43
History
Receive Date:
03
August
2020
Accepted Date:
29
March
2026
Available online:
29
March
2026
© 2020 ITMO University.
This is an open access article under the terms
of the CC BY-NC 4.0 license.
Metadata is available under the terms of the CC BY 4.0 license
This is an open access article under the terms
of the CC BY-NC 4.0 license.
Metadata is available under the terms of the CC BY 4.0 license