A pile-up of edge dislocations to relax Misfit strain

Aziz Soufi, Ayoub Aitoubba, Khalil EL-HAMI, Mohamed Talea, Assia Bakali, Jean Grilhé


It is shown that very large stresses may be present in the thin films that comprise integrated circuits and magnetic disks and that these stresses can cause deformation and fracture of the material. For a crystalline film on a non-deformable substrate, a key problem involves the movement of dislocations in the thin film. An analysis of this problem provides insight into both the formation of misfit dislocations in epitaxial thin films and the high strengths of thin metal films on substrates. We develop in this paper, theoretical calculations for dislocation nucleation phenomena in nanomaterials obtained by hetero-epitaxial growth of thin films on substrates having lattice mismatch defects. Atomic force microscopy observations showed the nucleation of dislocations from free lateral surfaces to relax the "misfit" strain, here we explain the principle of nucleating edge dislocations from these surfaces by the theoretical calculation, using the method of image stress and energy study. We begin, by treating the case of a single dislocation and then generalize the work at a pile-up of n interface dislocations.



Thin film; Heteroepitaxial growth; Misfit Strain; Misfit dislocation

Full Text:



- D. Hull, D.J. Bacon, Introduction to Dislocations, fourth ed, Butterworth Heinemann, 2001.

- J.P. Hirth, J. Lothe, Theory of dislocations. Materials Science and Engineering Series, Second edition, 1982.

- R. Hill, The mathematical theory of plasticity, Oxford Classic Texts, 1998.

- I.S. Sokolnikoff, Mathematical Theory of Elasticity, University of California, 1946.

- A.M. Kossevich, The Crystal Lattice: Phonons, Solitons, Dislocations, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. 1999.

- S. Timoshenko, J.N. Goodier, Theory of Elasticity, New York-Toronto-London : McGraw-Hill Book Co., 1951.

- C.C. Wu, E.A. Stach, R. Hull, Nanoscale mechanisms of misfit dislocation propagation in undulated Si1-xGex/Si (100) epitaxial thin films. Nanotechnology 18 (2007) 165705. doi:10.1088/0957-4484/18/16/165705

- T. Shimokawa, S. Kitada, Dislocation Multiplication from the Frank-Read Source in Atomic Models, Mater. Trans. 55(1) (2014) 58-63. doi:10.2320/matertrans.MA201319

- F.C. Frank, W.T. Read, Jr., Multiplication Processes for Slow Moving Dislocations, Phys. Rev. 79(1950) 722. doi:10.1103/PhysRev.79.722

- H. H. Wang, S. Y. Byrapa, F. Wu, B. Raghothamachar, M. Dudley, E. K. Sanchez, D. M. Hansen, R. Drachev, S. G. Mueller, M. J. Loboda, Basal Plane Dislocation Multiplication via the Hopping Frank-Read Source Mechanism and Observations of Prismatic Glide in 4H-SiC. Mater. Sci. Forum 717-720(2012) 327-330. doi:10.4028/www.scientific.net/MSF.717-720.327

- P.G. Neudeck, J.A. Powell. Homoepitaxial and Heteroepitaxial Growth on Step-Free SiC Mesas. In: Silicon Carbide, Part II, (2004) 179-205. doi:10.1007/978-3-642-18870-1_8

- X. Wu, G.C. Weatherly, The first stage of stress relaxation in tensile strained In1-xGaxAs1-sPy films, Philosophal Magazine A. 81(6) (2001) 1489-1506. doi:10.1080/01418610108214359

- E. Le Bourhis, G. Patriarche, Deformations induced by a Vickers indentor in InP at room temperature. Eur. Phys. J. Appl. Phys. 12 (2000) 31-36. doi:10.1051/epjap:2000168

- L. Largeau, G. Patriarche, E. Le Bourhis, Subsurface deformations induced by a Vickers indenter in GaAs/AlGaAs superlattice, J. Mater. Sci. Lett. 21(5) (2002) 401-404. doi:10.1023/A:1014971619783

- J.W. Matthews, Defects associated with the accommodation of misfit between crystals, J. Vac. Sci. Technol. 12(1) (1975). doi:10.1116/1.568741

- W.D. Nix. Mechanical Properties of Thin Films. Stanford University, 2005.

- T. Zhu, J. Li, A. Samanta, A. Leach, K. Gall, Temperature and Strain-Rate Dependence of Surface Dislocation Nucleation, Phys. Rev. Lett. 100 (2008) 025502. doi:10.1103/PhysRevLett.100.025502

- A. Subramaniam. Critical thickness of equilibrium epitaxial thin films using finite element method. J. Appl. Phys. 95(12) (2004) 8472. doi:10.1063/1.1745115

- R. Rabe, J.-M. Breguet, P. Schwaller, S. Stauss, F.-J. Haug, J. Patscheider, J. Michler, Observation of fracture and plastic deformation during indentation and scratching inside the scanning electron microscope. In: Proceedings of International Conference on Metallurgical Coatings and Thin Films No31, San Diego, California, 2004, pp. 206-213.

- M.F. Doerner, W.D. Nix, A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res 1(1986) 601-609. doi:10.1557/JMR.1986.0601

- J. Dunstan, Strain and strain relaxation in semiconductors, J. Mater. Sci. Materials in Electronic 8(6) (1997) 337-375. doi:10.1023/A:1018547625106

- S.C. Jain, A.H. Harker, R.A. Cowley, Misfit strain and misfit dislocations in lattice mismatched epitaxial layers and other systems, Phil. Mag. A 75; (1997) 1461-1515. doi:10.1080/01418619708223740

- F.C. Frank, W.T. Read Jr., In: Proceedings of the Symposium on plastic deformation of crystalline solids. Mellon Institute of Industrial Research, Pittsburgh U.S. Government Printing Office, 1950.

- S.V. Kamat, J.P. Hirth, Dislocation injection in strained multilayer structures, J. Appl. Phys. 67(1990) 6844. doi:10.1063/1.345074

- G.E. Beltz, L.B. Freund, On the Nucleation of Dislocations at a Crystal Surface. Phys. Stat. Sol. B 180(1993), 303-313.

- J.H. Van Der Merwe, Crystal Interfaces. Part II. Finite Overgrowths. J. Appl. Phys. 34(1963) 123. doi:10.1063/1.1729051

- J.W. Matthews, A.E. Blakeslee, Defects in epitaxial multilayers: I. Misfit dislocations. J. Cryst. Growth, 27(1974) 118-125. doi:10.1016/S0022-0248(74)80055-2


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

ISSN 2170-127X

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at http://revue.ummto.dz.