Isotropic Stress Distribution in Cu/(001) Fe Two Sheets

The nanotechnology based on epitaxial systems includes single or arranged misfit dislocations. In general, whatever is the type of dislocation or the geometry of the array formed by the dislocations; it is important for experimental studies to know exactly the stress distribution for which there is no analytical expression [1, 2]. This work, using a numerical analysis, deals with relaxation of epitaxial layers having at their interface a periodic network of edge misfit dislocations. The stress distribution is estimated by using isotropic elasticity. The results show that the thickness of the two sheets is a crucial parameter in the stress distributions and then in the profile of the two sheets. A comparative study between the case of single dislocation and the case of parallel network shows that the layers relaxed better when the interface is covered by a parallel arrangement of misfit. Consequently, a single dislocation at the interface produces an important stress field which can be reduced by inserting a parallel network of dislocations with suitable periodicity.

Authors:

• A. Derardja
• L. Baroura
• M. Brioua

Keywords:

• Parallel array of misfit
• interface
• isotropic elasticity
• single crystalline substrates
• coherent interface

References:

[1] V. Martin, W. Meyer, C. Giovanardi, L. Hammer, and K. Heinz, Z.
Tian, D. Sander, and J. Kirschner, Pseudomorphic growth of Fe
monolayers on Ir(001)-(1×1): From a fct precursor to a bct film, Phys.
Rev. B 76, 205418, 2007.
[2] Dirk Sander, Zhen Tian and J├╝rgen Kirschner, Cantilever
measurements of surface stress, surface reconstruction, film stress and
magnetoelastic stress of Monolayers, Sensosrs 8, p 4466-4486, 2008.
[3] P. H. Pumpharey, H. Gleiter, P. J. Goodhew, Phil. Mag.vol. 36, issue 5,
1977, pp 1099-1107.
[4] A. Lakshmanan, V. Gopal, A. H. King and E. P. Kvam, Dislocation
array in the interfaces between substrates and epitaxial islands, Mat. Res.
Soc. Symp. Proc. Vol. 672, 2001.
[5] T. Furuhara and T. Maki, Interfacial structure of grain boundary
precipitate in a Ni-45% Cr alloy, Materials Transactions, JIM, Vol. 33,
N 8, 1992, pp 734-739.
A. M. Andrews, R. Le Sar, M. A. Kerner, J. S. Speck, A. E. Romanov,
A. L. Kolesnikova, M. Bobeth and W. Pompe, Modeling Crosshatch
surface morphology in growing mismatched layers,Part II: Periodic
boundary conditions and dislocation groups, Journal of Applied Physics
vol.95,N11, 2004.
[6] L. B. Freund, Advances in applied mechanics, Vol. 30, edited by John
W. Hutchinson, Y. Wu Theodore, 1994.
[7] Nye JF. Acta Metall 1953; 1 pp 153.
[8] D. Le Bolloc-h, V.L. Jacques, N. Kirova, J. Dumas, S. Ravy, J. Marcus,
F. Livet, Phys. Rev. Lett.vol. 100,2008.
[9] R. Bonnet and J. L. Verger Gaugry, Phil. Mag. A., Vol. 66,1992, p 849.