Nonlinear Finite Element and Atomistic Modelling of Dislocations in Heterostructures (original) (raw)

Abstract

A continuum and atomistic approach to the modelling of dislocations observed by the High Resolution Transmission Electron Microscopy (HRTEM) is discussed. We present a methodology for the analysis of dislocations, stacking faults and interfacial regions in crystal heterostructures by using experimental measurements, and atomistic/continuum models. The derived method is capable of handling dense arrays of dislocations as well as large areas of the interface between two crystal structures. As an example, we consider stacking faults in bulk GaN and a misfit dislocation network in a GaN/sapphire interfacial region through relaxation of strain and associated residual stresses; where the quantification of the latter is beyond the reach of experiment alone.

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References (26)

  1. Béré, A., Serra, A.: Atomic structure of dislocation cores in GaN. Physical Review B 65, 205323 (2002)
  2. Béré, A., Serra, A.: Atomic structure of dislocation cores in GaN. Phys. Rev. B 65(20), 205323 (2002)
  3. de Wit, R.: Theory of dislocations II, continuous and discrete dislocations in anisotropic elasticity. J. Research of Nat. Bur. Stand (USA) -A. Phys. Chem. 77A, 608 (1973)
  4. Dłużewski, P.: Anisotropic hyperelasticity based upon general strain measures. Journal of Elasticity 60(2), 119-129 (2000)
  5. Dłużewski, P., Jurczak, G., Antúnez, H.: Logarithmic measure of strains in finite ele- ment modelling of anisotropic deformations of elastic solids. Computer Assisted Me- chanics and Engineering Science 10, 69-79 (2003)
  6. Dłużewski, P., Maciejewski, G., Jurczak, G., Kret, S., Laval, J.-Y.: Nonlinear FE analy- sis of residual stresses induced by misfit dislocations in epitaxial layers. Computational Materials Science 29(3), 379-395 (2004)
  7. Dłużewski, P., Young, T., Dimitrakopoulos, G., Komninou, P.: Continuum and atomistic modelling of the mixed straight dislocation. Int. J. Multiscale Computational Engineer- ing (2009) (accepted for publication)
  8. Fall, C.J., Jones, R., Briddon, P.R., Blumenau, A.T., Frauenheim, T., Heggie, M.I.: In- fluence of dislocations on electron energy-loss spectra in gallium nitride. Phys. Rev. B 65(24), 245304 (2002)
  9. Hÿtch, M., Putaux, J.-L., Pénisson, J.-M.: Measurement of the displacement field of dislocations to 0.03Å by electron microscopy. Nature 423, 270-273 (2003)
  10. Hÿtch, M.J., Snoeck, E., Kilaas, R.: Quantitative measurement of displacement and strain fields from HTEM micrographs. Ultramicroscopy 74, 131-146 (1998)
  11. Kioseoglou, J., Dimitrakopulos, G., Komninou, P., Kehagias, T., Karakostas, T.: Phys. Status Solidi A 203, 2156 (2006)
  12. Kioseoglou, J., Dimitrakopulos, G.P., Komninou, P., Karakostas, T.: Atomic structures and energies of partial dislocations in wurtzite GaN. Phys. Rev. B 70(3), 035309 (2004)
  13. Kioseoglou, J., Dimitrakopulos, G.P., Komninou, P., Karakostas, T., Aifantis, E.: Dislo- cation core investigation by geometric phase analysis and the dislocation density tensor. J. Phys. D: Appl. Phys. 41, 035408 (2007)
  14. Komninou, P., Kioseoglou, J., Dimitrakopulos, G., Kehagias, T., Karakostas, T.: Phys. Status Solidi A 202, 2888 (2005)
  15. Kret, S., Dłużewski, P., Dłużewski, P., Laval, J.-Y.: On the measurement of disloca- tion cores distribution in GaAs/ZnTe/CdTe heterostructure by transmission electron mi- croscopy. Philosophical Magazine A 83, 231-244 (2003)
  16. Kröner, E.: Continuum theory of defects. In: Balian, R., Kleman, M., Poiries, J.-P. (eds.) Physics of Defects, pp. 215-315. North-Holland, Amsterdam (1981)
  17. Lee, S.M., Belkhir, M.A., Zhu, X.Y., Lee, Y.H., Hwang, Y.G., Frauenheim, T.: Elec- tronic structures of gan edge dislocations. Phys. Rev. B 61(23), 16033-16039 (2000)
  18. Leung, K., Wright, A., Stechel, E.: Charge accumulation at a threading edge dislocation in gallium nitride. Applied Physics Letters 74, 2495 (1999)
  19. Love, A.E.H.: Mathematical Theory of Elasticity. Cambridge University Press, Cam- bridge (1927)
  20. Lymperakis, L.: Ab-Initio Based Multiscale Calculations of Extended Defects in and on Group III -Nitrides. PhD thesis, Department Physik der Fakultät für Naturwis- senschaften an der Universität Paderborn (2005)
  21. Lymperakis, L., Neugebauer, J., Albrecht, M., Remmele, T., Strunk, H.P.: Strain induced deep electronic states around threading dislocations in GaN. Phys. Rev. Lett. 93(19), 196401 (2004)
  22. Potin, V., Ruterana, P., Nouet, G., Pond, R.C., Morkoç, H.: Mosaic growth of gan on (0001) sapphire: A high-resolution electron microscopy and crystallographic study of threading dislocations from low-angle to high-angle grain boundaries. Phys. Rev. B 61(8), 5587-5599 (2000)
  23. Read Jr., W.T.: Dislocations in Crystals. McGraw-Hill, London (1953)
  24. Spaepen, F.: Interfaces and stresses in thin films. Acta Materialia 48, 31-42 (2000)
  25. Stadelmann, P.: EMS -A software package for electron diffraction analysis and hrem image simulation in materials science. Ultramicroscopy 21, 131 (1987)
  26. Wright, A., Grossner, U.: The effect of doping and growth stoichiometry on the core structure of a threading edge dislocation in GaN. Applied Physics Letters 73, 2751 (1998)