Physics of the Solid State

, Volume 58, Issue 8, pp 1611–1621 | Cite as

Initial stages of misfit stress relaxation through the formation of prismatic dislocation loops in GaN–Ga2O3 composite nanostructures

Mechanical Properties, Physics of Strength, and Plasticity


The initial stages of misfit stress relaxation through the formation of rectangular prismatic dislocation loops in model composite nanostructures have been considered. The nanostructures are either spherical or cylindrical GaN shells grown on solid or hollow β-Ga2O3 cores or planar thin GaN films on β-Ga2O3 substrates. Three characteristic configurations of prismatic dislocation loops, namely, square loops, loops elongated along the GaN/Ga2O3 interface, and loops elongated along the normal to the GaN/Ga2O3 interface, have been analyzed. The generation of prismatic dislocation loops from the interface into the bulk of the GaN shell (film), from the free surface into the GaN shell (film), and from the interface into the β-Ga2O3 core (substrate) has been investigated. It has been shown that, for the minimum known estimate of the lattice misfit (2.6%) in some of the considered nanostructures, no any prismatic dislocation loops can be generated. If the generation of prismatic dislocation loops is possible, then in all the considered nanostructures, the energetically more favorable case corresponds to prismatic dislocation loops elongated along the GaN/Ga2O3 interfaces, and the more preferred generation of prismatic dislocation loops occurs from the GaN free surface. The GaN/Ga2O3 nanostructures that are the most and least resistant to the formation of prismatic dislocation loops have been determined. It has been found that, among the considered nanostructures, the planar two-layer GaN/Ga2O3 plate is the most resistant to the generation of prismatic dislocation loops, which is explained by the action of an alternative mechanism for the relaxation of misfit stresses due to the bending of the plate. The least resistant nanostructure is the planar three-layer GaN/Ga2O3/GaN plate, in which GaN films have an identical thickness and which itself as a whole does not undergo bending. The critical thicknesses of the GaN shells (films), which must be exceeded to ensure the growth of these shells (films) so as to avoid the formation of prismatic dislocation loops, have been calculated for all the studied nanostructures and three known estimates of the lattice misfits (2.6, 4.7, and 10.1%).


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  1. 2.
    L. Y. Kuritzky and J. S. Speck, MRS Commun. 5, 463 (2015).CrossRefGoogle Scholar
  2. 3.
    Z. Alaie, S. Mohammad Nejad, and M. H. Yousefi, Mater. Sci. Semicond. Proc. 29, 16 (2015).CrossRefGoogle Scholar
  3. 4.
    S. Fujita, Jpn. J. Appl. Phys. 54, 030101 (2015).ADSCrossRefGoogle Scholar
  4. 5.
    S. Kumar and R. Singh, Phys. Status Solidi RRL 7, 781 (2013).CrossRefGoogle Scholar
  5. 6.
    M. Higashiwaki, K. Sasaki, A. Kuramata, T. Masui, and S. Yamakoshi, Phys. Status Solidi A 211, 21 (2014).CrossRefGoogle Scholar
  6. 7.
    W. Tian, H. Lu, and L. Li, Nano Res. 8, 382 (2015).CrossRefGoogle Scholar
  7. 8.
    E. G. Víllora, K. Shimamura, K. Aoki, and K. Kitamura, Thin Solid Films 500 (1–2), 209 (2006).ADSCrossRefGoogle Scholar
  8. 9.
    E. G. Víllora, K. Shimamura, K. Kitamura, K. Aoki, and T. Ujiie, Appl. Phys. Lett. 90 (23), 234102 (2007).ADSCrossRefGoogle Scholar
  9. 10.
    M. M. Muhammed, M. Peres, Y. Yamashita, Y. Morishima, S. Sato, N. Franco, K. Lorenz, A. Kuramata, and I. S. Roqan, Appl. Phys. Lett. 105 (4), 042112 (2014).ADSCrossRefGoogle Scholar
  10. 11.
    K. Shimamura, E. G. Víllora, K. Domen, K. Yui, K. Aoki, and N. Ichinose, Jpn. J. Appl. Phys. 44, L7 (2005).ADSCrossRefGoogle Scholar
  11. 12.
    S. Ohira, N. Suzuki, H. Minami, K. Takahashi, T. Araki, and Y. Nanishi, Phys. Status Solidi C 4, 2306 (2007).ADSCrossRefGoogle Scholar
  12. 13.
    Z. L. Xie, R. Zhang, C. T. Xia, X. Q. Xiu, P. Han, B. Liu, H. Zhao, R. L. Jiang, Y. Shi, and Y. D. Zheng, Chin. Phys. Lett. 25, 2185 (2008).ADSCrossRefGoogle Scholar
  13. 14.
    S. Ito, K. Takeda, K. Nagata, H. Aoshima, K. Takehara, M. Iwaya, T. Takeuchi, S. Kamiyama, I. Akasaki, and H. Amano, Phys. Status Solidi C 9, 519 (2012).ADSCrossRefGoogle Scholar
  14. 15.
    K. Kachel, M. Korytov, D. Gogova, Z. Galazka, M. Albrecht, R. Zwierz, D. Siche, S. Golka, A. Kwasniewski, M. Schmidbauer, and R. Fornari, CrystEng- Comm 14, 8536 (2012).CrossRefGoogle Scholar
  15. 16.
    V. I. Nikolaev, A. I. Pechnikov, V. N. Maslov, A. A. Golovatenko, V. M. Krymov, S. I. Stepanov, N. K. Zhumashev, V. E. Bougrov, and A. E. Romanov, Mater. Phys. Mech. 22, 59 (2015).Google Scholar
  16. 17.
    R. Korbutowicz, J. Wnek, P. Panachuda, J. Serafinczuk, and R. Srnanek, Opt. Appl. XLIII, 73 (2013).Google Scholar
  17. 18.
    H. H. Hsueh, S. L. Ou, D. S. Wuu, and R. H. Horng, Vacuum 118, 8 (2015).ADSCrossRefGoogle Scholar
  18. 19.
    H. S. Oon and K. Y. Cheong, Mater. Sci. Semicond. Proc. 16, 1217 (2013).CrossRefGoogle Scholar
  19. 20.
    S. Nakagomi, T. Sato, Y. Takahashi, and Y. Kokubun, Sens. Actuators, A 232, 208 (2015).CrossRefGoogle Scholar
  20. 21.
    C. Tang, Y. Bando, and Z. Liu, Appl. Phys. Lett. 83 (15), 3177 (2003).ADSCrossRefGoogle Scholar
  21. 22.
    J. H. Choi, M. H. Ham, W. Lee, and J. M. Myoung, Solid State Commun. 142, 437 (2007).ADSCrossRefGoogle Scholar
  22. 23.
    S. Lee, M. H. Ham, J. M. Myoung, and W. Lee, Acta Mater. 58, 4714 (2010).CrossRefGoogle Scholar
  23. 24.
    L. W. Chang, J. H. Chang, J. W. Yeh, H. N. Lin, and H. C. Shih, AIP Adv. 1, 032114 (2011).ADSCrossRefGoogle Scholar
  24. 25.
    Y. K. Lee, H. Medina, and P. W. Chiu, J. Vac. Sci. Technol., B: Microelectron. Nanometer Struct.—Process., Meas., Phenom. 30, 011802 (2012).ADSCrossRefGoogle Scholar
  25. 26.
    J.-W. Yu, P.-C. Yeh, S.-L. Wang, Y.-R. Wu, M.-H. Mao, H.-H. Lin, and L.-H. Peng, Appl. Phys. Lett. 101 (18), 183501 (2012).ADSCrossRefGoogle Scholar
  26. 27.
    C.-K. Li, P.-C. Yeh, J.-W. Yu, L.-H. Peng, and Y.-R. Wu, J. Appl. Phys. 114 (16), 163706 (2013).ADSCrossRefGoogle Scholar
  27. 28.
    J. Miao, C.-C. Chen, C. Song, Y. Nishino, Y. Kohmura, T. Ishikawa, D. Ramunno-Johnson, T.-K. Lee, and S. H. Risbud, Phys. Rev. Lett. 97 (21), 215503 (2006).ADSCrossRefGoogle Scholar
  28. 29.
    H. Xiao, H. Pei, W. Hu, B. Jiang, and Y. Qiu, Mater. Lett. 64, 2399 (2010).CrossRefGoogle Scholar
  29. 30.
    J. Q. Ning, S. J. Xu, P. W. Wang, Y. P. Song, D. P. Yu, Y. Y. Shan, S. T. Lee, and H. Yang, Mater. Charact. 73, 153 (2012).CrossRefGoogle Scholar
  30. 31.
    H. D. Xiao, H. L. Ma, C. S. Xue, H. Z. Zhuang, J. Ma, F. J. Zong, and W. R. Hu, Mater. Lett. 59, 4041 (2005).CrossRefGoogle Scholar
  31. 32.
    P. Sahoo, J. Basu, S. Dhara, H. C. Fang, C. P. Liu, T. R. Ravindran, S. Dash, and A. K. Tyagi, J. Mater. Sci. 47, 3447 (2012).ADSCrossRefGoogle Scholar
  32. 33.
    J. W. Matthews, in Dislocations in Solids, Ed. by F. R. N. Nabarro (North-Holland, Amsterdam, 1979), Vol. 2, p. 461.Google Scholar
  33. 34.
    Yu. A. Tkhorik and L. S. Khazan, Plastic Deformation and Misfit Dislocations in Heteroepitaxial Systems (Naukova Dumka, Kiev, 1983) [in Russian].Google Scholar
  34. 35.
    M. Yu. Gutkin, A. L. Kolesnikova, and A. E. Romanov, Mater. Sci. Eng., A 164, 433 (1993).CrossRefGoogle Scholar
  35. 36.
    L. B. Freund and S. Suresh, Thin Film Materials: Stress, Defect Formation and Surface Evolution (Cambridge University Press, Cambridge, 2004).CrossRefMATHGoogle Scholar
  36. 37.
    M. Yu. Gutkin and A. M. Smirnov, Acta Mater. 88, 91 (2015).CrossRefGoogle Scholar
  37. 38.
    L. I. Trusov, M. Yu. Tanakov, V. G. Gryaznov, A. M. Kaprelov, and A. E. Romanov, J. Cryst. Growth 114, 133 (1991).ADSCrossRefGoogle Scholar
  38. 39.
    M. Yu. Gutkin, Int. J. Eng. Sci. 61, 59 (2012).CrossRefGoogle Scholar
  39. 40.
    M. Yu. Gutkin, Nanomater. Energy 2, 180 (2013).CrossRefGoogle Scholar
  40. 41.
    M. Yu. Gutkin and A. M. Smirnov, Phys. Solid State 56 (4), 731 (2014).ADSCrossRefGoogle Scholar
  41. 42.
    M. Yu. Gutkin, A. L. Kolesnikova, S. A. Krasnitckii, and A. E. Romanov, Phys. Solid State 56 (4), 723 (2014).ADSCrossRefGoogle Scholar
  42. 43.
    M. Yu. Gutkin, A. L. Kolesnikova, S. A. Krasnitckii, A. E. Romanov, and A. G. Shalkovskii, Scr. Mater. 83, 1 (2014).CrossRefGoogle Scholar
  43. 44.
    A. L. Kolesnikova, M. Yu. Gutkin, S. A. Krasnitckii, and A. E. Romanov, Int. J. Solids Struct. 50, 1839 (2013).CrossRefGoogle Scholar
  44. 45.
    M. Yu. Gutkin, S. A. Krasnitskii, A. M. Smirnov, A. L. Kolesnikova, and A. E. Romanov, Phys. Solid State 57 (6), 1177 (2015).ADSCrossRefGoogle Scholar
  45. 46.
    J. P. Hirth and J. Lothe, Theory of Dislocations (McGraw-Hill, New York, 1968; Atomizdat, Moscow, 1972).Google Scholar
  46. 47.
    B. Cheng and E. T. Samulski, J. Mater. Chem. 11, 2901 (2001).CrossRefGoogle Scholar
  47. 48.
    J. Hu, Q. Li, J. Zhan, Y. Jiao, Z. Liu, S. P. Ringer, Y. Bando, and D. Golberg, ACS Nano 2, 107 (2008).CrossRefGoogle Scholar
  48. 49.
    G. Guzmán-Navarro, M. Herrera-Zaldívar, J. Valenzuela-Benavides, and D. Maestre, J. Appl. Phys. 110 (3), 034315 (2011).ADSCrossRefGoogle Scholar
  49. 50.
    T. Y. Tsai, S. L. Ou, M. T. Hung, D. S. Wuu, and R. H. Horng, J. Electrochem. Soc. 158, H1172 (2011).CrossRefGoogle Scholar
  50. 51.
    Ga 2 O 3 Technical Data (Tamura, Escondido, California, United States, 2014). http://wwwtamurasscojp/en/ indexhtml.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Institute of Problems of Mechanical EngineeringRussian Academy of SciencesSt. PetersburgRussia
  2. 2.Peter the Great St. Petersburg State Polytechnic UniversitySt. PetersburgRussia
  3. 3.St. Petersburg National Research University of Information TechnologiesMechanics and Optics (ITMO University)St. PetersburgRussia

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