Kinetics of growth of nanowhiskers (nanowires and nanotubes)

Nanoscale Research Letters20072:235

DOI: 10.1007/s11671-007-9054-8

Received: 3 January 2007

Accepted: 13 March 2007

Published: 1 May 2007

Abstract

The kinetics of nanowhiskers growth is studied theoretically taking into account the adatom diffusion from the surface to the top of needle. An exponential growth with time is expected for the initial stages of the process, when the lengthl of the whisker is smaller than the average diffusion length λ of adatoms. It transforms to linear growth rate forl > λ. The formation of nanotubes with a hollow core dislocation is explained by accounting for the role of the stress in the middle of screw dislocations. When the magnitude of the Burgers vector exceeds a critical value, it is energetically more favorable to remove the highly strained material around the dislocation line and to create a tube with an additional free surface. Additionally, there is an important size effect, due to the small radiusR of the nanowhisker. The interplay, between the contributions from the size effects and from the diffusion, explains why for the very thin nanowhiskers the lengthl is proportional to the radiusR while, otherwise the length is inversely proportional to it, i.e.,l∼1/R.

Keywords

Nanotubes Nanowires Nanowhiskers

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Declarations

Acknowledgment

The support of the EU Project INTERCONY, Contract no NMP4-CT-2006-033200 is appreciated.

Authors’ Affiliations

(1)
Institute of Physical Chemistry, Bulgarian Academy of Sciences

References

  1. Givargizov E: J. Cryst. Growth. 1975, 31: 20. COI number [1:CAS:528:DyaE28Xot1KmtQ%3D%3D] 10.1016/0022-0248(75)90105-0View Article
  2. Duan X, Wang J, Lieber C: Appl. Phys. Lett.. 2000, 76: 1116. ; COI number [1:CAS:528:DC%2BD3cXhtlSgtb4%3D]; Bibcode number [2000ApPhL..76.1116D] 10.1063/1.125956View Article
  3. Lew K, Redwing J: J. Cryst. Growth. 2003, 254: 14. View Article
  4. Plante M, LaPierre R: J. Cryst. Growth. 2006, 286: 394. COI number [1:CAS:528:DC%2BD28XjsFan] 10.1016/j.jcrysgro.2005.10.024View Article
  5. Sears GW: Acta Metall.. 1955, 3: 367. COI number [1:CAS:528:DyaG2MXns1ajsQ%3D%3D] 10.1016/0001-6160(55)90042-0View Article
  6. Sears GW: J. Chem. Phys.. 1956, 25: 637. COI number [1:CAS:528:DyaG2sXotF2q] 10.1063/1.1743018View Article
  7. Gomer R: J. Chem. Phys.. 1958, 28: 457. COI number [1:CAS:528:DyaG1cXltl2htg%3D%3D] 10.1063/1.1744158View Article
  8. Dittmar W, Neumann K: Growth and Perfection of Crystals.. Edited by: Doremus R.H., Roberts B.W., Turnball D.. Wiley, New York; 1958.
  9. Dittmar W, Neumann K: Z. Elektrochem.. 1960, 64: 297.
  10. Frank FC: Acta Crystallogr.. 1951, 4: 497. COI number [1:CAS:528:DyaG38XivVymtg%3D%3D] 10.1107/S0365110X51001690View Article
  11. Heindl J, Dorsch W, Strunk HP, St. Müller G, Eckstein R, Hofmann D, Winnacker A: Phys. Rev. Lett.. 1998, 80: 740. ; COI number [1:CAS:528:DyaK1cXlsVyhug%3D%3D]; Bibcode number [1998PhRvL..80..740H] 10.1103/PhysRevLett.80.740View Article
  12. Scapski A: Acta Met.. 1956, 4: 576. 10.1016/0001-6160(56)90159-6View Article
  13. D. Turnbull, M. Cohen, in Modern Aspects of vitreous State ed. by S.D. Mackenzie (Butterworths, London, 1960) p. 38
  14. Avramov I, Russel C, Avramova K: J. Non-Cryst. Sol.. 2004, 337: 220. COI number [1:CAS:528:DC%2BD2cXlsVehsbw%3D] 10.1016/j.jnoncrysol.2004.04.012View Article
  15. Budurov S, Stojcev N, Avramov I: Krist. Technik. 1972, 7: 387. COI number [1:CAS:528:DyaE38XlsFOhsLk%3D] 10.1002/crat.19720070403View Article
  16. Dubrovskii VG, Cirlin GE, Soshnikov IP, Tonkikh AA, Sibirev NV, Samsonenko YuB, Ustinov VM: Phys. Rev. B. 2005, 71: 205325. Bibcode number [2005PhRvB..71t5325D] Bibcode number [2005PhRvB..71t5325D] 10.1103/PhysRevB.71.205325View Article
  17. Ruth V, Hirth P: J. Chem. Phys.. 1964, 41: 3139. COI number [1:CAS:528:DyaF2cXkvVylsL8%3D] 10.1063/1.1725687View Article
  18. E.I. Givargizov, A.A. Chernov, Kristallografiya 18, 147 (1973)
  19. Avramov I, Hoeche Th, Russel C: J. Chem. Phys.. 1999,110(17):8676. ; COI number [1:CAS:528:DyaK1MXisFCgsbg%3D]; Bibcode number [1999JChPh.110.8676A] 10.1063/1.478775View Article
  20. Soshnikov I: Lett. JTF. 2005, 31: 29. in Russian in Russian
  21. V.G. Dubrovskii, G.E. Cirlin, I.P. Soshnikov, A.A. Tonkikh, N.V. Sibirev, Yu. B. Samsonenko, V.M. Ustinov, Phys. Rev. B 71, 205325 (2005)View Article
  22. Dubrovskii VG, Sibirev NV, Cirlin GE: Tech. Phys. Lett. 2004, 30: 682. COI number [1:CAS:528:DC%2BD2cXntVKrtLw%3D] 10.1134/1.1792313View Article
  23. Kashchiev D: Cryst. Growth Design. 2006, 6: 1154. COI number [1:CAS:528:DC%2BD28XjtlOis7o%3D] 10.1021/cg050619iView Article

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© to the authors 2007