Skip to main content
SpringerLink
Log in

Characterization of Surface Roughness for Growth Models

  • Conference paper
  • First Online:
Vehicle and Automotive Engineering 2 (VAE 2018)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Included in the following conference series:

  • 3536 Accesses

Abstract

The technique of growth surfaces under Molecular Beam Epitaxy (MBE) has received considerable attention for a wide range of technological and industrial applications. This approach provides a unique capability to grow crystalline thin films with precise control of thickness, composition and morphology. This enables scientists to build nanostructures as pyramidal objects or mounds. The evolution of the surface morphology during MBE growth results from a competition between the molecular flux and the relaxation of the surface profile through surface diffusion. The richness of patterns forming during MBE is determined solely by processes which occur locally at the surface.

Our aim is to describe the coarsening process by mathematical models. Analytical results on the surface roughness are provided. Numerical simulations are presented to show the roughening of the surface pattern and the evolution of the surface morphology in time in one-dimension.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Barabási, A.L., Stanley, H.E.: Fractal Concepts in Surface Growth. Cambridge University Press, Cambridge (1995)

    Book  Google Scholar 

  2. Clarke, C.: The Science of Ice Cream. The Royal Society of Chemistry, Cambridge (2004)

    Google Scholar 

  3. Frisch, T., Verga, A.: Effect of step stiffness and diffusion anisotropy on the meandering of a growing vicinal surface. Phys. Rev. Lett. PRL 96, 166104 (2009)

    Article  Google Scholar 

  4. Gillet, F., Pierre-Luis, O., Misbah, C.: Non-linear evolution of step meander during growth of a vicinal surface with no desorption, arXiv:cond-mat/0005422v1 (2000)

  5. Gillet, F., Csahók, Z., Misbah, C.: Continuum nonlinear surface evolution equation for conserved step-bunching dynamics. Phys. Rev. B 63, 241401(R) (2001)

    Article  Google Scholar 

  6. Golovin, A.A., Davis, S.H., Vorhees, P.W.: Self-organization of quantum dots in epitaxially strained solid films. Phys. Rev. E 68, 056203 (2003)

    Article  Google Scholar 

  7. Golovin, A.A., Nepomnyashchy, A.A.: Self-assembly, Pattern Formation and Growth Phenomena in Nano-systems. Springer, Dordrecht (2004)

    Google Scholar 

  8. Kardar, K., Parisi, G., Zhang, Y.Z.: Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56, 889–892 (1986)

    Article  Google Scholar 

  9. Kharchenko, D.O., Kharchenko, V.O., Kokhan S.V.: Properties of nano-pattern formation in reaction-diffusion systems with hyperbolic transport and multiplicative noise. arXiv:1101.3189v1 (2011)

  10. Krim, J., Palasantzas, G.: Experimental observations of self-affine scaling and kinetic roughening at sub-micron length scales. Int. J. Modern Phys. B 9, 599–632 (1995)

    Article  Google Scholar 

  11. Krug, J.: Power laws in surface physics: the deep, the shallow and the useful. Phys. A-Stat. Mech. Appl. 340(4), 647–655 (2004)

    Article  Google Scholar 

  12. Marsh, B.D.: Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallization 1: Theory. Contrib. Miner. Pet. 99(3), 277–291 (1988)

    Article  Google Scholar 

  13. Ostwald, W.: Lehrbruck der Allgemeinen Chemie, vol. 2. W. Engelmann, Leipzig (1896)

    Google Scholar 

  14. Patravale, V.B., Date, A.A., Kulkarni, R.M.: Nanosuspensions: a promising drug delivery strategy. J. Pharm. Pharmacol. 56(7), 827–840 (2004)

    Article  Google Scholar 

  15. Politi, P., Vaia, R.: Steady states of the conserved Kuramoto-Sivashinsky equation. arXiv:0609545v

  16. Silk, J., White, S.D.: The development of structure in the expanding universe. Astrophys J 223, L59–L62 (1978)

    Article  Google Scholar 

  17. Sivashinsky, G.I.: Nonlinear analysis of hydrodynamic instability in laminar flames I: derivation of basic equations. Acta Astronaut. 4(11–12), 1177–1206 (1977)

    Article  MathSciNet  Google Scholar 

  18. Valbusa, U., Boragno, C., Buatier de Mongeot, F.: Nanostructuring surfaces by ion sputtering. J. Phys.: Condens. Matter 14, 8153–8175 (2002)

    Google Scholar 

Download references

Acknowledgement

The described article was carried out as part of the EFOP-3.6.1-16-2016-00011 “Younger and Renewing University – Innovative Knowledge City – institutional development of the University of Miskolc aiming at intelligent specialisation” project implemented in the framework of the Szechenyi 2020 program. The realization of this project is supported by the European Union, co-financed by the European Social Fund.

Author information

Authors and Affiliations

  1. University of Miskolc, Miskolc-Egyetemváros, 3515, Hungary

    Gabriella Bognár

Authors
  1. Gabriella Bognár
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gabriella Bognár .

Editor information

Editors and Affiliations

  1. University of Miskolc , Miskolc, Hungary

    Károly Jármai

  2. University of Miskolc , Miskolc, Hungary

    Betti Bolló

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bognár, G. (2018). Characterization of Surface Roughness for Growth Models. In: Jármai, K., Bolló, B. (eds) Vehicle and Automotive Engineering 2. VAE 2018. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-75677-6_47

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-75677-6_47

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-75676-9

  • Online ISBN: 978-3-319-75677-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation