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A vicinal surface model for epitaxial growth with logarithmic free energy

Publication ,  Journal Article
Gao, Y; Ji, H; Liu, JG; Witelski, TP
Published in: Discrete and Continuous Dynamical Systems - Series B
December 1, 2018

We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation, ut = -u2(u3 + au)hhhh, gives the evolution for the surface slope u as a function of the local height h in a monotone step train. Subject to periodic boundary conditions and positive initial conditions, we prove the existence, uniqueness and positivity of global strong solutions to this PDE using two Lyapunov energy functions. The long time behavior of u converging to a constant that only depends on the initial data is also investigated both analytically and numerically.

Duke Scholars

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Published In

Discrete and Continuous Dynamical Systems - Series B

DOI

ISSN

1531-3492

Publication Date

December 1, 2018

Volume

23

Issue

10

Start / End Page

4433 / 4453

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Gao, Y., Ji, H., Liu, J. G., & Witelski, T. P. (2018). A vicinal surface model for epitaxial growth with logarithmic free energy. Discrete and Continuous Dynamical Systems - Series B, 23(10), 4433–4453. https://doi.org/10.3934/dcdsb.2018170
Gao, Y., H. Ji, J. G. Liu, and T. P. Witelski. “A vicinal surface model for epitaxial growth with logarithmic free energy.” Discrete and Continuous Dynamical Systems - Series B 23, no. 10 (December 1, 2018): 4433–53. https://doi.org/10.3934/dcdsb.2018170.
Gao Y, Ji H, Liu JG, Witelski TP. A vicinal surface model for epitaxial growth with logarithmic free energy. Discrete and Continuous Dynamical Systems - Series B. 2018 Dec 1;23(10):4433–53.
Gao, Y., et al. “A vicinal surface model for epitaxial growth with logarithmic free energy.” Discrete and Continuous Dynamical Systems - Series B, vol. 23, no. 10, Dec. 2018, pp. 4433–53. Scopus, doi:10.3934/dcdsb.2018170.
Gao Y, Ji H, Liu JG, Witelski TP. A vicinal surface model for epitaxial growth with logarithmic free energy. Discrete and Continuous Dynamical Systems - Series B. 2018 Dec 1;23(10):4433–4453.

Published In

Discrete and Continuous Dynamical Systems - Series B

DOI

ISSN

1531-3492

Publication Date

December 1, 2018

Volume

23

Issue

10

Start / End Page

4433 / 4453

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics