Abstract
We study a variational problem that has been introduced to describe step-terraces on surfaces of so-called "unorthodox" crystals. Motivated by physical considerations, we use Γ-convergence to derive a simplified model that can be solved explicitly.
References
- G. Alberti: Variational models for phase transitions, an approach via γ-convergence, in: Calculus of Variations and Partial Differential Equations, Topics on Geometrical Evolution Problems and Degree Theory, G. Buttazzo et al. (ed.), Springer, Berlin (2000) 17–32.https://doi.org/10.1007/978-3-642-57186-2_3Google Scholar
- G. Dal Maso: An Introduction to Γ-Convergence, Birkhäuser Boston, Boston, MA (1993).https://doi.org/10.1007/978-1-4612-0327-8Google Scholar
- J. Hannon et al.: Step faceting at the (001) surface of boron doped silicon, Phys. Rev. Letter 79 (1997) 4226–4229.https://doi.org/10.1103/PhysRevLett.79.4226Google Scholar
- J. Hannon, M. Marcus, Victor J. Mizel: A variational problem modelling behavior of unorthodox silicon crystals, ESAIM Control Optim. Calc. Var. 9 (electronic) (2003) 145–149.https://doi.org/10.1051/cocv:2003004Google Scholar
- H. C. Jeong, E. D. Williams: Steps on surfaces: Experiment and theory, Surface Science Reports 34 (1999) 175–294.https://doi.org/10.1016/S0167-5729(00)80000-XGoogle Scholar
- L. Modica, S. Mortola: Il limite nella γ-convergenza di una famiglia di funzionali ellittici, Boll. Un. Mat. Ital. A (5) 14(3) (1977) 526–529.Google Scholar
- W. W. Mullins: Theory of thermal grooving, J. Appl. Physics 28 (1957) 333–339.https://doi.org/10.1063/1.1722742Google Scholar
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Published by Heldermann Verlag, 2004. Rights now held by Banach Press LLC.
