Controlling growth at crystalline surfaces requires a detailed and quantitative understanding of the thermodynamic and kinetic parameters governing mass transport. Many of these parameters can be determined by analyzing the isothermal wandering of steps at a vicinal [“step-terrace”] type surface [for a recent review see [4]]. In the case of crystals one finds that these meanderings develop larger amplitudes as the equilibrium temperature is raised (as is consistent with the statistical mechanical view of the meanderings as arising from atomic interchanges). The classical theory due to Herring, Mullins and others [5], coupled with advances in real-time experimental microscopy techniques, has proven very successful in the applied development of such crystalline materials. However in 1997 a series of experimental observations on vicinal defects of heavily boron-doped Silicon crystals revealed that these crystals were quite in the sense that a lowering of the equilibrium temperature led to increased amplitude for the isothermal wanderings of a step edge [3]. In addition, at low temperatures the step profile adopted a periodic saw-tooth structure rather than the straight profile predicted by the classical theories. This article examines a stored free energy model for such crystals involving a (higher order) Landau/de Gennes type order parameter term and provides a proof for the existence of a minimizer.
Mots clés : Landau/de Gennes order parameter, parametric problem
@article{COCV_2003__9__145_0,
author = {Hannon, J. and Marcus, M. and Mizel, Victor J.},
title = {A variational problem modelling behavior of unorthodox silicon crystals},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {145--149},
publisher = {EDP-Sciences},
volume = {9},
year = {2003},
doi = {10.1051/cocv:2003004},
mrnumber = {1957095},
zbl = {1066.49011},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2003004/}
}
TY - JOUR AU - Hannon, J. AU - Marcus, M. AU - Mizel, Victor J. TI - A variational problem modelling behavior of unorthodox silicon crystals JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2003 SP - 145 EP - 149 VL - 9 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2003004/ DO - 10.1051/cocv:2003004 LA - en ID - COCV_2003__9__145_0 ER -
%0 Journal Article %A Hannon, J. %A Marcus, M. %A Mizel, Victor J. %T A variational problem modelling behavior of unorthodox silicon crystals %J ESAIM: Control, Optimisation and Calculus of Variations %D 2003 %P 145-149 %V 9 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2003004/ %R 10.1051/cocv:2003004 %G en %F COCV_2003__9__145_0
Hannon, J.; Marcus, M.; Mizel, Victor J. A variational problem modelling behavior of unorthodox silicon crystals. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 145-149. doi : 10.1051/cocv:2003004. http://www.numdam.org/articles/10.1051/cocv:2003004/
[1] and, Wulff theorem and best constant in Sobolev inequality. J. Math. Pures Appl. 71 (1992) 97-118. | MR | Zbl
[2] , The Wulff theorem revisited. Proc. Roy. Soc. Lond. A 432 (1991) 125-145. | MR | Zbl
[3] et al., Step Faceting at the (001) Surface of Boron Doped Silicon. Phys. Rev. Lett. 79 (1997) 4226-4229.
[4] and, Steps on Surfaces: Experiment and Theory. Surface Sci. Reports 34 (1999) 175-294.
[5] , Theory of thermal grooving. J. Appl. Phys. 28 (1957) 333-339.
[6] -Mean curvature and weighted mean curvature. Acta Metall. Mater. 40 (1992) 1475-1485.
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