Transient regimes and crossover for epitaxial surfaces
We apply a formalism for deriving stochastic continuum equations associated with lattice models to obtain equations governing the transient regimes of epitaxial growth for various experimental scenarios and growth conditions. The first step of our methodology is the systematic transformation of the...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2011
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| Online Access: | http://hdl.handle.net/1721.1/64983 |
| _version_ | 1826214656778174464 |
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| author | Haselwandter, Christoph A. Vvedensky, Dimitri D. |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Haselwandter, Christoph A. Vvedensky, Dimitri D. |
| author_sort | Haselwandter, Christoph A. |
| collection | MIT |
| description | We apply a formalism for deriving stochastic continuum equations associated with lattice models to obtain equations governing the transient regimes of epitaxial growth for various experimental scenarios and growth conditions. The first step of our methodology is the systematic transformation of the lattice model into a regularized stochastic equation of motion that provides initial conditions for differential renormalization-group (RG) equations for the coefficients in the regularized equation. The solutions of the RG equations then yield trajectories that describe the original model from the transient regimes, which are of primary experimental interest, to the eventual crossover to the asymptotically stable fixed point. We first consider regimes defined by the relative magnitude of deposition noise and diffusion noise. If the diffusion noise dominates, then the early stages of growth are described by the Mullins-Herring (MH) equation with conservative noise. This is the classic regime of molecular-beam epitaxy. If the diffusion and deposition noise are of comparable magnitude, the transient equation is the MH equation with nonconservative noise. This behavior has been observed in a recent report on the growth of aluminum on silicone oil surfaces [Z.-N. Fang et al., Thin Solid Films 517, 3408 (2009)]. Finally, the regime where deposition noise dominates over diffusion noise has been observed in computer simulations, but does not appear to have any direct experimental relevance. For initial conditions that consist of a flat surface, the Villain-Lai-Das Sarma (VLDS) equation with nonconservative noise is not appropriate for any transient regime. If, however, the initial surface is corrugated, the relative magnitudes of terms can be altered to the point where the VLDS equation with conservative noise does indeed describe transient growth. This is consistent with the experimental analysis of growth on patterned surfaces [H.-C. Kan et al., Phys. Rev. Lett. 92, 146101 (2004); T. Tadayyon-Eslami et al., Phys. Rev. Lett. 97, 126101 (2006)]. |
| first_indexed | 2024-09-23T16:09:17Z |
| format | Article |
| id | mit-1721.1/64983 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:09:17Z |
| publishDate | 2011 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/649832022-10-02T06:41:09Z Transient regimes and crossover for epitaxial surfaces Haselwandter, Christoph A. Vvedensky, Dimitri D. Massachusetts Institute of Technology. Department of Physics Haselwandter, Christoph A. Haselwandter, Christoph A. We apply a formalism for deriving stochastic continuum equations associated with lattice models to obtain equations governing the transient regimes of epitaxial growth for various experimental scenarios and growth conditions. The first step of our methodology is the systematic transformation of the lattice model into a regularized stochastic equation of motion that provides initial conditions for differential renormalization-group (RG) equations for the coefficients in the regularized equation. The solutions of the RG equations then yield trajectories that describe the original model from the transient regimes, which are of primary experimental interest, to the eventual crossover to the asymptotically stable fixed point. We first consider regimes defined by the relative magnitude of deposition noise and diffusion noise. If the diffusion noise dominates, then the early stages of growth are described by the Mullins-Herring (MH) equation with conservative noise. This is the classic regime of molecular-beam epitaxy. If the diffusion and deposition noise are of comparable magnitude, the transient equation is the MH equation with nonconservative noise. This behavior has been observed in a recent report on the growth of aluminum on silicone oil surfaces [Z.-N. Fang et al., Thin Solid Films 517, 3408 (2009)]. Finally, the regime where deposition noise dominates over diffusion noise has been observed in computer simulations, but does not appear to have any direct experimental relevance. For initial conditions that consist of a flat surface, the Villain-Lai-Das Sarma (VLDS) equation with nonconservative noise is not appropriate for any transient regime. If, however, the initial surface is corrugated, the relative magnitudes of terms can be altered to the point where the VLDS equation with conservative noise does indeed describe transient growth. This is consistent with the experimental analysis of growth on patterned surfaces [H.-C. Kan et al., Phys. Rev. Lett. 92, 146101 (2004); T. Tadayyon-Eslami et al., Phys. Rev. Lett. 97, 126101 (2006)]. Austrian Science Fund (FWF) 2011-07-29T14:32:19Z 2011-07-29T14:32:19Z 2010-02 2009-09 Article http://purl.org/eprint/type/JournalArticle 1539-3755 1550-2376 http://hdl.handle.net/1721.1/64983 Haselwandter, Christoph A., and Dimitri D. Vvedensky. “Transient Regimes and Crossover for Epitaxial Surfaces.” Physical Review E 81.2 (2010) : 021606. © 2010 The American Physical Society en_US http://dx.doi.org/10.1103/PhysRevE.81.021606 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Haselwandter, Christoph A. Vvedensky, Dimitri D. Transient regimes and crossover for epitaxial surfaces |
| title | Transient regimes and crossover for epitaxial surfaces |
| title_full | Transient regimes and crossover for epitaxial surfaces |
| title_fullStr | Transient regimes and crossover for epitaxial surfaces |
| title_full_unstemmed | Transient regimes and crossover for epitaxial surfaces |
| title_short | Transient regimes and crossover for epitaxial surfaces |
| title_sort | transient regimes and crossover for epitaxial surfaces |
| url | http://hdl.handle.net/1721.1/64983 |
| work_keys_str_mv | AT haselwandterchristopha transientregimesandcrossoverforepitaxialsurfaces AT vvedenskydimitrid transientregimesandcrossoverforepitaxialsurfaces |