Anisotropic surface energy formulations and their effect on stability of a growing thin film
| dc.contributor.author | Korzec, Maciek D. | |
| dc.contributor.author | Münch, Andreas | |
| dc.contributor.author | Wagner, Barbara | |
| dc.date.accessioned | 2019-01-10T09:18:29Z | |
| dc.date.available | 2019-01-10T09:18:29Z | |
| dc.date.issued | 2012 | |
| dc.description | Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich. | de |
| dc.description | This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively. | en |
| dc.description.abstract | In this paper we revisit models for the description of the evolution of crystalline films with anisotropic surface energies.We prove equivalences of symmetry properties of anisotropic surface energy models commonly used in the literature. Then we systematically develop a framework for the derivation of surface diffusion models for the self-assembly of quantum dots during Stranski-Krastanov growth that include surface energies also with large anisotropy as well as the effect of wetting energy, elastic energy and a randomly perturbed atomic deposition flux. A linear stability analysis for the resulting sixth-order semilinear evolution equation for the thin film surface shows that that the new model allows for large anisotropy and gives rise to the formation of anisotropic quantum dots. The nonlinear three-dimensional evolution is investigated via numerical solutions. These suggest that increasing anisotropy stabilizes the faceted surfaces and may lead to a dramatic slow-down of the coarsening of the dots. | en |
| dc.identifier.eissn | 1463-9971 | |
| dc.identifier.issn | 1463-9963 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/8970 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-8096 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 510 Mathematik | de |
| dc.subject.other | anisotropic surface energy | en |
| dc.subject.other | high order partial differential equations | en |
| dc.subject.other | pseudospectral methods | en |
| dc.subject.other | surface diffusion | en |
| dc.title | Anisotropic surface energy formulations and their effect on stability of a growing thin film | en |
| dc.type | Article | en |
| dc.type.version | publishedVersion | en |
| dcterms.bibliographicCitation.doi | 10.4171/IFB/291 | en |
| dcterms.bibliographicCitation.issue | 4 | en |
| dcterms.bibliographicCitation.journaltitle | Interfaces and free boundaries | en |
| dcterms.bibliographicCitation.originalpublishername | European Mathematical Society | en |
| dcterms.bibliographicCitation.originalpublisherplace | Zürich | en |
| dcterms.bibliographicCitation.pageend | 567 | en |
| dcterms.bibliographicCitation.pagestart | 545 | en |
| dcterms.bibliographicCitation.volume | 14 | en |
| tub.accessrights.dnb | domain | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |