Scaling theory for two-dimensional single domain growth driven by attachment of diffusing adsorbates
Epitaxial growth methods are a key technology used in producing large-area thin films on substrates but as a result of various factors controlling growth processes the rational optimization of growth conditions is rather difficult. Mathematical modeling is one approach used in studying the effects o...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2019-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/ab3fca |
| _version_ | 1797749971633569792 |
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| author | Kazuhiko Seki |
| author_facet | Kazuhiko Seki |
| author_sort | Kazuhiko Seki |
| collection | DOAJ |
| description | Epitaxial growth methods are a key technology used in producing large-area thin films on substrates but as a result of various factors controlling growth processes the rational optimization of growth conditions is rather difficult. Mathematical modeling is one approach used in studying the effects of controlling factors on domain growth. The present study is motivated by a recently found scaling relation between the domain radius and time for chemical vapor deposition of graphene. Mathematically, we need to solve the Stefan problem; when the boundary moves, its position should be determined separately from the boundary conditions needed to obtain the spatial profile of diffusing adsorbates. We derive a closed equation for the growth rate constant defined as the domain area divided by the time duration. We obtain approximate analytical expressions for the growth rate; the growth rate constant is expressed as a function of the two-dimensional diffusion constant and the rate constant for the attachment of adsorbates to the solid domain. In experiments, the area is decreased by stopping the source gas flow. The rate of decrease of the area is obtained from theory. The theoretical results presented provide a foundation to study controlling factors for domain growth. |
| first_indexed | 2024-03-12T16:26:14Z |
| format | Article |
| id | doaj.art-32365c34672c499fa02c965360d573ad |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:26:14Z |
| publishDate | 2019-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-32365c34672c499fa02c965360d573ad2023-08-08T15:42:09ZengIOP PublishingNew Journal of Physics1367-26302019-01-0121909305910.1088/1367-2630/ab3fcaScaling theory for two-dimensional single domain growth driven by attachment of diffusing adsorbatesKazuhiko Seki0https://orcid.org/0000-0001-9858-2552Nanomaterials Research Institute(NMRI), National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 5, Higashi 1-1-1, Tsukuba, Ibaraki 305-8565, JapanEpitaxial growth methods are a key technology used in producing large-area thin films on substrates but as a result of various factors controlling growth processes the rational optimization of growth conditions is rather difficult. Mathematical modeling is one approach used in studying the effects of controlling factors on domain growth. The present study is motivated by a recently found scaling relation between the domain radius and time for chemical vapor deposition of graphene. Mathematically, we need to solve the Stefan problem; when the boundary moves, its position should be determined separately from the boundary conditions needed to obtain the spatial profile of diffusing adsorbates. We derive a closed equation for the growth rate constant defined as the domain area divided by the time duration. We obtain approximate analytical expressions for the growth rate; the growth rate constant is expressed as a function of the two-dimensional diffusion constant and the rate constant for the attachment of adsorbates to the solid domain. In experiments, the area is decreased by stopping the source gas flow. The rate of decrease of the area is obtained from theory. The theoretical results presented provide a foundation to study controlling factors for domain growth.https://doi.org/10.1088/1367-2630/ab3fcadiffusionreactionStefan problemgraphene |
| spellingShingle | Kazuhiko Seki Scaling theory for two-dimensional single domain growth driven by attachment of diffusing adsorbates New Journal of Physics diffusion reaction Stefan problem graphene |
| title | Scaling theory for two-dimensional single domain growth driven by attachment of diffusing adsorbates |
| title_full | Scaling theory for two-dimensional single domain growth driven by attachment of diffusing adsorbates |
| title_fullStr | Scaling theory for two-dimensional single domain growth driven by attachment of diffusing adsorbates |
| title_full_unstemmed | Scaling theory for two-dimensional single domain growth driven by attachment of diffusing adsorbates |
| title_short | Scaling theory for two-dimensional single domain growth driven by attachment of diffusing adsorbates |
| title_sort | scaling theory for two dimensional single domain growth driven by attachment of diffusing adsorbates |
| topic | diffusion reaction Stefan problem graphene |
| url | https://doi.org/10.1088/1367-2630/ab3fca |
| work_keys_str_mv | AT kazuhikoseki scalingtheoryfortwodimensionalsingledomaingrowthdrivenbyattachmentofdiffusingadsorbates |