Inequalities for Single Crystal Ribbon Growth by Edge-Defined Film-Fed Growth Technique
<p>Abstract</p> <p>A second-order nonlinear differential equation, of which some solutions describe the static meniscus free surface (the static liquid bridge free surface between the shaper and the crystal surface) occurring in single crystal ribbon growth, is analyzed. The analys...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2008-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2008/381604 |
| _version_ | 1818289832840921088 |
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| author | Balint AgnetaM Balint Stefan |
| author_facet | Balint AgnetaM Balint Stefan |
| author_sort | Balint AgnetaM |
| collection | DOAJ |
| description | <p>Abstract</p> <p>A second-order nonlinear differential equation, of which some solutions describe the static meniscus free surface (the static liquid bridge free surface between the shaper and the crystal surface) occurring in single crystal ribbon growth, is analyzed. The analysis is focusing on the dependence of the solutions of the equation on the pressure difference <inline-formula> <graphic file="1029-242X-2008-381604-i1.gif"/></inline-formula> across the free surface. Inequalities are deduced for <inline-formula> <graphic file="1029-242X-2008-381604-i2.gif"/></inline-formula>, which are necessary or sufficient conditions for the stable and convex free surface of a static meniscus. The obtained results are numerically illustrated in the case of a silicon single crystal ribbon growth. The advantage of these kinds of inequalities is that from them special results can be gleaned concerning the experiment planning and technology design. With this aim this study was undertaken.</p> |
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| id | doaj.art-d79ae91217c44bb8b1e69d61c6dfa244 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-13T02:18:33Z |
| publishDate | 2008-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-d79ae91217c44bb8b1e69d61c6dfa2442022-12-22T00:02:49ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2008-01-0120081381604Inequalities for Single Crystal Ribbon Growth by Edge-Defined Film-Fed Growth TechniqueBalint AgnetaMBalint Stefan<p>Abstract</p> <p>A second-order nonlinear differential equation, of which some solutions describe the static meniscus free surface (the static liquid bridge free surface between the shaper and the crystal surface) occurring in single crystal ribbon growth, is analyzed. The analysis is focusing on the dependence of the solutions of the equation on the pressure difference <inline-formula> <graphic file="1029-242X-2008-381604-i1.gif"/></inline-formula> across the free surface. Inequalities are deduced for <inline-formula> <graphic file="1029-242X-2008-381604-i2.gif"/></inline-formula>, which are necessary or sufficient conditions for the stable and convex free surface of a static meniscus. The obtained results are numerically illustrated in the case of a silicon single crystal ribbon growth. The advantage of these kinds of inequalities is that from them special results can be gleaned concerning the experiment planning and technology design. With this aim this study was undertaken.</p>http://www.journalofinequalitiesandapplications.com/content/2008/381604 |
| spellingShingle | Balint AgnetaM Balint Stefan Inequalities for Single Crystal Ribbon Growth by Edge-Defined Film-Fed Growth Technique Journal of Inequalities and Applications |
| title | Inequalities for Single Crystal Ribbon Growth by Edge-Defined Film-Fed Growth Technique |
| title_full | Inequalities for Single Crystal Ribbon Growth by Edge-Defined Film-Fed Growth Technique |
| title_fullStr | Inequalities for Single Crystal Ribbon Growth by Edge-Defined Film-Fed Growth Technique |
| title_full_unstemmed | Inequalities for Single Crystal Ribbon Growth by Edge-Defined Film-Fed Growth Technique |
| title_short | Inequalities for Single Crystal Ribbon Growth by Edge-Defined Film-Fed Growth Technique |
| title_sort | inequalities for single crystal ribbon growth by edge defined film fed growth technique |
| url | http://www.journalofinequalitiesandapplications.com/content/2008/381604 |
| work_keys_str_mv | AT balintagnetam inequalitiesforsinglecrystalribbongrowthbyedgedefinedfilmfedgrowthtechnique AT balintstefan inequalitiesforsinglecrystalribbongrowthbyedgedefinedfilmfedgrowthtechnique |