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An analytical solution for quantum size effects on Seebeck coefficient
Istanbul Technical University, Energy Institute.
Istanbul Technical University, Energy Institute.ORCID iD: 0000-0002-7431-5115
Istanbul Technical University, Energy Institute.
2016 (English)In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 91, article id 035803Article in journal (Refereed) Published
Abstract [en]

There are numerous experimental and numerical studies about quantum size effects on Seebeckcoefficient. In contrast, in this study, we obtain analytical expressions for Seebeck coefficientunder quantum size effects. Seebeck coefficient of a Fermi gas confined in a rectangular domainis considered. Analytical expressions, which represent the size dependency of Seebeckcoefficient explicitly, are derived in terms of confinement parameters. A fundamental form ofSeebeck coefficient based on infinite summations is used under relaxation time approximation.To obtain analytical results, summations are calculated using the first two terms of Poissonsummation formula. It is shown that they are in good agreement with the exact results based ondirect calculation of summations as long as confinement parameters are less than unity. Theanalytical results are also in good agreement with experimental and numerical ones in literature.Maximum relative errors of analytical expressions are less than 3% and 4% for 2D and 1D cases,respectively. Dimensional transitions of Seebeck coefficient are also examined. Furthermore, adetailed physical explanation for the oscillations in Seebeck coefficient is proposed byconsidering the relative standard deviation of total variance of particle number in Fermi shell.

Place, publisher, year, edition, pages
2016. Vol. 91, article id 035803
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:uu:diva-380283OAI: oai:DiVA.org:uu-380283DiVA, id: diva2:1299044
Available from: 2019-03-26 Created: 2019-03-26 Last updated: 2019-03-26

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