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A thermosize junction consists of two different sized structures made by the same material. Classical and quantum thermosize effects (CTSE and QTSE), which are opposite to each other, induce a thermosize potential in a thermosize junction. A semi-analytical method is proposed to calculate thermosize potentials in wide ranges of degeneracy and confinement by considering both CTSE and QTSE in thermosize junctions made by semiconductors. Dependencies of thermosize potential on temperature, size and degeneracy are examined. It is shown that a potential difference in millivolt scale can be induced as a combined effect of CTSE and QTSE. The highest potential is obtained in non-degenerate limit where the full analytical solution is obtained. The model can be used to design semiconductor thermosize devices for a possible experimental verification of CTSE and QTSE, which may lead to new nano energy conversion devices.

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There are numerous experimental and numerical studies about quantum size effects on Seebeck coefficient. In contrast, in this study, we obtain analytical expressions for Seebeck coefficient under quantum size effects. Seebeck coefficient of a Fermi gas confined in a rectangular domain is considered. Analytical expressions, which represent the size dependency of Seebeck coefficient explicitly, are derived in terms of confinement parameters. A fundamental form of Seebeck coefficient based on infinite summations is used under relaxation time approximation. To obtain analytical results, summations are calculated using the first two terms of Poisson summation formula. It is shown that they are in good agreement with the exact results based on direct calculation of summations as long as confinement parameters are less than unity. The analytical 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, a detailed physical explanation for the oscillations in Seebeck coefficient is proposed by considering the relative standard deviation of total variance of particle number in Fermi shell.