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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >An analytical solution for quantum size effects on Seebeck coefficient
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An analytical solution for quantum size effects on Seebeck coefficient

机译：量子尺寸对塞贝克系数影响的解析解

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摘要

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.
机译：关于塞贝克系数的量子尺寸效应，有大量的实验和数值研究。相反，在这项研究中，我们获得了量子尺寸效应下塞贝克系数的解析表达式。考虑被限制在矩形域中的费米气体的塞贝克系数。根据限制参数推导了明确表示塞贝克系数大小相关性的解析表达式。在松弛时间近似下使用基于无限求和的塞贝克系数的基本形式。为了获得分析结果，使用泊松求和公式的前两个项来计算求和。结果表明，只要约束参数小于1，它们与基于直接求和的精确结果非常吻合。分析结果也与文献中的实验和数值结果相吻合。对于2D和1D情况，分析表达式的最大相对误差分别小于3％和4％。还检查了塞贝克系数的尺寸变化。此外，通过考虑费米壳中粒子数总方差的相对标准偏差，提出了塞贝克系数振荡的详细物理解释。

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