Abstract The energy conversion efficiency of thermoelectric systems can be greatly improved via the process known as “hole-doping” in which small-scale holes are introduced into constituent thermoelectric materials. However, the associated thermal stress induced by the introduction of the holes is known to be one of the main factors contributing to failure of the thermoelectric system. In this paper, we perform a detailed and rigorous analysis of the thermal stress distribution around a small-scale (micro- and nano-scale) elliptic hole by taking into consideration the contribution of size effects. Numerical solutions describing electric, thermal and elastic fields in the vicinity of the hole are obtained using complex variable techniques and Fourier series expansions. In particular, we obtain closed-form analytical solutions for the special case of a circular hole to verify the results of our numerical solutions. We find that the dominant stress distribution around the hole is that induced by the hoop stress which is significantly influenced by surface phonon scattering. Specifically, the maximum hoop stress decreases sharply with the increase of the Knudsen number and reaches a minimum value which therefore identifies an optimal stress distribution.

中文翻译：

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表面声子散射对热电材料中小尺度椭圆孔周围热应力的影响

摘要 热电系统的能量转换效率可以通过被称为“空穴掺杂”的过程大大提高，在这个过程中，小尺寸的空穴被引入组成的热电材料中。然而，已知由孔的引入引起的相关热应力是导致热电系统故障的主要因素之一。在本文中，我们通过考虑尺寸效应的贡献，对小尺度（微米和纳米尺度）椭圆孔周围的热应力分布进行了详细而严格的分析。使用复变量技术和傅立叶级数展开可以获得描述孔附近电场、热和弹性场的数值解。特别是，我们获得了圆孔特殊情况的封闭形式解析解，以验证我们的数值解的结果。我们发现孔周围的主要应力分布是由受表面声子散射显着影响的环向应力引起的。具体而言，最大环向应力随着 Knudsen 数的增加而急剧下降，并达到最小值，因此确定了最佳应力分布。