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.

摘要

通过以下方式可以大大提高热电系统的能量转换效率一种称为“空穴掺杂”的过程，其中将小规模的空穴引入组成热电材料中。然而，已知由于引入孔而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影响，对小尺寸（微米和纳米级）椭圆孔周围的热应力分布进行了详细而严格的分析。使用复杂变量技术和傅立叶级数展开获得描述孔附近电场，热场和弹性场的数值解。特别是，我们针对特殊情况下的圆孔获得了封闭形式的解析解，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环向应力引起的，环向应力主要受表面声子散射的影响。具体地，最大环向应力随着克努森数的增加而急剧减小，并且达到最小值，因此确定了最佳应力分布。