Effect of surface phonon scattering on thermal stress around small-scale elliptic holes in a thermoelectric material

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.

Keywords:

• Micro- or nano-scale hole
• surface phonon scattering
• thermal stress
• thermoelectric material

Additional information

Funding

Schiavone thanks the Natural Sciences and Engineering Research Council of Canada for their support through a Discovery Grant [Grant # RGPIN 155112].