Improved maximum cooling by optimizing the geometry of thermoelectric leg elements

In this paper, we investigate the effect of the thermoelectric leg geometry and boundary conditions on the overall device cooling performance. We present a detailed 3D electrothermal analysis of heat and current distribution in a Bi₂Te₃ single-leg element with 50×50 μm² cold side contact area, which is smaller than the element cross section (410×410 μm²). We compared the cases when a uniform voltage is applied at the contact and when a uniform current density is applied. The finite element calculation results demonstrate that in the latter case the 3D single-leg element has a very non-uniform temperature distribution at the contact area. Maximum cooling in the center region is 92°C, which is 20% higher than the 1D limit (76°C) for a typical Bi₂Te₃ material with ZT∼1. Calculations show that it is possible to take away 600 W/cm² at the center 20×20 μm² region, which is 6 times better than the 1D device with the same thickness. In contrast, with a boundary condition of uniform voltage at the cold side contact area, the temperature distribution is as uniform as 1D device and reaches the same maximum cooling temperature as 1D. We also propose the possibility of using array contact structures to achieve the uniform current boundary condition that can improve the maximum device cooling performance. These findings add contact geometry as another degree of freedom to engineer the performance of single and multi stage TE devices.