Heat Transfer Optimization in Microscale Thermoelectric Devices

Abstract

Microscale thermoelectric generators are attractive for harvesting waste heat from compact electronics, but their
achievable power density is limited less by bulk material properties than by thermal contact resistance and leg
geometry effects that grow disproportionately important as device size shrinks. We present a coupled
thermal-electrical numerical model of a bismuth telluride microscale thermoelectric leg array, validated against a
fabricated 64-leg test module, and use it to optimize leg aspect ratio (height-to-cross-section) and contact-layer
thickness across 54 device geometries at leg heights from 20 to 300 micrometers. Across this geometry sweep,
output power density varied by a factor of 5.7, from 0.31 to 1.77 W/cm^2, with the maximum occurring at an
intermediate leg height of 80 micrometers rather than at the shortest legs tested, contradicting a naive bulk-limited
expectation that power density should increase monotonically as leg height decreases. Decomposing total thermal
resistance showed that contact resistance accounted for 61% of total thermal resistance at the shortest leg height
(20 micrometers) but fell to 18% at the longest (300 micrometers), while the leg's own bulk thermal resistance
showed the inverse trend, explaining the interior power-density maximum as the point where reducing further leg
height stops yielding a proportional temperature-difference gain because contact resistance increasingly dominates
the total thermal budget. At the optimal 80-micrometer geometry, the device achieved a measured-to-predicted
power agreement within 6.4% (model: 1.77 W/cm^2; fabricated module: 1.66 W/cm^2) and a device-level figure of
merit ZT_device of 0.58, 34% below the bulk material ZT of 0.88, with the gap attributed almost entirely to parasitic
contact and spreading resistances. A sensitivity analysis varying contact resistivity by a factor of 3 above and below
its measured baseline value shifted the optimal leg height by 35 micrometers and changed peak power density by
28%, identifying contact-layer quality as the single fabrication parameter with the greatest leverage over achievable
device performance. These findings provide quantitative design guidance for microscale thermoelectric leg
geometry and underscore that contact engineering, not bulk material improvement alone, is likely to yield the largest
near-term gains in microscale thermoelectric power density.