Abstract

Thermoelectric materials for power generation are typically compared using the dimensionless figure-of-merit ZT because it relates directly to the device efficiency. However, for practical applications, the cost of power generation – as governed by material, manufacturing, and heat exchanger costs – is also a critical factor which is not captured in ZT. The necessary analysis derived herein yields the first expressions for optimizing the thermoelectric leg length and the system fill factor, F, as a function of these costs. This optimization yields the minimum $/W value for thermoelectric power generation and a framework for comparing materials beyond ZT. Even very expensive thermoelectric materials have the potential to be the most cost effective at the system level, if incorporated with sufficiently short legs and small fill factor. Furthermore, an approximate scaling analysis delineates various cost-dominant regimes with different priorities for materials development: (i) a heat exchanger cost dominated regime, where ZT should be increased regardless of material or manufacturing costs; (ii) an areal cost, C’’, dominated regime at fixed F, where ZT/C’’ should be maximized, and (iii) a volumetric cost, C’’’, dominated regime at fixed F, where ZT/(kC’’’) should be maximized, reinforcing the need for low thermal conductivity, k. The cost-performance framework derived in this work is applied to a number of practical materials and manufacturing processes in a concurrent manuscript.