Thermal switching ratio of semiconducting polymers with spatially graded doping

Abstract

The switching ratio of a thermal switch is a key design parameter, and electrically activated switches based on thermoelectric effects have been reported to produce large switching ratios over a wide range of temperatures. Previous switches based on the Seebeck effect have switching ratios that are limited by the thermoelectric figure-of-merit zT. Perhaps, more importantly, they are limited by their device construction of alternating p-type and n-type materials with soldered junctions. Alternatively, we show that semiconducting polymers with spatially graded doping can offer similar switching ratios due to a volumetric heat absorption effect. This occurs in heavily doped polymers, which exhibit a sharp decrease in the Seebeck coefficient as charge carriers become fully delocalized. Such heat absorption is analogous to the Thomson effect, where heat is locally absorbed due to temperature-dependent variation of the Seebeck coefficient. Here, a theoretical model is derived to solve the 1D heat equation with spatially graded doping, allowing for optimization of the doping profile for a given material system. Four different material systems are compared according to an analysis of reported measurements to determine the upper limit of the switching ratio. A hypothetical Thomson switch based on poly(3,4-ethylenedioxythiophene) doped with ferric tosylate can produce switching ratios up to 12 under a thermal bias of 10 K, a threefold increase compared to a Peltier switch of the same material. Like a Peltier switch, the switching ratio of a Thomson switch diverges under a small thermal bias. Under a large thermal bias, the switching ratio converges toward that of an equivalent Peltier switch.