Thickness optimization of the output power and effective thermoelectric figure of merit of thin thermoelectric generator

The conventional thermoelectric figure of merit and the power factor are not sufficient as a measure of thin film quality of thermoelectric materials, where the power conversion efficiency depends on the film dimensions. By considering the film size, the effective thermoelectric figure of merit and effective Seebeck coefficient are introduced to guarantee that the maximum energy conversion efficiency increases as the effective thermoelectric figure of merit increases. Similarly, the effective power factor is defined. By introducing typical material properties for Bi${}_2$Te${}_3$ and PEDOT, we study the thickness dependence of the effective figure of merit and the effective power factor.