Thermoelectric power in very thin film thermocouples: Quantum size effects

The thermoelectric power SF of thin film thermocouples is related to the bulk thermopower Sbulk by ΔSF(t)=Sbulk−SF as a linear function of 1∕t when t⪢ℓ, where ℓ is the electron mean free path and t the film thickness. For these conditions quantum size effects (QSEs) are negligible. However, when t<ℓ QSEs become relevant. In recent work we have shown that for Pt∕Au thermocouples with film thickness t<ℓPt≈10nm, ΔSF(t)=0.194+26.7(1∕t)−93.6(1∕t)2+112.0(1∕t)3. Here we show that this nonlinear 1∕t behavior is due to QSE.