Determination of modified figure of merit validity for thermoelectric thin films with heat transfer model: Case of CuCrO2:Mg deposited on fused silica

Thermoelectric performance of a material is determined using a figure of merit (FOM) determined as ZT (ZT = σS2T/κ where σ is the electrical conductivity, S is the Seebeck coefficient, κ is the thermal conductivity, and T is the temperature). In the case of a thin film, it is normal in the first approach to consider calculating the FOM by using the thermal conductivity of the film. However, both the thermal influence of the substrate and the emissivity of the film must also be taken into account. In the present work, the heat transfer model is used in order to study the influence of the thermal conductivity, the thickness, and the emissivity of the film on the thermal gradient of the stack (substrate + thin film). The limits of these three parameters are determined in order to have the temperature variation due to the presence of the film compared to the substrate alone that remains less than 1%. Under these limits, the thermal conductivity of the substrate can be taken into account instead of the thermal conductivity of the thin film, and a modified FOM (Z’T) can be calculated. The present study leads to the determination of the validity of modified ZT. In the case of CuCrO2:Mg thin films, the model shows that the use of Z’T is valid. The calculated value of Z’T with the measured Seebeck coefficient and the electrical conductivity as a function of the temperature for 100 nm thick films and the temperature dependent thermal conductivity taken from the literature reached 0.02 at 210 °C. A thermoelectric module made with this material showed 10.6 nW when 220 °C is applied at the hot side.