Mechanical model for a thermoelectric thin film bonded to an elastic infinite substrate

A thermoelectric thin film bonded to an elastic infinite substrate is modeled with consideration of the bending stiffness of the film. Through the stress balance and the strain compatibility between the film and the substrate, a pair of integral equations is derived. The results show that the interfacial tensile and shear stresses exhibit singularity at the end of the thin film. For this, the concept of stress intensity factor is used to describe the singularity behavior of the film/substrate interface. The effects of the electric current density, the thermal conductivity of the film, the film to substrate stiffness ratio and the half-length to thickness ratio of the film on the stress intensity factors are examined. Comparison between beam model and membrane model for thermoelectric thin film analysis is made and the results suggest that consideration of film stiffness is essential for correct evaluation of the thermal stress level in the thermoelectric film.