Thermal stress analysis in a graded thermoelectric film bonded to a homogeneous substrate

In this paper, the thermoelastic behavior of a functionally graded thermoelectric thin film attached to a homogeneous substrate is investigated. First assuming a one-dimensional temperature field, the steady-state temperature distribution is obtained using the equations governing the physics of thermoelectric material. Then, the integral equations are derived for the problem by combining the equilibrium and strain compatibility equations. The simple shearing deformation is adopted for the bonding layer since its tensile strength is much smaller than that of the film and the substrate. Finally, employing the Gauss-Chebyshev discretization method, the integral equation is solved for the interfacial stress distribution. A detailed parametric study is conducted to explore the effect of non-homogeneity parameters on the stress components for the film and the substrate. The numerical results indicate that proper adjustment of the non-homogeneity parameters for the functionally graded thermoelectric thin film can extend the service life and the mechanical stability of the device. Additionally, choosing a softer and/or thicker bonding layer can reduce the stress concentration near the film ends as well as the delamination edges. The interfacial shear stress distribution changes direction when the delamination length exceeds 40% of the film length. Depositing a thinner thermoelectric film on an elastic substrate can delay delamination failure driven by interfacial shear stress.