<p>This study investigates the interface effects in thermoelectric generators composed of functionally graded materials (FGMs) using the differential transformation method (DTM). A steady-state thermal model is developed to analyze the impacts of FGM parameters and interfacial layer characteristics on the performance of thermoelectric generators. Varying thermoelectric properties including thermal conductivity, Seebeck coefficient, and electrical resistivity along the axial direction of thermoelectric legs are considered. By incorporating external and internal interface layers, this model examines their impact on temperature distribution, heat flux distribution, thermal stress, and energy conversion efficiency. The results demonstrate that DTM provides an accurate and efficient solution for nonlinear thermoelectric governing equations, exhibiting excellent agreement with finite element method (FEM) simulations. The study reveals that optimizing the material property gradients and interface layer configurations can simultaneously enhance energy conversion efficiency and reduce thermal stress. The findings show that the exponential profile yields a higher maximum thermomechanical performance index (<i>ζ</i> = 2.87 1/GPa at <i>J</i> = −83 A/cm²) than the linear profile (<i>ζ</i> = 2.65 1/GPa at <i>J</i> =  −88 A/cm²). This work advances theoretical understanding of FGMs and interface layer design in thermoelectric systems, providing valuable insights for high performance thermoelectric device.</p> Graphical abstract <p></p>