The recent advances in the inelastic background analysis of XPS spectra recorded with hard X-rays (HAXPES) make this method a powerful, non-destructive solution to retrieve the depth distribution of deeply buried elements. In this work, we apply this technique to study diffusion phenomena, upon annealing, in power transistor devices. We present a complete analysis of a sample under different stages of the fabrication process. We investigate the accuracy of the determination of the elemental depth distributions and concentrations with the inelastic background analysis. This is done by cross-checking with destructive techniques such as TEM/EDX and XPS depth profiling, and we shed light on the complementarities with HAXPES core-level analysis. We obtain consistent results which show the formation of an inhomogeneous structure, consisting of a blend of Al, Ga, and Ta, created during annealing. The inelastic background analysis permits us to successfully retrieve the depth distributions of Al, Ga, and Ta as well as the concentration of these elements in each layer, over 70 nm below the surface. This is a reliable solution to investigate diffusion phenomena and improve the fabrication processes of devices with critical and deeply buried interfaces.