The analytical solution of the contact problem of spherical indenters on layered materials: Application for the investigation of TiN films on silicon

Utilising an analytical solution of the contact problem of spherical indentation into layered materials we investigated TiN layers of various thicknesses on single-crystal silicon. We used Heaviside functions to describe the discontinuity of the mechanical parameters at the interface of the TiN-silicon compound. A spherical 5 mu m diamond indenter was used to obtain the penetration depth-force curves. In spite of this small indenter we only obtained good utilizable results for film thicknesses of more than 0.8 mu m. For thinner films the influence of failure effects such as roughness of the film, not an exactly known film thickness and substrate parameters, deviation of the shape of the diamond indenter from the ideal spherical one and the failure caused by the indentation apparatus themselves becomes too influential. Thus, here we show an investigation of a 1.4 and an 0.8 mu m TiN layer on silicon including calculation of the films Young's modulus and the stresses, and for an 0.4 and an 0.2 mu m TiN layer on silicon a stress calculation only using estimated Young's moduli from the thicker films. We paid special attention to the investigation of the non-elastic behaviour of the compounds utilising the von-Mises criterion.