THE ANALYTICAL SOLUTION OF THE CONTACT PROBLEM OF SPHERICAL INDENTERSON LAYERED MATERIALS - APPLICATION FOR THE INVESTIGATION OF TIN FILMSON SILICON

Utilising an analytical solution of the contact problem of spherical i ndentation into layered materials we investigated TiN layers of variou s thicknesses on single-crystal silicon. We used Heaviside functions t o describe the discontinuity of the mechanical parameters at the inter face of the TiN-silicon compound. A spherical 5 mu m diamond indenter was used to obtain the penetration depth-force curves. In spite of thi s small indenter we only obtained good utilizable results for film thi cknesses of more than 0.8 mu m. For thinner films the influence of fai lure effects such as roughness of the film, not an exactly known film thickness and substrate parameters, deviation of the shape of the diam ond indenter from the ideal spherical one and the failure caused by th e 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 silico n 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 calculat ion only using estimated Young's moduli from the thicker films. We pai d special attention to the investigation of the non-elastic behaviour of the compounds utilising the von-Mises criterion.