Strain gradients and normal stresses in textured Mo thin films

Abstract

The high-resolution x-ray-diffraction technique was used to explore strain variations in sputtered Mo films with thicknesses of 170, 260, and 800 nm that possess a (110) out-of-plane texture. The strains in crystallographic planes perpendicular to the surface of each film were found to be nominally constant and compressive at all x-ray penetration depths. Near the surface of each film, the inclined-plane strains were compressive, and then relaxed as the penetration depths approached each entire film thickness. The strain tensor in a laboratory reference frame for each film, as a function of penetration depth, revealed that the normal strain εzz was tensile near the surface of each film, and then relaxed to a nominally constant value as the penetration depths approached the entire film thickness. The penetration depth over which the normal strain decayed to a nominally constant value increased as the total film thickness increased. A consequence of the large normal strains near the free surface of each film is that the corresponding normal stresses were nonzero.