A unified theoretical model for tensile and compressive residual film stress

• Published in: Thin solid films Vol. 370; no. 1; pp. 232 - 237
• Main Authors: Knuyt, G., Lauwerens, W., Stals, L.M.
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 17.07.2000; Elsevier Science
• Subjects: Coatings; Condensed matter: structure, mechanical and thermal properties; Exact sciences and technology; Mechanical and acoustical properties; Physical properties of thin films, nonelectronic; Physical vapour deposition; Physics; Stress; Surfaces and interfaces; thin films and whiskers (structure and nonelectronic properties); Tungsten; Physical vapour deposition; Coatings; Tungsten; Stress; Compressive stress; Tensile stress; Films; Physical vapor deposition; Theoretical study; Mechanical properties; Energy density; Models; Residual stresses; Fabrication property relation; Ion beams
• ISSN: 0040-6090; 1879-2731
• DOI: 10.1016/S0040-6090(00)00944-5

A relative simple model is elaborated for the overall behaviour of the residual stress in a coating layer, grown under continuous bombarding of energetic particles. It concentrates on the transition from tensile to compressive stress under increasing energetic particle flux, a phenomenon frequently observed in experiments. The energy density E in the film is written as a sum of an elastic deformation contribution, and a contribution due to depletion zones between the growing columns. Minimization of E leads to the value of the lateral stress in the film. It is found that the film stress shows a characteristic behaviour on the ratio J ion/ J at (ion to atom flux ratio). Generally, for increasing J ion/ J at the stress will first attain a maximum tensile value, and then will change from tensile to compressive values. Further we find that the maximum tensile stress and the tensile/compressive transition occur at lower J ion/ J at ratios for higher energies of the incoming energetic particles. These findings agree with a number of experimental results.