A Quantitative Model for Interpreting Nanometer Scale Hardness Measurements of Thin Films
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A QUANTITATIVE MODEL FOR INTERPRETING NANOMETER SCALE HARDNESS MEASUREMENTS OF THIN FILMS W.H. POISL', B.D. FABES, and W.C. OLIVER" "Dept.ofand Materials Science and Engineering, University of Arizona, Tucson, AZ 85721. "-Metals Ceramics Division, Oak Ridge National Laboratories, Oak Ridge, TN, 37831. ABSTRACT A model has been developed to determine the hardness of thin films from the measured change in hardness with indenter displacement using a depth-sensing indentation instrument. The model is developed by dividing the measured hardness into film and substrate contributions based on the projected areas of both the film and substrate under the indenter. The model incorporates constraints on the deformation of the film by the surrounding material in the film, the substrate, and friction at the indenter/film and film/substrate interfaces. These constraints increase the pressure that the film can withstand and account for the increase in measured hardness as the indenter approaches the substrate. The model is evaluated by fitting the predicted hardness versus depth curves to data obtained from titanium and Ta2O5 films of varying thicknesses on sapphire substrates. The model predicts a lower interfacial strength for Ta20 5 films on sapphire with a carbon layer between the film and the substrate than that obtained for a film without an interfacial carbon layer. INTRODUCTION Depth-sensing indentation instruments have been used to determine the mechanical properties, especially Young's modulus, E, and hardness, H, of thin films and coatings on the nanometer scale. In measuring the hardness of a thin film, it is often observed that, for the same depth of penetration, hardness increases as the thickness of the film decreases. The interactions between the intrinsic (dislocation density, crystal structure, etc.) and extrinsic (substrate hardness, film/substrate adhesion, film thickness, etc.) properties on the measured hardness are not well understood. Various models of the indentation process have been proposed to calculate the hardness versus depth curves of thin films on substrates. These have included finite element models,' as well as physical models based on weighted volumes 24 or areas5' 6 of material affected by the indenter. Many of these models, however, have not used the actual cross-sectional area to depth function of the indenter, have not included the full range of indentation depths (both less than and greater than the film thickness), or included changes in film/substrate adhesion. If a soft film adheres to a hard substrate, or if there is friction between the film and substrate, the substrate will constrain the plastic flow of the film. This will induce a hydrostatic pressure under the indenter, making penetration by the indenter more difficult. As the hardness of the system is defined as the maximum load divided by the projected permanent area of the indent, this will cause an increase in hardness as the indenter approaches the substrate. For films of the same thickness, an increase in friction between the
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