Indentation Fracture Toughness Measurements of Low Dielectric Constant Materials
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Indentation Fracture Toughness Measurements of Low Dielectric Constant Materials Dylan J. Morris and Robert F. Cook Department of Chemical Engineering and Materials Science, University of Minnesota Minneapolis, MN 55455 U.S.A. ABSTRACT The physics and mechanics of a fracture toughness measurement technique for low-k films are described. It has been observed experimentally that it is possible to generate reproducible stable cracks at indentation sites in thin low-k films using cube-corner indentation. The fracture response depends on the film thickness and follows no simple scaling laws. The physics of a model that takes into account the stress fields from indentation and film stress, with particular attention paid to the Poisson’s ratio of the film, are described. The model is able to predict the changes in observables when the film thickness is changed, which allows one to estimate film toughness independent of the configuration of the material. INTRODUCTION Indentation fracture toughness measurements have been used with great success for over 20 years in characterizing engineering ceramic and glassy materials. The technique has rarely been extended to characterize films of thicknesses less than 10 µm, and never successfully implemented as a technique to characterize coatings that are porous and densifying. A “wedging” phenomenon for indentation crack propagation is proposed that operates in lieu of the elastic-plastic mismatch stress field normally present in dense ceramics and glasses. Wedging, elastic contact stresses and intrinsic film stresses are combined with fracturemechanics descriptions of crack shapes to form a complex two-regime description of the fracture phenomena. The effects of film thickness and Poisson’s ratio on both contact mechanics and fracture mechanics are demonstrated. The model successfully predicts changes in fracture response when the film thickness is changed, which is a necessary condition for any model to extract the film property from a composite material system. EXPERIMENTAL Standard hardness and elastic modulus measurements were performed with a Berkovich probe using a MTS Corp. Nano Indenter® Dynamic Contact Module (DCM). Cube-corner indentation for the purpose of generating cracks was performed with a MTS Corp. Nano Indenter® XP. Cube-corner indentations were made under constant indentation strain-rate [1] loading, and a 10 s hold at peak load. Continuous stiffness measurements [2] were made during the loading half-cycle and at peak load. Imaging of the indentation impressions, and the cracks surrounding the impressions, was performed with low-voltage field-emission-gun scanning electron microscopy (FEG-SEM) at magnifications ranging from 15,000 to 50,000. An example of an indentation flaw in a low-k film is shown in Figure 1. Delamination of the film at large indentation loads was obvious as uplift at the indentation site, determined from Nomarski imaging. Data where there was delamination was discounted. Crack-length measurements were made with image analysis software.
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