Indentation fracture of low-dielectric constant films: Part II. Indentation fracture mechanics model
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Part I [D.J. Morris and R.F. Cook, J. Mater. Res. 23, 2429 (2008)] of this two-part work explored the instrumented indentation and fracture phenomena of compliant, low-dielectric constant (low-) films on silicon substrates. The effect of film thickness and probe acuity on the fracture response, as well as the apparent connection of this response to the perceived elastic modulus, were demonstrated. These results motivate the creation of a fracture model that incorporates all of these variables here in Part II. Indentation wedging is identified as the mechanism that drives radial fracture, and a correction is introduced that adjusts the wedging strength of the probe for the attenuating influence of the relatively stiff substrate. An estimate of the film fracture toughness can be made if there is an independent measurement of the film stress; if not, a critical film thickness for channel-cracking under the influence of film stress may be estimated.
I. INTRODUCTION
Part I of this work outlined some of the phenomena of radial crack initiation and propagation in low-dielectric constant (low-) films at contacts by sharp probes.1 It was shown that the conventional analysis for estimation of fracture toughness by indentation is inapplicable due to the clear dependence of the indentation fracture response on the film thickness and the apparently complex crack-length–indentation-load scaling involved. Furthermore, one of the core physical assumptions of the conventional indentation fracture model (volume conserving plastic deformation) is likely broken for low- films, as the incorporation of porosity for low-dielectric constants will almost necessarily result in densification being the dominant irreversible deformation mode. This paper develops concepts and a model that attempt to capture the important physics of the indentation fracture response of thin, porous films. With this, a method for the estimation of the fracture toughness of low- films is presented. Section II modifies the “wedging” radial crack development model of Morris and Cook2 for the presence of a stiff, constraining substrate in two ways: by consideration of the constraint of the substrate on crack shape and on the attenuation of the indentation crack-driving stresses within the film by the substrate.
Section III outlines the effect of pre-existing film stress on the fracture response. In Sec. IV, the complete fracture model is developed and compared with experimental data. Simulation of fracture responses in Sec. V shows the way that all three substrate effects (crack shape change, indentation stress attenuation, and film stresses) play a role in the fracture response. II. INDENTATION CRACK DRIVING FORCES A. Indentation stress-intensity factors for different crack shapes
Estimation of fracture properties in small volumes, or on samples ill-suited to conventional fracture-specimen preparation, requires a local mechanical property probe such as indentation. In most ceramics and glasses, the hoop-tensile residual stress field caused by the reaction of
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