Abstract
Length scales are essential to the understanding of small volume deformation and fracture in emerging technologies. Recent analysis by two groups at the atomistic (Horstmeyer and Baskes, 1999) and mesoscopic (Gerberich et al., 2002) levels have shown the importance of the volume to surface ratio to the indentation size effect (ISE) at small depths of penetration. We have interpreted this in terms of the plastic work under the contact and the surface work associated with the creation of new surface or the excess surface stress. Treating this as a modified Griffith criterion the case is made that this same length scale should apply to the delamination of thin films. By making this simple equivalency in length scales, an R-curve analysis for crack growth resistance, GR ,i n thin film delamination emerges. This recovers the classic σ 2 ysh/E term as well as the fact that interfacial toughness should scale with the square root of incremental crack growth. Here σys is yield strength, h is thickness and E is modulus of the film. As applied to thin Cu and Au films bonded to silicon substrates, the model is in good agreement.
Highlights
Current research into nanotechnology is increasingly aware of the limitations of small scales in micromachines, MEMS, microelectric interconnects and magnetic recording heads
We believe we have fortuitously arrived at a single length scale parameter that controls both small volume deformation and fracture behavior of thin films
E is essentially the leading term in most thin film resistance models involving plasticity. This proposed R-curve behavior for forced thin film crack extension is seen to evolve directly from a simple volume to surface length scale. We propose that both indentation and fracture occurring from small volume deformation are controlled by the same length scale and that this leads to a delamination resistance criteria
Summary
Current research into nanotechnology is increasingly aware of the limitations of small scales in micromachines, MEMS, microelectric interconnects and magnetic recording heads. We believe we have fortuitously arrived at a single length scale parameter that controls both small volume deformation and fracture behavior of thin films. From previous works [2] on the indentation size effect (ISE) we had shown that the volume to surface ratio could explain the increases in hardnesses observed at very small depths of penetration with δ ≤ 300 nm.
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