Quantitative adhesion measures of multilayer films: Part I. Indentation mechanics

The mechanics for calculating the quantitative driving force of indentation -induced delamination of thin-film multilayers is presented. The solution i s based on the mechanics developed by Marshall and Evans [D.B. Marshall and A.G. Evans, J. Appl. Phys. 56, 2632 (1984).] and extended to the general c ase of a multilayer by use of standard bending and thin-plate analyses. Pre sented and discussed are the specific solutions for the bilayer case that s how that in the limit of zero thickness of either layer, the solution conve rges to the single-layer case. In the range of finite thickness, the presen ce of the superlayer increases the driving force relative to that possible for the original film alone and can be optimized to the experimental situat ion by proper choice of thickness, elastic constants, and residual stress. The companion paper "Quantitative adhesion measures of multilayer films: Pa rt II. Indentation of W/Cu, W/W, Cr/W" discusses experimental results with copper, tungsten, and chromium thin films.