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The mechanics for calculating the quantitative driving force of indentation-induced delamination of thin-film multilayers is presented. The solution is 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 case of a multilayer by use of standard bending and thin-plate analyses. Presented and discussed are the specific solutions for the bilayer case that show that in the limit of zero thickness of either layer, the solution converges to the single-layer case. In the range of finite thickness, the presence of the superlayer increases the driving force relative to that possible for the original film alone and can be optimized to the experimental situation by proper choice of thickness, elastic constants, and residual stress. The companion paper “Quantitative adhesion measures of multilayer films: Part II. Indentation of W/Cu, W/W, Cr/W” discusses experimental results with copper, tungsten, and chromium thin films.

Sputtered copper and tungsten thin films both with and without tungsten and chromium superlayers were tested by using nanoindentation probing to initiate and drive delamination. The adhesion energies of the films were calculated from the induced delaminations using the analysis presented in “Quantitative adhesion measures of multilayer films: Part I. Indentation mechanics.” Copper films ranging in thickness from 150 to 1500 nm in the as-sputtered condition had measured adhesion energies ranging from 0.2 to 2 J/m2, commensurate with the thermodynamic work of adhesion. Tungsten films ranging in thickness from 500 to 1000 nm in the as-sputtered condition had measured adhesion energies ranging from 5 to 15 J/m2. The superlayer was shown to induce radial cracking when under residual tension, resulting in underestimation of the adhesion energy when the film was well adhered. Under conditions of weak adherence or residual compression, the superlayer provided an excellent means to induce a delamination and allowed an accurate and reasonably precise quantitative measure of thin film adhesion.

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Numerous mechanisms have been identified as fundamental to the adhesion of thin metallic films. The primary mechanism is the thermodynamic work of adhesion of the interface, which in its most basic description is the difference between the surface energies of the two materials and that of the interface. This quantity is often described as leveraging the contributions of other mechanisms. One of the more important mechanisms is that of plasticity occurring in a process zone in the vicinity of the delamination boundary. A quantitative model to characterize the contributions of plastic energy dissipation has been developed and used to rationalize experimental adhesion assessments. This model incorporates the functional dependence of the film thickness and constitutive properties. Orders of magnitude increases in the practical work of adhesion were both observed and predicted. Experimentally, the films used for model comparison were sputter-deposited copper ranging from 40 to 3300 nm in thickness, with and without a thin 10 nm Ti underlayer. Nanoindentation induced delamination of the Cu from SiO 2 /Si wafers were evaluated in the context of composite laminate theory to determine adhesion energies ranging from 0.6 to 100 J/m 2 for bare Cu and from 4 to 110 J/m 2 for Cu with the Ti underlayer.