The yield strength of thin copper films on Kapton

Thin films of copper, with thickness between 0.1 and 3 μm, were vapor-deposited on 12.7 or 7.6-μm-thick polyimide (Kapton) substrates. They were tested in a microtensile tester in which the strain is measured by optical diffraction from a microlithographically applied grid. The Young modulus is independent of film thickness and is about 20% below the value calculated from single-crystal elastic constants. The yield stress depends strongly on the film thickness and is fit by ${\sigma }_y{\text{=116+355(t)}}^{\text{−0.473}},$ where t is the thickness in μm and ${\sigma }_y$ is in MPa. The microstructure of the films was studied by focused ion-beam microscopy. The grains are heavily twinned and the microstructural lengths (grain size, twin spacing, twin width) depend only weakly on the film thickness. A substantial part of the yield stress is therefore attributable to an effect of the film thickness, such as that predicted by strain gradient plasticity theory. The lower limit and some estimates of the thickness contribution to the yield stress are calculated. The estimated characteristic length of strain gradient plasticity theory is 0.6 μm for these materials.