Thin film characterization

The film thickness was evaluated by an optical 3D white light profiling system (Veeco Wyko NT 1000). The chemical composition of the films on Si substrate was analyzed with an EDX detector (Oxford Instruments INCA) attached to the scanning electron microscope (Zeiss Evo-50). The crystallographic structure was investigated by X-ray diffraction in θ/2θ and grazing incidence (2° incidence angle) geometry utilizing a Bruker-AXS D8 Advance diffractometer equipped with Cu-K_α radiation and parallel beam optics. The lattice parameter was determined from the θ/2θ measurements by Rietveld refinement⁴⁹ using the fundamental parameter approach⁵⁰ contained within the software TOPAS V4 (Bruker AXS).

Nanoindentation on the 500 nm thin films on Si was performed in a Hysitron TI 950 TriboIndenter equipped with a Berkovich diamond tip. The area function of the tip was determined before and after the experiments using a fused silica sample, yielding the same result. On each sample, 25 load-controlled quasi-static indents were carried out. To cover a suitable range of indentation depths, the indentation load was incrementally decreased with each indent, from a maximum load of 1.5 mN to a minimum of 0.5 mN. The elastic modulus was obtained from the unloading segment applying the Oliver and Pharr method⁵¹ using elastic modulus, E, and Poisson’s ratio, ν, of the diamond indenter (E = 1141 GPa and ν = 0.07). At least 18 indents on each film with a maximum indentation depth of 10% of the film thickness were performed to achieve reasonable statistics.

The macroscopic biaxial residual stress, σ_r, of the films on Si substrates was determined using the curvature method applying the modified Stoney’s equation⁵²

where M _s is the biaxial modulus of the (100) oriented Si substrate (M _s = 180 GPa⁵³), t _s and t are the substrate and film thickness, and r the radius of curvature. The curvature of the substrate was measured with a custom-built device utilizing the reflection of two parallel laser beams. A Jandel RM2 four-point probe was used to evaluate the influence of alloying with Re on the electrical sheet resistivity of the films.

The fracture process of the 50 nm thin films on PI under uniaxial tensile load was monitored in situ by measuring the change in electrical resistance, which is a useful technique to evaluate the critical COS. For each film-substrate system, three samples (5 mm × 35 mm) were strained with an MTS Tyron 250 universal testing machine. The electrical resistance during loading and unloading was determined by four-point probes which were incorporated into the grips of the tensile stage as described in ref. ⁵⁴. The samples were loaded continuously to a maximum elongation of 15% with an initial gauge length and displacement rate of 20 mm and 5 μm/s, respectively. The failure strain (COS) was defined as the strain at which the measured resistance deviates from the theoretical resistance ratio

where R/R ₀ is the relative resistance and L/L ₀ the relative elongation. The engineering strain, ε, is defined as ε = (L − L₀)/L₀. Thus, Eq. (²) was employed to calculate the theoretical resistance ratio for each engineering strain, which is valid as long as no structural changes arise during the experiment and volume conservation is satisfied. However, once the formation of cracks occurs, the resistance ratio of the films cannot longer be describe by an analytical formula^{54, 55}.

In situ optical fragmentation tests were conducted in order to observe crack initiation and growth during straining as well as to assess the COS independently from the electrical measurements. The experiments were carried out by mounting an Anton Paar TS600 straining device under an Olympus BX51 optical microscope. The samples (7 mm × 35 mm) were strained with a loading rate of 10 μm/s in small increments until the maximum tensile strain of 12% was reached. During straining, surface images were taken which were analyzed with the software Image J⁵⁶ to obtain the crack density at each strain. In every micrograph three lines were plotted perpendicularly to the direction of the cracks and the number of cracks intersecting with the lines was counted. The average crack density was calculated as ratio between the average number of cracks and the length of the lines.