Influence of film thickness on critical concentration and critical stress

The influence of the film ated for Nb

films with thicknesses between

and 1 mm. According to theory for buckling to the square

root of inverse film

stress for buckling should be sm

and 100 nm Nb thicknesses, deposited onto

thickness on critical concentration and critical stress thickness on the critical system parameters was investig

50 nm and 200 nm on PC substrates with thicknesses of 0.5 mm a linear dependency of ccrit and σ_crit

thickness is expected. Thus the critical hydrogen concentration and critical aller for films with larger thickness (see Eq. (1.34)).

In Fig. 3.4, a), b) results on the stress evolution in Pd/Nb/Pd with 50 nm 0.5 mm PC, are shown.

___3. Experimental results______________________________________________________

b) a)

In all cases compressive stresses increase linearly with increasing hydrogen concentration at the beginning of the loading sequence, as expected from linear elastic theory. The slope of the corresponding straight parts in Fig. 3.4 are in agreement with previous measurements of Nb on Si-substrates and their theoretical interpretation based on Eq. (1.6) [B98]. The critical stress was set to the value where the stress curve deviates from the linear increase by 2%. In chapter 3.1.1 it has been shown that the critical hydrogen concentration of 200 nm Nb is 8 % H/Nb (Fig. 3.1c).

For the 100 nm Nb-layer a ccrit of 17% H/Nb (optically 16 %) is observed, for 50 nm Nb-layer this value increases to 33 % H/Nb (optically 31 %). The initial stress increase is 3.4-4.5 GPa/cH. Thinner films debond from their substrates at higher hydrogen concentrations and larger stress.

To investigate the influence of the substrate thickness on critical stress and critical hydrogen concentration Pd (10 nm)/Nb/Pd (10 nm) //PC (1 mm) films with Nb-layer of 50-, 100- and 200- nm thickness have been measured. The stress curves of these samples are shown in Fig. 3.5 for stepwise hydrogen loading.

Figure 3.5: Increase of the mechanical stresses in a Pd/Nb/Pd//PC(1 mm) multilayer with different Nb-layer thicknesses (50-200 Nm). The critical stress clearly decreases with decreasing Nb thickness. The arrows mark the concentrations at which formation of wrinkles was detected by optical light-microscopy.

The critical concentration for 200 nm film was 7 % H/Nb, for 100 nm film 11 %, for 50 nm film 17 %, determined by 2 % stress-deviation from the initial linear stress increase.

Similar initial slope of the stress for all films on the substrates with the same thickness was expected, but it deviates from sample to sample and amounts 4.1-5.9 GPa/cH. These deviations might occur due to different microstructure of the substrates or /and due to the small differences in the substrate thickness, for example. Laudahn [Lau98] has measured for Nb on silicon the

___3. Experimental results______________________________________________________

In Fig. 3.6 the evolution of the buckles morphologies during hydrogen loading is shown for the Nb films for which the stress measurement has been presented in Fig. 3.5. The width of the buckles is smaller for the thinner films, while the shape of the buckles is similar. The buckles morphology corresponds to the straight–sided Euler buckle morphology.

The light microscopical images confirm the critical hydrogen concentration for delamination derived from the stress curves.

Figure 3.6: Comparison of the buckle morphology during hydrogen loading for Pd/Nb/Pd films with Pd 20nm/ Nb 50 nm (left), 100 nm (middle), 200 nm (right)/ Pd 20nm on 1mm PC. The buckle morphologies at the critical hydrogen concentrations are marked with the red rectangle. The hydrogen content in the metal film is increasing from top to bottom, as marked above each image.

The evaluation of the critical H-concentration for the Pd (10 nm)/Nb/Pd (10 nm) //PC (1 mm) films from light microscopy is shown in Fig. 3.7.

0 200nm 100nm 50nm

0 0

16 22

100μm

7 11 17

10

___3. Experimental results______________________________________________________

a) b)

c)

Figure 3.7: a) Fraction of delaminated area of metal films on 1-mm thick PC substrate as a function of H-concentration. The thicknesses of the Nb layers are d=200 nm (closed circles), d=100 nm (triangles) and d= 50 nm (open circles). The increasing area of detached film is approximated by straight lines and their intercepts with the lines of initial values. These yield a critical H-concentration for the onset of buckling. b) Comparison of critical concentrations determined optically and from stress curves (2%

deviation). c) The relation between hydrogen concentration and film thickness for 20% fraction of detached area is shown.

As shown in the Fig. 3.7(a), with increasing hydrogen concentration the detached film area increases steadily after the onset of buckling. The critical stresses for these critical concentrations can be determined. The stress values obtained in this way are included in Fig. 3.8. In this figure the critical stresses for delamination are plotted versus inverse square root of film thickness d, as this relation represents Eq. (1.33). From the slope of the resulting curve the adhesion energy can be calculated.

___3. Experimental results______________________________________________________

Figure 3.8: Critical stress for delamination of Pd (10 nm)/ Nb (50,100,200 nm) /Pd (10 nm) on 0.5 mm and 1 mm PC substrate. The critical stresses for buckling are obtained from stress measurements as presented in Fig. 3.1 and plotted versus the inverse square root of film thickness d. (Closed circles: 0.5 mm PC, open circles: 1 mm PC). The triangles are obtained from light microscopy investigations of the critical hydrogen concentration H/Nb.

Summarizing the measurements of critical stresses and hydrogen concentrations for films with different film thicknesses it can be pointed out that thinner films require larger critical stress and higher hydrogen concentration for buckling. This result is in accordance with Eq. (1.31), which shows that more elastic energy can be stored in thicker films. The influence of Pd top layer on the critical hydrogen concentration is not significant because of the much higher stresses for buckling than the tensile stress for stretching the Pd layer. However, it should influence the buckle height. This effect of Pd top layer will be discussed in Chap. 3.4.4 by buckle geometry investigations using the white-light interferometer.