The idea of this method

The idea of this method is shown in Fig. 1.2. A high compressive stress can be introduced in a metal film by charging with solute atoms. The increase of elastic energy leads to film detachment by overcoming the adhesion energy. The critical stress for film delamination provides information about the adhesion energy of the film to the substrate.

a) b) c)

1. Controlled buckling method___________________________________

In this work controlled hydrogen loading of metal films was applied, leading to stress formation and delamination of the film from the substrate. Why do we use hydrogen as a solute? It is known that hydrogen diffuses much faster than any other atoms in solids, because small, light weight atoms diffuse faster than larger, more massive atoms. In Fig. 1.3 some examples of diffusion coefficients of some elements in Nb and α-Fe are shown.

Figure 1.3: Diffusion coefficients of H, N, and O in Nb and C in a α−Fe [AV78]. The diffusion coefficient of H in Nb is much larger than that of other gases in a wide temperature range. Room temperature is shown with the dashed line.

Diffusion coefficients of H in Nb at room temperature and in the wide temperature range are much larger than the diffusion coefficients of other gases in Nb.

In this work the Nb has been applied for the hydrogen absorption. The choice of Nb resulted from its large capability of absorbing hydrogen. For example, the solubility of hydrogen in niobium within the low concentration range at room temperature is 2.8·10⁵ times larger than that in palladium at the same hydrogen pressure [W82]. The phase diagram of hydrogen in bulk Nb crystals is shown in Fig. 1.4, where cH/Nb is hydrogen concentration. Above room temperature depending on the hydrogen concentration three phases appear: α, α´, and β, where the α and α´

phases are disordered solutions of low and high hydrogen concentrations, respectively.

The solid solution α-Nb-H-phase has a cubic body-centred (bcc) crystal structure. It solves H up to a concentration cH = 0.06 H/Nb at 300 K, above which the formation of the Nb-H-Hydride

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phase. In the α and α´ phases hydrogen atoms are randomly distributed in the host lattice, and the Nb crystal retains its cubic symmetry, while the lattice constants are different. Because of the similarity to gas and liquid phase transition, α and α´ are called lattice gas and lattice liquid phase. The α´-Nb-H-phase is thermodynamically stable for T > 361 K. For hydrogen in bulk Nb, the critical temperature of the α−α´ phase transition is 444 K, and the related critical hydrogen concentration is cH = 0.31 H/Nb [H96].

With increasing H-concentration above 0.06 H/Nb and at room temperature the ordered β-Nb-H phase is formed. The crystal lattice of the β-Nb-H phase is face centred orthorhombic. Compared to the α-phase the lattice is stretched and orthogonally deformed. The deformation is small, c/a=1.005 [WR70]. The β-Nb-H phase exists from cH =0.70 H/Nb up to 1.0 H/Nb. The (α,β)-miscibility gap at room temperature extends from cH = 0.06 H/Nb to cH = 0.72 H/Nb. The δ−Nb-H phase is formed up to cH =1.1 H/Nb [WR70].

c

Figure 1.4: The phase diagram of hydrogen in bulk Nb crystals [SchW78].

Compressive stresses are built up in a film on a substrate by absorbing solute atoms or molecules in the film. In a metal film not attached to a substrate, due to hydrogen absorption isotropic volume expansion ΔV/V occur. The volume expansion depends linearly on the hydrogen

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c_H/Nb Atomicvolumev0/Å3

c_H/Nb

Atomicvolumev0/Å3

Figure 1.5: Increasing of Nb volume vs. hydrogen concentration [SchW78].

In Fig. 1.5 the linear increase of the Nb bulk volume with increasing hydrogen concentration is shown. For the volume expansion in the α-Nb-H phase Peisl [P78] gives

c_H c_H cubic crystal with a lattice constant a and a random occupation of the interstitial sites by H-atoms it is Therefore the lattice expansion for bulk Nb can be calculated with Eq. (1.6) as

_H For a well-adhering film on a rigid substrate lattice expansion is prevented in-plane, while expansion is possible only in the out of plane direction. Therefore, within the plane of the film compressive stresses up to several GPa are induced. For hydrogen in metal films the corresponding strains and stresses can be calculated as [B98]

( ) (

)

where υp is the partial molar volume of the solute and c its concentration. Thus, compressive

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For an isotropic Nb-film, clamped to a rigid substrate, the expansion in direction normal to the film layer is [Lau98]

ε₃^' =0.131⋅c_H (1.10) while the in-plane stress increases as

σ_xx =σ_yy =−9.7GPa⋅c_H (1.11)

Thus, by hydrogen loading it is possible to achieve high in-plane compressive stress up to several GPa in strongly bond Nb thin films, linearly depending on hydrogen concentrations for low values of cH. Laudahn has observed stresses up to −9.7GPa/c_H for laser deposed Nb-films. In this work this effect is used in controlled hydrogen induced delamination method and applied for the evaluation of the adhesion energy between thin films and substrates.

In order to enable hydrogen absorption by the niobium film, a thin (10 to 20 nm) palladium film can be deposited onto the niobium film. Thereby palladium films with the thickness of 10 nm are closed [Wag05]. This top palladium layer prevents oxidation of the niobium film and acts as catalyst for hydrogen absorption. Since hydrogen solubility of niobium is 2.8·10⁵ times larger than that of palladium, dissolved hydrogen atoms diffuse into the niobium layer after dissociation of hydrogen molecules at the palladium surface. Therefore, hydrogen is preferentially absorbed in the Nb-layer and the hydrogen content within the Pd-layer can be neglected, and the Nb-layer is regarded as active layer generating and transferring mechanical stress in the systems Nb/Pd or Me/Nb/Pd (with Me=metal).

To summarize, the idea of the controlled buckling method is to apply in-plane stresses in a controlled way using the electrochemical hydrogen loading technique which will be explained in the next chapter. Hydrogen loading of a Pd-covered Nb film generates high in-plane stress up to several GPa. This stress increases linearly at low hydrogen concentration (i.e.: in the elastic region). At the critical hydrogen concentration (critical stress) the buckling occurs. Thereby elastic stress in the metal film sample is reduced. The critical stress for buckling can be measured by determining the curvature of the substrate.