First-principles study of thermodynamical and mechanical stabilities of thin copper film on tantalum

The adhesion, stability, and wetting behavior at interfaces between thin Cu films and clean Ta (110) substrates are investigated by first-principles calculations using density functional theory (DFT) in the local-density approximation. Interfaces between pseudomorphic body-centered-tetragonal thin films of Cu, strained face-centered-cubic thin films of Cu, and a single pseudomorphic monolayer of Cu on body-centered-cubic Ta (110) surfaces are studied. Various high-symmetry interface configurations are considered for each case. The mechanical stability of the interfaces is studied by the ideal work of separation, while the thermodynamic stability is investigated by Gibbs’ excess interface energy. All three interfaces are found to be thermodynamically unstable. An energy-weighting scheme extends the use of the DFT calculations to the case of an incoherent misfitting interface. The incoherent monolayer of Cu on Ta is thereby found to be thermodynamically stable. For coverages by more than a monolayer, the Cu atoms are expected to form three-dimensional islands on top of the Cu monolayer. With respect to interface separation, the monolayer is found to be bound more strongly to the Ta substrate than the thin film. Hence, failure is expected to occur not at the $\mathrm{Cu}∕\mathrm{Ta}$ interface but inside the Cu.

Figure 1

Schematic drawing indicating the interface and surface energies in the thin-film growth-mode criterion of Eq. (1).

Figure 2

A schematic sketch of the supercell models for the thin film in (a) and the monolayer in (b). The supercell is shown here from the $\left[1\overline{1}1\right]$ direction (pointing out of the page).

Figure 3

A schematic view of the Ta bcc (110) (black) and Cu fcc (111) (white) surface unit cells. The calculated bulk lattice parameters are 3.25, and $3.56\mathrm{\AA }$ for Ta and Cu, respectively. In (a), the incommensurate cells are shown on top of each other. In (b), the commensurate cells (strained Cu on unstrained Ta) are shown together with the different locations considered in this study for the Cu monolayers with respect to the Ta substrate.

Figure 4

The interfacial binding energy (the negative of $W_{\mathit{sep}}$) for a thin Cu film (a) and a Cu monolayer (b) on a Ta substrate, shown as a function of interfacial distances for the various translations considered in the current study. Note the similarity of the work of separation curves for the pseudomorphic (PM) and the bcc-stacking site cases.

Figure 5

Relaxation of fcc Cu on bcc Ta with interfacial bcc-stacking sites. In (a), the axial strain ${ϵ}_{\perp }$ normal to the interface in Cu and Ta is plotted as a function of the layer position. In (b), the stacking periods along the ${\left[1\overline{1}0\right]}_{\mathit{bcc}}$ and ${\left[11\overline{2}\right]}_{\mathit{fcc}}$ directions of bcc Ta and fcc Cu, respectively, are shown. The dashed lines in the lower panel at $1∕3$ and $1∕2$ indicate the ideal stacking periods of Cu (111) and Ta (110) planes, respectively.

Figure 6

An interfacial cross section of a general incoherent but commensurate Cu-Ta interface in the NW orientation relationship. Only one Cu layer and one Ta layer are shown at the interface. Ta atoms in the bcc (110) plane are shown as large dark spheres, while Cu atoms in the fcc (111) plane are shown by small spheres represented with different shades of gray corresponding to the local effective excess energy for $n=1$ [see Eq. (3)]. Dark small spheres represent Cu atoms with low local energy, while bright small spheres represent Cu atoms with high local energy.