Simulation of electromigration effects on voids in monocrystalline Ag films

We developed a three-dimensional, atomistic model based on the kinetic Monte Carlo method to investigate how voids penetrating a monocrystalline silver film are affected by electromigration. The simulations show a clear dependency between the nonequilibrium shape of the voids and the crystallographic orientation of the film. The simulation results are in accordance with experimental results on bicrystalline silver wires.

Figure 1

Schematic outline of the $E_{\mathrm{a}}$ composition for atom hops to stable (a) and unstable (b) fcc sites. (a) Binding energy curve for an atom detaching from a step. The saddle point is between the neighboring fcc sites. This is not the case in (b), which shows the binding-energy curve for an atom hopping over a step. There, the final fcc site is a saddle point.

Figure 2

Vicinity of a fcc site (green circle) on a $\left\{100\right\}$/$\left\{111\right\}$ edge (a) and a $\left\{111\right\}$/$\left\{111\right\}$ edge (b), respectively (neighboring fcc sites are represented by green crosses). To reach an fcc site on the upper facet, an intermediate, unstable position (red atom) is taken on with $Z=2$ (a) and $Z=1$ (b). The latter is especially important, because due to the nonimplemented hcp sites (red triangles) traversing a $\left\{111\right\}$/$\left\{111\right\}$ edge would be impossible otherwise.

Figure 3

The simulation setup: An initially cylindrical void is cut into a Ag stripe of $120\times 120\times 16$ atoms. $\vec{x}$ points in the $\left[11\overline{2}\right]$ or $\left[110\right]$ direction, $\vec{y}$ points in the $\left[1\overline{1}0\right]$ direction and $\vec{z}$ points in the $\left[001\right]$ or $\left[111\right]$ direction.

Figure 4

Void shapes in a $\left(111\right)$-oriented system. (a) Without an electromigration force, the initially round void (see Fig. 3) becomes hexagonal. (b) Upper half of the system in (a) shown from the side. (c) Schematic view of the inner void surface. (d)–(f) Corresponding figures with $\Delta E_{\mathrm{EM}}=0.005\mathrm{eV}$. This time the void becomes pointed against the ${\vec{F}}_{\mathrm{EM}}$ direction.

Figure 5

SEM image of an electromigration test structure of ten parallel bicrystalline Ag wires after electrical stressing. On the left side of the grain boundary (indicated by the orange dashed line) the $\left[001\right]$ direction of the Ag crystal is normal to the surface. On the right side, the $\left[111\right]$ direction of the grain is oriented normal to the surface. For 193 min a current of $119\text{mA}$ was applied to the wires. The direction of electron motion was from the left to the right [from the Ag$\left(111\right)$ part of the wires to the Ag$\left(001\right)$ part]. Voids of the characteristic triangular shape, corresponding to the symmetry of the Ag$\left(111\right)$ part, are visible on the right-hand side of the image.

Figure 6

Void shapes in a $\left(001\right)$-oriented system. (a) Without an electromigration force, the initially round void (see Fig. 3) becomes rectangular. (b) Upper half of the system in (a) shown from the side. (c) Schematic scheme of the inner void surface. (d)–(f) Corresponding figures with $\Delta E_{\mathrm{EM}}=0.005\mathrm{eV}$.

Figure 7

SEM image of an electromigration test structure of ten parallel bicrystalline Ag wires after electrical stressing. On the left side of the grain boundary (indicated by the orange dashed line) the $\left[001\right]$ direction of the Ag crystal is normal to the surface. On the right side, the $\left[111\right]$ direction of the grain is oriented normal to the surface. For 1189 min a current of $141\text{mA}$ was applied to the wires. The direction of electron motion was from the Ag$\left(001\right)$ part of the wires to the Ag$\left(111\right)$ part. Voids of the characteristic rectangular shape, corresponding to the symmetry of the Ag$\left(001\right)$ part, are visible on the left side of the image.