Nonlinear evolution of a morphological instability in a strained epitaxial film

A strained epitaxial film deposited on a deformable substrate undergoes a morphological instability, relaxing the elastic energy by surface diffusion. The nonlinear dynamical equation of such films with wetting interactions are derived and solved numerically in two and three dimensions. Nonlocal nonlinearities together with wetting effects are crucial to regularize the instability, leading to an island morphology. The island chemical potential decreases with its volume, and the system consistently experiences a noninterrupted coarsening evolution described by power laws with a marked dimension dependence.

Figure 1

Space-time evolution of a 2D film according to Eq. (7) with $h_0=0.1$. Surface diffusion induces a noninterrupted coarsening until only one island is left surrounded by a wetting layer with height $h^{wl}$.

Figure 2

(Color online) Space-time evolution obtained by Eq. (4) with $t=3.9$ (a), 8.3 (b), and 13.9 (c).

Figure 3

Equilibrium surface chemical potential (2) as function of the flat film volume $V=V^f$ when $h<h_c$, and of the island volume $V$ when $h>h_c$ in (a) two dimensions and (b) three dimensions.

Figure 4

Maximal height of an equilibrium island as function of the initial height in (a) two dimensions and (b) three dimensions.

Figure 5

Roughness as function of time with (a) $L=6700$ in two dimensions and (b) $L=209$ in three dimensions.

Figure 6

Evolution of the number of islands with the same parameters as in Fig. 5.

Figure 7

Evolution of the surface coverage with the same parameters as in Fig. 5.