Collapse of an adsorbate island on substrate pillars

We study an equilibrium shape of an adsorbate solid island on a substrate surface patterned with arrays of pillars. For a large island with a weak wettability to the substrate, an island sits on top surfaces of pillars, in a state called Cassie-Baxter (CB) state. In the opposite case of a small island with a strong wettability, the island collapses in the space between pillars, forming the so-called Wenzel (W) state. The collapse transition from CB to W state is studied in the phase space of the island volume and the wettability. Theory leads to collapse transition lines for an island with only (100) facets at zero temperature. They are in good agreement with the transitions observed in kinetic Monte Carlo simulations of an island with additional (110) and (111) facets at a finite temperature.

Figure 1

(Color online) Two typical island morphologies on substrate pillars: (a) CB state and (b) W state. The reduced volume is the same $v=800$, but the wettability is different, (a) $\chi =0.390$ and (b) $\chi =0.405$. For visualization purpose, the flat base of the substrate has different color from the pillar parts.

Figure 2

(Color online) Side views of a CB island as it grows. (a) Inner state, (b) inner-to-pinned state, (c) pinned-to-outer state, and (d) outer state.

Figure 3

(Color online) Side views of collapsing processes for (a) the inner state and (b) the outer state.

Figure 4

Island excess energy $\Delta E=E-E_{\text{CB}}$ from a CB state as a function of a wetting length of a pillar sidewall $h^{\ast }$ at a wettability $\chi =0.395$. A large island with a volume $v=V/{\ell }_p^3=750$ has an energy barrier, whereas a small island with a volume $v=720$ has none. The critical volume is calculated as $v_0=V_0/{\ell }_p^3=738$.

Figure 5

The CB-W collapse transition line in the phase space of the reduced volume $v=V/{\ell }_p^3$ and the wettability $\chi$ for $\alpha =3.0$ and $n=4$. Dashed lines separate regions of inner, pinned, and outer states.

Figure 6

The phase space $v\text{−}\chi$ is divided into zones where $n$ CB state is the most stable one for $n=1–5$. Lines indicate the collapse transition lines for various CB state.

Figure 7

Summary of KMC simulation results on collapse transition for $n=4$ and $\alpha =3$. Circles correspond to the stable CB states and crosses to the W states. The line corresponds to the theory on the collapse of a (100)-faceted island.

Figure 8

Phase space close to $n=3$ and 4 zones.

Figure 9

(Color online) Variation of a number of pillars in touch of a base facet at a level of pillar top. (a) At the time $t{\nu }_0=2\times {10}^4$, base sits on $3\times 3$ pillars, (b) at $t{\nu }_0=6\times {10}^4$, it is on $3\times 4$ pillars, and eventually (c) at $t{\nu }_0=5\times {10}^5$, it is on $4\times 4$ pillars. The island volume is $v=1050$ and the wettability is $\chi =0.40$.

Figure 10

Critical wettability ${\chi }_c$ versus relative periodicity $\alpha$.