Kinetic phase diagram for island nucleation and growth during homoepitaxy

The impact of small-island dissociation and mobility on island nucleation and growth during vapor deposition of thin films is analyzed using mean field rate equations. The dominant island nucleation and growth mechanism is mapped onto a temperature/deposition-rate kinetic phase diagram, using Cu(100) homoepitaxy as an example. The methodology provides analytical expressions for the boundaries on the diagram and encourages a deeper understanding of the growth mechanisms. A kinetic Monte Carlo simulation incorporating the small-island dynamics is also presented and used to test the kinetic phase diagram, and satisfactory agreement is found throughout.

Figure 1

Snapshots at 10% coverage of the island arrays grown during the simulation at $T=300\mathrm{K}$ (top row) and $T=600\mathrm{K}$ (bottom row) on a $2000\times 2000$ lattice. In all cases, the ratio of deposition to monomer diffusion rate is $2\times {10}^8$ (the deposition rates are $2.65\times {10}^{-5}$ and $0.83\mathrm{ML}∕\mathrm{s}$, respectively). The middle image in both rows is for the full simulation with both small-island mobility and dissociation active; the left-hand images are with dissociation only active, and the right-hand images are for mobility only active.

Figure 2

(Color online) Boundaries between $i=8$ behavior and (a) lower-$i$ regimes; (b) mobility regimes. The new regimes can occur above the lines. In (b), the black solid line is the boundary between $i=8$ and $i=3$ from (a).

Figure 3

(Color online) Boundaries between the $i=3$ regime and a lower critical island size or a mobility-dominated regime, where the new regimes can occur above the lines. The threshold for the dimer-mobility regime giving way to critical island size $i=1$ is also shown. The black solid line is the boundary between $i=8$ and $i=3$ from Fig. 2.

Figure 4

The kinetic phase diagram deduced from Fig. 3. The dominant nucleation mechanism is indicated in each region of the diagram. The $(T,F)$ $\text{points}+\text{are}$ used to test the diagram with the Monte Carlo simulation. The circles are points from Ref. 31, as discussed in the text.

Figure 5

(Color online) The simulated island density at 10% coverage as a function of $R=D_1∕F$, using the test points indicated in Fig. 4. The negative of the gradients of the lines fitted through the sets of data points (“chi”) are given in the legend.