Influence of morphology of islands and of mobile clusters on island formation in molecular-beam epitaxy

We investigated by Monte Carlo simulations the influence of island morphology and of the mobility of small clusters, such as dimers and trimers, on island formation in molecular beam epitaxy. We considered two growth models, fractal growth model and compact growth model, both with and without the mobility of dimers and trimers. It was found that the mobility of small islands affected significantly the power-law behavior of the island density, while island morphology influences weakly the power-law behavior of the monomer density. The dynamic scaling function for island-size distribution was also found to be influenced by both morphology and mobility.

Figure 1

Pictures of the morphology from the two growth models for $R={10}^9$ and $\theta =0.1\mathrm{ML}$ on a $400\times 400$ lattice substrate. (a) and (b) represent the morphology from the fractal growth, and (c) and (d) represent the morphology from the compact growth with $r_e=0.02$. The two figures on the left are those without mobility of dimers and trimers and the two on the right are those with mobility with $r_2=0.02$ and $r_3=0.003$.

Figure 2

The scaled density values of the monomers and islands against the coverage. (a) and (b) represent those for the fractal growth (i.e., $r_e=0$); (a) without mobile islands and (b) with $r_2=0.02$ and $r_3=0.003$, and (c) and (d) are for the compact growth with $r_e=0.02$; (c) without mobile islands and (d) with $r_2=0.02$ and $r_3=0.003$. The trial values of $\gamma$ and $\chi$ and the regression slopes of ${\rho }_1$ are denoted in each plot.

Figure 3

Plots of $\rho$ and ${\rho }_1$ against $R$ for the fractal growth model, i.e., for $r_e=0$. The upper sets are the data for $\rho$ calculated at $\theta =0.1\mathrm{ML}$, and the lower sets for ${\rho }_1$ calculated at $\theta =0.005\mathrm{ML}$. Different symbols correspond to the different degrees of mobility for the dimers and trimers, and the dashed lines represent the regression fit.

Figure 4

Scaling function in Eq. (4) for the fractal growth of $R={10}^9$ and $r_e=0$. The lower set at the peak is for $r_2=r_3=0$ (i.e., without mobile dimers and trimers) and the upper set is for $r_2=0.02$ and $r_3=0.003$. The coverage from the solid line to the dashed line is $\theta =0.1$, 0.2, 0.3, and 0.4.

Figure 5

The scaling function in Eq. (4) regarding the compact growth for $R={10}^9$ and $r_e=0.02$. The lower set at the peak is for $r_2=r_3=0$ and the upper set is for $r_2=0.02$ and $r_3=0.003$. The coverages from the solid line to the dashed line is $\theta =0.1$, 0.2, 0.3, and 0.4.