Submonolayer Growth with Anomalously High Island Density in Hyperthermal Deposition

We present a rate equation model for submonolayer island growth under conditions where hyperthermal deposition techniques such as low-energy ion deposition are employed to achieve smooth layer-by-layer growth. By asymptotic analysis, we demonstrate that the model exhibits stationary behavior with well-defined dynamic and growth exponents $\beta$ and $\chi$, respectively, in the limit of small and high detachment rates. We verify these predictions by using the particle coalescence simulation method. The simulations reveal the existence of a relatively sharp transition regime with an increasing detachment rate of adatoms from high values of the growth exponent $\beta \approx 1$ to much smaller values of $\beta$ determined by detachment and island diffusion processes. Our numerical results for the island size distribution indicate an anomalously high number of small islands, in agreement with available experimental data.

Figure 1

Growth exponent $\beta$ for systems with $(\mu ,\alpha )=(1,1/2)$, $(3/2,1/2)$, $(2,1/2)$, $(3,1/2)$, and (2,1) (inset) as a function of the parameter $\kappa R^{(\alpha +1)/2}$. Note the sharp transition to growth characterized by $\beta$ given by Eq. (3) (solid lines).

Figure 2

Fits to the simulation results for the scaling function (solid lines) and data for cases $(2,1/2)$, $R={10}^5$, and $\kappa ={10}^{-2}$ (circles) and $(1,1/2)$, $R={10}^6$, and $\kappa ={10}^{-2}$ (squares). In the inset the experimental data on LEID from Ref. 1 are compared with PCM simulations for $(2,1/2)$, $R={10}^5$, and $\kappa ={10}^{-2}$.