Kinetic Optimum of Volmer-Weber Growth

We find that the molecular beam epitaxy of ${\mathrm{Fe}}_3\mathrm{Si}$ on GaAs(001) observed by real-time x-ray diffraction begins by the abrupt formation of 3 monolayer (ML) high islands and approaches two-dimensional layer-by-layer growth at a thickness of 7 ML. A surface energy increase is confirmed by ab initio calculations and allows us to identify the growth as a strain-free Volmer-Weber transient. Kinetic Monte Carlo simulations incorporating this energy increase correctly reproduce the characteristic x-ray intensity oscillations found in the experiment. Simulations indicate an optimum growth rate for Volmer-Weber growth in between two limits, the appearance of trenches at slow growth and surface roughening at fast growth.

Figure 1

(a) Epitaxy of ${\mathrm{Fe}}_3\mathrm{Si}$ on GaAs(001) and (b) crystal truncation rods measured during growth (circles) with the fits assuming a complete coverage of the substrate by the film (lines). The substrate temperature is $180°\mathrm{C}$, the x-ray diffraction measurements are performed with an energy of 10 keV at a grazing incidence angle of 0.3°.

Figure 2

(a) ${\mathrm{Fe}}_3\mathrm{Si}$ epitaxial film thickness and (b) the fraction of the substrate covered by the film as obtained from the CTR measurements.

Figure 3

(a) Diffraction peak profiles measured during epitaxial growth by rotating the sample about its normal through the reflection. The measured curves are fitted to a sum of two Lorentzians. (b) Lateral sizes of the 3D islands obtained from the broad component of the peak profile. The narrow component represents the constant average terrace width of 100 nm.

Figure 4

Diffraction intensity oscillations during epitaxial growth of (a) ${\mathrm{Fe}}_3\mathrm{Si}$ and (b) Ge on GaAs(001). In addition to the heteroepitaxy of ${\mathrm{Fe}}_3\mathrm{Si}$ on the substrate, homoeptaxial growth after an anneal is shown for comparison.

Figure 5

Kinetic Monte Carlo simulations of Volmer-Weber growth: (a) snapshots at different depositions for the deposition rate $F=1/1200\mathrm{s}$ (size of the simulation cell is $200\times 200$ atoms), (b) calculated intensity oscillations during deposition, and (c) time evolution of the root-mean-squared (rms) roughness. The simulations are performed with the same lowering of the surface diffusion barrier between substrate and film by $\Delta E_S=0.11\mathrm{eV}$.