Faceting at the step flow threshold in epitaxial growth on patterned surfaces

We identify a kinetic mechanism responsible for the emergence of low-angle facets in recent epitaxial regrowth experiments on patterned surfaces. Kinetic Monte Carlo simulations of vicinal surfaces show that the preferred slope of the facets matches the threshold slope for the transition between step flow and growth by island nucleation. At this crossover slope, the surface step density is minimized and the adatom density is maximized, respectively. A model is developed that predicts the temperature dependence of the crossover slope and hence the facet slope.

Figure 1

(Color online) (a) Experimental atomic force microscope cross sections of 1D gratings on GaAs (001) with the [110] direction in the plane of the page. The bottom line shows the initial microfabricated grating profile before any growth has taken place. The next line is after deposition of 600 nm of GaAs at $580°\text{C}$. The straight line indicates the facet slope ${\theta }_f$. (b) Grating profiles for kMC simulations on a patterned surface at two different temperatures after deposition of 6000 monolayers on a surface with $2600\times 600$ sites. Each point in the 2D profile is an average over the 600 surface sites in the third dimension. The inset shows the profile slope in the area surrounding the grating peak at 560 (upper curve) and $600°\text{C}$ (lower curve).

Figure 2

Experimental atomic force microscope cross sections of 1D gratings on GaAs (110) with the $\left[1\overline{1}0\right]$ direction in the plane of the page after deposition of 200 nm of GaAs at $590°\text{C}$ and a deposition rate of 0.29 ML/s. Other experimental parameters are similar to Ref. 9. The starting surface has a trapezoidal shape similar to that shown in Fig. 1a.

Figure 3

(Color online) (a) Step density $S$ and (b) adatom density $n$ on vicinal surfaces as a function of slope for 400, 450, 550, and $600°\text{C}$ (○,▽,◇,◻). The inset shows one step edge pattern at $400°\text{C}$ and two patterns at $600°\text{C}$ at the slopes indicated by symbols in the main figure.

Figure 4

(Color online) Schematic plot of facet development at the step density minimum (see text). Shaded arrows represent adatom diffusion away from areas of low $S$ and the dashed arrows represent the areas of lowest growth rate.

Figure 5

(Color online) Temperature dependence of the facet slope ${\theta }_f(\times )$ from the regrowth simulations [as shown in Fig. 1b], the slope at the minimum in the step density ${\theta }_{\text{min}}$ (○) as determined from simulations on vicinal surfaces [Fig. 3b], and the experimental data point ${\theta }_f$ (◼) from Fig. 1a. Also shown are (- -) the reciprocal of the nucleation length at zero slope represented by $a{S}_0/2$, where $S_0$ is the step density at zero slope (see text), and (—) the threshold slope for step flow growth predicted from Eq. (2).