Roughening Rates of Strained-Layer Instabilities

We study the evolution of the morphology of ${\mathrm{S}\mathrm{i}}_{0.75}{\mathrm{G}\mathrm{e}}_{0.25}$ strained layers using a wide range of deposition times, $60<\tau <2400\mathrm{s}$, at $600°\mathrm{C}$ on laser textured substrates with miscuts $\theta <15°$ off Si(001). Ripple-shaped morphologies form spontaneously on miscuts along the $⟨110⟩$ directions. At the shortest deposition times, roughening is suppressed as predicted by a linear stability analysis that uses previously measured values for the mass transport rate on the surface. The measured time constant of the roughening is $\approx 80\mathrm{s}$, a factor of 4 larger than predicted by theory.

Figure 1

Selected AFM micrographs of 100 ML thick ${\mathrm{S}\mathrm{i}}_{0.75}{\mathrm{G}\mathrm{e}}_{0.25}$ layers grown with different layer deposition times. The images are high-pass filtered to separate the nanometer-scale features from the micron-scale curvature of the dimples. The numbers below each micrograph indicate the deposition time. For (f), $60+600$ indicates 60 s deposition time and 600 s annealing time. The images are cropped near the top of the rim of the dimple. The diameter of each cropped image is $\approx 3\mu \mathrm{m}$.

Figure 2

Plot of average width (circles) and amplitudes (squares) of the ripple-shaped instability vs time. The error bars indicate the standard deviations in the measurements of $\approx 25$ ripples. The widths have been corrected for $\sim 5\mathrm{n}\mathrm{m}$ overestimate due to the finite tip radius. The data from Fig. 1f, 60 s deposition followed by 600 s anneal, are plotted as an open circle and an open square. The solid line indicates a 0.30 power-law fit to the instability widths. For the two shortest times, amplitudes are shown with bars and arrows pointing down to indicate the upper limit. An exponential function $z_0=z_m\exp ({\omega }_{m}t)$ has been fit to the data, $z_m=0.036\mathrm{n}\mathrm{m}$ and ${\omega }_m=0.012{\mathrm{s}}^{-1}$.