One-Dimensional Defect-Mediated Diffusion of Si Adatoms on the $\mathrm{Si}(111)\mathrm{\text{−}}(5\times 2)\mathrm{\text{−}}\mathrm{Au}$ Surface

Using scanning tunneling microscopy, we determine that the one-dimensional diffusion of Si adatoms along the $\mathrm{Si}(111)\mathrm{\text{−}}(5\times 2)\mathrm{\text{−}}\mathrm{Au}$ surface reconstruction occurs by a defect-mediated mechanism. Distinctive diffusion statistics, especially correlations between sequential adatom displacements, imply that the displacements are triggered by an interaction with a defect that is localized to the adatom. The defect is intrinsic and thermally activated. The measured diffusion statistics are modeled accurately by a Monte Carlo simulation. The measured adatom diffusion activation barrier is $1.24\pm 0.08\mathrm{eV}$.

Figure 1

(a) A STM image showing a typical $(5\times 2)\mathrm{\text{−}}\mathrm{Au}$ surface ($50\times 50{\mathrm{nm}}^2$, $-1.5\mathrm{V}$, 0.1 nA). A clean $7\times 7$ domain (upper left) coexists with the $(5\times 2)\mathrm{\text{−}}\mathrm{Au}$ reconstruction. (b)–(e) Excerpts from a STM movie at 457 K illustrating a burst of displacements ($11\times 7{\mathrm{nm}}^2$, $-2.0\mathrm{V}$, 0.1 nA, $7.1\mathrm{s}/\mathrm{\text{frame}}$). (b) The adatom in the circle rests for 19 frames (135 s), then moves in three consecutive frames (c)–(e) by $-8a$, $+4a$, and $-2a$, as indicated by arrows. It then remains at rest for 14 frames (99 s). The circle indicates the adatom position in the preceding frame.

Figure 2

Arrhenius plot of the mean-square adatom displacement versus temperature. The effective activation barrier, $1.24\pm 0.08\mathrm{eV}$, is extracted from the fit (solid line) to the displacements (solid circles) measured with $0.25\pm 0.03\mathrm{\text{adatoms}}/5\times 2\mathrm{\text{cell}}$. Open circles are for lower coverages (0.14–0.2). The broken line, activation barrier 1.15 eV and prefactor ${10}^{11}{\mathrm{s}}^{-1}$, shows the temperature-dependence predicted by using our model to fit the displacement distributions. Statistical error bars in displacements are smaller than plot symbols, temperature error bars are $\pm 5\mathrm{K}$. (Inset) Mean-square displacements vs time.

Figure 3

Diffusion statistics for Si adatoms on the $(5\times 2)\mathrm{\text{−}}\mathrm{Au}$ surface. Experimental measurements are represented by symbols. Solid lines, with shaded error bars, are the results of our defect-mediated model. (a) Time correlations between adatom displacements. (b) Wait-time distributions. The inset shows a comparison with a random-walk model (broken line), which fails for short wait times. (c) Displacement distributions. Broken lines are for a random walk.

Figure 4

(a) Schematic for our model of 1D defect-mediated hopover diffusion. The diffusive hops of the adatom (large ball) are mediated by a localized defect (black ball). (b) The potential energy surface which determines the lifetime of the defect.