Thermal decay of superheated $7\times 7$ islands and supercooled “$1\times 1$” vacancy islands on Si(111)

Low-energy electron microscopy was used to clarify how the thermal decay of two-dimensional (2D) islands and 2D vacancy islands depends on the surface structure. Using the first-order “$1\times 1$”–$7\times 7$ phase transition on Si(111), we produce 2D islands with superheated $7\times 7$ phases above the critical temperature $T_{\mathrm{c}}$, and compare their decay kinetics with that of islands with equilibrium surface phases of coexisting “$1\times 1$” and $7\times 7$ structures. 2D vacancy islands with supercooled “$1\times 1$” phases are also compared with 2D vacancy islands with coexisting “$1\times 1$” and $7\times 7$ phases below $T_{\mathrm{c}}$. The superheated islands decay faster than the coexisting islands, indicating that the equilibrium adatom concentration, $c_{eq}$, of the superheated island is higher than that of the coexisting island. The supercooled vacancy islands also decay faster than the coexisting vacancy islands, because the supercooled vacancy islands have lower $c_{eq}$ than coexisting vacancy islands. These differences in $c_{eq}$ give us an estimate of the energy difference between the “$1\times 1$” and $7\times 7$ structures.

Figure 1

Schematic illustrations of islands and vacancy islands studied in this work. (a) Supercooled and coexisting vacancy islands below $T_{\mathrm{c}}$. (b) Superheated and coexisting islands above $T_{\mathrm{c}}$.

Figure 2

LEEM images of an array of 3D mounds at (a) $t=0\mathrm{s}$ and (b) $t=12\mathrm{s}$. Islands $A–C$ are superheated islands, and islands $D$ and $E$ are coexisting islands. The measured areas of the islands are plotted as a function of time by the different symbols in (c). The solid and dotted lines in (c) are calculation results under the condition that $c_{eq}$ of the superheated island is 0.3% larger than that of the coexisting island. The inset shows how the calculated decay curve of island $A$ depends on the percentage difference in $c_{eq}$ between 0.1% and 0.5%.

Figure 3

LEEM images of an array of 3D craters at (a) $t=0\mathrm{s}$ and (b) $t=90\mathrm{s}$. Vacancy islands $A–C$ are supercooled vacancy islands, and $D–F$ are coexisting vacancy islands. The measured areas of the vacancy islands are plotted as a function of time by the different symbols in (c). The solid and dotted lines in (c) are calculation results under the condition that $c_{eq}$ of the supercooled vacancy island is 0.6% smaller than that of the coexisting vacancy island.

Figure 4

(Color online) LEEM images of islands inside a large vacancy island at (a) $t=0\mathrm{s}$, (b) $t=10\mathrm{s}$, (c) $t=20\mathrm{s}$, and (d) $t=28\mathrm{s}$. (e) The size evolution of the islands. Open and filled symbols denote the data for the superheated and coexisting islands. The thin solid and dotted lines are respective calculations for the superheated and coexisting islands under the condition that the superheated island has $c_{eq}$ equal to the coexisting island. The thick solid and dotted lines were obtained under the condition that $c_{eq}$ of the superheated island is 0.17% larger than that of the coexisting island. $D{c}_{eq}^0=2.8\times {10}^7{\mathrm{s}}^{-1}$ and $D{c}_{eq}^0=3.6\times {10}^7{\mathrm{s}}^{-1}$ were used in the calculations of the thick and thin lines, respectively. Cusps in the calculated time evolution of some islands correspond to the disappearance of other islands. Their magnitudes mainly depend on the arrangement of the islands, but are somewhat enhanced because of the finite time step in the calculations.