Surface Phase Metastability during Langmuir Evaporation

We have directly imaged the spontaneous formation of metastable surface phase domains on GaAs(001) during Langmuir evaporation. Eventually, these metastable phases transform to the thermodynamically stable parent phase, producing a dynamic phase coexistence with a temperature dependent, time-averaged coverage. Monte Carlo simulations are used to identify the key kinetic processes and investigate the interplay between phase metastability and evolving surface morphology. This is used to explain the measured temperature dependence of the time-averaged coverage.

Figure 1

Snapshots taken from a LEEM movie [20] revealing the fundamental mechanism of surface-phase metastability. The $c(8\times 2)$ phase appears bright, while $(6\times 6)$ and steps [indicated with arrows in (a)] appear dark. The scale bar in (a) is $0.1\mu \mathrm{m}$ and the sample temperature is $598°\mathrm{C}$.

Figure 2

Cross-sectional schematic of Lochkeim formation and surface-phase metastability. (a) A Lochkeim formation forms in the $c(8\times 2)$ phase (green line) and bilayer height steps propagate as atoms evaporate into the vacuum. The freshly exposed surface is the $(6\times 6)$ phase (purple line). (b) $c(8\times 2)$ nucleates within the $(6\times 6)$ phase and the phase boundaries propagate until only $c(8\times 2)$ is present. (c) Schematic representation of the change in surface free energy (per unit area) of the exposed surface. The exposed surface is unstable and transforms into the metastable $(6\times 6)$ phase. An activation energy barrier $\mathrm{\Delta }G$ exists for the conversion of the metastable $(6\times 6)$ to the thermodynamically stable $c(8\times 2)$.

Figure 3

Time-averaged $(6\times 6)$ coverage as a function of temperature. The circles are experimental values and the crosses were calculated from the MC simulations. The inset shows the time evolution of the $(6\times 6)$ coverage produced by the MC simulation at $592°\mathrm{C}$. The dashed line shows the time-averaged coverage obtained from the shaded region (see text). Error bars are computed as standard deviations from the mean.

Figure 4

Measured rates of the key kinetic processes used in the MC simulations as a function of $T$. $\ln (J_w)$, $\ln (J_b)$, $\ln (\rho )$, and $\ln (v)$ are plotted against $1/kT$ with $J_w$, $J_b$, and $\rho$ in units of $\mu {\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$ and $v$ in $\mu \mathrm{m}{\mathrm{s}}^{-1}$. The respective prefactors of $J_w$, $J_b$, $\rho$, and $v$ obtained from the linear fits to the measured data are $7.0\times {10}^{31}\mu {\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$, $1.6\times {10}^5\mu {\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$, $2.0\times {10}^{51}\mu {\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$, and $2.3\times {10}^{17}\mu \mathrm{m}{\mathrm{s}}^{-1}$ and the respective energy barriers are 6.0, 1.0, 9.0, and 3.7 eV (see text).

Figure 5

Snapshots of evolving surface morphology taken from LEEM movies at (a) $581°\mathrm{C}$, (b) $598°\mathrm{C}$, and (c) $639°\mathrm{C}$ and MC simulation movies at (d) $581°\mathrm{C}$, (e) $598°\mathrm{C}$, and (f) $639°\mathrm{C}$. Dark areas correspond to $(6\times 6)$ terraces. The scale bar in (a) is $0.2\mu \mathrm{m}$.