Wetting Layer Super-Diffusive Motion and QSE Growth in Pb/Si

The unusual growth mode of uniform height islands discovered in Pb/Si was related to the electronic energy modulation with island height due to quantum size effects (QSEs). In addition to these energetic reasons provided by QSE, there is also the question of kinetics, i.e., how atoms move at relatively low temperatures (as low as 150 K) to build the islands in the short time of minutes. Controlled experiments with different techniques have shown the intriguing role of the dense wetting layer in transporting mass. STM experiments monitoring how unstable islands transform into stable islands have shown that the wetting layer between the islands moves selectively to the unstable islands, climbs over their sides, forms quickly rings of constant width ∼ 20 nm, and finally it completes the island top, but at a slower rate than the ring completion. This growth is independent of the starting interface, whether it is the amorphous wetting layer on the Si(111) (7 × 7) or the well-ordered Si(111)–Pb \(\alpha (\surd 3\times \surd 3)\) surface (except Pb diffusion on the latter interface is faster by a factor of ∼ 5). Real-time low-energy electron microscopy (LEEM) observations of mass transport phenomena have confirmed the fast mobility of the wetting layer in Pb/Si and in addition have revealed some unusual features that are unexpected from classical diffusion behavior. The experiment monitors the refilling of a circular vacant area generated by a laser pulse. The concentration profile does not disperse as in normal diffusion, the refilling speed \(\Delta x/\Delta t\) is constant (instead of \(\Delta x/\surd \Delta t = \mathrm{constant}\)), and the equilibration time diverges below a critical coverage, θ c, as \(1/\tau \sim (\theta _{\mathrm{c}} - \theta)^{-\kappa}\). The absolute value of the refilling speed 0.05 nm/s at 190 K is orders of magnitude higher than what is expected from Pb diffusion on Pb crystals at higher temperatures. These results are compared with predictions of three candidate models: (i) a conventional diffusion model with a step-like coverage-dependent diffusion coefficient \(D_{\mathrm{c}}(\theta)\), (ii) a model with mass transport due to adatoms on top of the wetting layer with coverage-dependent adatom vacancy formation energy, and (iii) the carpet unrolling mechanism proposed for other systems. None of these models can account for the unusual observations, which suggests that the wetting layer most likely enters a novel state of very high mobility for \(\theta > \theta _{\mathrm{c}}\), similar to a phase transition that needs to be better understood theoretically.