Interlayer Mass Transport and Quantum Confinement of Electronic States

Abstract

A numerical analysis of the ripening of multilayer islands on Cu(111) shows that the EhrlichSchwoebel barrier for interlayer mass transport is independent of the terrace width w as long as w . w c 14 6 2 Å, but vanishes for w , w c . The critical width w c corresponds exactly to the terrace width below which the surface state is pushed above the Fermi level due to quantum confinement. The Ehrlich-Schwoebel barrier is therefore correlated with the occupation of surface states.[ S0031-9007(99)08912-7] PACS numbers: 68.35.Fx, 73.20.Dx The growth of atomically flat epitaxial films requires a facile mass transport across the step edges which separate terraces of different height. Diffusion across a step edge is frequently hindered by an activation barrier for interlayer mass transport (Ehrlich-Schwoebel barrier [1,2]). The existence of a significant EhrlichSchwoebel barrier (ES barrier) is well documented for the (111) surfaces of Pt, Rh, Ag,. In these and other experiments, merely an average ES barrier is typically determined. Total energy calculations based on the embedded atom model (EAM) [8][9][10] as well as recent ab initio calculations in the local density approximation [11] have shown that activation energies for mass transport across a step depend on the type of steps and involve an exchange of the adatom with a step atom. For the experimentally rather extensively studied Pt(111) surface Feibelman [11] has shown that the activation energy is practically zero (0.02 eV) for crossing the A step [displaying a (100) facet], but large (0.35 eV) for the B step [(111) facet]. This result is at variance with the large effective ES barrier observed in earlier experiments [3]. However, according to a recent study [12] the large ES barrier in earlier work was caused by preferential adsorption of CO on A steps from the residual gas. On clean Cu(111) surfaces on the other hand, a significant ES barrier was found experimentally also for the A type step [13]. EAM calculations have further revealed significant differences in the ES barrier on a straight step and at kink sites [9,10]. Whether the calculated differences are always significant for the interlayer mass transport depends on the preexponential factors which are presently not known and may (partly) compensate different activation barriers (see, e.g., [14]).Faced with the unpleasantly complex situation, both on the experimental and theoretical side, a better understanding as to why and when larger ES barriers exist, would be rather welcome. An attempt in that direction was made several years ago by Memmel and Bertel [15] who conjectures that the existence of an ES barrier on (111) oriented fcc surfaces is correlated with the nearly free electron surface state [16]. It was argued that the boundary condition for the surface state wave function at the steps leads to a reduction of the binding energy at steps and hence to an ES barrier. While the concept is appealing, convincing evidence for a correlation between the existence of surface states and the ES barrier ...

Fast scanning tunnelling microscopy as a tool to understand changes on metal surfaces: from nanostructures to single atoms

“…On Cu(111) and Ag(111) surfaces the decay rate of double-layer islands increases by orders of magnitude when the distance between the island edges falls below a critical width [6,[55][56][57][58][59]]. An example is shown in Fig.…”

“…This phenomenon was first described for stacks of adatom islands on Cu(111) [55]. It was assigned to a breakdown of the step-edge barrier due to quantum confinement [56], because the critical width coincides on Cu(111) with a critical step distance, below which the electronic surface state is pushed above the Fermi level as a result of quantum confinement [60]. The comparison with Ag(111) showed that this explanation of the phenomenon is not correct [57].…”

Quantum size effects in ultrathin epitaxial Mg films on Si(111)

“…Also the formation of small islands would lead to energy shifts in the surface state due to lateral localization of its wave function. [27][28][29] After annealing to 200°C for a few minutes, surface photovoltage induces a 200-meV shift of the Fermi edge. This is again indicative of island formation.…”

Effects of surface vibrations on interlayer mass transport: Ab initio molecular dynamics investigation of Ti adatom descent pathways and rates from TiN/TiN(001) islands

“…More recently, Giesen et al observed that the rates of Cu island decay on Cu(111) greatly increase when the separation distance, d, between island-and terrace-step edges is smaller than a critical value w c ≈ 14Å [10,11]. The effect was attributed to ES barriers becoming vanishingly small for d < w c , in accordance with theoretical models, which showed that quantum confinement of electronic surface states in metals occurs for terrace widths < w c = λ F / √ 2, where λ F is the Fermi-electron wavelength [12].…”