Measuring surface diffusion from nucleation island densities

Abstract

We present a critical view of the analysis of experimental island densities acquired as a function of temperature in terms of barriers and prefactors for tracer diffusion at surfaces. We investigate the achievable precision for methods ranging from simple application of scaling laws, via integration of mean-field rate equations within various approximations for the capture rates, to kinetic Monte Carlo simulations that account for the various island shapes realized on square and hexagonal lattices. The discussion of theoretical models will be accompanied by variable temperature STM data for the nucleation of Ag on a Pt͑111͒ surface. We introduce experimental methods to test for dimer diffusion and dissociation, as well as for transient mobility of monomers. Density scaling is analyzed in the presence of post-deposition mobility and easy adatom attachment to islands and other monomers. From extended kinetic Monte Carlo simulations we establish density scaling for the various island shapes on square and hexagonal lattices for coverages up to percolation, which is particularly relevant for methods working in reciprocal space. ͓S0163-1829͑99͒01231-X͔

Equilibrium island-size distribution in one dimension

“…14 However, for Ag on Pt͑111͒ dimer dissociation starts already at 120 K, 44 while both density functional calculations 45 and experiments 46 indicate that, for certain systems, dimers might break up more easily at step sites rather than on terrace sites. Finally, it is interesting to note that the dimer bond energy per Ag atom on Pt͑111͒ estimated by STM, 75± 10 meV, 47 compares well with E b = 83 meV calculated using Eqs. ͑8͒-͑10͒ and the experimental N, M, K values.…”

Dynamics of Surface Migration in the Weak Corrugation Regime

“…Similar, albeit less drastic effects, exist for the migration of Ag on various fcc surfaces [18,24,27], where, with the migration barrier decreasing from 168 6 5 to 60 6 10 meV, the corresponding preexponential factor drops from the universal value D 0 1.4 3 10 2260.3 ͑n 0 7 3 10 1360.3 s 21 ͒ to D 0 2 3 10 2760.6 cm 2 ͞s ͑n 0 1 3 10 960.6 s 21 ͒. Note that with all these systems dimer stability ͑i 1͒ and the absence of cluster mobility were ensured by investigating the onset of coarsening for dimers [24] or by analyzing the island size distributions [26].…”

“…Dimer mobility can be similarly excluded for the present temperature range, based on the theoretical value of the dimer migration barrier [21] and on the scaling laws in the presence of cluster diffusion [22,23]. The saturation island density is thus solely controlled by the tracer diffusion coefficient and the deposition flux F. Then the following scaling law relates D ‫ء‬ to n x [19,24]:…”

Time-dependent annealing and deposition on substrates with repulsive interactions

“…But it has been included in recent papers on nucleation and growth 7,13 , because it must become more important at higher coverage θ.…”

“…The case when τ is finite (i.e. τ −1 > 0) is a general way of introducing competing loss processes, such as re-evaporation, or capture by other clusters, in the uniform depletion, or mean-field approximation 1,7,12,13 .…”