Exact island-size distributions for submonolayer deposition: Influence of correlations between island size and separation

Long Time Behaviour and Self-similarity in an Addition Model with Slow Input of Monomers

“…is a solution of system (3) then (c 1 , c j ), j ≥ 2 is a solution of system (2). The proof can be done as in [5, Theorem 2.1].…”

“…One way to externally supply monomers is to define the input term J 1 (t) independently of the state of the system. This is a reasonable assumption in a number of applications, including in simple models of polymerization and of epitaxial growth [2]. The easiest hypothesis about J 1 (t), which turns out to be very useful in applications, is to make it a time independent constant.…”

“…We study two aspects of the dynamical behaviour of solutions to (2). First, we want to establish the componentwise behaviour of the solution as time t → +∞ and the behaviour of the total amount of clusters.…”

Formation and Equilibration of Submonolayer Island Distributions in Ag/Ag(100) Homoepitaxy

“…As an aside, we note that the characteristic shape of this distribution has only recently been understood as being controlled by subtle correlations between the size and separation of islands. 4 We believe that the absence of small islands in the experimental distribution, compared to the simulation results, could be due to a number of factors: we have chosen scanning conditions with lower resolution, as noted in section II, and these conditions are not sensitive to small islands; subsequent automated processing of the original STM images to obtain island size distributions (using NIH software) can "lose" small islands; mobility of dimers and other small clusters could modify the distribution without significantly affecting N av behavior; 14 small islands could be lost due to coarsening following deposition and before the STM image is obtained; and finally, the STM tip could disrupt small islands. Correspondingly, theoretical predictions with various cutoffs for minimum observable size match the observed behavior better (see Figure 2).…”

“…2,3 For example, such studies have finally led to an understanding of the characteristic shape of the island size distribution at low (precoalescence) coverages. 4 Such studies also facilitate the characterization of the nonrandom spatial distribution of islands on the surface. 1,2 Another issue of basic interest is the postdeposition coarsening of the adlayer, starting from the far-fromequilibrium island distribution created by the above nucleation and growth processes.…”