Decay of isolated surface features driven by the Gibbs-Thomson effect in an analytic model and a simulation

Abstract

A theory based on the thermodynamic Gibbs-Thomson relation is presented which provides the framework for understanding the time evolution of isolated nanoscale features (i.e., islands and pits) on surfaces. Two limiting cases are predicted, in which either diffusion or interface transfer is the limiting process. These cases correspond to similar regimes considered in previous works addressing the Ostwald ripening of ensembles of features. A third possible limiting case is noted for the special geometry of "stacked" islands. In these limiting cases, isolated features are predicted to decay in size with a power law scaling in time: A ∝ (t 0 − t) n , where A is the area of the feature, t 0 is the time at which the feature disappears, and n = 2/3 or 1. The constant of proportionality is related to parameters describing both the kinetic and equilibrium properties of the surface. A continuous time Monte Carlo simulation is used to test the application of this theory to generic surfaces with atomic scale features. A new method is described to obtain macroscopic kinetic parameters describing interfaces in such simulations. Simulation and analytic theory are compared directly, using measurements of the simulation to determine the constants of the analytic theory. Agreement between the * Communicating author. Present Address:

Decay characteristics of two-dimensional islands on strongly anisotropic surfaces

“…[2][3][4][5][6][7][8][9][10][11] The thermal decay of such islands was found to reduce the island area with time t proportional to (t 0 Ϫt) 2␤ , where t 0 is the time at which the island is fully dissolved. 12 The value of the exponent ␤ is a signature of the dominant microscopic mechanism governing the rate of decay. In the case where attachment and detachment of atoms from the island edges dominate the rate of decay, ␤ equals 1/2 whereas for the diffusion-limited case, i.e., where diffusion of adatoms on the terrace limits the decay rate, ␤ is 1/3.…”

“…Three successive atomic processes are involved: ͑i͒ the interface transfer of atoms at the island edge, i.e., detachment and attachment events, ͑ii͒ the adatom diffusion on the surface, and ͑iii͒ the incorporation of the adatoms into the environment at the outer boundary, i.e., at sinks. 12 A decaying island must have a net detachment of atoms from the island. Thus the atom current…”

Facet evolution on supported nanostructures: Effect of finite height

“…Inset shows a local maximum of E n / N 4 for n / N Ϸ 0.45. 4 and t ‫ء‬ has been documented for a wide range of g values in Ref. 26.…”

“…As a result, in the absence of material deposition, the perimeter of a single isolated step generally shrinks-a phenomenon that is well understood in terms of a step line tension. 4,5 In addition to step curvature, another quantity that is clearly finite is the number of monolayers that make up the nanostructure. However, the effects of finite height have received much less attention in theoretical treatments compared to infinite and periodic surface features.…”

Slope selection-driven Ostwald ripening in ZnO thin film growth

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