# Kinetic 3D Lattice Monte-Carlo model of ion erosion of fcc(111) surfaces

Introduction

We have developed a very efficient K3DLMC method, which allows to study ion erosion of fcc(111) surfaces due to low-energy ion bombardment. As an application we modeled 1 keV Xe ion erosion of Pt(111), for which a fairly large amount of experimental data exist. A specific feature of this model is the fact, that the distribution of damage at the surface (surface vacancies and adatoms) is properly taken into account.

**Fig. 1:** Simulated microstructure after erosion of six monolayers. Coloring according to depth. For clarity, the simulated area (indicated by the slightly shaded box) is quadrupled.

## Basic Description

A rhombohedric fcc simulation cell of size *L* x *L* x *H* is used with periodic boundary conditions in lateral directions. The thermodynamical aspects of the surface dynamics are determined by nearest-neighbor interactions within the Ising model. The bond strength is chosen to be *E*_{b} = 0.25 eV. The frequencies of jump attempts and the activation energies for nearest-neighbor jumps depend on coordination: Adatoms (all atoms with coordination < 4): *f* = 5 x 10^{12} 1/s, *E*_{a} = 0.3 eV. For all other atoms with 3 < coordination < 9: *f* = 1 x 10^{12} 1/s, *E*_{a} = 0.6 eV. The remaining higher coordinated atoms are considered to be immobile. The transition probabilities are computed with the help of the Metropolis algorithm.

For 1 keV Xe ion bombardment a sputter coefficient of 2.8, and an adatom generation rate of 5 has been measured. Thus, per ion incident 7.8 surface vacancies and 5 adatoms are distributed according to radial, exponentially decaying distributions.

**Fig. 2:** Microstructure right after the first ion impact showing a typical distribution of adatoms and surface vacancies.

## Application

The following animation (1.8 MB mpeg-movie) shows the evolution for erosion up to 6 monolayers (ML) for a system size of 64 x 64 atoms. The simulation temperature is T = 500 K and an erosion rate of 25 s/ML is applied. A closer look to the coalescence of two pits is available in the following animation (4.9 MB mpeg-movie).

The MC model allows to apply ad-hoc rules in order to control surface kinetics processes and to study their effect on the surface morphology evolution during ion erosion. For instance, step-edge diffusion can be effectively suppressed by prohibiting the thermal generation of step-adatoms from kinks. The following animation (7.8 MB mpeg-movie) shows the corresponding surface evolution during erosion.

## Publications

M. Strobel, K.-H. Heinig, and T. Michely, *Three-dimensional kinetic lattice Monte-Carlo simulation of ion erosion of fcc(111) surfaces*, Nucl. Instr. Meth. B, in press.

T. Michely, M. Kalff, G. Comsa, M. Strobel and K.-H. Heinig, *Step-edge diffusion and step atom detachment in surface evolution: Ion erosion of Pt(111)*, Phys. Rev. Lett., submitted.

M. Strobel, K.-H. Heinig, and T. Michely, *Mechanisms of pit coarsening in ion erosion of fcc(111) surfaces: A kinetic 3D lattice Monte-Carlo study*, Surf. Sci., submitted.