Atomistic surface erosion and thin film growth modelled over realistic time scales

Abstract

We present results of atomistic modelling of surface growth and sputtering using a multi-time scale molecular dynamics–on-the-fly kinetic Monte Carlo scheme which allows simulations to be carried out over realistic experimental times. The method uses molecular dynamics to model the fast processes and then calculates the diffusion barriers for the slow processes on-the-fly, without any preconceptions about what transitions might occur. The method is applied to the growth of metal and oxide materials at impact energies typical for both vapour deposition and magnetron sputtering. The method can be used to explain growth processes, such as the filling of vacancies and the formation of stacking faults. By tuning the variable experimental parameters on the computer, a parameter set for optimum crystalline growth can be determined. The method can also be used to model sputtering where the particle interactions with the surface occur at a higher energy. It is shown how a steady state can arise in which interstitial clusters are continuously being formed below the surface during an atom impact event which also recombine or diffuse to the surface between impact events. For fcc metals the near surface region remains basically crystalline during the erosion process with a pitted topography which soon attains a steady state roughness.

Influence of the prefactor to defect motion inα-Iron during long time scale simulations

“…To determine the various transition pathways a combination of the Dimer [2] and the minimum mode following [19] methods have been implemented into an otf-KMC technique [6] in order to achieve the best mixture of low computational costs and accuracy for finding the various saddle states surrounding a local minimum. The switch from the Dimer to the minimum mode method occurs when the Dimer's curvature value becomes negative and there is at least one negative eigenvalue in the system by which the minimum mode method can converge to a saddle.…”

“…They suggested to characterise systems by local energy minima, do multiple saddle searches and calculate rates for each individual transition using hTST and to select an event and advance the simulation clock according to the KMC algorithm. It has become widespread practise to use fixed τ values, usually ranging from 10 12 to 10 13 s −1 , in such KMC simulations [4,5,6,7], with the assumption that the attempt frequency does not vary greatly. This is because an accurate determination is computationally expensive and 'small' variations in the energy barrier ∆E affect the transition rates much more than 'small' variations in τ .…”

Thermal dynamics of silver clusters grown on rippled silica surfaces

“…MD simulations are limited to time scales up to microseconds at best and experimental time scales are generally not accessible by MD alone. Recently a multi-time scale technique has been developed that uses MD to model individual particle impacts over picosecond time scales followed by an off-lattice KMC approach to model diffusion between particle impacts 26 . This works well when the diffusion barriers are large so that atom movement only occurs as series of rare events.…”

Reaction pathways in atomistic models of thin film growth

“…The approach that is the basis of the main results described here uses MD to simulate the particle impacts onto the surface and AKMC to model the transitions that occur between successive particle impacts. 13 In the AKMC approach, the transition pathways are determined directly by numerical algorithms that perform open ended searches for the saddle points around a local minimum directly 9,11 rather than waiting for the system dynamics to find them. At first sight, therefore, it might appear that such methods should be more efficient but the AKMC method itself can also be limited by, for example, low transition energy barriers and large search volumes.…”