Dynamical Monte Carlo methods for plasma-surface reactions

Abstract

Different dynamical Monte Carlo algorithms to investigate molecule formation on surfaces are developed, evaluated and compared with the deterministic approach based on reaction-rate equations. These include a null event algorithm, the n-fold way / BKL algorithm and an "hybrid" variant of the latter. NO 2 formation by NO oxidation on Pyrex and O recombination on silica with the formation of O 2 are taken as case studies. It is shown that dynamical Monte Carlo schemes are flexible, simple to implement, describe easily elementary processes that are not straightforward to include in deterministic simulations, can run very efficiently if appropriately chosen and give highly reliable results. Moreover, the present approach provides a relatively simple procedure to describe fully coupled surface and gas phase chemistries. The influence of the grid size on the CPU calculation time and the accuracy of the results, the effect of back diffusion and its inclusion in a deterministic formulation, and the influence of Langmuir-Hinsehlwood recombination involving two physisorbed atoms, are investigated and discussed.

Deterministic and Monte Carlo methods for simulation of plasma‐surface interactions

“…In the first approximation in case of a square grid, the correction factor is equal to 3/4 which corresponds to the probability of 1/4 for an atom to return to its initial position after two successive hops. This effect is called back diffusion and it can be shown that it is important for processes that have elementary probabilities close to one, such as the occupation of empty chemisorption sites by diffusion (R5), but it should be neglected for processes with a low elementary probability, such as L‐H recombination (R6), (R7) …”

“…The elementary probability can be calculated in the same way as P R with the appropriate values of the energy barrier and the pre‐exponential factor. In Guerra et al it is assumed that upon an encounter between two physisorbed atoms the recombination occurs with probability 1. This assumption can be justified by the fact that physisorbed atoms interact only weakly with the surface and hence reaction (R7) is similar to a 3‐body gas phase recombination which proceeds with no barrier for many atomic species .…”

“…Now, the system of Equation and can be solved to follow the time evolution of θ F and θ S towards the steady state. Once the steady state is reached, the recombination probability of atoms on the surface can be calculated as follows: where …”

“…Different KMC algorithms exist to choose processes and locations at which these processes occur. This includes the so called null event method proposed in ref and later implemented for plasma‐surface systems . In null event algorithms, first a surface site is randomly selected and then, depending on the occupancy of this site, one of the available processes is executed with a probability that depends on the transition rate of this process.…”

“…Furthermore, the deterministic approach fails when the fluctuations of the number of particles become important (e.g., interstellar dust grains that receive extremely low fluxes of reactive species). Moreover, the treatment of the diffusion of physisorbed species in DD models always involves additional assumptions regarding the rates of reactions of physisorbed species (e.g., Langmuir‐Hinshelwood recombination); the accuracy of such assumptions is discussed in ref …”