Ernst-Moritz-Arndt University, Griefswald, Germany
Tools and strategies for the description of plasma-wall interaction
1. General considerations
PWI modeling has to deal with very complex and different problems such as arcs (field emission coefficients), NNBI (surface ionization, effect of Cs layers) and hot spots (SEE coefficients for ions and electrons). Therefore, interaction with other fields is needed and multi-scale physics requires a combination of methods. The real structure of the material is quite important, because it determines diffusion and impurities can strongly affect surface binding energies. Molecular dynamic simulations can help to overcome some shortcomings of simpler models, but they are only as good as the quality of the interaction potentials. Also, they can deal mostly with idealized systems and have problems for realistic fusion wall materials (mixed materials with a lot of damage and impurities). For fundamental understanding model systems are needed for validation.
Sputtering of a surface exposed to a flux of energetic ions is one of the best studied effects of ion-surface interactions. The details of ion-surface interactions depend greatly on the target-projectile combination. When the projectile is an ion of a volatile (recycling) element then sputtering usually dominates and the surface is eroded. In this case experiments are well described theoretically. The sputtering yield is the main parameter that is used to validate theoretical models against experiments. Existing models such as the TRIM code show good agreement with experiment for many target-projectile combinations.
If the projectile is a solid-state (non-recycling) ion then its interaction with the surface can lead to implantation if the ion, after penetration and deceleration in the solid, remains in the surface. This leads to formation of a mixed surface of target and projectile atoms. The properties of the mixed surface may deviate significantly from the properties of original materials. Additionally, the surface composition is dynamically changed by sputtering and implantation. The study of such interactions cannot be described just by the sputtering yield behavior; it depends strongly on the elemental composition of the surface, which is, in turn, modified continuously by ion bombardment. Similar difficulties are encountered when volatile ions interact with compounds or when a surface is exposed to a mixed flux of volatile and solid-state ions. To solve this problem a dynamic version of the TRIM code called TRIDYN (later re-written as SDTrimSP) was developed. This is a 1D version of TRIM, where the distance from the surface into the solid is discretized on a grid and dynamical change of the surface composition along the depth due to implantation of projectiles and relocation of recoils during collisional cascades are considered. There have been a number of studies comparing experiments with TRIDYN simulations showing generally good agreement.
The existing models assume that a plane and perfectly smooth surface exists and they demonstrate good agreement with experiments if well-polished specimens are used. Surface roughness is prone to increase the sputtering yield by up to a factor of 5. There were a few approaches to predict sputtering yields of rough surfaces. Ruzic suggested considering the surface to have a fractal geometry, and Kuestner et.al. assumed that the surface can be represented as aggregates of simple surfaces at tilted angles. These approaches yield reasonable agreement, but their intrinsic limitations have prevented further development of the models. One of the limitations is their inability to simulate surface morphology changes by deposition and implantation.
The limitations of the approaches can be overcome by extending the grid of the existing model into the second and third lateral dimensions. The first step in this direction has been made in developing the SDTrimSP-2D code, which is capable to treat the interaction of ions with a 2D surface. An example of such a surface is a diffraction lattice. The code belongs to the TRIM family and it incorporates the same physical model, but due to existing of second lateral dimension, it requires also an advanced relaxation mechanism. It has been shown that the code predicts the evolution of a Si pitch grating exposed to 6 keV Ar ions with a good accuracy. Although this system is rather simple and governed mainly by sputtering and relaxation, the agreement between the experiment and numerical simulation demonstrates the validity of the basic physics included in the model. The code has also been used to evaluate the effect of the surface roughness of W exposed to C and C+D flux.
Another extension of the code is the inclusion of chemical sputtering by combining the local chemistry model of Mech et al. (based on work by Küppers et al.) with the experimental flux scaling from Roth et al. and the concept of escape probabilities for hydrocarbons depending on the distance to the surface (see Jacob et al.). This code reproduces a large number of experiments including the observation that a hydrocarbon surface bombarded with Neon (producing damage) and in parallel exposed to thermal hydrogen influx shows strong chemical sputtering.