Cu self-sputtering MD simulations for 0.1–5 keV ions at elevated temperatures

Abstract

Self-sputtering of copper under high electric fields is considered to contribute to plasma buildup during a vacuum breakdown event frequently observed near metal surfaces, even in ultra high vacuum condition in different electric devices. In this study, by means of molecular dynamics simulations, we analyze the effect of surface temperature and morphology on the yield of self-sputtering of copper with ion energies of 0.1–5 keV. We analyze all three low-index surfaces of Cu, {1 0 0}, {1 1 0} and {1 1 1}, held at different temperatures, 300 K, 500 K and 1200 K. The surface roughness relief is studied by either varying the angle of incidence on flat surfaces, or by using arbitrary roughened surfaces, which result in a more natural distribution of surface relief variations. Our simulations provide detailed characterization of copper self-sputtering with respect to different material temperatures, crystallographic orientations, surface roughness, energies, and angles of ion incidence.

Introduction

Particle accelerators, free electron lasers, fusion reactors and other devices using high electric fields in ultra high vacuum, often experience spontaneous plasma discharges happening on the material surface, known as vacuum arcing or electrical breakdowns. Surface electric fields in these devices can reach up to 300 MV/m as, e.g., in the accelerating structures of the Compact Linear Collider (CLIC) with the target energy of electron-positron collisions of 0.5–5 TeV [1]. It is strongly believed that the breakdowns are preceded by strong field emission [2], [3], however, it is still a puzzle how the plasma densities build up in the ultrahigh vacuum condition. Even though the very initial atoms may be found at random above the surface, these are not sufficient to develop a full self-sustainable plasma, detected as electrical breakdowns disturbing the operation of the machine [4], [5], [6]. It is believed that the plasma is fueled by atoms sputtered from the surface by ions forming above the surface due to interaction with electrons [6]. The main component of such a plasma are the ions of the surface material. Thus the self-sputtering may play a crucial role for understanding of the plasma buildup process.

It has been proposed that the increase of the surface temperature through field emission and plasma arc heating may intensify the amount of neutral Cu atoms emerging from Cu self-bombardment [6]. In other words, the temperature might be increasing the sputtering yield—the number of atoms kicked out of the surface per incident ion accelerated by the plasma sheath potential [7]. Experimentally, thermally enhanced sputtering has been observed in linear plasma devices [8].

It is well known that sputtering yields depend on many irradiation parameters, such as incident angle, energy, and mass of the incoming ion, as well as the mass and surface binding energy of the target atoms [9]. In addition, for a crystalline target such as Cu, the crystallographic orientation of the surface with respect to the direction of the projectile may play an important role [10]. Moreover, surface roughness may also affect the sputtering yield. For example, a study by Makeev and Barabási [11], found an up to 100% increase of the sputtering yield, compared to flat surface values.

Currently, no fundamental equation, which would be able to predict the effect of all the aforementioned variables on the sputtering yield, exist—although several phenomenological expressions developed to fit experimental observations were suggested throughout the last few decades [12], [13], [14], [15], [16], [17]. These models work best for the elements, which are neither too heavy (as, for instance, Au) nor too light (as, e.g. H, He), with not too low energy of incident ions, and the target surface being free of any contaminants. One of the major disadvantages of the existing semi-empirical models is the lack of a description of the temperature dependence of sputtering yields, although this dependence sometimes can show intriguing patterns [18]. Comparing the available fits to experimental data for Cu self-sputtering in Refs. [14], [15], [19], the formula by Yamamura [12], [19] shows the best agreement.

At elevated temperatures, the thermal vibration energies also increases, leading towards the decrease of the effective binding energy on the surface. However, as the experiments suggest, this explanation is not sufficient to explain the temperature dependence of sputtering yield [20], [8].

It has also been hypothesized that at elevated temperatures, the kinetic energy of the projectile is more easily dissipated, i.e. there are less focused few-body collisions and the sputtering yield drops [21]. On the other hand, it was also shown that in thermal spikes, which can be expected in metal irradiated by ions with energies higher than 2 keV, ambient thermal effects are negligible as the temperature of atoms in the spikes is very high [22], [23]. Normally, elevated temperatures may cause annealing of radiation defects, especially in metals, which may potentially decrease the sputtering yield, however, this process is usually neglected as small defects created in the cascades move relatively fast already at room temperature [24], [25].

A computer simulation study indicates up to ∼10 times increase of the sputtering yield as compared to the value at room temperature [26], [27]. Additionally, an exponential increase of the sputtering yield due to thermal evaporation has been observed near melting temperatures, although in this regime ballistic and thermal effects may overlap [10], [28].

Experimentally it has been reported that for Cu and Al—both face centered cubic (FCC) metals—the sputtering yield either stays rather constant [29] or experiences a small-scale deviation with an increase of the target surface temperature (up to 20–30%) [30]. Furthermore, no difference in the sputtering yield with increasing target temperature was observed for the {1 0 0} and {1 1 0} surfaces bombarded at the normal incidence, while a minor decrease in the sputtering yield with increasing temperature was observed for the normal bombardment of the {1 1 1} surface. This clearly indicates an anisotropy in temperature dependencies for different surface orientations [21].

The aim of this study is to test the hypothesis that the temperature has a dramatic effect on the primary sputtering process during the self-bombardment process of Cu, the main material for accelerating structures of CLIC, and thereby produces more unbound atoms upon which an electric breakdown can occur. We focus in this paper on the effects induced directly by collision cascades, i.e. we do not in this paper examine the possibility that thermal evaporation may enhance atom desorption between the actual collision cascades [31] or during overlapping cascades [32]. However, the possible role of these effects will be touched on in the discussion section.

In Section 2, we describe the molecular dynamics simulation setup and the interatomic potentials used in the current study. In Section 3.1, we investigate the angular dependencies of the sputtering yields by considering a wide range of different incident ion angles at different temperatures and different surface crystallographic orientations. In Section 3.2, we study the channeling effects for different crystallographic orientations. The dependence of the target temperature is investigated in Section 3.3 and in Section 3.4 we consider the effect of surface roughness on sputtering yield. The results are discussed and the paper is concluded in Section 4.