Mechanism of surface modification in the plasma-surface interaction in electrical arcs

Electrical sparks and arcs are plasma discharges that carry large currents and can strongly modify surfaces. This damage usually comes in the form of micrometer-sized craters and frozen-in liquid on the surface. Using a combination of experiments, plasma and atomistic simulation tools, we now show that the observed formation of deep craters and liquidlike features during sparking in vacuum is explained by the impacts of energetic ions, accelerated under the given conditions in the plasma sheath to kiloelectron volt energies, on surfaces. The flux in arcs is so high that in combination with kiloelectron volt energies it produces multiple overlapping heat spikes, which can lead to cratering even in materials such as Cu, where a single heat spike normally does not.

Figure 1

Craters produced during arcing at the dc arc setup at CERN. (a) and (b) show SEM images of two different sparking events. The experiments show craters of similar shape in a wide variety of sizes in the range $\sim 0.1–10\mu \text{m}$, justifying the comparison with smaller simulated craters.

Figure 2

(Color) Comparison of experimental and simulated craters. Top left: tilted SEM experimental image of a few nearby craters. Top right: tilted AFM experimental image of the same experimental crater. Bottom left: tilted MD simulated image of a single crater. Bottom right: MD simulated image of the same simulated crater. In the simulated case the total-energy deposition was $4.34\text{keV}/{\text{nm}}^2$. The inset in the bottom left part shows a complex double crater from the MD simulations.

Figure 3

(Color online) Results from PIC simulations of the development of an arc plasma. The figure shows the total flux of Cu ions from the plasma against the cathode material. Due to the acceleration in the sheath potential, the energy distribution has a strong maximum around the high kinetic energy/atom of 8 keV. The inset shows the distribution of electric potential between the cathode (at $x=0$) and anode $\left(x=20\mu \text{m}\right)$ after the arc plasma has formed. The plasma sheath leads to a strong gradient in the potential near the cathode, leading to the acceleration of Cu ions toward it.

Figure 4

(Color online) Development of the average temperature in the system for different numbers of bombarding ions. The bombardment of the surface started at $t=1\text{ps}$. Atoms that are above the original surface are not included in the temperature calculation since sputtered atoms can have high kinetic energies which do not contribute to the substrate temperature. The total number of atoms in these systems was 7 million.

Figure 5

(Color online) Self-similarity of craters of different size produced in the MD simulations. The simulations show craters of similar shape in the whole simulated range of $r=3–25\text{nm}$, justifying the comparison with larger experimental craters. Only a thin slice from the top of the simulation cells is shown. The height scale is indicated on the right-hand side in units of angstrom, and both the lateral, depth and height of the plotting region is exactly the same in all frames. The frame for $r=15\text{nm}$ and energy deposition $E_{dep}=1.88\text{keV}/{\text{nm}}^2$ shows the same crater as that in the left-hand side of Fig. 6. The crater for $r=25\text{nm}$ was produced by a relatively low-energy deposition, and hence the crater is split into several parts, similar to some of the craters in Fig. 1.

Figure 6

(Color online) Snapshots of the time development of cratering by arcs. Left: crater produced by energetic plasma ion flux obtained from dc plasma simulations. Right: crater produced by nonballistic (thermal) energy deposition but depositing the same amount of energy as in the plasma ion case. Only a thin slice from the top of the simulation cells is shown. Each dot shows the position of an atom, due to the large number of atoms involved individual atoms cannot be distinguished at the surface. The atoms are colored according to the height above the surface, with dark yellow (medium gray in grayscale) giving the original surface position, and light yellow (light gray) and red (dark gray) positions of atoms above the surface. The height scale is given in angstrom to the right. In both cases the total-energy deposition was $1.88\text{keV}/{\text{nm}}^2$. Note how in the dc case massive fingers of atoms come up, which eventually break up and lead to the formation of complex surface features and cluster emission.

Figure 7

(Color online) Results from MD simulations of the crater formation due to the flux of particles from the plasma for a bombarding area of $r=15\text{nm}$. The sputtering yield signifies the total amount of particles that leave the sample because of the intense particle bombardment over the whole duration of one arcing event. The crater rim size is the total number of atoms above the surface but still connected to the sample. We also calculated the sizes of the excavated areas (crater wells), but this data is not shown for clarity, since it is almost exactly equal to the sum of the sputtering and crater rim size and thus carries no additional information. Also shown are the same quantities due to nonballistic (thermal) energy deposition that does not involve high kinetic energies.

Figure 8

(Color online) Crater shape profiles obtained from experiments and simulations. The experimental shapes were obtained from AFM measurements and the simulated ones from a simulation of a spherical AFM tip approaching the atomic coordinates obtained from the MD simulations. However, since the experimental tip radius was below 35 nm, tip convolution effects were negligible. One of the experimental shapes has been multiplied by 0.2 to illustrate that the experimental crater shapes are self-similar over different scales. Computer capacity limitations prevented simulation of micron-sized craters, but after multiplication by a factor of 30–40, the simulated crater shapes obtained from the plasma ions agree very well with the experimental shapes. However, the nonballistic (thermal) energy deposition crater shape is clearly different from the experimental ones. Note also that in the two simulated cases of plasma bombardment, the shapes are similar with only a difference of 1.3 in the multiplication factor, although the fluence was a factor of 2.5 different.