Dynamic coupling between particle-in-cell and atomistic simulations

We propose a method to directly couple molecular dynamics, the finite element method, and particle-in-cell techniques to simulate metal surface response to high electric fields. We use this method to simulate the evolution of a field-emitting tip under thermal runaway by fully including the three-dimensional space-charge effects. We also present a comparison of the runaway process between two tip geometries of different widths. The results show with high statistical significance that in the case of sufficiently narrow field emitters, the thermal runaway occurs in cycles where intensive neutral evaporation alternates with cooling periods. The comparison with previous works shows that the evaporation rate in the regime of intensive evaporation is sufficient to ignite a plasma arc above the simulated field emitters.

Figure 1

The relation between different components in the proposed multiscale-multiphysics model.

Figure 2

Boundary regions and geometry of the simulation domain, which consists of an atomistic region and an extension.

Figure 3

Electric field calculation by means of particle-in-cell method.

Figure 4

Generation and usage of Voronoi cells for surface charge calculation.

Figure 5

Current-voltage dependence from various models.

Figure 6

Relative difference between the surface charges obtained with HELMOD [31] and with the current model. The difference is calculated along the surfaces of a $\left\{100\right\}$ and a $\left\{110\right\}$ slice of the apex.

Figure 7

Time evolution of the averaged nanotip heights (left) and some characteristic excerpts from the simulation (right). Labels (a)–(h) on the left correspond to the frames on the right side. Error bars show the variation of the data between parallel runs in a form of standard error of the mean.

Figure 8

Time evolution of averaged apex temperature (left) and total field emission current (right) from the nanotips. The inset shows the magnification of the first 10 fs, during which the space charge is formed.

Figure 9

Time evolution of the relative height of molten region.

Figure 10

Four separate height profiles of thin nanotips that illustrate the variation in shape and timings of the curves. Dashed lines demonstrate the method for determining $t_{\mathrm{evap}}$ and $t_{\mathrm{cool}}$. Labels (a)–(h) correspond to snapshots in Fig. 7.

Figure 11

Cumulative number of emitted atoms (right lines on the graph) and electrons (left lines). The slope of the linear fit (bold dashed lines) gives evaporation and injection rates.

Figure 12

Simulation flowchart for the model described in Sec. 2.

Figure 13

Generation of a superparticle into a quadrangle, which in turn is located inside a triangle.