Particle-resolved dynamics during multilayer growth of ${\text{C}}_{60}$

Using large-scale kinetic Monte Carlo (KMC) simulations, we investigate the nonequilibrium surface growth of the fullerene ${\text{C}}_{60}$. Recently we have presented a self-consistent set of energy barriers that describes the nucleation and multilayer growth of ${\text{C}}_{60}$ for different temperatures and adsorption rates in quantitative agreement with experiments [Bommel et al., Nat. Commun. 5, 5388 (2014)]. We found that ${\text{C}}_{60}$ displays lateral diffusion resembling colloidal systems, however it has to overcome an atomlike energetic step-edge barrier for interlayer diffusion. Here we focus on the particle-resolved dynamics, and the interplay between surface morphology and particle dynamics during growth. Comparing ${\text{C}}_{60}$ growth with an atomlike system, we find significant differences in the evolution of the surface morphology, as well as the single-particle dynamics on the growing material landscape. By correlating the mean-squared displacement of particles with their current neighborhood, we can identify the influence of the different time scales that compete during growth and can pinpoint the differences between the two systems.

Figure 1

Pair potentials for ${\text{C}}_{60}$ (blue continuous line) and argon atoms (red dashed line). Both are scaled to a potential well depth of $-1$, and the range is expressed in terms of particle diameters [30, 31].

Figure 2

Island density for $T=40{}^{\circ }\text{C}$ and a relatively small adsorption rate $(f=0.1\text{ML} {\text{min}}^{-1})$ as a function of the average surface height $\overline{h}=f\times t$.

Figure 3

Height of surface structures after the growth of 1.5 ML for (a) ${\text{C}}_{60}$ on ${\text{C}}_{60}$(111) and (b) Ag on Ag(111). The black lines depict trajectories of a particle which arrived on an island. Both systems are simulated on a triangular lattice with equal energy barriers $E_{\text{free}}=0.54$ eV and $E_{\text{ES}}=0.11$ eV, but different neighbor binding energies $E_{\text{n}}=0.13$ eV and $E_{\text{n}}{\left(\text{Ag}\right)}^{{}^{\prime }}=0.72$ eV, respectively.

Figure 4

(a) Height-height correlation function $G(d,t)$ as a function of the distance $d$ after the growth of 0.5 ML ($t\approx 22$ s) for ${\text{C}}_{60}$ and Ag. The inset depicts a snapshot of size $75a\times 125a$ of the surfaces. (b) The dependence of the average island size on the radius of gyration $x_{\text{gyr}}$ in a double-logarithmic representation. Included are values for the resulting scaling exponents $D$ [see Eq. (7)].

Figure 5

Height-height correlation functions $G(d,t)$ of ${\text{C}}_{60}$ and Ag as a function of time for two distances (a) $d=0a$ and (b) $d=1a$.

Figure 6

The MSD of particles that arrive (a) between islands or (b) on top of islands after the growth of 0.5 ML for different interaction energies $E_{\text{n}}\left({\text{C}}_{60}\right)=0.13$ eV, $E_{\text{n}}{\left(\text{Ag}\right)}^{{}^{\prime }}=0.72$ eV, and $E_{\text{n}}{\left(\text{Pt}\right)}^{{}^{\prime }}=0.92$ eV. All systems are simulated on a triangular lattice with equal energy barriers $E_{\text{free}}=0.54$ eV and $E_{\text{ES}}=0.11$ eV. The turquoise lines represent the MSD for free diffusion (linear time dependence).

Figure 7

(a) and (c) The MSD of the ${\text{C}}_{60}$ and Ag systems already plotted in Fig. 6 (i.e., diffusion in between islands), while (b) and (d) correlate these data to the time dependence of the fraction of particles doing a certain process. These processes can be free diffusion $\left(n=0\right)$ and diffusing away from a site with $n=1\text{or}2$ neighbor particles. Also plotted are the fractions of particles that are immobilized (bound). All other processes are negligible.