Structure Formation of C₆₀ on Insulating CaF₂ Substrates: Matching Experiments with Simulations

Abstract

An extensively studied organic molecule that has become a paradigmatic choice as an adsorbate for deposition experiments is the fullerene C 60 , which has been shown to produce a vast assortment of resulting cluster morphologies on metallic [10][11][12][13][14][15] and insulating [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] substrates. However, even for the self-assembly of such a well-studied molecule, reliable structure predictions and design principles are mostly lacking. Computer simulations can be used to fill this gap and to explore the parameter space efficiently. While first principle and atomistic simulations can account for molecular details, they are prohibitively expensive to access the length and time scales needed to determine cluster morphologies. On large lengths, continuum approaches [35] including phase-field modeling [36] require the input of effective parameters (mobilities, interfacial tensions, etc.). An intermediate particle-resolved technique is the kinetic Monte Carlo (KMC) method, which has been shown to be able to achieve the necessary length and time scales to simulate the cluster growth of several deposition experiments. [37][38][39][40][41][42][43] KMC stochastically advances a number of molecules moving between discrete lattice sites through elementary transitions that depend on the interactions with neighboring molecules.A major issue one faces with KMC simulations is the modeling of the elementary transition rates of the system, which can involve a large amount of free parameters. Typically one reduces that amount by assuming an Arrhenius law for the transition rates and by applying some constraints (like bond counting approaches) on the remaining energy barrier and attempt rate parameters. Pure top-down modeling can easily lead to models that are oversimplified, contain invalid assumptions, or can lead to model parameters that lose their intended physical interpretation. Experimental data is used to tune the remaining parameters of such rate models and one can make use of machine learning techniques [44,45] to optimize the parameter tuning. However, experimental data alone is often insufficient to determine the transition rates of all relevant elementary processes (free diffusion, edge diffusion, ascension, descension, dissociation, etc.).A bottom-up approach to help with the determination of KMC rate models is the use of molecular dynamics (MD) simulations. By assuming interaction potentials for the adsorbate and substrate interactions, one can set up systems in which one can directly measure the transition rates of interest. [37] In refs. [46,47] we have recently developed such an approach and gathered an extensive amount of data from MD simulations to inform KMC rate modelsThe epitaxial growth of metallic thin films has been studied intensively, leading to computational models that can predict diverse morphologies depending on thermodynamic and kinetic growth parameters. Much less is known about thin films of organic molecules. Here kinetic Mont...

FandMcenters in alkali halides: A theoretical study applying self-consistent dielectric-dependent hybrid density functional theory

“…The kinetic Monte Carlo (kMC) method is an established method in solid state physics to simulate diffusion and migration processes in the bulk or on the surface. [127][128][129][130][131][132] In this work, the same method was implemented according to the equations by Voter [133] and employed to simulate a system as it moves from a reagent to a product across a network of reactions, as the fundamental kinetic principles are the same as for a diffusion or migration process. In principle, the Gibbs free activation energy Δ𝐺 ‡ 𝑖 𝑗 at temperature 𝑇 is the only property required for the kMC simulation, yielding the corresponding rate constant 𝑘 𝑖 𝑗 for a reaction from state 𝑖 to 𝑗 as…”