Low-coverage surface diffusion in complex periodic energy landscapes: Analytical solution for systems with symmetric hops and application to intercalation in topological insulators

Abstract

This is the first of two papers that introduce a general expression for the tracer diffusivity in complex, periodic energy landscapes with M distinct hop rates in one-, two-, and three-dimensional diluted systems (low-coverage, single-tracer limit). The present report focuses on the analysis of diffusion in systems where the end sites of the hops are located symmetrically with respect to the hop origins (symmetric hops), as encountered in many ideal surfaces and bulk materials. For diffusion in two dimensions, a number of formulas are presented for complex combinations of the different hops in systems with triangular, rectangular, and square symmetry. The formulas provide values in excellent agreement with kinetic Monte Carlo simulations, concluding that the diffusion coefficient can be directly determined from the proposed expressions without performing the simulations. Based on the diffusion barriers obtained from first-principles calculations and a physically meaningful estimate of the attempt frequencies, the proposed formulas are used to analyze the diffusion of Cu, Ag, and Rb adatoms on the surface and within the van der Waals (vdW) gap of a model topological insulator, Bi2Se3. Considering the possibility of adsorbate intercalation from the terraces to the vdW gaps at morphological steps, we infer that, at low coverage and room temperature, (i) a majority of the Rb atoms bounce back at the steps and remain on the terraces, (ii) Cu atoms mostly intercalate into the vdW gap, the remaining fraction staying at the steps, and (iii) Ag atoms essentially accumulate at the steps and gradually intercalate into the vdW gap. These conclusions are in good qualitative agreement with previous experiments. The companion report (M. A. Gosálvez et al., Phys. Rev. B, submitted] extends the present study to the description of systems that contain asymmetric hops.