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In an accompanying article we showed that surface morphologies obtained through codeposition of a small quantity (2%) of impurities with Cu during growth (step-flow mode, ? = 40 ML) significantly depends on the lateral nearest-neighbor binding energy (ENN) to Cu adatom and the diffusion barrier (Ed) of the impurity atom on Cu(0 0 1). Based on these two energy parameters, ENN and Ed, we classify impurity atoms into four sets.

Using Monte Carlo simulations, we compute the terrace-width distributions (TWDs) of surfaces in which steps can touch each other, forming multiple-atomic height steps, but cannot cross (no overhangs), and so inconsistent with the standard mapping to spinless fermions. Our results show that the generalized Wigner distribution with minor modifications at small step separations, gives a very good fit for TWDs of touching steps. The interaction strength derived from the fit parameter indicates an effective attraction between steps. The strength of this effective attraction decreases for larger mean-step separations and decreasing step-touching energies; describable via finite-size scaling. Hence, accurate extraction of the true repulsion strength requires multiple vicinalities.

A unified explanation of the physics underlying all the distinctive features of the growth instabilities observed on Cu vicinals has long eluded theorists. Recently, kinetic Monte Carlo studies showed that codeposition of impurities during growth could account for the key distinctive experimental observations (Hamouda et al., Phys. Rev. B 77, 245430 (2008)). To identify the responsible impurity atom, we compute the nearest-neighbor binding energies (ENN) and terrace diffusion barriers (Ed) for several candidate impurity atoms on Cu(0 0 1) using DFT-based VASP. Our calculations show that codeposition (with Cu) of midtransition elements, such as Fe, Mn, and W, could—in conjunction with substantial Ehrlich-Schwoebel barriers—cause the observed instabilities; when the experimental setup is considered, W emerges to be the most likely candidate. We discuss the role of impurities in nanostructuring of surfaces.

Using both density-functional theory calculations and Monte Carlo simulations, we compute various key parameters that are used to model steps on vicinal surfaces. In the first part, we discuss the importance of multi-site interactions (trios and quartos) in the lattice-gas characterization of adatom interactions. Using density-functional theory calculations, we show that multi-site interactions with substantial contributions from direct interactions are sensitive to adatom relaxations. Such sensitivity to adatom relaxations complicates the lattice-gas approach to modeling overlayer systems. Our results show that a careful consideration of relaxation effects is required to make connections with experiments. In the second part, we use both density-functional theory calculations and kinetic Monte Carlo simulations to identify the impurity atom responsible for growth instabilities on Cu vicinals. In addition to that, we also show that a small quantity of codeposited impurities significantly alters the growth behavior. Our results indicate that growth morphologies could be controlled through the codeposition of an appropriate impurity. Hence, impurities could play a crucial role in nanostructuring of surfaces. Step configurations have fruitfully been related to the worldlines of spinless fermions in one dimension. However, in addition to the realistic no-crossing condition, the fermion picture imposes a more restrictive non-touching condition. in the third part of this thesis, we use Metropolis Monte Carlo method to study the effects of loosening this non-touching condition on the resulting TWDs. Our results show that allowing step touching leads to an effective attraction in the step-step interaction strength measurements. We show that this effective attraction can be incorporated into the fermion picture as a finite-size effect.