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.