Kinetic modelling of epitaxial film growth with up- and downward step barriers

TL;DR

This paper introduces a generalized kinetic model for epitaxial film growth that accounts for particle coordination-dependent barriers, resulting in stable mound formation and consistent roughening behavior across temperatures.

Contribution

It extends existing models by incorporating coordination-dependent barriers, avoiding spurious morphologies, and providing a more accurate description of epitaxial growth dynamics.

Findings

Standard models produce unstable morphologies with step barriers.

The new model yields stable, well-formed mounded structures.

Surface roughness and correlation length follow power-law scaling with exponents ~0.31 and ~0.22.

Abstract

The formation of three-dimensional structures during the epitaxial growth of films is associated to the reflection of diffusing particles in descending terraces due to the presence of the so-called Ehrlich-Schwoebel (ES) barrier. We generalize this concept in a solid-on-solid growth model, in which a barrier dependent on the particle coordination (number of lateral bonds) exists whenever the particle performs an interlayer diffusion. The rules do not distinguish explicitly if the particle is executing a descending or an ascending interlayer diffusion. We show that the usual model, with a step barrier in descending steps, produces spurious, columnar, and highly unstable morphologies if the growth temperature is varied in a usual range of mound formation experiments. Our model generates well-behaved mounded morphologies for the same ES barriers that produce anomalous morphologies in the standard model. Moreover, mounds are also obtained when the step barrier has an equal value for all particles independently if they are free or bonded. Kinetic roughening is observed at long times, when the surface roughness w and the characteristic length $\xi$ scale as $w ~ t^\beta$ and $\xi ~ t^\zeta$ where $\beta \approx 0.31$ and $\zeta \approx 0.22$, independently of the growth temperature.