A simple solid-on-solid model of epitaxial thin films growth: surface roughness and dynamics

TL;DR

This paper presents a Monte Carlo simulation of epitaxial thin film growth incorporating surface diffusion barriers, revealing how these factors influence surface roughness and morphology, and confirming a power-law relationship between roughness and film thickness.

Contribution

It introduces an extended solid-on-solid model with Ehrlich-Schwoebel barriers to better simulate surface roughness and growth dynamics in epitaxial films, aligning simulations with experimental observations.

Findings

Surface roughness follows a power law with film thickness.

Ehrlich-Schwoebel barriers increase surface roughness and influence morphology.

Growth exponent β is approximately 0.2, affected by diffusion range and barriers.

Abstract

The random deposition model must be enriched to reflect the variety of surface roughness due to some material characteristics of the film growing by vacuum deposition or sputtering. The essence of the computer simulation in this case is to account for possible surface migration of atoms just after the deposition, in connection with binding energy between atoms (as the mechanism provoking the diffusion) and/or diffusion energy barrier. The interplay of these two factors leads to different morphologies of the growing surfaces from flat and smooth ones, to rough and spiky ones. In this paper we extended our earlier calculation by applying some extra diffusion barrier at the edges of terrace-like structures, known as Ehrlich-Schwoebel barrier. It is experimentally observed that atoms avoid descending when the terrace edge is approach and these barriers mimic this tendency. Results of our Monte Carlo computer simulations are discussed in terms of surface roughness, and compared with other model calculations and some experiments from literature. The power law of the surface roughness $\sigma$ against film thickness $t$ was confirmed. The nonzero minimum value of the growth exponent $\beta$ near 0.2 was obtained which is due to the limited range of the surface diffusion and the Ehrlich-Schwoebel barrier. Observations for different diffusion range are also discussed. The results are also confronted with some deterministic growth models.