# Interplay of Quantum Size Effect and Tensile Strain on Surface Morphology of β‑Sn(100) Islands

## TL;DR

This study explores how quantum size effects and strain influence the surface patterns of tin islands grown on a silicon carbide substrate.

## Contribution

The paper reveals an inverse surface roughness effect due to the interplay of quantum size effects and tensile strain in β-Sn(100) islands.

## Key findings

- β-Sn(100) islands with thickness N ≤ 10 have flat surfaces.
- For N ≥ 26, surfaces become corrugated and patterned.
- Intermediate thicknesses show coexisting flat and patterned surfaces with oscillating pattern coverage.

## Abstract

The quantum size
effect (QSE) and strain effect are two
key factors
influencing the surface morphology of thin films, which can increase
film surface roughness through QSE-induced thickness oscillation and
strain-induced island formation, respectively. Surface roughness usually
manifests in the early stages of film growth and diminishes beyond
a critical thickness. In this work, we employ molecular beam epitaxy
(MBE) to grow β-Sn(100) islands with varying thickness N on bilayer graphene-terminated 6H-SiC(0001) substrates.
Scanning tunneling microscopy and spectroscopy measurements reveal
an inverse surface roughness effect that highlights the interplay
of QSE and misfit strain in shaping the surface morphology of β-Sn(100)
islands. For N ≤ 10, the islands exhibit flat
surfaces, while for N ≥ 26, the island surfaces
become corrugated and patterned. For the intermediate range, i.e.,
12 ≤ N ≤ 24, both flat and patterned
surfaces coexist, with the percentage coverage of the patterned surface
oscillating as a function of N. By performing density
functional theory calculations, we demonstrate that the unusual surface
pattern evolution in our MBE-grown β-Sn(100) islands is a result
of the interplay between QSE-induced surface roughing and tensile
strain-induced smoothening effect.