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

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 <i>N</i> 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 <i>N</i> ≤ 10, the islands exhibit flat surfaces, while for <i>N</i> ≥ 26, the island surfaces become corrugated and patterned. For the intermediate range, i.e., 12 ≤ <i>N</i> ≤ 24, both flat and patterned surfaces coexist, with the percentage coverage of the patterned surface oscillating as a function of <i>N</i>. 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.