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

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 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 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 Sn(100) islands is a result of the interplay between QSE-induced surface roughing and tensile strain-induced smoothening effect.