Slab Thickness Effects for the Clean and Adsorbed Ge(001) Surface with Comparison to Si(001)

Quantum confinement effects on the electronic structure of thin Ge(001) slabs with one clean and one H-terminated surface are discussed based on density functional theory calculations for periodic slabs. Recent work has shown that while the geometry of the clean Ge(001) surface is reliably reproduced by relatively thin asymmetric slabs, the associated electronic structure can be quite sensitive to the number of layers in the slab. Here we show that the changes in the character and energy of the states near the Fermi energy of such slabs are related to the description of the bulk states and the width of the valence band, both of which are sensitive to the thickness of the slabs. Calculations performed for an isolated H or Cl atom adsorbed on the surface of a Ge(001) slab show that the effect of bulk electron confinement within thin slabs significantly influences the geometries, electronic structures, and relative thermodynamic stability of the single-atom adsorbates and the associated reconstructed surface. By contrast, the corresponding Si(001) surface does not exhibit any significant slab thickness dependence. We believe that these differences are a direct consequence of the nature of the states in the vicinity of the Fermi energy. Our results highlight the importance of employing an appropriate number of layers in slab calculations of the Ge(001) surface and imply that the surface electronic properties of Ge(001) slabs may be manipulated by employing a thin film technology.