Density Functional Theory Calculations Revealing Metal-like Band Structures for Ultrathin Germanium (111) and (211) Surface Layers

To find out if germanium possesses facet-dependent electrical-conductivity properties, surface-state density functional theory (DFT) calculations were performed on one to six layers of germanium (100), (110), (111), and (211) planes. Tunable Ge(100) and Ge(110) planes always present the same semiconducting band structure with a band gap of 0.67 eV expected of bulk germanium. In contrast, one, two, four, and five layers of Ge(111) and Ge(211) plane models show metal-like band structures with continuous density of states (DOS) throughout the entire band. For three and six layers of Ge(111) and Ge(211) plane models, the normal semiconducting band structure was obtained. The plane layers with metal-like band structures also show Ge-Ge bond-length deviations and bond distortions, as well as significantly different 4s and 4p frontier-orbital electron counts and relative percentages integrated over the valence and conduction bands from those of the semiconducting state. These differences should contribute to strikingly dissimilar band structures. The calculation results suggest the observation of facet-dependent electrical-conductivity properties of germanium materials; when making transistors from germanium, the facet effects with shrinking dimensions approaching 3 nm may also need to be considered.