Electronic properties of germanium quantum films

The electronic band structures of hydrogen-terminated freestanding nanometer size (0.5--2.4 nm) germanium films have been calculated from first principles for three main low-index orientations. A quantum confinement-induced direct band gap appears for (100) and (111) oriented films, whereas the (110) oriented films are characterized by an indirect band gap. For the same film thickness there is an anisotropy in the fundamental band gap Eg with respect to the film orientation, e.g., Eg〈111〉<Eg〈110〉<Eg〈100〉. This is explained in terms of electron effective mass anisotropy. The thickness dependence of the band gap is investigated and the results are fitted to an empirical expression. We find that the band-gap blueshift is determined by the quantum confinement in both valence and conduction bands.