Indirect to direct gap transition in low-dimensional nanostructures of Silicon and Germanium

The electronic band structures of Si and Ge low-dimensional nanostructure such as nanofilms and nanowires have been calculated using first principles based on density functional theory (DFT) with the generalized gradient approximation (GGA). The calculation results show that a direct band gap can be obtained from Si orientation [100] or in Ge orientation [111] confined low dimensional nanostructure. However, an indirect band gap is still kept in the Si orientation [111] or in the Ge orientation [110] confined low dimensional nanostructure. The calculation results are interesting and the transition mechanism from indirect to direct band gap in low dimensional nanostructures is given in the physical structures model.