  We used density-functional theory based first principles simulations to study
the effects of uniaxial strain and quantum confinement on the electronic
properties of germanium nanowires along the [110] direction, such as the energy
gap and the effective masses of the electron and hole. The diameters of the
nanowires being studied are up to 50 {\AA}. As shown in our calculations, the
Ge [110] nanowires possess a direct band gap, in contrast to the nature of an
indirect band gap in bulk. We discovered that the band gap and the effective
masses of charge carries can be modulated by applying uniaxial strain to the
nanowires. These strain modulations are size-dependent. For a smaller wire (~
12 {\AA}), the band gap is almost a linear function of strain; compressive
strain increases the gap while tensile strain reduces the gap. For a larger
wire (20 {\AA} - 50 {\AA}), the variation of the band gap with respect to
strain shows nearly parabolic behavior: compressive strain beyond -1% also
reduces the gap. In addition, our studies showed that strain affects effective
masses of the electron and hole very differently. The effective mass of the
hole increases with a tensile strain while the effective mass of the electron
increases with a compressive strain. Our results suggested both strain and size
can be used to tune the band structures of nanowires, which may help in design
of future nano-electronic devices. We also discussed our results by applying
the tight-binding model.
