Computational modeling of the size effects on the optical vibrational modes of H-terminated Ge nanostructures

The vibrational dispersion relations of porous germanium (pGe) and germanium nanowires (GeNWs) were calculated using the ab initio density functional perturbation theory with a generalized gradient approximation with norm-conserving pseudopotentials. Both pores and nanowires were modeled using the supercell technique. All of the surface dangling bonds were saturated with hydrogen atoms. To address the difference in the confinement between the pores and the nanowires, we calculated the vibrational density of states of the two materials. The results indicate that there is a slight shift in the highest optical mode of the Ge-Ge vibration interval in all of the nanostructures due to the phonon confinement effects. The GeNWs exhibit a reduced phonon confinement compared with the porous Ge due to the mixed Ge-dihydride vibrational modes around the maximum bulk Ge optical mode of approximately 300 cm⁻¹; however, the general effects of such confinements could still be noticed, such as the shift to lower frequencies of the highest optical mode belonging to the Ge vibrations.