Theoretical investigation of the surface vibrational modes in germanium nanocrystals

We have used a microscopic lattice dynamical model to study phonon modes in germanium (Ge) NC with size varying between 47 to 7289 atoms (diametersimilar to6.8 nm). By separating these atoms into bulk and surface atoms we have found that surface modes can exist in Ge NC both at low frequencies (<50 cm(-1)) and at high frequency (similar to260 cm(-1)). The latter mode is a resonant mode which occurs in the "pseudogap" between the acoustic and optical phonon branches in bulk Ge. From the low frequency surface modes we have been able to reconstruct the spheroidal and torsional Lamb modes which have been used to interpret experimental results. Finally, we found that the Lamb model starts to deviate from the lattice dynamical results for Ge NC with diameter <4 nm and breaks down for NC smaller than 3 nm.