Theory of Raman Scattering by Phonons in Germanium Nanostructures
1 Instituto Politécnico Nacional, ESIME-Culhuacan, Av. Santa Ana 1000, Mexico, 04430, DF, Mexico
2 Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apartado Postal 70-360, Mexico, 04510, DF, Mexico
Nanoscale Research Letters 2007, 3:55-59 doi:10.1007/s11671-007-9114-0Published: 21 December 2007
Within the linear response theory, a local bond-polarization model based on the displacement–displacement Green’s function and the Born potential including central and non-central interatomic forces is used to investigate the Raman response and the phonon band structure of Ge nanostructures. In particular, a supercell model is employed, in which along the  direction empty-column pores and nanowires are constructed preserving the crystalline Ge atomic structure. An advantage of this model is the interconnection between Ge nanocrystals in porous Ge and then, all the phonon states are delocalized. The results of both porous Ge and nanowires show a shift of the highest-energy Raman peak toward lower frequencies with respect to the Raman response of bulk crystalline Ge. This fact could be related to the confinement of phonons and is in good agreement with the experimental data. Finally, a detailed discussion of the dynamical matrix is given in the appendix section.