The One Phonon Raman Spectrum of Silicon Nanostructures

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 [001] 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.

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“…The p-Ge is modeled by means of the supercell technique, in which columns of Ge atoms are removed along the [001] direction [ 15 ]. In Fig.…”

Section: Resultsmentioning

confidence: 99%

Theory of Raman Scattering by Phonons in Germanium Nanostructures

2007

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“…The use of supercells with periodic boundary conditions in the three directions creates foldings of the first Brillouin zone and then there are several active Raman modes at the G point. 19 The highest frequency of first-order Raman peaks (u R ) is plotted as a function of the porosity in Fig. 2 for ordered square pores of Si (orange open squares) and Ge (green dotted squares) in a supercell of 648 atoms, while its shift (Du h u 0 À u R ) with respect to the crystalline case (u 0 ), being u 0 ¼ u Si or u Ge , is shown in the inset (b) of Fig.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…An additional weighting function of exp(À|u À u 0 |/x) with u 0 ¼ 497 cm À1 and x ¼ 13 cm À1 is considered to eliminate spurious Raman peaks at lower energies due to the use of the supercell technique, since the artificial periodic boundary condition (absent in the real samples) leads to the appearance of many active Raman modes at the G point as a consequence of the folding processes of the first phonon Brillouin zone in the reciprocal space. 19 In other words, in a porous sample the phonon momentum selection rule is relaxed due to the topological disorder and confinement effects, i.e. the complete Brillouin zone could be active for the Raman scattering.…”

Section: Measured Raman Spectramentioning

confidence: 99%

Raman scattering by confined optical phonons in Si and Ge nanostructures

et al. 2011

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A microscopic theory of the Raman scattering based on the local bond-polarizability model is presented and applied to the analysis of phonon confinement in porous silicon and porous germanium, as well as nanowire structures. Within the linear response approximation, the Raman shift intensity is calculated by means of the displacement-displacement Green's function and the Born model, including central and non-central interatomic forces. For the porous case, the supercell method is used and ordered pores are produced by removing columns of Si or Ge atoms from their crystalline structures. This microscopic theory predicts a remarkable shift of the highest-frequency of first-order Raman peaks towards lower energies, in comparison with the crystalline case. This shift is discussed within the quantum confinement framework and quantitatively compared with the experimental results obtained from porous silicon samples, which were produced by anodizing p--type (001)-oriented crystalline Si wafers in a hydrofluoric acid bath.

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