RAMAN SPECTROSCOPY Scattering mechanisms Random motions Vibrations Rotations Rayleigh Mie Raman - local modes, vibrations, rotations Brillouin - collective modes (sound) Elastic

Raman scattering Detects normal modes Fingerprint of bonds (elements) Vibrations or rotations in gases or liquids Phonon modes in solids Fingerprint of bonds (elements) Sensitive to State of matter, crystalline or amorphous Defects Particle size Temperature …. Experimental: narrow laser line + good spectrometer

Raman lines of semiconductors

Raman scattering Interaction between applied field and normal modes Applied optical field: Induces polarization Polarizability Vibrations: Displacement Raman active modes: Small amplitudes -e +e

Raman Lines Polarization Momentum sele ction rule: k₀ - k  q +G=0 Only transitions at q=0

Selection rules – Raman active modes: Polarizability ellipsoids of molecule. is Raman active: the polarizability is different at the two extremes. On the other hand and are not Raman active.

Raman scattering from Si nanocrystals Bonds in Si (Diamond structure) S1: Vibrational frequencies (0.1 eV) S2: Optical frequencies (3.4 eV)

Raman spectrum of Si

Phonons in bulk Si Experiments: Neutron scattering

Size effects in phonon modes Well-known for thin films 0-D systems: No band gap in amorphous matrix - reduce confinement effects Fluctuations in size, shape, and orientation Effect on Raman spectrum: Shift of peak Broadening of line selection rule lifted -

Raman spectrum Faraci et al. PRB 73, 033307 (2006)

Confinement function Decays towards edge of nanocrystal

Calculating spectrum

Calculated spectra Large shift with size Asymmetric shape of spectrum

Comparison to experiments

Bond charge model

Bond charge model

Transition from amorphous to nano crystalline Si film Yue, Appl. Phys. Lett., 75, 492 (1999) PECVD deposition at 230˚C on glass PL spectra: a-Si at 1.3 eV c-Si at 0.9 eV

Temperature dependence Si nc’s on graphite. Shift of Stokes and Anti Stokes lines. Ratio between Stokes and Anti Stokes determine temperature Faraci et al. PRB 80 193410 (2009)

Raman spectroscopy on carbon nanotubes Jung, Bork, Holmgaard, Kortbek 8th semester report 𝐶 ℎ =𝑛 𝑎 1 +𝑚 𝑎 2 (n,m) tube

Metallic and semiconducting tubes

Radial and transverse modes

Radial breadingmodes

Conclusions Raman spectroscopy Elemental specific optical technique Fast and reliable Distinguish crystalline and amorphous phases Size sensitive for nc’s ~1-10 nm