Resonant Raman study of phonon states in gas-evaporated Ge small particles

We have studied phonon states of Ge small particles by Raman scattering resonating with the ${\mathit{E}}_1$∼${\mathit{E}}_1$+${\mathrm{\Delta }}_1$ gaps. Those particles are prepared by evaporation in Ar gas atmosphere and their sizes range from about 2 through 30 nm. Since the electronic transition energy depends on the particle size as a result of confinement of the electron and hole in the particle, we can selectively excite the particle with a specific diameter by tuning the incident laser wavelength to match the transition energy. Thus we can study the size dependence of the phonon states with a good size resolution even if the particle size is distributed in a wide range in a sample. The Raman spectra consist of nonresonant broadbands and a sharp line whose frequency and width depend on the incident laser wavelength reflecting the resonance behavior. The Raman spectra have been analyzed by a model assuming the discrete value of wave vector for the confined phonon and relaxation of the momentum conservation in the scattering process. The diameter of the particle deduced from the analysis of the Raman spectra turns out to be roughly half the size expected from the resonance energy of the electronic excitation. This result is discussed in connection with the softening of the optical phonons in the small particle. The nonresonant broadbands are attributed to very small particles with their diameter of about 1 nm and/or to amorphous Ge coexisting with larger particles in the sample.