Raman theory of quantum wires. Evidence of ripples in Raman spectra of thin wall Si nanotubes

In the present paper we develop for the first time a general theory calculating the Raman spectrum of a quantum wire, using the phonon modes active in the wire. No Raman theory is at present available for quantum wires. In fact, to date only phenomenological models with arbitrary parameters, or unidimensional approaches have been published specifically for quantum dots. In our approach the confinement effects due to the reduced size are introduced directly by means of the Heisenberg Uncertainty Principle. The present theory, applied to silicon nanowires, permits the evaluation of Raman frequency shift and linewidth broadening as a function of the size. The results obtained by this model for Si nanowires are in close agreement with the few experimental data available in the literature. The model also shows evidence of ripples in the Raman spectra of thin wall Si nanotubes. This theory can be applied as well to any semiconductor of known phonon branches.