An analytical form for the Raman shift dependence on size of nanocrystals

SALIS, MARCELLO;RICCI, PIER CARLO;ANEDDA, ALBERTO

2009-01-01

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Abstract

An analytical form of the Raman shift dependence on the size of nanocrystals is presented. On the basis of the hard confinement model, this form describes the deviations from Raman shifts in infinite crystals as Δω = π2A[1 - exp(-η)] /12x2η2, where η = L/12ax and x = (A/Γ0)1/2, L standing for the crystal size, Γ0 for the intrinsic band linewidth, a for the lattice parameter and A for a suitable phonon curve parameter. It works in those cases where the average phonon curve shows a quadratic dependence on the phonon quasi-momentum in the range of interest.