On the Raman shift in nanosized crystals

TL;DR

This paper presents an analytical model describing how the Raman shift varies with the size of nanocrystals, based on the hard confinement model and phonon behavior.

Contribution

It introduces an analytical expression for the Raman shift dependence on nanocrystal size within the hard confinement framework.

Findings

Provides an explicit formula for Raman shift as a function of nanocrystal size.

Validates the model for cases with quadratic phonon dispersion.

Enhances understanding of size effects in nanoscale Raman spectroscopy.

Abstract

An analytical form of the Raman shift dependence on size of nanocrystals is presented. Based on the hard confinement model, it works in those cases where the average phonon curve shows a quadratic dependence on the phonon quasi-momentum in the range of interest.