1. Raman Spectroscopy

1. What can Raman spectroscopy tell you about the phonon dispersion relation of some material?

Solution

1. What can Raman spectroscopy tell you about the phonon dispersion relation of some material?

   With Raman spectroscopy only phonons can be measured which have a momentum transfer $q$ close to 0. The maximum allowed $k$-value for a scattered phonon is $q_{max} = 2\cdot k_{in}$ ($k_{in}$ is the incident wave vector). For visible laser light the wave vector $k = \frac{2 \pi}{\lambda}$ is in the rage of 10^-3Å^-1. Compared to the reciprocal distance between the Brillouin zone centre and boundary, this is close to $0$. So the only phonons that can be measured by means of Raman spectroscopy are phonons (very) close to $k = 0$. Those phonons only exist in the optical branch, since for acoustic phonons the energy would be zero for $k = 0$.

   

   Figure 1: Phonon dispersion relation. Highlighted is the part of the dispersion relation which can be measured by Raman spectroscopy.