# How to find out the temperature of phonons using the Raman anti-Stokes and Stoke intensities ratio?

Basically the title, the concept is simple, but I`m having a hard time trying to9 find an explicit solution.

New contributor
Pedro is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
• have you done some preliminary calculations or given some thoughts to this problem, or do you just want a formula? – ZeroTheHero Dec 8 at 20:02

## 1 Answer

The Stokes signal intensity $$I_S \propto n+1$$, while the anti-Stokes intensity $$I_A \propto n$$, where $$n$$ is the phonon population following the Bose-Einstein distribution, and the constants of proportionality are the same. $$n = \frac{1}{e^{\epsilon/kT}-1}$$ Here, $$\epsilon$$ is the energy of the phonon (= $$h c$$ times measured wavenumber), and $$k$$ is the Boltzmann constant. I will leave it as an exercise for the reader to determine $$T$$ from $$I_S/I_A$$.