  We have investigated the effects of ozone treatment on graphene by Raman
scattering. Sequential ozone short-exposure cycles resulted in increasing the
$p$ doping levels as inferred from the blue shift of the 2$D$ and $G$ peak
frequencies, without introducing significant disorder. The two-phonon 2$D$ and
2$D'$ Raman peak intensities show a significant decrease, while, on the
contrary, the one-phonon G Raman peak intensity remains constant for the whole
exposure process. The former reflects the dynamics of the photoexcited
electrons (holes) and, specifically, the increase of the electron-electron
scattering rate with doping. From the ratio of 2$D$ to 2$D$ intensities, which
remains constant with doping, we could extract the ratio of electron-phonon
coupling parameters. This ratio is found independent on the number of layers up
to ten layers. Moreover, the rate of decrease of 2$D$ and 2$D'$ intensities
with doping was found to slowdown inversely proportional to the number of
graphene layers, revealing the increase of the electron-electron collision
probability.
