We theoretically study the inelastic scattering rate and the carrier mean free path for energetic hot electrons in graphene, including both electron-electron and electron-phonon interactions. Taking account of optical phonon emission and electron-electron scattering, we find that the inelastic scattering time $tau sim 10^{-2}-10^{-1} mathrm{ps}$ and the mean free path $l sim 10-10^2 mathrm{nm}$ for electron densities $n = 10^{12}-10^{13} mathrm{cm}^{-2}$. In particular, we find that the mean free path exhibits a finite jump at the phonon energy $200 mathrm{meV}$ due to electron-phonon interaction. Our results are directly applicable to device structures where ballistic transport is relevant with inelastic scattering dominating over elastic scattering.
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