  For most optoelectronic applications of graphene a thorough understanding of
the processes that govern energy relaxation of photoexcited carriers is
essential. The ultrafast energy relaxation in graphene occurs through two
competing pathways: carrier-carrier scattering -- creating an elevated carrier
temperature -- and optical phonon emission. At present, it is not clear what
determines the dominating relaxation pathway. Here we reach a unifying picture
of the ultrafast energy relaxation by investigating the terahertz
photoconductivity, while varying the Fermi energy, photon energy, and fluence
over a wide range. We find that sufficiently low fluence ($\lesssim$ 4
$\mu$J/cm$^2$) in conjunction with sufficiently high Fermi energy ($\gtrsim$
0.1 eV) gives rise to energy relaxation that is dominated by carrier-carrier
scattering, which leads to efficient carrier heating. Upon increasing the
fluence or decreasing the Fermi energy, the carrier heating efficiency
decreases, presumably due to energy relaxation that becomes increasingly
dominated by phonon emission. Carrier heating through carrier-carrier
scattering accounts for the negative photoconductivity for doped graphene
observed at terahertz frequencies. We present a simple model that reproduces
the data for a wide range of Fermi levels and excitation energies, and allows
us to qualitatively assess how the branching ratio between the two distinct
relaxation pathways depends on excitation fluence and Fermi energy.
