  For many of the envisioned optoelectronic applications of graphene it is
crucial to understand the sub-picosecond carrier dynamics immediately following
photoexcitation, as well as the effect on the electrical conductivity - the
photoconductivity. Whereas these topics have been studied using various
ultrafast experiments and theoretical approaches, controversial and incomplete
explanations have been put forward concerning the sign of the
photoconductivity, the occurrence and significance of the creation of
additional electron-hole pairs, and, in particular, how the relevant processes
depend on Fermi energy. Here, we present a unified and intuitive physical
picture of the ultrafast carrier dynamics and the photoconductivity, combining
optical pump - terahertz probe measurements on a gate-tunable graphene device,
with numerical calculations using the Boltzmann equation. We distinguish two
types of ultrafast photo-induced carrier heating processes: At low
(equilibrium) Fermi energy ($E_{\rm F} \lesssim$ 0.1 eV for our experiments)
broadening of the carrier distribution involves interband transitions -
interband heating. At higher Fermi energy ($E_{\rm F} \gtrsim$ 0.15 eV)
broadening of the carrier distribution involves intraband transitions -
intraband heating. Under certain conditions, additional electron-hole pairs can
be created (carrier multiplication) for low $E_{\rm F}$, and hot carriers
(hot-carrier multiplication) for higher $E_{\rm F}$. The resultant
photoconductivity is positive (negative) for low (high) $E_{\rm F}$, which
originates from the effect of the heated carrier distributions on the screening
of impurities, consistent with the DC conductivity being mostly due to impurity
scattering. The importance of these insights is highlighted by a discussion of
the implications for graphene photodetector applications.
