  GaN is a key material for lighting technology. Yet, the carrier transport and
ultrafast dynamics that are central in GaN light emitting devices are not
completely understood. We present first-principles calculations of carrier
dynamics in GaN, focusing on electron-phonon (e-ph) scattering and the cooling
and nanoscale dynamics of hot carriers. We find that e-ph scattering is
significantly faster for holes compared to electrons, and that for hot carriers
with an initial 0.5$-$1 eV excess energy, holes take a significantly shorter
time ($\sim$0.1 ps) to relax to the band edge compared to electrons, which take
$\sim$1 ps. The asymmetry in the hot carrier dynamics is shown to originate
from the valence band degeneracy, the heavier effective mass of holes compared
to electrons, and the details of the coupling to different phonon modes in the
valence and conduction bands. We show that the slow cooling of hot electrons
and their long ballistic mean free paths (over 3 nm) are a possible cause of
efficiency droop in GaN light emitting diodes. Taken together, our work sheds
light on the ultrafast dynamics of hot carriers in GaN and the nanoscale origin
of efficiency droop.
