  Carrier multiplication (CM), where the absorption of a single photon results
in the generation of several electron-hole pairs via impact ionization, plays a
pivotal role in the quest for enhancing the performance of solar cells beyond
the Shockley-Queisser limit. The combination of its narrow bandgap relative to
the photon energy of visible light, along with its low phonon frequencies that
hinder efficient energy dissipation into phonons, makes the topological
insulator Bi$_2$Se$_3$ an optimal candidate material for efficient CM. Here we
use time- and angle-resolved photoemission spectroscopy (trARPES) to trace the
number of electron-hole pairs after photoexcitation of Bi$_2$Se$_3$ with
visible pump pulses at $\hbar\omega=2$ eV. We find that both the number of
electrons inside the conduction band as well as the number of holes inside the
valence band keep increasing long after the pump pulse is gone, providing
direct evidence for CM. We also analyze the transient band structure as well as
the hot carrier dynamics inside the conduction band, providing a complete
picture of the non-equilibrium carrier dynamics in photoexcited Bi$_2$Se$_3$
which can now serve as a basis for novel optoelectronic applications.
