  We study dynamics of incoherent exciton formation under interband
photoexcitation in Cu$_2$O using time-and angle-resolved photoemission
spectroscopy at 90 K. Hot electrons injected by allowed optical transitions
with 3.40-eV photons show ultrafast relaxation to the conduction-band minimum
(CBM), surviving up to 500 fs after excitation. While hot-electron states with
high excess energy show a rapid population decay of ~25 fs, an abrupt increase
to 130 fs is observed for states with excess energies of 0.15 eV. This latter
is interpreted in terms of phonon bottleneck dynamics characteristic of
LO-phonon mediated energy relaxation. Excitons, having a small binding energy
of 60 meV, are formed below the CBM quasi-instantaneously and subsequently
relax to the 1S-exciton state of the yellow series within 1.5 ps. We find that,
together with possible plasma screening for electron-hole interaction, the
cooling of exciton center-of-mass motion plays an important role in the exciton
relaxation dynamics. The characteristic features of exciton photoionization
process are critically discussed based on the detailed analysis of
angle-resolved photoemission results for the 1S excitons formed 1.5 ps after
excitation.
