  Excitons - the particle-hole bound states - composed of localized
electron-hole states in semiconducting systems are crucial to explaining the
optical spectrum. Spectroscopic measurements can contain signatures of these
two particle bound states and can be particularly useful in determining the
characteristics of these excitons. We formulate an expression for evaluating
the angle-resolved photoemission spectrum arising from the ionization of
excitons given their steady-state distribution in a semiconductor. We show that
the spectrum contains information about the direct/indirect band gap nature of
the semiconductor and is located below the conduction band minimum displaced by
the binding energy. The dispersive features of the spectrum contains remnants
of the valence band while additional interesting features arise from different
exciton distributions. Our results indicate that for most exciton probability
distributions, the energy integrated photoemission spectrum provides an
estimate of the exciton Bohr radius.
