  Compared to traditional nonlinear optical crystals, like BaB$_2$O$_4$,
KTiOPO$_4$ or LiNbO$_3$, semiconductor integrated sources of photon pairs may
operate at pump wavelengths much closer to the bandgap of the materials. This
is also the case for Bragg-reflection waveguides (BRW) targeting parametric
down-conversion (PDC) to the telecom C-band. The large nonlinear coefficient of
the AlGaAs alloy and the strong confinement of the light enable extremely
bright integrated photon pair sources. However, under certain circumstances, a
significant amount of detrimental broadband photoluminescence has been observed
in BRWs. We show that this is mainly a result of linear absorption near the
core and subsequent radiative recombination of electron-hole pairs at deep
impurity levels in the semiconductor. For PDC with BRWs, we conclude that
devices operating near the long wavelength end of the S-band or the short
C-band require temporal filtering shorter than 1 ns. We predict that shifting
the operating wavelengths to the L-band and making small adjustments in the
material composition will reduce the amount of photoluminescence to negligible
values. Such measures enable us to increase the average pump power and/or the
repetition rate, which makes integrated photon pair sources with on-chip
multi-gigahertz pair rates feasible.
