  Quantum repeaters - fundamental building blocks for long-distance quantum
communication - are based on the interaction between photons and quantum
memories. The photons must fulfil stringent requirements on central frequency,
spectral bandwidth and purity in order for this interaction to be efficient. We
present a design scheme for monolithically integrated resonant photon-pair
sources based on parametric down-conversion in nonlinear waveguides, which
facilitate the generation of such photons. We investigate the impact of
different design parameters on the performance of our source. The generated
photon spectral bandwidths can be varied between several tens of MHz up to
around $1\,$GHz, facilitating an efficient coupling to different memories. The
central frequency of the generated photons can be coarsely tuned by adjusting
the pump frequency, poling period and sample temperature and we identify
stability requirements on the pump laser and sample temperature that can be
readily fulfilled with off-the-shelve components. We find that our source is
capable of generating high-purity photons over a wide range of photon
bandwidths. Finally, the PDC emission can be frequency fine-tuned over several
GHz by simultaneously adjusting the sample temperature and pump frequency. We
conclude our study with demonstrating the adaptability of our source to
different quantum memories.
