  Integrated quantum photonics, which allows for the development and
implementation of chip-scale devices, is recognized as a key enabling
technology on the road towards scalable quantum networking schemes. However,
many state-of-the-art integrated quantum photonics demonstrations still require
the coupling of light to external photodetectors. On-chip silicon single-photon
avalanche diodes (SPADs) provide a viable solution as they can be seamlessly
integrated with photonic components, and operated with high efficiencies and
low dark counts at temperatures achievable with thermoelectric cooling.
Moreover, they are useful in applications such as LIDAR and low-light imaging.
In this paper, we report the design and simulation of silicon waveguide-based
SPADs on a silicon-on-insulator platform for visible wavelengths, focusing on
two device families with different doping configurations: p-n+ and p-i-n+. We
calculate the photon detection efficiency (PDE) and timing jitter at an input
wavelength of 640 nm by simulating the avalanche process using a 2D Monte Carlo
method, as well as the dark count rate (DCR) at 243 K and 300 K. For our
simulated parameters, the optimal p-i-n+ SPADs show the best device
performance, with a saturated PDE of 52.4 +/- 0.6% at a reverse bias voltage of
31.5 V, full-width-half-max (FWHM) timing jitter of 10 ps, and a DCR of < 5
counts per second at 243 K.
