  The requirements in quantum optics experiments for high single photon
detection efficiency, low timing jitter, low dark count rate and short dead
time have been fulfilled with the development of superconducting nanowire
single photon detectors. Although they offer a detection efficiency above 90%,
achieving a high time resolution in devices made of amorphous materials is a
challenge, particularly at temperatures above 0.8 K. Devices made from niobium
nitride and niobium titanium nitride allow to reach the best timing jitter, but
in turn have stronger requirements in terms of film quality to achieve a high
efficiency. Here we take advantage of the flexibility of reactive co-sputter
deposition to tailor the composition of NbxTi1-xN superconducting films, and
show that a Nb fraction of x = 0.62 allows for the fabrication of detectors
from films as thick as 9 nm and covering an active area of 20 {\mu}m, with a
wide detection saturation plateau at telecom wavelengths and in particular at
1550 nm. This is a signature of an internal detection efficiency saturation,
achieved while maintaining the high time resolution associated with NbTiN and
operation at 2.5K. With our optimized recipe, we reliably fabricated detectors
with high critical current densities reaching a saturation plateau at 1550 nm
with 80% system detection efficiency, and with a FWHM timing jitter as low as
19.47 ps.
