  Free-running InGaAs/InP single-photon detectors (SPDs) based on
negative-feedback avalanche diodes (NFADs) are the key components for
applications requiring asynchronous single-photon detection in the
near-infrared region. From the perspective of practical applications, the
features of SPDs in terms of high photon detection efficiency (PDE), low noise,
large sensitive area, and compactness are highly desired for system integration
and performance enhancement. Here, we present the implementation of a compact
four-channel multimode fiber coupling free-running InGaAs/InP SPD, with the
best overall performance to date. On the one hand, we design and fabricate
structure-optimized InGaAs/InP NFAD devices with 25 $\mu$m diameter active area
and integrated thin film resistors to enhance the maximum achievable PDE. On
the other hand, we apply a compact thermoacoustic cryocooler to regulate the
operating temperature of NFADs within a large range, and design a dedicated
readout circuit with minimized parasitic parameters and tunable settings of
hold-off time to suppress the afterpulsing effect. The SPD is then
characterized to achieve remarkable overall performance simultaneously at 1550
nm, i.e., 40% PDE, 2.3 kcps dark count rate, 8% afterpulse probability and 49
ps timing jitter (full width at half maximum) under the conditions of 5.9 V
excess bias voltage, 10 $\mu$s hold-off time and 213 K operation temperature.
Such performance and the results of the long-term stability tests indicate that
the SPD could be a favorable solution for practical applications.
