We report on $\mathrm{Mo}$-$\mathrm{Si}$-based superconducting nanowire single-photon detectors on a gallium arsenide substrate. $\mathrm{Mo}$-$\mathrm{Si}$ deposited on a passivated $\mathrm{Ga}\mathrm{As}$ surface has the same critical temperature as $\mathrm{Mo}$-$\mathrm{Si}$ deposited on silicon. The critical temperature decreases slightly on depositing $\mathrm{Mo}$-$\mathrm{Si}$ directly on the native oxide of $\mathrm{Ga}\mathrm{As}$. Hence, $\mathrm{Mo}$-$\mathrm{Si}$ works well as a thin-film superconductor on $\mathrm{Ga}\mathrm{As}$. We propose that the amorphous structure of $\mathrm{Mo}$-$\mathrm{Si}$ ensures compatibility with the $\mathrm{Ga}\mathrm{As}$ matrix. Superconducting nanowire single-photon detectors (SNSPDs) are fabricated with $\mathrm{Mo}$-$\mathrm{Si}$ on $\mathrm{Ga}\mathrm{As}$ using a meander-wire design. The SNSPD metrics are very similar to those of devices fabricated with the same procedure on a silicon substrate. We observe a plateau in the response-versus-bias curve, signaling a saturated internal quantum efficiency. The plateau remains even at an elevated temperature, 2.2 K, at a wavelength of 980 nm. We achieve a timing jitter of 50 ps and a recovery time of 29 ns. These results point to the promise of integrating $\mathrm{Mo}$-$\mathrm{Si}$ SNSPDs with $\mathrm{Ga}\mathrm{As}$ photonic circuits.
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