We analyze the influence of the surface passivation produced by oxides on the superconducting properties of $gamma$-Mo$_2$N ultra-thin films. The superconducting critical temperature of thin films grown directly on Si (100) with those using a buffer and a capping layer of AlN are compared. The results show that the cover layer avoids the presence of surface oxides, maximizing the superconducting critical temperature for films with thicknesses of a few nanometers. We characterize the flux-flow instability measuring current-voltage curves in a 6.4 nm thick Mo$_2$N film with a superconducting critical temperature of 6.4 K. The data is analyzed using the Larkin and Ovchinnikov model. Considering self-heating effects due to finite heat removal from the substrate, we determine a fast quasiparticle relaxation time $approx$ 45 ps. This value is promising for its applications in single-photon detectors.
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