We study the homogeneously disordered MoC thin films with thicknesses of 10 and 5 nm and the superconducting transition temperatures near 6 and 4 K, significantly decreased as compared to the bulk T_{c}=8.32 K due to a disorder. The scanning tunnelling spectroscopy reveals in the thicker sample a BCS superconducting energy gap Δ with a broadening parameter Γ equal to about 10 per cent of Δ. Remarkably, Γ increases with temperature. The thinner, more disordered sample shows a gapped superconducting density of states but without any coherence peaks at the gap edge, which could not be approximated by the BCS DOS. Moreover, the reduced DOS around the Fermi level persists above the resistive transition temperature reminding the pseudo-gap known from high-T_{c} cuprates.
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