Ellipsometric measurements of thin CVD Si3N4 films deposited on Si reveal a graded composition of silicon oxynitride with increasing oxygen content as the Si-Si3N4 interface is approached. Measurements of steady-state dark currents, injected into Si 3N4 from negatively biased Al contacts at constant average field, Eav=Vτ-1=6 MV/cm, have been fitted to an empirical relation, J=J0 exp(τ0/τ), where τ is the film thickness and τ0=1039 Å. Increased film conductivity with decreasing thickness τ is attributed to diminished electron trapping as τ approaches the centroid of trapped charge, δ∼100 Å.