Electrical transport through molecular monolayers being very sensitive to disorder effects, admittance and current density characteristics of Hg//C12H25-n Si junctions incorporating covalently bonded n-alkyl molecular layers, were investigated at low temperature (150-300 K), in the as-grafted state and after ageing at the ambient. This comparison reveals local oxidation effects both at the submicron scale in the effective barrier height distribution and at the molecular scale in the dipolar relaxation. In the bias range dominated by thermionic emission and modified by the tunnel barrier (TB) attenuation, expd(-beta(0)d(T)), where d(T) is the thickness of the molecular tunnel barrier and beta(0) is the inverse attenuation length at zero applied bias, some excess current is attributed to a distribution of low barrier height patches. Complementary methods are used to analyze the current density J(V, T) characteristics of metal-insulator-semiconductor tunnel diodes. Assuming a Gaussian distribution of barrier heights centered at q Phi(B) provides an analytical expression of the effective barrier height, q Phi(EFF)(T) = q Phi(B) + (kT)beta(0)d(T) - (q delta Phi)(2)/2kT; this allows fitting of the distribution standard deviation delta Phi and tunnel parameter (beta(0)d(T)) over a wide temperature range. In a more realistic modeling including the voltage dependence of barrier height and circular patch area, the so-called "pinch-off" effect is described by a distribution of parameter gamma = 3(Delta R-P(P)2/4)(1/3), which combines interface potential modulation and patch area variations. An arbitrary distribution of gamma values, fitted to low-temperature J(V) data, is equally well described by Gaussian or exponential functions. Ageing in air also increases the interface oxidation of Si substrate and affects the density of localized states near mid gap, which typically rises to the high 10(11) eV(-1) cm(-2) range, as compared with D-S < 10(11) eV(-1) cm(-2) in the as-grafted state. The bias-independent relaxation observed near 1 kHz at low temperature may be attributed either to dipoles in the alkyl chain induced by the strong permanent dipoles of interface silicon oxide or to a local relaxation of water molecules trapped at the OML/silicon interface. The respective roles of SiO2 formation and water physisorption on the decrease of patch barrier height are also discussed. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767121]