The effect of a high current density on the measured admittance of ultrathin Metal-Insulator-Semiconductor (MIS) tunnel junctions is investigated to obtain a reliable energy distribution of the density, D-S(E), of defects localized at the semiconductor interface. The behavior of admittance Y(V, T, omega) and current density J(V, T) characteristics is illustrated by rectifying Hg//C12H25-Si junctions incorporating n-alkyl molecular layers (1.45 nm thick) covalently bonded to n-type Si(111). Modeling the forward bias admittance of a nonequilibrium tunnel junction reveals several regimes which can be observed either in C(omega approximate to 0) vs. (J) plots of the low frequency capacitance over six decades in current or in M ''(omega) plots of the electrical modulus over eight decades in frequency. At low current density, the response of interface states above mid-gap is unaffected and a good agreement is found between the interface states densities derived from the modeling of device response time tau(R)(V) and from the low-high frequency capacitance method valid for thick MIS devices; the low defect density near mid-gap (D-S < 10(11) eV(-1) cm(-2)) results from a good passivation of dangling bonds at the C12H25-n Si interface. In the high current density regime (J > 1 mA cm(-2)), the admittance depends strongly on both the density of localized states and the dc current density, so that the excess capacitance method overestimates D-S. For very high current densities > 10 mA cm(-2)), the observation of a linear C(omega approximate to 0) vs. (J) dependence could indicate some Fermi level pinning in a high interface density of states located near the Si conduction band. The temperature-independent excess capacitance C(omega approximate to 0) - C(1 MHz) observed at very small J, not predicted by the admittance model, is attributed to some dipolar relaxation in the molecular junction. (C) 2012 Elsevier Ltd. All rights reserved.