The one dimensional density-of-states (DOS) in the inversion layers of MOSFETs with ultra-thin gate oxides is known to broaden in energy due to gate leakage. The existing self-consistent formulation does not take the: effects of this broadening into account. We have calculated the DOS as functions of energy and position. It is shown that if the energy broadening of the inversion layer states are much smaller than the separation between the inversion layer eigenenergies, the DOS can be expressed as a product of an energy-dependent and a position-dependent function. This provides the justification for the use of the existing formulation in devices where the broadening is not negligible and it becomes unnecessary to explicitly incorporate the broadening into the model. We also estimate the lifetimes of the quasi-bound inversion layer states from the calculated resonance widths. We find that the lifetimes of the higher energy states, instead of saturating, begins to increase with increasing energy. A. qualitative explanation for this unusual behavior is also provided.