  A theoretical technique which allows to include contributions from
non-orthogonality of the electron states in the leads connected to a tunneling
junction is derived. The theory is applied to a single barrier tunneling
structure and a simple expression for the time-dependent tunneling current is
derived showing explicit dependence of the overlap. The overlap proves to be
necessary for a better quantitative description of the tunneling current, and
our theory reproduces experimental results substantially better compared to
standard approaches.
