  Measurements of current-voltage (I-V) characteristics of a high quality
Al/Al$_2$O$_3$/Al junction at temperatures ranging from 3.5 K to 300 K have
been used to extract the barrier properties. Fitting results using Simmons'
model led to a constant value of barrier width $s$$\sim$20.8~$\textrm{\AA}$ and
a continuous increase in the barrier height with decreasing temperature. The
latter is used to determine the energy band gap temperature dependence and
average phonon frequency $\omega$ = 2.05 $\times$ 10$^{13}$ sec$^{-1}$ in
Al$_2$O$_3$, which adds confidence to the precision of our measurements. The
barrier parameters are used to extract the temperature dependent dwell times in
tunneling ($\tau_D$ = 3.6 $\times$ 10$^{-16}$ sec at mid-barrier energies) and
locate resonances above the barrier.
