  Sandwich-type MgB2 Josephson tunnel junctions (MgB2/AlOx/MgB2) have been
fabricated using as-grown MgB2 films formed by molecular beam epitaxy. The
junctions exhibited substantial supercurrent and a well-defined superconducting
gap (D=2.2~2.3mV). The superconducting gap voltage (D) agrees well with those
of the smaller gap in the multi-gap scenario. The IcRN product is 0.4-1.3 mV at
4.2K, but approaches to 2.0 mV at 50 mK. The Ic has peculiar temperature
dependence far from the Ambegaokar-Baratoff formula. It rapidly decreases with
temperature, and disappears above T = 20 K, which is much lower than the gap
closing temperature. Interface microstructure between AlOx and MgB2 were
investigated using cross-sectional transmission electron microscopy to clarify
the problems in our tunnel junctions. There are poor-crystalline MgB2 layers
and/or amorphous Mg-B composite layers of a few nanometers between AlOx barrier
and the upper MgB2 layer. The poor-crystalline upper Mg-B layers seem to behave
as normal metal or deteriorated superconducting layers, which may be the
principal reason for all non-idealities of our MgB2/AlOx/MgB2 junctions.
