  A formally exact expression for the tunneling current, for its separation
into specular and diffuse components, and for its directionality, is given for
a thick tunnel junction with rough interfaces in terms of the properties of
appropriately defined scattering amplitudes. An approximate evaluation yields
the relative magnitudes of the specular and diffuse components, and the angular
dependence of the diffuse component, in terms of certain statistical properties
of the junction interfaces.
