Trilayer tunneling structures consisting of cuprate electrodes and tit
anate barriers were grown by atomic layer-by-layer molecular beam; epi
taxy and processed into c-axis transport samples. Barriers of SrTiO3 a
nd related titanates with thicknesses ranging from 4 Angstrom to 28 An
gstrom (one to seven unit cells of the titanate) were grown. While no
supercurrent was observed for even the thinnest barrier, the zero bias
resistance was an exponential function of barrier thickness for sampl
es with five or fewer titanate unit cell barriers, indicating tunnelin
g transport. Each additional titanate unit cell caused the zero bias r
esistance to increase by one order of magnitude. A detailed investigat
ion of the properties of the cuprate layers immediately adjacent to th
e titanate layers revealed that they were depleted of charge carriers
and exhibited variable range hopping transport. Thus the electron stat
es in these layers were localized. The trilayer transport process is m
odeled as one phonon assisted tunneling between localized states.