  Fluidic devices exhibiting ion current rectification (ICR), or ionic diodes,
are of broad interest for applications including desalination, energy
harvesting, and sensing, amongst others. For such applications a large
conductance is desirable which can be achieved by simultaneously using thin
membranes and wide pores. In this paper we demonstrate ICR in micron sized
conical channels in a thin silicon membrane with pore diameters comparable to
the membrane thickness but both much larger than the electrolyte screening
length. We show that for these pores the entrance resistance is not only key to
Ohmic conductance around 0 V, but also for understanding ICR, both of which we
measure experimentally and capture within a single analytic theoretical
framework. The only fit parameter in this theory is the membrane surface
potential, for which we find that it is voltage dependent and its value is
excessively large compared to literature. From this we infer that surface
charge outside the pore strongly contributes to the observed Ohmic conductance
and rectification by a different extent. We experimentally verify this
hypothesis in a small array of pores and find that ICR vanishes due to
pore-pore interactions mediated through the membrane surface, while Ohmic
conductance around 0 V remains unaffected. We find that the pore-pore
interaction for ICR is set by a long-ranged decay of the concentration which
explains the surprising finding that the ICR vanishes for even a sparsely
populated array with a pore-pore spacing as large as 7 $\mu$m.
