  We investigate tunneling in metal-insulator-metal junctions employing few
atomic layers of hexagonal boron nitride (hBN) as the insulating barrier. While
the low-bias tunnel resistance increases nearly exponentially with barrier
thickness, subtle features are seen in the current-voltage curves, indicating
marked influence of the intrinsic defects present in the hBN insulator on the
tunneling transport. In particular, single electron charging events are
observed, which are more evident in thicker-barrier devices where direct
tunneling is substantially low. Furthermore, we find that annealing the devices
modifies the defect states and hence the tunneling signatures.
