  Defects in hexagonal boron nitride (h-BN) layer can facilitate tunneling
current through thick h-BN tunneling barriers. We have investigated such
current-mediating defects as local probes for materials in two dimensional
heterostructure stacks. Besides $IV$ characteristics and negative differential
conductance, we have characterized the electrical properties of h-BN defects in
vertical graphene-h-BN-Cr/Au tunnel junctions in terms of low frequency current
noise. Our results indicate a charge sensitivity of 1.5$\times$$ 10^-5$e/$\sqrt
Hz$ at 10 $Hz$, which is equal to good metallic single electron transistors.
The noise spectra at low frequency are governed by a few two-level fluctuators.
For variations in electrochemical potential, we achieve a sensitivity of
0.8$\mu$eV/$\sqrt Hz$.
