Defects in h-BN tunnel barrier for local electrostatic probing of two dimensional materials.

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/$\sqrt Hz$.