Electronic devices using graphene and other two dimensional (2D) materials have shown interesting performances. However, the interaction of conductive and semiconducting 2D materials with traditional dielectrics (which are necessary to build up the devices) is still very poor (i.e. the fabrication is challenging and it generates abundant interface defects). Hexagonal Boron Nitride (h-BN) is a layered insulating material that could be used as dielectric stack in 2D materials based devices, as it shows excellent insulating ability and a perfect interaction with graphene and other 2D materials. Here we show the first device-level reliability study of h-BN dielectric stacks and describe the dielectric breakdown (BD) process.