  In view of the extensive use of hexagonal boron nitride (hBN) in 2D material
electronics, it becomes important to refine its dielectric characterization in
terms of low-field permittivity and high-field strength and conductivity up to
the breakdown voltage. The present study aims at filling this gap using DC and
RF transport in two Au-hBN-Au capacitor series of variable thickness in the
10--100 nm range, made of large high-pressure, high-temperature (HPHT) crystals
and a polymer derivative ceramics (PDC) crystals. We deduce an out-of-plane low
field dielectric constant $\epsilon_\parallel=3.4\pm0.2$ consistent with the
theoretical prediction of Ohba et al., that narrows down the generally accepted
window $\epsilon_\parallel=3$--$4$. The DC-current leakage at high-field is
found to obey the Frenkel-Pool law for thermally-activated trap-assisted
electron transport with a dynamic dielectric constant
$\epsilon_\parallel\simeq3.1$ and a trap energy $\Phi_B\simeq1.3\;\mathrm{eV}$,
that is comparable with standard technologically relevant dielectrics.
