  Sub-micron-thick layers of hexagonal boron nitride (hBN) exhibit high
in-plane thermal conductivity and useful optical properties, and serve as
dielectric encapsulation layers with low electrostatic inhomogeneity for
graphene devices. Despite the promising applications of hBN as a heat spreader,
the cross-plane phonon mean free paths in hBN have not been measured. We
measure the cross-plane thermal conductivity of hBN flakes exfoliated from bulk
crystals. We find that the thermal conductivity is extremely sensitive to film
thickness. We measure a forty-fold increase in the cross-plane thermal
conductivity between 7 nm and 585 nm flakes at 285 {\deg}K. We attribute the
large increase in thermal conductivity with increasing thickness to
contributions from phonons with long mean free paths (MFPs), spanning many
hundreds of nanometers in the thickest flakes. When planar twist interfaces are
introduced into the crystal by mechanically stacking multiple thin flakes, the
cross-plane thermal conductivity of the stack is found to be a factor of seven
below that of individual flakes with similar total thickness, thus providing
strong evidence that phonon scattering at twist boundaries limits the maximum
phonon MFPs. These results improve our understanding of thermal transport in
two-dimensional materials and have important implications for hBN integration
in nanoelectronics.
