  Recently, the in-plane thermal transport in van der Waals (vdW) materials
such as graphene, hexagonal boron nitride (h-BN), and transition metal
dichalcogenides (TMDs) has been widely studied. Whereas, the cross-plane one is
far from sufficient. Based on the non-equilibrium molecular dynamics
simulations and Boltzmann transport equation, here we reveal the stacking and
thickness effects on the cross-plane thermal conductivity (K) of h-BN. We find
that K can be significantly modulated by both the stacking structure and
thickness (d) of h-BN, which is unexpected from the viewpoint of its smooth
in-plane structure and weak interlayer interaction. In the small thickness
region (d<6 nm), K of h-BN at room temperature significantly increases with
thickness, following a power law of K ~ d^b with b=0.84, 0.66, and 0.92 for
AA', AB, and AB' stacking structures, respectively. Moreover, K of AB'
structure reaches up to 60% larger than that of AA' and AB structures with
d=5.3 nm, showing the remarkable stacking effect. We also find that the
stacking effect on K changes dramatically with d increasing, where AA' stacking
has the largest K with d > 200 nm. We finally clarify that such exotic stacking
and thickness dependence of K is owing to the competing effect of excited
number of phonons and phonon relaxation time, both of which directly affect the
thermal conductivity. Our findings may provide new insights into the
cross-plane thermal management in vdW materials.
