  The formation of a Schottky barrier at the interface between a metal and
hexagonal boron nitride (h-BN) is studied using density functional theory. For
metals whose work functions range from 4.2 to 6.0 eV, we find Schottky barrier
heights for holes between 1.2 and 2.3 eV. A central role in determining the
Schottky barrier height is played by a potential step of between 0.4 and 1.8 eV
that is formed at the metal|h-BN interface and effectively lowers the metal
work function. If h-BN is physisorbed, as is the case on fcc Cu, Al, Au, Ag and
Pt(111) substrates, the interface potential step is described well by a
universal function that depends only on the distance separating h-BN from the
metal surface. The interface potential step is largest when h-BN is
chemisorbed, which is the case for hcp Co and Ti (0001) and for fcc Ni and Pd
(111) substrates.
