  Graphene demonstrated potential for practical applications owing to its
excellent electronic and thermal properties. Typical graphene field-effect
transistors and interconnects built on conventional SiO2/Si substrates reveal
the breakdown current density on the order of 1 uA/nm2 (i.e. 10^8 A/cm2) which
is ~100\times larger than the fundamental limit for the metals but still
smaller than the maximum achieved in carbon nanotubes. We show that by
replacing SiO2 with synthetic diamond one can substantially increase the
current-carrying capacity of graphene to as high as ~18 uA/nm2 even at ambient
conditions. Our results indicate that graphene's current-induced breakdown is
thermally activated. We also found that the current carrying capacity of
graphene can be improved not only on the single-crystal diamond substrates but
also on an inexpensive ultrananocrystalline diamond, which can be produced in a
process compatible with a conventional Si technology. The latter was attributed
to the decreased thermal resistance of the ultrananocrystalline diamond layer
at elevated temperatures. The obtained results are important for graphene's
applications in high-frequency transistors, interconnects, transparent
electrodes and can lead to the new planar sp2-on-sp3 carbon-on-carbon
technology.
