  We use numerical simulations to investigate the properties of metal contacts
to three-dimensional arrays of carbon nanotubes (CNTs). For undoped arrays
top-contacted with high or low work function metals, electrostatic screening is
very strong, resulting in a small Schottky barrier for current injection in the
top layer and large Schottky barriers for current injection in the deeper
layers. As a consequence, the majority of the current flows through the top
layer of the array. Our simulations show that doping of the CNT array can
alleviate this problem, even without direct contact to each tube in the array;
however, we find that the charge transfer length is unusually long in arrays
and increases with the number of CNT layers under the contact. We also show
that a bottom gate can modulate the contact resistance, but only very weakly.
These results are important for the design of electronic and optoelectronic
devices based on CNT arrays, because they suggest that increasing the thickness
of the array does little to improve the device performance unless the film is
strongly doped at the contacts and the contact is long, or unless each tube in
the array is directly contacted by the metal.
