  A first-principles investigation of the electronic properties of boron
nitride nanoribbons (BNNRs) having either armchair or zigzag shaped edges
passivated by hydrogen with widths up to 10 nm is presented. Band gaps of
armchair BNNRs exhibit family-dependent oscillations as the width increases
and, for ribbons wider than 3 nm, converge to a constant value that is 0.02 eV
smaller than the bulk band gap of a boron nitride sheet owing to the existence
of very weak edge states. The band gap of zigzag BNNRs monotonically decreases
and converges to a gap that is 0.7 eV smaller than the bulk gap due to the
presence of strong edge states. When a transverse electric field is applied,
the band gaps of armchair BNNRs decrease monotonically with the field strength.
For the zigzag BNNRs, however, the band gaps and the carrier effective masses
either increase or decrease depending on the direction and the strength of the
field.
