  We have theoretically investigated the electronic properties of neutral and
$n$-doped dangling bond (DB) quasi-one-dimensional structures (lines) in the
Si(001):H and Ge(001):H substrates with the aim of identifying atomic-scale
interconnects exhibiting metallic conduction for use in on-surface circuitry.
Whether neutral or doped, DB lines are prone to suffer geometrical distortions
or have magnetic ground-states that render them semiconducting. However, from
our study we have identified one exception -- a dimer row fully stripped of
hydrogen passivation. Such a DB-dimer line shows an electronic band structure
which is remarkably insensitive to the doping level and, thus, it is possible
to manipulate the position of the Fermi level, moving it away from the gap.
Transport calculations demonstrate that the metallic conduction in the DB-dimer
line can survive thermally induced disorder, but is more sensitive to imperfect
patterning. In conclusion, the DB-dimer line shows remarkable stability to
doping and could serve as a one-dimensional metallic conductor on $n$-doped
samples.
