  The unknown quantum electronic conductance across nanojunctions made of
silicon-doped carbon wires between carbon leads is investigated. This is done
by an appropriate generalization of the phase field matching theory for the
multi-scattering processes of the electronic excitations at the nanojunction,
and the use of the tight-binding method. Our calculations of the electronic
band structures for carbon, silicon and diatomic silicon carbide, are matched
with the available corresponding density functional theory results to optimize
the required tight-binding parameters. The silicon and carbon atoms are treated
on the same footing by characterizing each with their corresponding orbitals.
Several types of nanojunctions are analyzed to sample their behavior under
different atomic configurations. We calculate for each nanojunction the
individual contributions to the quantum conductance for the propagating
$\sigma$, $\pi$, and $\sigma^{*}$ electrons incident from the carbon leads. The
calculated results show a number of remarkable features, which include the
influence of the ordered periodic configurations of silicon-carbon pairs, and
the suppression of the quantum conductance due to minimum substitutional
disorder and to artificially organized symmetry on these nanojunctions. Our
results also demonstrate that the phase field matching theory is an efficient
tool to treat the quantum conductance of complex molecular nanojunctions.
