  We have theoretically investigated the thermoelectric properties of
impurity-doped one-dimensional semiconductors, focusing on nitrogen-substituted
(N-substituted) carbon nanotubes (CNTs), using the Kubo formula combined with a
self-consistent $t$-matrix approximation. N-substituted CNTs exhibit extremely
high thermoelectric power factor ($PF$) values originating from a
characteristic of one-dimensional materials where decrease in the carrier
density increase both the electrical conductivity and the Seebeck coefficient
in the low-N regime. The chemical potential dependence of the $PF$ values of
semiconducting CNTs has also been studied as a field-effect transistor and it
turns out that the $PF$ values show a noticeable maximum in the vicinity of the
band edges. This result demonstrates that "band-edge engineering" will be
crucial for solid development of high-performance thermoelectric materials.
