  We theoretically investigate the interplay between the confinement length $L$
and the thermal de Broglie wavelength $\Lambda$ to optimize the thermoelectric
power factor of semiconducting materials. An analytical formula for the power
factor is derived based on the one-band model assuming nondegenerate
semiconductors to describe quantum effects on the power factor of the low
dimensional semiconductors. The power factor is enhanced for one- and
two-dimensional semiconductors when $L$ is smaller than $\Lambda$ of the
semiconductors. In this case, the low-dimensional semiconductors having $L$
smaller than their $\Lambda$ will give a better thermoelectric performance
compared to their bulk counterpart. On the other hand, when $L$ is larger than
$\Lambda$, bulk semiconductors may give a higher power factor compared to the
lower dimensional ones.
