Quantum effects in the thermoelectric power factor of low-dimensional semiconductors

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.