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

TL;DR

This paper provides a theoretical analysis of how quantum confinement effects influence the thermoelectric power factor in low-dimensional semiconductors, showing conditions for enhanced performance based on confinement length and thermal wavelength.

Contribution

It derives an analytical formula for the power factor considering quantum effects, highlighting the conditions under which low-dimensional semiconductors outperform bulk materials.

Findings

Power factor is enhanced when confinement length is smaller than the thermal de Broglie wavelength.

Low-dimensional semiconductors outperform bulk when L < Lambda.

Bulk semiconductors may have higher power factor when L > Lambda.

Abstract

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.