Thermoelectric properties of periodic quantum structures in the Wigner-Rode formalism

Improving the thermoelectric Seebeck coefficient, while simultaneously reducing thermal conductivity, is required in order to boost thermoelectric (TE) figure of merit (ZT). A common approach to improve the Seebeck coefficient is electron filtering where 'cold' (low energy) electrons are restricted from participating in transport by an energy barrier (Kim and Lundstrom 2011 J. Appl. Phys. 110 034511, Zide et al 2010 J. Appl. Phys. 108 123702). However, the impact of electron tunneling through thin barriers and resonant states on TE properties has been given less attention, despite the widespread use of quantum wells and superlattices (SLs) in TE applications. In our work, we develop a comprehensive transport model using the Wigner-Rode formalism. We include the full electronic bandstructure and all the relevant scattering mechanisms, allowing us to simulate both energy relaxation and quantum effects from periodic potential barriers. We study the impact of barrier shape on TE performance and find that tall, sharp barriers with small period lengths lead to the largest increase in both Seebeck coefficient and conductivity, thus boosting power factor and TE efficiency. Our findings are robust against additional elastic scattering such as atomic-scale roughness at side-walls of SL nanowires.