Optimizing thermoelectric power factor by means of a potential barrier

Large efforts in improving thermoelectric energy conversion are devoted to energy filtering by nanometer size potential barriers. In this work, we perform an analysis and optimization of such barriers for improved energy filtering. We merge semiclassical with quantum mechanical simulations to capture tunneling and reflections due to the barrier and analyze the influence of the width W, the height V_b, and the shape of the barrier, and the position of the Fermi level (E_F) above the band edge, η_F. We show that for an optimized design, ∼40% improvement in the thermoelectric power factor can be achieved if the following conditions are met: η_F is large; V_b−E_F is somewhat higher but comparable to k_BT; and W is large enough to suppress tunneling. Finally, we show that a smooth energy barrier is beneficial compared to a sharp (square) barrier for increasing the thermoelectric power factor.