We study the effect of quantum reflection over the barrier (ROB) in a thermionic cooling device. We find that the performance of refrigerators can be enhanced by the ROB effect if the bias voltage and the lattice thermal resistance of the semiconductor in the barrier region are both sufficiently high. Furthermore, the figure of merit ZT can be higher due to the ROB effect if the workfunction of the cathode is low and the lattice thermal resistance is high. The overall optimum ZT calculated with and without the ROB effect are 6.5 and 7.1, respectively. The origin of the ROB correction to ZT is that the quantum reflection becomes asymmetric for the carrier transport in opposite directions.

Two-dimensional (2D) materials and their heterostructures have been widely explored for high-performance energy conversion applications. The Thomson effect—a higher order transport process—plays an important role in thermoelectric devices, yet its effect on the performance of thermionic devices remains unknown thus far. Here, we investigate the performance of thermionic refrigeration in vertically stacked heterostructure (VHS) and laterally stitched heterointerface (LHS) composed of a graphene and a 2D semiconductor (i.e., MoS2 and WSe2) in the presence of the Thomson effect. Using a temperature-dependent Seebeck coefficient, we derived the analytical expressions of the cooling efficiency and the effective ZT. We shall show that the Thomson effect improves the coefficient of performance (COP) by up to 20%, particularly, in the case where the temperature difference between the cold and the hot electrodes is large. However, the Carnot efficiency decreases with the temperature difference. The overall COP is reduced by the Thomson effect. We calculate the COP in graphene/MoS2/graphene and graphene/WSe2/graphene VHS and LHS devices. We show that the LHS composed of WSe2 significantly outperforms the VHS and MoS2 counterpart. These findings provide an understanding of thermionic processes in the higher-order transport regime and shall offer insights into the design of novel 2D material heterostructure thermionic energy converters.