We consider the effect that the barrier shape has on the electron energy spectrum and lattice thermal conductivity, and together the effect of these coefficient of performance of thermionic refrigerators. Whilst it is shown that wide barriers are also desirable to enhance the electron energy spectrum, the primary motivation to increase barrier width to the maximum allowable value with ballistic transport is to reduce thermal conductivity. It is shown that the barriers which produce the highest electronic coefficient of performance do not necessarily give the highest coefficient of performance when thermal conductivity is considered if electronic heat current is reduced. While mean free path length multibarrier geometries may offer reduced thermal conductivity due to the possibility of interface scattering and phonon miniband formation, this effect needs to be significant to achieve coefficient of performance comparable with a single barrier device. Finally, we show that maximum refrigerator coefficient of performance is achieved by transmitting electrons over a tuned energy range only, which may be approximated by the transmission probability associated with a Gaussian modulated superlattice.
展开▼
