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Thermionic refrigerators with non-Richardson current

Most models of solid-state thermionic devices assume that all electrons with energy in the direction of transport greater than the barrier height are transmitted and utilize the Richardson equation. Here we consider a number of thermionic systems where the electron energy spectrum differs from the Richardson model. The electron energy spectra for maximum refrigeration coefficient of performance and maximum power are presented. We then consider multilayer solid-state nanostructures with currents not given by the Richardson equation and discuss the optimization of their energy spectrum. Nanometre gap vacuum thermionic refrigerators are also treated, where significant current is provided by below the barrier tunnelling. Finally, equations are developed for devices that select electrons for emission according to their total momentum, rather than simply the value in the direction of transport as is the case with conventional devices.