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.