Solid-state thermionics and thermoelectrics in the ballistic transport regime

A study is conducted to demonstrate that the equations for electrical current in solid-state thermionic and thermoelectric devices converge for devices with a width equal to the mean free path of electrons, yielding a common expression for the intensive electronic efficiency in the two types of devices. The obtained result is used to show that the material parameters for thermionic and thermoelectric refrigerators are equal, rather than differing by a multiplicative factor as previously thought.