Electronic efficiency in nanostructured thermionic and thermoelectric devices

Abstract

Advances in solid-state device design now allow the spectrum of transmitted electrons in thermionic and thermoelectric devices to be engineered in ways that were not previously possible. Here we show that the shape of the electron energy spectrum in these devices has a significant impact on their performance. We distinguish between traditional thermionic devices where electron momentum is filtered in the direction of transport only and a second type, in which the electron filtering occurs according to total electron momentum. Such "total momentum filtered" thermionic devices could potentially be implemented in, for example, quantum dot superlattices. It is shown that whilst total momentum filtered thermionic devices may achieve an efficiency equal to the Carnot value, traditional thermionic devices are limited to an efficiency below this. Our second main result is that the electronic efficiency of a device is not only improved by reducing the width of the transmission filter as has previously been shown, but also strongly depends on whether the transmission probability rises sharply from zero to full transmission. The benefit of increasing efficiency through a sharply rising transmission probability is that it can be achieved without sacrificing device power, in contrast to the use of a narrow transmission filter which can greatly reduce power. We show that devices that have a sharply rising transmission probability significantly outperform those that do not and that such transmission probabilities may be achieved with practical single and multibarrier devices. We discuss how the shape of the electron energy spectrum will also have an effect on the electronic efficiency of thermoelectric devices due to mathematical equivalences in the ballistic and diffusive formalisms. Finally, we present an experimental measure that might be used to provide an indication of the nature of the electron energy spectrum and the electronic efficiency of a ballistic device.

From Thermal Rectifiers to Thermoelectric Devices

“…As remarked above, Carnot efficiency is obtained in the limit of zero particle current, corresponding to zero entropy production and zero output power. However, high values of ZT can still be achieved with sharply-peaked transmission functions without greatly reducing the output power [109,144].…”

Solid-state thermionics and thermoelectrics in the ballistic transport regime

“…The theoretical differences between thermionic devices in which the transmission probability is a function of k and k x are explored in detail in other papers. [7][8][9] In thermoelectric devices the energy-resolved diffusive electron current density may be obtained from the Boltzmann transport equation under the relaxation-time approximation, and can be written as…”

Efficiency at maximum power of thermochemical engines with near-independent particles

“…Many strategies have been proposed to find the suitable engine in various practical surroundings, including the construction of heat engines, the choice of the working substance, and some optimization measures on working conditions [1][2][3][4][5][6][7][8][9][10][11][12][13]. Among the possible energy conversion apparatuses, thermochemical engines are the easiest to control as they can work without moving parts [7][8][9][14][15][16][17][18][19]. Especially for thermoelectric engines, two-reservoir [8,16,17], three-reservoir [18,19], and four-reservoir [20,21] constructions have been proposed to produce electrical power from thermal energy effectively and in controllable manners.…”