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.

Conventional thermionic power generators and refrigerators utilize a barrier in the direction of transport to selectively transmit high-energy electrons, resulting in an energy spectrum of electrons that is not optimal for high efficiency or high power. Here, we derive the ideal energy spectrum for achieving maximum power in thermionic refrigerators and power generators. By using energy barriers that block or transmit electrons according to their total momentum rather than their momentum in the direction of transport, the power of thermionic devices can, in principle, be doubled and the electronic efficiency improved by 25%.

Materials capable of highly efficient, direct thermal-to-electric energy conversion would have substantial economic potential. Theory predicts that thermoelectric efficiencies approaching the Carnot limit can be achieved at low temperatures in one-dimensional conductors that contain an energy filter such as a double-barrier resonant tunneling structure. The recent advances in growth techniques suggest that such devices can now be realized in heterostructured, semiconductor nanowires. Here we propose specific structural parameters for InAs/InP nanowires that may allow the experimental observation of near-Carnot efficient thermoelectric energy conversion in a single nanowire at low temperature.

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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.