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.
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