Advances in solid-state device design now allow the spectrum of transmittedelectrons in thermionic and thermoelectric devices to be engineered in waysthat were not previously possible. Here we show that the shape of the electronenergy spectrum in these devices has a significant impact on their performance.We distinguish between traditional thermionic devices where electron momentumis filtered in the direction of transport only and a second type, in which theelectron filtering occurs according to total electron momentum. Such 'totalmomentum filtered' kr thermionic devices could potentially be implemented in,for example, quantum dot superlattices. It is shown that whilst total momentumfiltered thermionic devices may achieve efficiency equal to the Carnot value,traditional thermionic devices are limited to efficiency below this. Our secondmain result is that the electronic efficiency of a device is not only improvedby reducing the width of the transmission filter as has previously been shown,but also strongly depends on whether the transmission probability rises sharplyfrom zero to full transmission. The benefit of increasing efficiency through asharply rising transmission probability is that it can be achieved withoutsacrificing device power, in contrast to the use of a narrow transmissionfilter which can greatly reduce power. We show that devices which have asharply-rising transmission probability significantly outperform those which donot and it is shown such transmission probabilities may be achieved withpractical single and multibarrier devices. Finally, we comment on theimplications of the effect the shape of the electron energy spectrum on theefficiency of thermoelectric devices.
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