Mark F. O'Dwyer

Power optimization in thermionic devices

Conventional thermionic power generators and refrigerators utilize a barrier in the direction of transport to selectively transmit high-energy electrons. Here we show that the energy spectrum of electrons transmitted in this way is not optimal, and we derive the ideal energy spectrum for operation in the maximum power regime. By using suitable energy filters, such as resonances in quantum dots, the power of thermionic devices can, in principle, be improved by an order of magnitude.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%.

Electronic and thermal transport in hot carrier solar cells with low-dimensional contacts

Hot carrier solar cells are a third generation solar cell device where electrons and holes, heated by solar radiation, are removed from the absorber via low-dimensional energy selective contacts before they can thermalise to the band edge. Here, a new model is presented for calculating the performance of these devices, which takes into account the energy spectrum of the contacts. It is shown that efficiency is maximised with a certain ideal number of contacts and that the energy spectra of these should be narrow.

Solid-state thermionics and thermoelectrics in the ballistic transport regime

It is shown that 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 intensive electronic efficiency in the two types of devices. This result is used to demonstrate that the materials parameters for thermionic and thermoelectric devices are equal, rather than differing by a multiplicative factor as previously thought.It is shown 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. This result is used to demonstrate that the material parameters for thermionic and thermoelectric refrigerators are equal, rather than differing by a multiplicative factor as previously thought.

Efficiency in nanometre gap vacuum thermionic refrigerators

The performance of vacuum thermionic refrigerators with emitter–collector separations of the order of a few nanometres is examined. The importance of the spectrum of transmitted electrons on device behaviour is highlighted. We find that for room temperature refrigeration applications, radiation losses are not negligible when the device is designed for high efficiency. A trade off between currents below and above the Fermi level is found to occur, with the optimal result not necessarily being achieved with minimum emitter–collector separation.

Thermionic refrigerators with non-Richardson current

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.

Low thermal conductivity short-period superlattice thermionic devices

A new solid-state thermionic device structure is proposed, which employs short-period superlattices to reduce heat backflow in the device while maintaining good electrical transport. Short-period superlattices have been shown to have thermal conductivities significantly lower than their bulk constituents or the relevant alloy. Here we discuss how this might be utilized to achieve higher efficiencies in thermionic devices. The barrier in a conventional device is replaced by a short-period superlattice with periodicity selected based on experiments reporting their low thermal conductivity. Calculations are performed showing how the nature of this structure affects the cooling current due to electrons flowing in the device and how it can be optimized. Such a device could significantly out-perform a conventional solid-state thermionic device. Finally, we discuss how this device structure provides a logical progression in design methodology from conventional multi-barrier thermionics to the current state-of-the-art thermoelectric devices.

Thermionic refrigeration in low-dimensional structures

The Richardson equation for thermionic emission is generalised to ND systems. An equation for thermionic emission heat current and an analytical expression for the coefficient of performance of ND thermionic refrigerators are also provided. It is found that when heat backflow is very small, lower-dimensional thermionic refrigerators outperform higher-dimensional systems. Conversely, when heat current backflow is significant, higher-dimensional thermionic refrigerators achieve higher COPs.

The effect of the electron energy spectrum on electronic efficiency and power in thermionic and thermoelectric devices

We show that the details of the energy spectrum of transmitted electrons in thermionic and thermoelectric devices have 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. Our main result is that the electronic efficiency of a device is not only improved by reducing the width of the transmission filter, but also strongly depends on whether the transmission probability rises sharply from zero to full transmission. Finally, we comment on the implications of the effect the shape of the electron energy spectrum has on the efficiency of thermoelectric devices and suggest an experimental measure for providing insight into the nature of the electron energy spectrum.

The effect of barrier shape on thermionic refrigerator performance

We consider the effect that the barrier shape has on the electron energy spectrum and lattice thermal conductivity, and together the effect of these coefficient of performance of thermionic refrigerators. Whilst it is shown that wide barriers are also desirable to enhance the electron energy spectrum, the primary motivation to increase barrier width to the maximum allowable value with ballistic transport is to reduce thermal conductivity. It is shown that the barriers which produce the highest electronic coefficient of performance do not necessarily give the highest coefficient of performance when thermal conductivity is considered if electronic heat current is reduced. While mean free path length multibarrier geometries may offer reduced thermal conductivity due to the possibility of interface scattering and phonon miniband formation, this effect needs to be significant to achieve coefficient of performance comparable with a single barrier device. Finally, we show that maximum refrigerator coefficient of performance is achieved by transmitting electrons over a tuned energy range only, which may be approximated by the transmission probability associated with a Gaussian modulated superlattice.

Energy-specific equilibrium in nanowires for efficient thermoelectric power generation

There is great scientific, economic and environmental interest in the development of thermoelectric materials capable of direct thermal-to-electric energy conversion with high efficiency. Recent theory predicts that in materials with a fine-tuned electronic density of states, electrons can be placed in energy-specific equilibrium, and the efficiency of thermoelectric power generation can approach the fundamental Carnot limit. Here we review the relevant theory of energy-specific equilibrium. We describe a concept for a proof-of principle demonstration of near-Carnot efficient power conversion involving a single, ballistic nanowire at low temperatures, and we discuss the potential for room-temperature applications in diffusive materials.