T. E. Humphrey

Reversible Thermoelectric Nanomaterials

Irreversible effects in thermoelectric materials limit their efficiency and economy for applications in power generation and refrigeration. While electron transport is unavoidably irreversible in bulk materials, here we derive conditions under which reversible diffusive electron transport can be achieved in nanostructured thermoelectric materials. We provide a fundamental thermodynamic explanation for why the optimum density of states in a thermoelectric material is a delta function and for why inhomogeneous doping and segmentation improve the thermoelectric figure of merit.

Reversible quantum brownian heat engines for electrons.

Brownian heat engines use local temperature gradients in asymmetric potentials to move particles against an external force. The energy efficiency of such machines is generally limited by irreversible heat flow carried by particles that make contact with different heat baths. Here we show that, by using a suitably chosen energy filter, electrons can be transferred reversibly between reservoirs that have different temperatures and electrochemical potentials. We apply this result to propose heat engines based on mesoscopic semiconductor ratchets, which can quasistatically operate arbitrarily close to Carnot efficiency.

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%.

Concept study for a high-efficiency nanowire based thermoelectric

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 tunnelling 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.

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.

Quantum, cyclic, and particle-exchange heat engines

Abstract Differences between the thermodynamic behavior of the three-level amplifier (a quantum heat engine based on a thermally pumped laser) and the classical Carnot cycle are usually attributed to the essentially quantum or discrete nature of the former. Here we provide examples of a number of classical and semiclassical heat engines, such as thermionic, thermoelectric and photovoltaic devices, which all utilize the same thermodynamic mechanism for achieving reversibility as the three-level amplifier, namely isentropic (but non-isothermal) particle transfer between hot and cold reservoirs. This mechanism is distinct from the isothermal heat transfer required to achieve reversibility in cyclic engines such as the Carnot, Otto or Brayton cycles. We point out that some of the qualitative differences previously uncovered between the three-level amplifier and the Carnot cycle may be attributed to the fact that they are not the same ‘type’ of heat engine, rather than to the quantum nature of the three-level amplifier per se.

Pumping heat with quantum ratchets

Abstract We describe how adiabatically rocked quantum electron ratchets can act as heat pumps. In general, ratchets may be described as non-equilibrium systems in which directed particle motion is generated using spatial or temporal asymmetry. In a rocked ratchet, which may also be described as a non-linear rectifier, an asymmetric potential is tilted symmetrically and periodically. The potential deforms differently during each half-cycle, producing a net current of particles when averaged over a full period of rocking. Recently, it was found that in the quantum regime, where tunnelling contributes to transport, the net current may change sign with temperature. Here we show that a Landauer model of an experimental tunnelling ratchet (Linke et al., Science 286 (1999) 2314) predicts the existence of a net heat current even when the net particle current goes through zero. We quantify this heat current and define a coefficient of performance for the ratchet as a heat pump, finding that more heat is deposited in each of the two electron reservoirs due to the process of rocking than is pumped from one reservoir to the other by the ratchet.

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.