Ideal efficiency of photon-enhanced thermionic emission energy converter driven by blackbody radiation

Reducing CO₂ emissions, particularly through the use of renewable energy resources, is crucially important for the mitigation of global warming. Direct solar-to-electrical energy conversion, which is possible using photovoltaics (PVs), is drawing increased attention despite low conversion efficiencies: PV-related costs have been decreasing steadily. In a recent report,¹⁾ Schwede et al. proposed a solar energy conversion scheme that exploits photon-enhanced thermionic emission (PETE). In a PETE device, electrons in a semiconductor cathode gain energy by a combination of direct photon excitation and thermal energy absorption. Electrons that have sufficient energy to overcome the material work function are emitted into a vacuum gap and are collected at an anode to generate an electric current through a load. The use of photo-excitation of electrons in a semiconductor cathode as opposed to heat in a metal emitter is the main feature distinguishing this PETE configuration from a conventional thermionic energy converter (TEC).^2,3) Photo-excitation reduces the thermal energy necessary for electrons to overcome the work function, thereby reducing the working temperature without greatly compromising the operating current density. Calculations conducted for an earlier study¹⁾ suggest that system energy conversion efficiencies from sunlight can exceed 50% with waste heat regeneration. Such efficiencies are considerably higher than those realized using conventional thermionic energy converters: typically 10–15%.^2,3) The potentially lower operating temperature resolves thermal issues that have plagued conventional TECs when emitters must operate at temperatures higher than 1500 K to achieve high current–energy densities. Energy densities that are afforded by PETE (10⁴–10⁶ W/m²) are higher than those of non-concentrated photovoltaics (typically less than 10² W/m²), potentially reducing the amounts of material and energy needed for the synthesis and maintenance of PV devices. Because of these interesting features, PETE has attracted great interest in the research community. Rapid progress has been made in the development of emitter materials and in the refinement of theoretical models of performance.^4–13)

Although ideal efficiencies of PETE have been estimated for sunlight,¹⁾ large flexibility by engineering the bandgap can probably afford conversions from other light sources. Sunlight is an extremely useful and clean energy source, but it is not stable. On Earth, many high-temperature materials can provide radiation stably, such as magma, geothermally heated rock, and exhaust pipes of heat engines. Consequently, this report describes the ideal conversion efficiencies of PETE device for the case driven by blackbody radiation (results are applicable also to gray radiation) to ascertain the feasibility of PETE devices for energy conversion of radiation from high-temperature materials.

The scheme for calculating ideal efficiency estimation is the same as that described in an earlier report.¹⁾ We have been able to reproduce results with the input variables used in that study and have identical efficiency curves. The only difference is the radiation source: the earlier study assumed sunlight, but the radiation source assumed for this study is blackbody radiation. The radiation collection angle is assumed to be 1 str. (If one collects radiation of the whole angle, the corresponding concentration, shown in the results, should be divided by 4π.) The collector temperature is assumed to be equal to the boiling temperature of water: 373 K. The collector work function is 0.9 eV. The effective mass of the hole is set as 0.57. The dope density is assumed to be 10⁻¹⁹ cm⁻³, resulting in a p-type semiconductor. The collector work function, the effective mass of the hole, and the dope density are chosen as described in an earlier report.¹⁾ The variables, which are adjusted to achieve the highest efficiency, are the emitter bandgap E_g, emitter temperature, and emitter electron affinity χ (or work function φ; being equal to χ + E_g − E_F, where E_F is the Fermi level), which is adjustable with Cs density on the electrode.

The calculation scheme is explained here only briefly. Details are available in the literature.¹⁾ The calculation solves two balances at the emitter: one is (a) the conduction band population of electrons; the other is (b) the energy budget for the emitter temperature. Those two balances are mutually dependent. The processes considered for (a) the electron density in the conduction band are (a-1) excitation by photon with energy equal to or higher than the bandgap, (a-2) radiative recombination, and (a-3) electron emission (collector-directed electron flux). The ones considered for (b) the emitter temperature are (b-1) photon-absorption assuming that the photon energy remaining from the excitation {(a-1)} is deposited as a heat, (b-2) radiative recombination (energy loss caused by recombining radiation), (b-3) electron emission (collector-directed electron flux), (b-4) electron absorption (emitter-directed electron flux), and (b-5) blackbody radiation. Calculations assume the absence of blackbody radiation between the electrodes.¹⁾ Finally the ideal output power (P_out) is found by the ideal voltage (work function difference between the electrodes) and net current (PETE current from the emitter minus small thermionic current from the collector). Then it is compared with the radiation input flux (P_rad) to extract the ideal conversion efficiency. It is noteworthy that "ideal" represents the total emitted current arriving to the other electrode, thereby assuming no resistance between the emitter and the collector.

Figure 1 presents the calculated conversion efficiencies as functions of the bandgap for four concentrations (based on 1 str. radiation) of the blackbody radiation of 1000 K. The 100 times concentrated radiation yields approx. 40% maximum efficiency, whereas the efficiency reaches approx. 20% with 10-times-concentrated radiation. The optimal bandgap that gives maximum efficiency is 0.45–5 eV, which is significantly lower than that for sunlight of approx. 1.4 eV.¹⁾ The difference is significant because blackbody radiation of 1000 K has few high-energy photons. For that reason, a lower bandgap is required to induce a marked effect of photo-excitation.

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For several concentrations, the maximum efficiencies are shown in Fig. 2 as functions of the radiation temperature. Efficiency increases with the temperature elevation of the radiating body and with increased concentrations. Figure 3 portrays the optimal bandgap for giving the maximum efficiencies. The optimal bandgap increases with the temperature elevation of the radiating body, because the fraction of high-energy photons increases. However it depends less on the concentrations, and the dependency is not simple. At the lower blackbody temperature, higher concentration of light functions best with a smaller bandgap, although with a high blackbody temperature, it functions best with a larger bandgap. This tendency is a result of a balance of photon-excitation and thermal excitation. The emitter temperature for the optimal conditions depends on the concentration and the blackbody temperature, as portrayed in Fig. 4. While it is a general trend that the optimal temperature increases with the concentration elevation, the dependency on the blackbody temperature (radiation spectrum) requires one to solve the balances.

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Figures 2 and 4 show that higher conversion efficiency requires higher emitter (cathode) temperature operation in the investigated conditions. For example, the conditions for 20% efficiency are achieved with an emitter temperature of approximately 1000 K, nearly independently from the concentration, whereas 40% efficiency is achieved with approx. 1600 K.

Although possible high conversion efficiency is shown, materials development, with desired bandgap and high melting temperature, is expected to be an important issue for realizing a PETE device driven by blackbody-like radiation. Among materials reported in the literature, InAs (bandgap of 0.35 eV and melting point of 1220 K) and PbS (0.41 eV and 1390 K) are apparently highly promising materials. Although this study assumes ideal converters, it should be noted finally that the resistance between the electrodes must be reduced to realize high-efficiency PETE devices, irrespective of the excitation source.

Acknowledgment