Thermionic emission and TICs. Thermionic energy converters are heat engines that convert heat directly to electricity at very high temperatures. Thermionic emission—the evaporation of electrons from a heated cathode once the electrons gain sufficient energy to overcome the potential barrier near the surface—is distinct from the thermoelectric phenomenon described by the Seebeck effect, which entails the direct conversion of heat differentials to electric voltage through the junction of two materials maintained at different temperatures.

A basic thermionic converter consists of two electrodes separated by a vacuum or a vapor. Click to enlarge.

The principle of thermionic emission and the development of devices exploiting it reach back to the late 19^th century. Frederick Guthrie is credited with the discovery of thermionic emission in 1873; in 1885, Thomas Edison showed that an electric current could be collected by placing an electrode near a hot filament; in 1912 and 1916, Owen Richardson published a basic theory of thermionic emission. He developed an expression for thermionic emission current density, now known as the Richardson-Dushman (RD) equation. Richardson was awarded the Nobel Prize in Physics for 1928 (awarded in 1929) for his work on the thermionic phenomenon and the equation.

In 1915, Schlichter published an investigation into the use of thermionic emission for converting heat into electricity. Broader investigation into thermionics began in the 1950s, with several groups producing TICs that operated at as low as 1400 K (1127 °C), delivering power densities of 3-10 W/cm² at efficiencies of 5-10%.

By 1980, a NASA Lewis Research Center report prepared for the US Department of Energy (DOE) suggested that then state-of-the-art thermionic converters could use tungsten electrodes with 1800 K (1527 °C) emitters to deliver 27.4 W/cm² at 26.6% efficiency with ~1000 K (727 °C) collectors or 22.6 W/cm² at 21.7% efficiency with ~1100 K (827 °C) collectors. Although the majority of the work with TICs was then related to space exploration, the focus of that report was the use of TICs with coal combustion.

Advances in nano/micro fabrication, together with engineered high-temperature materials, two-dimensional materials, and powerful computing methods have spurred renewed interest in thermionics. Stanford University, for example, has a thermionic energy conversion research effort underway as part of its Nano-electrochemical Systems (NEMS) group. The Stanford team is working to develop more robust thermionics with higher efficiency by fabricating thermally robust emitters, ultra-low work function collectors, and micron-meter scale inter-electrode gap.

The work function is the surface property that determines how easily electrons can escape into the vacuum or gas; a lower work function generally facilitates electron emission. Traditional methods of lowering the work function use alkali coatings, first developed in the first half of the 20^thcentury. However, these coatings typically enable work functions only as low as 1.5 to 1.0 eV.

Previous calculations have shown that with a work function of 0.5eV a TEC device can theoretically reach an efficiency of over 50% under 1000x concentrated solar radiation, which almost doubles the efficiency of the theoretical limit of single junction solar cell. By using DFT, combining with various of experimental approaches, we are looking for ultra-low work function materials.

—Stanford NEMS

The SUTD work. Shi-Jun Liang and L. K. Ang proposed a model to investigate the electron thermionic emission from single-layer graphene. They derived a formula—a function of the temperature, work function, and Fermi energy level—that is significantly different from the traditional Richardson-Dushman (RD) equation.

The Richardson-Dushman equation. J is the current density, T is the cathode temperature, Φ is the work function of the metal (independent of T), kB is the Boltzmann constant, A is the Richardson constant, which is related to the electron charge and the electron mass. Click to enlarge.

The amount of current density J from the thermionic emission is determined by the Richardson-Dushman (RD) law … In general, the RD law works well only for metallic-like materials, and a corresponding modification using quantum models is required for wide-band-gap materials and low-electron-affinity materials. Since monolayer graphene was exfoliated experimentally in 2004, many unique properties have been reported, such as linear band structure, ultrahigh mobility (up to 400000 cm V⁻¹ s⁻¹), and excellent conductivity. Fundamentally, the linear band structure of graphene, the most intriguing property, makes it different from other three-dimensional or bulk materials.

For electron emission, it has been recently shown that the traditional emission processes, such as field emission and photo-assisted overbarrier electron emission, may require further revisions to account for the unique properties of graphene. As the crystalline allotrope of carbon, the thermionic and field emission from carbon nanotubes (CNT) have also been studied both experimentally and theoretically, which indicates that traditional emission models may not be valid for CNT. Recent experiments confirm that the RD law is not valid for thermionic emission from CNT.

In this paper, we are interested to know if the RD law is valid for thermionic emission from single-layer suspended graphene by assuming that the effect of the substrate is not important. Electrons in graphene behave as massless quasiparticles (m=0), so the mass-dependent expression of the prefactor A in the RD law is questionable, as the supply function of the electron behaving like massless particles in graphene is not included. On the other hand, the electrons in graphene must exhibit a nonzero mass when they are collectively excited, which is only a few percentage points (0.01-0.03) of the intrinsic electron mass.

—Liang and Ang

In essence, their findings suggest that the traditional thermionic emission law governed by the RD equation is no longer valid if the effect of the substrate is not important—as is the case, they propose, with graphene.

One of the principles of thermionic emissions is that the electrons emitted per unit area from the cathode depends on the temperature. The classic RD scaling is that the number of emitted electrons is proportional to the square of cathode temperature (T²).

However, the SUTD team, working with the results of a recent Tsinghua University study measuring electron thermionic emission from suspended single-layer graphene (Zhu et al.), suggested that the scaling with graphene is cubic (T³) instead. In other words, the heat temperature could be lowered if graphene is used as the hot cathode.

The SUTD model predicts that the intrinsic work function of single-layer graphene is about 4.514 eV with a Fermi energy level of 0.083 eV.

If the work function of the graphene is lowered to 2.5–3 eV and the Fermi energy level is increased to 0.8–0.9 eV, it is possible to design a graphene-cathode-based TIC operating at around 900 K or lower, as compared with a metal-based cathode TIC operating at about 1500 K. With a graphene-based cathode (work function=4.514  eV) at 900 K and a metallic-based anode (work function=2.5  eV) such as LaB6 at 425 K (152 °C), the efficiency of the proposed TIC would be about 45%.

Due to the properties of graphene, the emitting current density can be further increased to 10 A/m² if the Fermi energy level can be tuned to 0.8 eV (or 0.9 eV) and the work function can be reduced to 2.5 eV (or 3 eV) based on the ongoing research.

Resources

• Shi-Jun Liang and L. K. Ang (2015) “Electron Thermionic Emission from Graphene and a Thermionic Energy Converter” Phys. Rev. Applied 3, 014002 doi: 10.1103/PhysRevApplied.3.014002

• F. Zhu, X. Lin, P. Liu, K. Jiang, Y. Wei, Y. Wu, J. Wang, and S. Fan (2014) “Heating graphene to incandescence and the measurement of its work function by the thermionic emission method,” Nano Res. 7, 4 doi: 10.1007/s12274-014-0423-1

• Westover, T.L. (2008) “Energy Transport and Conversion in Electron Emission Processes”

• Morris, J. F. (1980) “Optimal thermionic energy conversion with established electrodes for high-temperature topping and process heating” DOE/NASA/1062-6; NASA-TM-81555