Photon-enhanced thermionic emission for solar concentrator systems

Photon-enhanced thermionic emission for solar concentrator systems

(Parte 1 de 3)

Photon-enhanced thermionic emission for solar concentrator systems

and Nicholas A. Melosh1,2,5*

Solar-energy conversion usually takes one of two forms: the ‘quantum’ approach, which uses the large per-photon energy of solar radiation to excite electrons, as in photovoltaic cells, or the ‘thermal’ approach, which uses concentrated sunlight as a thermal-energy source to indirectly produce electricity using a heat engine. Here we present a new concept for solar electricity generation, photon-enhanced thermionic emission, which combines quantum and thermal mechanisms into a single physical process. The device is based on thermionic emission of photoexcited electrons from a semiconductor cathode at high temperature. Temperature-dependent photoemission-yield measurements from GaN show strong evidence for photon-enhanced thermionic emission, and calculated efficiencies for idealized devices can exceed the theoretical limits of single-junction photovoltaic cells. The proposed solar converter would operate at temperatures exceeding 200◦C, enabling its waste heat to be used to power a secondary thermal engine, boosting theoretical combined conversion efficiencies above 50%.

In a photovoltaic (PV) cell, solar photons with energies above the semiconductor’s bandgap excite electrons into the conduction band, which diffuse to electrodes and generate current. In high-performance solar cells, charge separation and collection are very efficient. However, the quantum approach of PV cells places intrinsic limitations on single-junction conversion efficiency. Photon energy in excess of the bandgap is lost as heat, known as thermalization loss, and sub-bandgap photons are not absorbed at all, known as absorption loss. In silicon solar cells, thermalization and absorption losses account for approximately 50% of the incident solar energy—most of the total energy loss1. In principle, these losses could be reclaimed by using this waste heat from the PV cell to power a secondary thermal cycle. Combinations of PV and thermal engines are predicted to have efficiencies greater than 60% (ref. 2), yet fail in practice because PV cells rapidly lose efficiency at elevated temperatures3, whereas heat engines rapidly lose efficiency at low temperatures4.

Thermionic energy converters (TECs) are less well-known heat engines, which directly convert heat into electricity. A simple thermionic converter consists of a hot cathode and cooler anode separated by a vacuum gap. In the TEC cathode, a fraction of the electrons have sufficient thermal energy to overcome the material’s work function and escape into vacuum, generating current between the two electrodes. The thermionic current density is dictated by the cathode work function and temperature according to the

Richardson–Dushman equation: J = AC∗TC2e−φ /kT , where φC is the cathode work function, TC the temperature and AC∗ the materials-specific Richardson constant5. Thermionic converters were first proposed and fabricated in the 1950s, with experimental conversion efficiencies eventually reaching 10–15% (refs 5,6). Both NASA and the Soviet space programme funded the development

1Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA, 2Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA, 3Department of Physics and Applied Physics, Stanford University, Stanford, California 94305, USA, 4Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA, 5Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA, 6Stanford Synchrotron Radiation Lightsource, Menlo Park, California 94025, USA. *

of TECs for deep-space missions and other applications requiring high-power autonomous generators, but the technology was never commercialized. Thermionic conversion’s main challenges relate to the very high temperatures and substantial current densities required for efficient operation7,8.

Photon-enhanced thermionic emission (PETE) combines photovoltaic and thermionic effects into a single physical process to take advantage of both the high per-quanta energy of photons, and the available thermal energy due to thermalization and absorption losses. A PETE device has the same vacuum-gap parallel-plate architecture as a TEC, except with a p-type semiconductor as the cathode (Fig. 1). PETE occurs in a simple three-step process: first, electrons in the PETE cathode are excited by solar radiation into the conduction band. Second, they rapidly thermalize within the conduction band to the equilibrium thermal distribution according to the material’s temperature and diffuse throughout the cathode. Finally, electrons that encounter the surface with energies greater than the electron affinity can emit directly into vacuum and are collected at the anode, generating current (Fig. 1a). Each emitted electron thus harvests photon energy to overcome the material bandgap, and also thermal energy to overcome the material’s electron affinity. The total voltage produced can therefore be higher than for a photovoltaic of the same bandgap owing to this ‘thermal boost’, thus more completely using the solar spectrum.

The ideal PETE current can be found by calculating the flux of photoexcited electrons that have sufficient energy to emit at the material surface. This calculation proceeds analogously to the calculation for thermionic current, except that for photoexcited electrons the population in the conduction band is distributed according to the quasi-Fermi level. In non-degenerate semiconduc- tors this is given by EF,n =EF+kTCln(n/neq) (ref. 1), where EF is the



EF EF,n φA

Photon-enhanced populationThermal population

Cathode Anode

X VOut ZLoad

Figure 1 | The PETE process. a, Energy diagram of the PETE process. Photoexcitation increases the conduction-band population, leading to larger thermionic currents and enabling the device to harvest both photon and heat energy. b, One possible implementation of a parallel-plate PETE converter. Photons impinge on a nanostructured cathode and excite electrons, which then emit into vacuum and are collected by an anode. Unused heat from the PETE cycle is used to drive a thermal engine.

Fermi level, n is the total electron concentration in the conduction band, neq is the equilibrium concentration without photoexcitation and TC is the cathode temperature. The larger the amount of photoexcitation, the higher the conduction-band concentration becomes, and thus the higher the quasi-Fermi level, EF,n. Following the derivation of ref. 9, the total emitted current density is

E +χ evx where e is the electron charge, vx the electron velocity perpendicular to the material surface, χ the electron affinity, m∗ the effective mass,

EC the energy at the conduction-band minimum, N(E) the density ofstatesandf (E)theFermidistribution.Theright-handexpression of equation (1) assumes that the density of states in the conduction band is parabolic and approximates the Fermi function by the Boltzmann distribution because the work function is much larger than kTC. If we assume that the effective mass is isotropic, then

exp kTC

0 dvy

0 dvz where vvac = √ 2χ/m∗ is the minimum velocity necessary to emit into vacuum. Significantly, evaluating equation (2) yields a result that is identical to the Richardson–Dushman equation for thermionic current, except that the energy barrier in the exponent is relative to the quasi-Fermi level instead of the equilibrium Fermi level:

TC2exp kTC kTC where A is the Richardson–Dushman constant. The right-hand expression explicitly shows that the effect of photo-illumination on semiconductor thermionic emission is to lower the energy barrier by the difference between the quasi-Fermi level with photoexcitation and the Fermi level without photoexcitation.

Substituting the expression for EF,n into equation (3) and rewriting in terms of the electron density in the conduction band, n, average velocity perpendicular to the surface, 〈vx〉, and electron affinity, χ, leads to an illuminating result:

This relation directly illustrates the effect of photoexcitation: illumination increases conduction-band concentration n over the equilibrium value neq, whereas the thermal energy determines the rate at which electrons emit over the electron affinity χ.

For p-type semiconductors, neq can be extremely low, such that photoexcitation can greatly increase the emission current. As the electron affinity can be almost arbitrarily tuned using surface coatings, such as Cs, the PETE process can be designed to operate overawiderangeoftemperatures,unlikethermionicemitters.

A plot of idealized PETE current as a function of temperature is shown in Fig. 2. At low temperatures, thermalized carriers in the conduction band cannot overcome the electron-affinity barrier and the PETE current is negligible. For high-energy photons

(hν > Eg + χ, where Eg is the bandgap) direct photoemission is also possible, but it is not included here for clarity. As temperature increases, the PETE process becomes more efficient and current increases, eventually reaching a plateau as every photoexcited electron is emitted. At even higher temperatures, purely thermionic emission dominates as thermal processes overshadow the effect of photoexcitation, and the emission current is no longer determined by the number of photoexcited electrons.

Despite the well-known individual physical mechanisms involved in PETE, the combined process has not previously been fully examined. Thermal energy has been suggested to assist electron emission over small interfacial barriers10,1, yet high-temperature photoemission from semiconductors has not been studied in detail. This is in part because caesium-based coatings, which are the most common work-function-lowering coatings in photocathode research, generally degrade at temperatures between 100 and 200◦C (refs12,13).Althoughapreviousreportnotedthatacombinationof photoemission and thermionic emission could be used to increase current from a commercial photocathode, photon enhancement of thermionicemissionwasnotconsideredasamechanism12.

PETE should show several physical signatures that differentiate it from photoemission or thermionic emission. PETE electrons should thermalize before emission, resulting in a thermal distribution of emitted electron energies regardless of the incident



Emitted electrons per above-gap photon

Cathode current Thermal current Photocurrent

Photon-enhancedthermionic regimePhotoemissionregime Thermionic regime

Figure 2 | Three regimes of electron emission. Depending on temperature, emission may be dominated by photoemission (not shown here), PETE or thermionic emission. This example assumes a cathode with χ =0.7eV,

Eg =1.0eV and ×100 solar concentration. Some high-temperature regions are not accessible at ×100 concentration without extra thermal energy but are shown for the purpose of illustration.

above-gap photon energy. Conversely, in the case of photoemission from a material with positive electron affinity, electrons excited above the vacuum level emit from the surface with minimal thermalization, resulting in a non-thermal energy distribution dependent on photon energy. In further contrast to PETE, overall photoemission yield decreases with temperature owing to increased scattering. PETE can be easily differentiated from thermionic emissionbycomparingthecurrentwithandwithoutillumination.

As a proof-of-principle of the PETE mechanism, we measured the temperature-dependent electron emission of caesiated GaN, an ultraviolet photocathode on which caesium forms a coating with unusually high thermal stability14. Samples were loaded into an ultrahigh-vacuum chamber (low-10−10 torr base pressure) with sample-heating, monochromatic-illumination and electronenergy-analysis capabilities. The GaN was carefully dosed with Cs vapour to lower the electron affinity to roughly 0.3–0.4eV, as determined by the low-energy cutoff of emitted electrons. In Fig. 3a, the emitted-electron energy distributions with 3.75eV (330nm) illumination are shown as a function of temperature. The distributions have the characteristic shape of thermally emitted electrons, and the distribution widths increase with temperature. The slight non-monotonic temperature dependence of the peak position is due to a ∼25meV change in the sample’s work function relative to that of the analyser over the course of measurement,butthisshiftdoesnotaffectthebroadeningresults.

Figure 3b provides further confirmation that at high temperatures the electrons thermalized before emission and provides a powerful example of the potential of PETE for power conversion. The sample was illuminated with either 3.75eV photons (330nm, energy approximately equal to the work function) or 3.3eV photons (375nm, energy barely exceeding the bandgap at 400 ◦C). The two distributions are virtually identical, indicating that the electron energy distribution immediately following photoexcitation was unimportant, as would be expected from PETE. Interestingly, as the average emitted-electron energy was approximately 3.8eV, each electron excited with 3.3eV light acquired ∼0.5eV in thermal energy before emission. In an energy converter this thermal boost could be harvested by using a proportionately higher operating voltage. For small-bandgap semiconductors, such as Si (1.1eV) or GaAs (1.4eV), a similar thermal boost would represent a considerable increase over the bandgap energy. The energy distribution without illumination was

Normalized counts (a.u.)

330 nm 375 nm

4.0 Normalized counts (a.u.)


350 nm 330 nm

Relative QE 0.5 b c

Figure 3|Temperature-dependent measurements of [Cs]GaN. a, Energy distributions of electrons emitted from GaN at 330nm. The inset shows that the electron distribution’s full-width at half-maximum (FWHM) increases with temperature. As noted in the Methods section, the temperature calibrations in parts a and b are with respect to a silicon reference and are only approximate. b, Electron energy distributions at 400◦C under 330nm and 375nm illumination. Measured photon energies are shown as vertical lines. These curves have been normalized to emphasize the line shape, and emission current under 375nm illumination is substantially less because absorption at this wavelength is weaker. Purely thermionic emission from this sample in the absence of illumination is considerably smaller but occurs in the same energy range. c, Emission current of a sample with electron affinity close to the positive–negative crossover as a function of temperature for 3.5eV (350nm) illumination. The emission current of the same sample near-optimally caesiated to a state of negative electron affinity at 350nm illumination is shown as a black dashed line for reference. These traces have been normalized to emphasize the temperature dependence. The temperature range is less than in parts a and b because the NEA coating does not survive to high temperature.

considerably smaller and has been subtracted from these curves, demonstratingthattheemissionisnotpurelythermionic.

Although electron thermalization most clearly identifies the

(Parte 1 de 3)