Photon-enhanced_thermionic_emission_for_solar_concentrator_systems

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PUBLISHED ONLINE: 1 AUGUST 2010 | DOI: 10.1038/NMAT2814
Photon-enhanced thermionic emission for solar concentrator systems
Jared W. Schwede1,2,3 , Igor Bargatin4 , Daniel C. Riley1,2,3 , Brian E. Hardin1,5 , Samuel J. Rosenthal1,5 , Yun Sun6 , Felix Schmitt1,2 , Piero Pianetta6 , Roger T. Howe4 , Zhi-Xun Shen1,2,3 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 ef?ciencies 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 ef?ciencies above 50%.
n 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 ? TC 2 e?φC /kTC , 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
I
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 semiconductors this is given by EF,n = EF +kTC ln(n/neq ) (ref. 1), where EF is the
1 Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA, 2 Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA, 3 Department of Physics and Applied Physics, Stanford University, Stanford, California 94305, USA, 4 Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA, 5 Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA, 6 Stanford Synchrotron Radiation Lightsource, Menlo Park, California 94025, USA. *e-mail: nmelosh@https://www.wendangku.net/doc/f99861314.html,.
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NATURE MATERIALS DOI: 10.1038/NMAT2814
a
Thermal population Photon-enhanced population Evacuum X EF,n EF Eg
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φA φA
VOut
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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
∞ ∞
JC =
EC +χ
evx N (E)f (E)dE =
EC +χ
evx
4π(2m? )3/2 h3
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: JC = en vx e?χ/kTC (4)
E ? EC (1)
× exp(?(E ? EF,n )/kTC )dE
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 of states and f (E) the Fermi distribution. The right-hand expression 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 2 E ? EC = m? v 2 /2, where v 2 = vx 2 + vy + vz 2 , and we can re-express the integral in terms of electron velocities: JC = 2e m? h
∞ 3
exp
? EC ? EF,n kTC
∞
∞
×
0
dvy
0
dvz
vvac
dvx vx exp(?m? v 2 /2kTC )
(2)
√ 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: JC = ? EC ? EF,n + χ 4πem? k 2 TC 2 exp h3 kTC ? φ ? EF,n ? EF kTC (3)
= ATC 2 exp
where A is the Richardson–Dushman constant. The right-hand expression explicitly shows that the effect of photo-illumination
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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 over a wide range of temperatures, unlike thermionic emitters. 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 barriers10,11 , 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 (refs 12,13). Although a previous report noted that a combination of photoemission and thermionic emission could be used to increase current from a commercial photocathode, photon enhancement of thermionic emission was not considered as a mechanism12 . 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
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NATURE MATERIALS DOI: 10.1038/NMAT2814
a
FWHM (eV)
0.20 0.19 0.18 0.17 200 300 400 Temperature (°C)
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0
500 Temperature (°C)
1,000
1,500
3.5 4.0 Energy above valence band maximum (eV) 330 nm 375 nm 4.5
Normalized counts (a.u.)
Relative QE
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 = 0.7 eV, Eg = 1.0 eV 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.
b
c
2.5 2.0 1.5 1.0 0.5 330 nm NEA 100 200 Temperature (°C) 350 nm
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 emission by comparing the current with and without illumination. 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 0.3–0.4 eV, as determined by the low-energy cutoff of emitted electrons. In Fig. 3a, the emitted-electron energy distributions with 3.75 eV (330 nm) 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 ～25 meV change in the sample’s work function relative to that of the analyser over the course of measurement, but this shift does not affect the broadening results. 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 3.75 eV photons (330 nm, energy approximately equal to the work function) or 3.3 eV photons (375 nm, 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 3.8 eV, each electron excited with 3.3 eV light acquired ～0.5 eV 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 (1.1 eV) or GaAs (1.4 eV), a similar thermal boost would represent a considerable increase over the bandgap energy. The energy distribution without illumination was
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400 °C
3.5 4.0 4.5 Energy above VBM (eV)
Figure 3 | Temperature-dependent measurements of [Cs]GaN. a, Energy distributions of electrons emitted from GaN at 330 nm. 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 330 nm and 375 nm illumination. Measured photon energies are shown as vertical lines. These curves have been normalized to emphasize the line shape, and emission current under 375 nm 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 af?nity close to the positive–negative crossover as a function of temperature for 3.5 eV (350 nm) illumination. The emission current of the same sample near-optimally caesiated to a state of negative electron af?nity at 350 nm 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, demonstrating that the emission is not purely thermionic. Although electron thermalization most clearly identifies the PETE process, the electron yield increased with temperature as well. The temperature-dependent emission current from a GaN sample with a small positive electron affinity was measured in a separate vacuum chamber (Fig. 3c). As the sample temperature varied from approximately 50 to 225 ? C, the emission current from 350 nm illumination more than doubled. The increase in yield for higherenergy photons was less dramatic, probably reflecting a contribution from direct photoemission, which decreases with temperature owing to increased scattering. More details on the quantum-yield measurements can be found in the Supplementary Information. For comparison, the same sample was further dosed with caesium to reach a state of negative electron affinity (NEA), with the result shown as a black dashed line in Fig. 3c. The stability of the NEA coating restricted the maximum temperature for these experiments to ～200 ? C. Because electrons do not need to overcome an
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NATURE MATERIALS DOI: 10.1038/NMAT2814
a
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Power conversion efficiency 0.5 0.4 0.3 0.2 0.1 0 200 400 600 800 Temperature (°C) 1,000 Eg = 1.4 eV X = 0.4 eV 0.6 eV 0.8 eV 1.0 eV
0.4 Power conversion efficiency
0.3 × 1,000 0.2 Heat fraction Photon × 100 fraction × 1,000 × 3,000 Ideal PV at × 3,000 1.0 1.5 Bandgap (eV) 2.0
c
Current density (A cm?2)
40 30 20 10 0
Eg = 1.4 eV
0.1
0.4 eV 0.6 eV 0.8 eV 1.0 eV
Flat-band condition 0.5 1.0 Voltage (V) 1.5 2.0
0.5
Figure 4 | Theoretical PETE ef?ciency. a, PETE ef?ciency for the AM1.5 direct + circumsolar spectrum as a function of bandgap. The cathode temperature and electron af?nity are chosen to maximize the overall ef?ciency. The anode temperature is 227 ? C to minimize the reverse current. In the inset, the power output at ×1,000 is shown to be due to roughly equal contributions from thermal (χ) and photon (Eg ) energy. b, Power-conversion ef?ciency increases with χ owing to larger voltage but requires higher temperatures. Power output decreases almost linearly with temperature after current saturation in the PETE regime owing to the increasing cathode Fermi level. The concentration is ×1,000. c, J–V curves for PETE devices with the same electron af?nities as in b, showing the ?at-band condition for χ = 0.4 eV. The temperatures are those at which the ef?ciencies in b are maximized.
extra barrier at the surface when the electron affinity is negative, the dominant temperature effect at 350 nm is a reduction in diffusion length. As a result, this trace shows a weak decrease in yield with temperature, clearly differentiating photoemission and PETE processes. Although caesiated GaN was convenient for demonstrating photon enhancement of thermionic emission, efficient solar-power conversion based on the PETE effect requires consideration of several factors in addition to thermal and chemical stability, most notably absorption and recombination. Only 1% of solar photons have energies exceeding the 3.3 eV bandgap of GaN, making the material unsuitable for solar applications. The high defect density and surface recombination of GaN, along with sub-optimal absorption due to the sample’s thin-film geometry, resulted in low PETE efficiencies: at 330 nm, the quantum efficiency was around 0.14%. One route to overcoming challenges relating to absorption and recombination is using nanostructures, which have shown long minority-carrier lifetimes15 due to high crystallinity and low defect densities as well as significantly enhanced absorption over thin films16 . However, to avoid complicating the analysis of theoretical PETE-device efficiency, in what follows, an idealized parallel-plate PETE converter is considered. The power output of a thermionic or PETE converter is calculated from the difference between the cathode current, JC , and the reverse thermionic current from the anode, JA , multiplied by the operating voltage. The operating voltage is given by the difference between the cathode and anode work functions and any extra voltage Vbias across the vacuum gap: PPETE = JV = (JC ? JA )(φC ? φA + Vbias ) (5)
Maximum power output for an idealized PETE converter occurs at Vbias = 0, called the flat-band condition (Fig. 4c), provided that φC ?φA > kTC and JC JA , and assuming that any electron absorbed from vacuum does not contribute to the cathode conduction-band population and hence cannot quickly re-emit (see Supplementary Information for further treatment).
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Although the optimal value of φC reflects a complicated balance between maximizing electron current and operating voltage, the anode work function φA should be as small as possible to maximize theoretical output voltage (equation (5)). In practice, this means that the anode temperature should be kept low enough to minimize reverse thermionic current. Work-function lowering is traditionally achieved by coating materials with alkali or alkali-earth metals, most notably caesium. Caesiated tungsten anodes are used in thermionic converters for their high-temperature stability and low work function (～1.7 eV), and caesiated titanium’s work function can reach nearly 1 eV (ref. 17). Caesium coatings can also controllably reduce a semiconductor anode’s (or cathode’s) electron affinity; for instance, in GaAs, χ can be reliably varied from ～4 to 0 eV depending on the surface coverage, and in some cases can even be negative18 . However, alkali or alkali-earth deposition is not the only path to realizing low work functions. Recently, phosphorus-doped diamond was reported to have a work function of 0.9 eV with thermal stability to at least 765 ? C (ref. 19). Although theoretical PETE conversion efficiencies can be extremely high if the choice of φA is not restricted, here we use a φA = 0.9 eV as an experimentally demonstrated value. The cathode emission current JC is calculated according to equation (4) by determining the steady-state conduction-band population n through balancing the rates of photoexcitation, thermionic emission and recombination. The rate of photoexcitation is determined by the flux of above-gap solar photons. Recombination in this analysis is treated in the detailed-balance limit, so that any photoexcited electron leaves the conduction band either through thermionic emission or through radiative recombination as determined by the Planck radiation law. A discussion of Auger recombination can be found in Supplementary Information, where it is seen that Auger can in some cases increase PETE device efficiency. Shockley–Read–Hall recombination is highly dependent on processing and impurities and is thus ignored in this theoretical analysis. Surface recombination is not considered for similar reasons, although it will be important for many materials, including GaN.
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0.5 Solar flux PETE device Cathode × 1,000
NATURE MATERIALS DOI: 10.1038/NMAT2814
Power conversion efficiency
Blackbody radiation
0.4
ZLoad
e? Anode
0.3
Electron current
0.2 Heat to thermal cycle 0.5
PETE alone Tandem PETE/thermal 1.0 1.5 Bandgap (eV) 2.0
Figure 5 | Theoretical tandem ef?ciency. a, Energy-?ow diagram for the PETE/thermal tandem device. Solar radiation is absorbed by the cathode. The cathode emits blackbody radiation both away from the device and towards the anode, whereas in Fig. 4 radiation exchange between cathode and anode is minimal. Electron current from the cathode JC is absorbed by the anode, delivering heat energy of JC (φA + 2kTC ). Excess heat in the anode due to electrons and photons from the cathode is released as blackbody radiation or reverse current, or delivered to a thermal cycle, which converts a fraction into useful work. b, Total PETE/thermal ef?ciency compared with PETE ef?ciency as a function of cathode bandgap at ×1,000 concentration, assuming a 285 ? C anode thermally coupled to a 31.5%-ef?cient thermal engine.
The PETE device is assumed to have a parallel-plate geometry (Fig. 1b), with the incident light striking the cathode through an infrared-absorbing substrate, so that sub-bandgap photons contribute to heating the cathode. The cathode is a thin semiconductor film with an electron diffusion length much longer than the relevant length for electron escape, so that the electron population is evenly distributed. Each above-gap photon is assumed to excite an electron into the conduction band. The total energy flux to the cathode is determined by comparing the rate of solar absorption with the rates of (detailed-balance-limited) blackbody emission and thermionic electron emission. After the PETE current is determined by self-consistently solving for the conduction-band population, the requirement of zero net energy flux at the cathode enables the total power generated for a given Eg to be optimized by suitable choices of TC and χ. Other cathode parameters such as the effective masses are based on p-type (doped at 1019 cm?3 ) Si (ref. 9), and dependent quantities such as neq and EF are found for each set of parameters using standard equations. Detailed descriptions of these calculations are provided in the Supplementary Information. The theoretical PETE conversion efficiency as a function of Eg and the concentration of the direct + circumsolar AM1.5 solar spectrum is shown in Fig. 4a. The optimal bandgap is between 1.1 and 1.7 eV, with a maximum at 1.35 eV. PETE is more efficient at higher solar concentrations, as expected from equation (4), with maximum efficiencies of 32% for ×100 concentration and 47% for ×3,000. Impressively, PETE efficiency exceeds the Shockley–Queisser limit for an ideal single-junction solar cell20 , as seen by a direct comparison of PETE and PV efficiencies at ×3,000 concentration. The PETE process’s main advantage over single-junction PV devices is that it successfully uses the heat produced by thermalization and sub-bandgap photon absorption to increase the output voltage, as was observed in the GaN experiments. Figure 4a (inset) shows that photon and thermal contributions (Eg and χ) are comparable at ×1,000 concentration and roughly correspond to the relative amounts of the solar spectrum absorbed as photons and heat for a given Eg . The temperature-dependent power output for a number of electron affinities is shown in Fig. 4b. Larger χ values produce higher output voltages yet require higher temperature to produce significant current. Although a device with χ = 0.4 eV reaches
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a maximum efficiency of ～25% at 200 ? C, for χ = 1.0 eV the maximum efficiency is 40% but requires a temperature of 800 ? C. The low temperatures necessary are also quite appealing compared with thermionic devices. The potential of PETE devices to improve solar-energy conversion is not just a more efficient single stage, but the opportunity to create a tandem cycle with a thermal engine. The high operating temperature in a PETE device matches well with thermal systems, such as a steam turbine or Stirling engine, enabling the waste heat from the PETE stage to drive a second thermal stage. A diagram of the energy flow in a PETE/solar-thermal tandem architecture is shown in Fig. 5a. Light is absorbed by the PETE cathode, which emits electrons and blackbody radiation that deliver heat energy to the anode. The anode is coupled to a thermal cycle, which removes the excess heat and uses it to generate electrical power. Tandem-PETE/thermal-engine efficiency for a concentration of ×1,000 suns is shown in Fig. 5b, assuming an anode temperature of 285 ? C and a thermal-to-electricity efficiency of 31.5% (refs 21,22). Total conversion efficiencies exceeding 53% are possible even at these low anode temperatures, constituting a 70% increase over the thermal cycle alone. The optimal bandgap shifts to a slightly lower value, ～1.15 eV, favouring more heat production than in a stand-alone PETE device. These calculations compare well with a previous report2 that found that an idealized photovoltaic/Carnot-engine tandem cycle at 500 K could reach 62% efficiency, provided that the PV cell could operate at arbitrary temperatures. In this context, the PETE device can be thought of as a high-temperature photovoltaic that can be used in combination with a thermal cycle. By using both thermal energy and photon energy, PETE can potentially achieve device efficiencies that exceed the fundamental limits on single-junction cells and rival those of complex multijunction cells, the best of which are around 40% efficient23 . PETE’s straightforward design could lead to inexpensive manufacturing, using processes derived from microelectromechanical systems (MEMS) technology, such as vacuum encapsulation by wafer-to-wafer bonding. In addition, high solar concentrations could potentially reduce material costs by scaling the device area. PETE devices are naturally synergistic with thermal engines and could be implemented as modular attachments to
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NATURE MATERIALS DOI: 10.1038/NMAT2814
existing solar-thermal infrastructure. Even a modestly efficient PETE module in tandem with a thermal engine could achieve a total system efficiency exceeding what is at present possible in a solely thermal or photovoltaic system, motivating research into combined quantum/thermal processes. Further efficiency improvements may be possible through new materials, nanostructures and plasmonic processes24 that can increase light absorption, carrier concentrations and emission probability. From the calculations and data shown here, the concept of harvesting photon and thermal energy together through PETE is a highly attractive mechanism for improving the efficiency of solar-energy collection that merits serious investigation.
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Methods
Energy-resolved electron-emission measurements in Fig. 3a,b were made at beamline 8-1 at the Stanford Synchrotron Radiation Lightsource (SSRL), maintained by Y.S. Yield measurements in Fig. 3c were made at a system on Stanford’s campus maintained by J.W.S., D.C.R. and F.S. Most experimental details are similar between the two set-ups, with differences noted below. Sample preparation. The 100 nm GaN samples were grown on sapphire substrates by SVT Associates and were Mg doped to a hole density of 5.3 × 1018 cm?3 (measured by SVT Associates, dopant concentration of approximately 1 × 1020 cm?3 ). The samples were cleaned in 98% sulphuric acid at 70 ? C for 5 min. A piece of tantalum foil was placed between the sample and a molybdenum sample holder to improve thermal contact, and the sample was affixed using molybdenum clips. The sample holder was put in a load lock, which reached a pressure in the 10?8 torr range. The sample was then transferred into the main chamber, whose base pressure was in the low-10?10 torr range. The sample was heat cleaned in vacuum at approximately 400 ? C. Caesium deposition and sample heating. The caesium evaporator was from Alvatec at Stanford and from SAES at SSRL. Caesium was incrementally deposited at the maximum sample temperature (220 ? C at Stanford and 400 ? C at SSRL) until measurements showed desired features. If an overdosage was achieved at Stanford, the sample temperature was raised by 50–150 ? C to induce desorption. The heater current was then decreased in steps lasting 30–60 min to ensure reliable temperature readings, and sample measurements were made at each step. Following this temperature sweep, the sample temperature was increased to check for degradation of the Cs coating. The temperature was read by a thermocouple on the heater assembly, which had been previously correlated to sample temperature. At Stanford, temperature calibration had been carried out with a thermocouple on a GaN reference. This calibration is expected to be accurate to ±20%. Temperature calibration at SSRL had been carried out using a silicon reference, and temperatures reported here are only approximate. Measurement. The light source for QE measurements was a monochromatized 150 W Xe lamp. After passing through a fibre bundle and an order-sorting filter, the monochromatized light was collimated, and a fraction was split off to a calibrated silicon photodiode to measure intensity for yield measurements. The remainder was focused through a viewport to make a spot of approximately 2 mm diameter on the sample surface at Stanford and approximately 4 mm at SSRL. The split-off beam and beam through the viewport, which was fused silica at Stanford and Pyrex at SSRL, had been previously calibrated, and this measurement is expected to be accurate to ±10%. The fibre bundle and optics were all fused silica. In the yield measurements at Stanford, a copper disc, which was located approximately 75 mm from the sample surface, was biased to 400 V to accelerate electrons away from the sample, which was near ground potential. Currents reported here were measured from the sample. At SSRL, the low-energy cutoff of the emitted electrons was measured using a PHI 10-360 hemispherical analyser at 5.85 eV pass energy, resulting in an analyser resolution estimated to be around 100 meV, consistent with manufacturer specifications. To overcome the 4.40 eV analyser work function, the sample was biased to 9.90 V. The energy-distribution curves shown in this report are corrected for this bias as well as for the calculated Fermi-level position relative to the valence-band maximum assuming a 170 meV activation energy for Mg, as detailed in the Supplementary Information. Cs coverage and the valence-band position at the surface were monitored with synchrotron radiation at 120 eV but are not reported here.
Acknowledgements
J.W.S., D.C.R. and S.J.R. were supported by the Global Climate and Energy Project, and J.W.S. was also partially supported by the US Department of Energy, Division of Materials Sciences, under Award DE-AC02-76SF00515. I.B. was partially supported by Robert Bosch Palo Alto Research and Technology Center and DARPA through the Center on Interfacial Engineering in Microelectromechanical Systems. Portions of this research were carried out at the SSRL, a national user facility operated by Stanford University on behalf of the US Department of Energy, Office of Basic Energy Sciences. The authors would like to thank Z. Hussain, J. Pepper, V. K. Narasimhan and K. Sahasrabuddhe for discussions.
Author contributions
J.W.S., D.C.R., Z-X.S. and N.A.M. designed experiments. Sample preparation was carried out by J.W.S. and Y.S. J.W.S., D.C.R. and Y.S. made energy-resolved measurements, and J.W.S. and D.C.R. made yield measurements with the help of F.S. All authors discussed the results and analysed data. N.A.M., Z-X.S, R.T.H. and P.P. supervised the project. J.W.S and N.A.M. carried out the simulations with the help of I.B. and D.C.R. J.W.S., I.B. and N.A.M. wrote the paper with editing from D.C.R., S.J.R. and B.E.H.
Received 9 October 2009; accepted 24 June 2010; published online 1 August 2010
Additional information
The authors declare no competing financial interests. Supplementary information accompanies this paper on https://www.wendangku.net/doc/f99861314.html,/naturematerials. Reprints and permissions information is available online at https://www.wendangku.net/doc/f99861314.html,/reprintsandpermissions. Correspondence and requests for materials should be addressed to N.A.M.
References
1. Würfel, P. Physics of Solar Cells: From Basic Principles to Advanced Concepts 2nd edn (Wiley-VCH, 2009).
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