ARTICLESPUBLISHED ONLINE: 1 AUGUST 2010 | DOI: 10.1038/NMAT2814

Photon-enhanced thermionic emission for solarconcentrator systemsJared 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 energyof solar radiation to excite electrons, as in photovoltaic cells, or the ‘thermal’ approach, which uses concentrated sunlightas a thermal-energy source to indirectly produce electricity using a heat engine. Here we present a new concept forsolar electricity generation, photon-enhanced thermionic emission, which combines quantum and thermal mechanisms intoa single physical process. The device is based on thermionic emission of photoexcited electrons from a semiconductorcathode at high temperature. Temperature-dependent photoemission-yield measurements from GaN show strong evidencefor photon-enhanced thermionic emission, and calculated efficiencies for idealized devices can exceed the theoretical limits ofsingle-junction photovoltaic cells. The proposed solar converter would operate at temperatures exceeding 200 ◦C, enabling itswaste 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 thesemiconductor’s bandgap excite electrons into the conductionband, which diffuse to electrodes and generate current. In

high-performance solar cells, charge separation and collectionare very efficient. However, the quantum approach of PV cellsplaces intrinsic limitations on single-junction conversion efficiency.Photon energy in excess of the bandgap is lost as heat, known asthermalization loss, and sub-bandgap photons are not absorbed atall, known as absorption loss. In silicon solar cells, thermalizationand absorption losses account for approximately 50% of theincident solar energy—most of the total energy loss1. In principle,these losses could be reclaimed by using this waste heat from the PVcell to power a secondary thermal cycle. Combinations of PV andthermal engines are predicted to have efficiencies greater than 60%(ref. 2), yet fail in practice because PV cells rapidly lose efficiency atelevated temperatures3, whereas heat engines rapidly lose efficiencyat low temperatures4.

Thermionic energy converters (TECs) are less well-known heatengines, which directly convert heat into electricity. A simplethermionic converter consists of a hot cathode and cooler anodeseparated by a vacuum gap. In the TEC cathode, a fraction of theelectrons have sufficient thermal energy to overcome the material’swork function and escape into vacuum, generating current betweenthe two electrodes. The thermionic current density is dictatedby the cathode work function and temperature according to theRichardson–Dushman equation: J = AC

∗TC2e−φC/kTC , where φC is

the cathode work function, TC the temperature and AC∗ the

materials-specific Richardson constant5. Thermionic converterswere first proposed and fabricated in the 1950s, with experimentalconversion efficiencies eventually reaching 10–15% (refs 5,6). BothNASA 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, StanfordUniversity, Stanford, California 94305, USA, 4Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA, 5Department ofMaterials Science and Engineering, Stanford University, Stanford, California 94305, USA, 6Stanford Synchrotron Radiation Lightsource, Menlo Park,California 94025, USA. *e-mail: nmelosh@stanford.edu.

of TECs for deep-space missions and other applications requiringhigh-power autonomous generators, but the technology was nevercommercialized. Thermionic conversion’s main challenges relateto the very high temperatures and substantial current densitiesrequired for efficient operation7,8.

Photon-enhanced thermionic emission (PETE) combines pho-tovoltaic and thermionic effects into a single physical process totake advantage of both the high per-quanta energy of photons, andthe available thermal energy due to thermalization and absorptionlosses. A PETE device has the same vacuum-gap parallel-platearchitecture as a TEC, except with a p-type semiconductor as thecathode (Fig. 1). PETE occurs in a simple three-step process: first,electrons in the PETE cathode are excited by solar radiation intothe conduction band. Second, they rapidly thermalize within theconduction band to the equilibrium thermal distribution accordingto the material’s temperature and diffuse throughout the cathode.Finally, electrons that encounter the surface with energies greaterthan the electron affinity can emit directly into vacuum and arecollected at the anode, generating current (Fig. 1a). Each emittedelectron thus harvests photon energy to overcome the materialbandgap, and also thermal energy to overcome the material’selectron affinity. The total voltage produced can therefore be higherthan for a photovoltaic of the same bandgap owing to this ‘thermalboost’, thusmore completely using the solar spectrum.

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

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NATURE MATERIALS DOI: 10.1038/NMAT2814 ARTICLES

φA

Evacuum

EF

EF,nφA

Photon-enhanced population

Thermal population

Cathode Anode

Eg

X

VOut

ZLoad

a b

Figure 1 | The PETE process. a, Energy diagram of the PETE process. Photoexcitation increases the conduction-band population, leading to largerthermionic 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 thePETE cycle is used to drive a thermal engine.

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

JC =∫∞

EC+χevxN (E)f (E)dE =

∫∞

EC+χevx

(4π(2m∗)3/2

h3

)√E−EC

× exp(−(E−EF,n)/kTC)dE (1)

where e is the electron charge, vx the electron velocity perpendicularto thematerial surface, χ the electron affinity,m∗ the effectivemass,EC the energy at the conduction-band minimum, N (E) the densityof states and f (E) the Fermi distribution. The right-hand expressionof equation (1) assumes that the density of states in the conductionband is parabolic and approximates the Fermi function by theBoltzmann distribution because the work function is much largerthan kTC. If we assume that the effective mass is isotropic, thenE−EC =m∗v2/2, where v2 = vx 2+v2y +vz 2, and we can re-expressthe integral in terms of electron velocities:

JC = 2e(m∗

h

)3

exp

(−(EC−EF,n

)kTC

)

×

∫∞

0dvy

∫∞

0dvz∫∞

vvac

dvxvx exp(−m∗v2/2kTC) (2)

where vvac =√2χ/m∗ is the minimum velocity necessary to

emit into vacuum. Significantly, evaluating equation (2) yieldsa result that is identical to the Richardson–Dushman equationfor thermionic current, except that the energy barrier in theexponent is relative to the quasi-Fermi level instead of theequilibrium Fermi level:

JC =(4πem∗k2

h3

)TC

2exp

(−(EC−EF,n+χ

)kTC

)

= ATC2exp

(−(φ−

(EF,n−EF

))kTC

)(3)

where A is the Richardson–Dushman constant. The right-handexpression explicitly shows that the effect of photo-illumination

on semiconductor thermionic emission is to lower the energybarrier by the difference between the quasi-Fermi level withphotoexcitation and the Fermi level without photoexcitation.Substituting the expression for EF,n into equation (3) and rewritingin terms of the electron density in the conduction band, n, averagevelocity perpendicular to the surface, 〈vx〉, and electron affinity, χ ,leads to an illuminating result:

JC= en〈vx〉e−χ/kTC (4)

This relation directly illustrates the effect of photoexcitation:illumination increases conduction-band concentration n over theequilibrium value neq, whereas the thermal energy determinesthe rate at which electrons emit over the electron affinity χ .For p-type semiconductors, neq can be extremely low, such thatphotoexcitation can greatly increase the emission current. As theelectron affinity can be almost arbitrarily tuned using surfacecoatings, such as Cs, the PETE process can be designed to operateover awide range of temperatures, unlike thermionic emitters.

A plot of idealized PETE current as a function of temperatureis shown in Fig. 2. At low temperatures, thermalized carriers inthe conduction band cannot overcome the electron-affinity barrierand the PETE current is negligible. For high-energy photons(hν > Eg + χ , where Eg is the bandgap) direct photoemission isalso possible, but it is not included here for clarity. As temperatureincreases, the PETE process becomes more efficient and currentincreases, eventually reaching a plateau as every photoexcitedelectron is emitted. At even higher temperatures, purely thermionicemission dominates as thermal processes overshadow the effect ofphotoexcitation, and the emission current is no longer determinedby the number of photoexcited electrons.

Despite the well-known individual physical mechanisms in-volved in PETE, the combined process has not previously been fullyexamined. Thermal energy has been suggested to assist electronemission over small interfacial barriers10,11, yet high-temperaturephotoemission from semiconductors has not been studied in detail.This is in part because caesium-based coatings, which are themost common work-function-lowering coatings in photocathoderesearch, generally degrade at temperatures between 100 and 200 ◦C(refs 12,13). Although a previous report noted that a combination ofphotoemission and thermionic emission could be used to increasecurrent from a commercial photocathode, photon enhancement ofthermionic emissionwas not considered as amechanism12.

PETE should show several physical signatures that differentiateit from photoemission or thermionic emission. PETE electronsshould thermalize before emission, resulting in a thermal dis-tribution of emitted electron energies regardless of the incident

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ARTICLES NATURE MATERIALS DOI: 10.1038/NMAT2814

Emitt

ed e

lect

rons

per

abo

ve-g

ap p

hoto

n Cathode currentThermal currentPhotocurrent

Photon-enhancedthermionic regime

Photoemissionregime

Thermionicregime

1.0

2.0

0.5

1.5

500 1,000Temperature (°C)

0 1,500

Figure 2 | Three regimes of electron emission. Depending on temperature,emission may be dominated by photoemission (not shown here), PETE orthermionic emission. This example assumes a cathode with χ =0.7 eV,Eg= 1.0 eV and×100 solar concentration. Some high-temperature regionsare not accessible at×100 concentration without extra thermal energy butare shown for the purpose of illustration.

above-gap photon energy. Conversely, in the case of photoemissionfrom a material with positive electron affinity, electrons excitedabove the vacuum level emit from the surface with minimalthermalization, resulting in a non-thermal energy distributiondependent on photon energy. In further contrast to PETE, overallphotoemission yield decreases with temperature owing to increasedscattering. PETE can be easily differentiated from thermionic emis-sion by comparing the current with andwithout illumination.

As a proof-of-principle of the PETE mechanism, we measuredthe temperature-dependent electron emission of caesiated GaN,an ultraviolet photocathode on which caesium forms a coatingwith unusually high thermal stability14. Samples were loadedinto an ultrahigh-vacuum chamber (low-10−10 torr base pressure)with sample-heating, monochromatic-illumination and electron-energy-analysis capabilities. The GaN was carefully dosed withCs 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 emittedelectrons, and the distribution widths increase with temperature.The slight non-monotonic temperature dependence of the peakposition is due to a ∼25meV change in the sample’s workfunction relative to that of the analyser over the course ofmeasurement, but this shift does not affect the broadening results.

Figure 3b provides further confirmation that at hightemperatures the electrons thermalized before emission andprovides a powerful example of the potential of PETE for powerconversion. The sample was illuminated with either 3.75 eVphotons (330 nm, energy approximately equal to the workfunction) or 3.3 eV photons (375 nm, energy barely exceeding thebandgap at 400 ◦C). The two distributions are virtually identical,indicating that the electron energy distribution immediatelyfollowing photoexcitation was unimportant, as would be expectedfrom PETE. Interestingly, as the average emitted-electron energywas approximately 3.8 eV, each electron excited with 3.3 eVlight acquired ∼0.5 eV in thermal energy before emission. In anenergy converter this thermal boost could be harvested by usinga proportionately higher operating voltage. For small-bandgapsemiconductors, such as Si (1.1 eV) or GaAs (1.4 eV), a similarthermal boost would represent a considerable increase over thebandgap energy. The energy distribution without illumination was

3.5 4.0 4.5Energy above VBM (eV)

Nor

mal

ized

co

unts

(a.

u.)

330 nm375 nm

400 °C

4.0

Nor

mal

ized

cou

nts

(a.u

.)

FWH

M (

eV)

100 200Temperature (°C)

NEA

350 nm

330 nm

0.17

0.18

0.19

0.20

3.5 4.5

Energy above valence band maximum (eV)

1.0

1.5

2.0

Rela

tive

QE

0.5

2.5

200 300Temperature (°C)

400

a

b c

Figure 3 | Temperature-dependent measurements of [Cs]GaN. a, Energydistributions of electrons emitted from GaN at 330 nm. The inset showsthat the electron distribution’s full-width at half-maximum (FWHM)increases with temperature. As noted in the Methods section, thetemperature calibrations in parts a and b are with respect to a siliconreference and are only approximate. b, Electron energy distributions at400 ◦C under 330 nm and 375 nm illumination. Measured photon energiesare shown as vertical lines. These curves have been normalized toemphasize the line shape, and emission current under 375 nm illuminationis substantially less because absorption at this wavelength is weaker. Purelythermionic emission from this sample in the absence of illumination isconsiderably smaller but occurs in the same energy range. c, Emissioncurrent of a sample with electron affinity close to the positive–negativecrossover as a function of temperature for 3.5 eV (350 nm) illumination.The emission current of the same sample near-optimally caesiated to astate of negative electron affinity at 350 nm illumination is shown as a blackdashed line for reference. These traces have been normalized to emphasizethe temperature dependence. The temperature range is less than in parts aand 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 thePETE process, the electron yield increased with temperature as well.The temperature-dependent emission current from a GaN samplewith a small positive electron affinity was measured in a separatevacuum chamber (Fig. 3c). As the sample temperature varied fromapproximately 50 to 225 ◦C, the emission current from 350 nmillumination more than doubled. The increase in yield for higher-energy photons was less dramatic, probably reflecting a contribu-tion from direct photoemission, which decreases with temperatureowing to increased scattering. More details on the quantum-yieldmeasurements can be found in the Supplementary Information. Forcomparison, the same sample was further dosed with caesium toreach a state of negative electron affinity (NEA), with the resultshown as a black dashed line in Fig. 3c. The stability of the NEAcoating restricted the maximum temperature for these experi-ments to ∼200 ◦C. Because electrons do not need to overcome an

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NATURE MATERIALS DOI: 10.1038/NMAT2814 ARTICLES

Flat-band condition

Eg = 1.4 eV1.0 eV

0.8 eV0.6 eV

Voltage (V)

Cur

rent

den

sity

(

A c

m¬

2 )

0.4 eV0.6 eV0.8 eV1.0 eV

× 100× 1,000× 3,000Ideal PV at × 3,000

Heat fraction

Photon fraction

× 1,000

X = 0.4 eV

Pow

er c

onve

rsio

n e

ffic

ienc

y

Pow

er c

onve

rsio

n ef

ficie

ncy

Eg = 1.4 eV

0.1

0.2

0.3

0.4

0.5

1.0 1.5

Bandgap (eV)

0.5 2.0

0.1

0.2

0.3

0.4

0.5

200 400 600 800Temperature (°C)

0 1,000

0

10

20

30

40

0.5 1.0 1.5 2.0

a b

c

Figure 4 | Theoretical PETE efficiency. a, PETE efficiency for the AM1.5 direct+circumsolar spectrum as a function of bandgap. The cathode temperatureand electron affinity are chosen to maximize the overall efficiency. The anode temperature is 227 ◦C to minimize the reverse current. In the inset, the poweroutput at×1,000 is shown to be due to roughly equal contributions from thermal (χ) and photon (Eg) energy. b, Power-conversion efficiency increaseswith χ owing to larger voltage but requires higher temperatures. Power output decreases almost linearly with temperature after current saturation in thePETE regime owing to the increasing cathode Fermi level. The concentration is×1,000. c, J–V curves for PETE devices with the same electron affinities asin b, showing the flat-band condition for χ =0.4 eV. The temperatures are those at which the efficiencies 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 indiffusion length. As a result, this trace shows a weak decreasein yield with temperature, clearly differentiating photoemissionand PETE processes.

Although caesiated GaN was convenient for demonstratingphoton enhancement of thermionic emission, efficient solar-powerconversion based on the PETE effect requires consideration ofseveral factors in addition to thermal and chemical stability, mostnotably absorption and recombination. Only 1% of solar photonshave energies exceeding the 3.3 eV bandgap of GaN, makingthe material unsuitable for solar applications. The high defectdensity and surface recombination of GaN, along with sub-optimalabsorption due to the sample’s thin-film geometry, resulted in lowPETE efficiencies: at 330 nm, the quantum efficiency was around0.14%. One route to overcoming challenges relating to absorptionand recombination is using nanostructures, which have shown longminority-carrier lifetimes15 due to high crystallinity and low defectdensities as well as significantly enhanced absorption over thinfilms16. However, to avoid complicating the analysis of theoreticalPETE-device efficiency, in what follows, an idealized parallel-platePETE converter is considered.

The power output of a thermionic or PETE converter iscalculated from the difference between the cathode current, JC,and the reverse thermionic current from the anode, JA, multipliedby the operating voltage. The operating voltage is given by thedifference between the cathode and anode work functions and anyextra voltage Vbias across the vacuum gap:

PPETE= JV = (JC− JA)(φC−φA+Vbias) (5)

Maximum power output for an idealized PETE converter occursat Vbias = 0, called the flat-band condition (Fig. 4c), provided thatφC−φA>kTC and JC� JA, and assuming that any electron absorbedfrom vacuum does not contribute to the cathode conduction-bandpopulation and hence cannot quickly re-emit (see SupplementaryInformation for further treatment).

Although the optimal value of φC reflects a complicated balancebetween maximizing electron current and operating voltage, theanode work function φA should be as small as possible to maximizetheoretical output voltage (equation (5)). In practice, this meansthat the anode temperature should be kept low enough tominimizereverse thermionic current.Work-function lowering is traditionallyachieved by coatingmaterials with alkali or alkali-earthmetals,mostnotably caesium. Caesiated tungsten anodes are used in thermionicconverters for their high-temperature stability and low workfunction (∼1.7 eV), and caesiated titanium’s work function canreach nearly 1 eV (ref. 17). Caesium coatings can also controllablyreduce a semiconductor anode’s (or cathode’s) electron affinity;for instance, in GaAs, χ can be reliably varied from ∼4 to 0 eVdepending on the surface coverage, and in some cases can even benegative18. However, alkali or alkali-earth deposition is not the onlypath to realizing low work functions. Recently, phosphorus-dopeddiamond was reported to have a work function of 0.9 eV withthermal stability to at least 765 ◦C (ref. 19). Although theoreticalPETE conversion efficiencies can be extremely high if the choice ofφA is not restricted, here we use a φA= 0.9 eV as an experimentallydemonstrated value.

The cathode emission current JC is calculated accordingto equation (4) by determining the steady-state conduction-bandpopulation n through balancing the rates of photoexcitation,thermionic emission and recombination. The rate of photo-excitation is determined by the flux of above-gap solar photons.Recombination in this analysis is treated in the detailed-balancelimit, so that any photoexcited electron leaves the conductionband either through thermionic emission or through radiativerecombination as determined by the Planck radiation law. Adiscussion of Auger recombination can be found in SupplementaryInformation, where it is seen that Auger can in some cases increasePETE device efficiency. Shockley–Read–Hall recombination ishighly dependent on processing and impurities and is thus ignoredin this theoretical analysis. Surface recombination is not consideredfor similar reasons, although it will be important for manymaterials, including GaN.

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ARTICLES NATURE MATERIALS DOI: 10.1038/NMAT2814

PETE device

Blackbody radiation

Cathode

Anode

Solarflux

ZLo

ad e¬

Heat to thermalcycle

Electroncurrent

× 1,000

PETE aloneTandem PETE/thermal

Pow

er c

onve

rsio

n ef

ficie

ncy

0.2

0.3

0.4

0.5

1.0 1.5Bandgap (eV)

0.5 2.0

a b

Figure 5 | Theoretical tandem efficiency. a, Energy-flow diagram for the PETE/thermal tandem device. Solar radiation is absorbed by the cathode. Thecathode emits blackbody radiation both away from the device and towards the anode, whereas in Fig. 4 radiation exchange between cathode and anode isminimal. 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 electronsand photons from the cathode is released as blackbody radiation or reverse current, or delivered to a thermal cycle, which converts a fraction into usefulwork. b, Total PETE/thermal efficiency compared with PETE efficiency as a function of cathode bandgap at×1,000 concentration, assuming a 285 ◦Canode thermally coupled to a 31.5%-efficient thermal engine.

The PETE device is assumed to have a parallel-plate geometry(Fig. 1b), with the incident light striking the cathode through aninfrared-absorbing substrate, so that sub-bandgap photons con-tribute to heating the cathode. The cathode is a thin semiconductorfilmwith an electron diffusion lengthmuch longer than the relevantlength for electron escape, so that the electron population is evenlydistributed. Each above-gap photon is assumed to excite an electroninto the conduction band. The total energy flux to the cathodeis determined by comparing the rate of solar absorption withthe rates of (detailed-balance-limited) blackbody emission andthermionic electron emission. After the PETE current is determinedby self-consistently solving for the conduction-band population,the requirement of zero net energy flux at the cathode enables thetotal power generated for a given Eg to be optimized by suitablechoices of TC and χ . Other cathode parameters such as the effectivemasses are based on p-type (doped at 1019 cm−3) Si (ref. 9), anddependent quantities such as neq and EF are found for each set ofparameters using standard equations. Detailed descriptions of thesecalculations are provided in the Supplementary Information.

The theoretical PETE conversion efficiency as a function ofEg and the concentration of the direct+ circumsolar AM1.5 solarspectrum is shown in Fig. 4a. The optimal bandgap is between 1.1and 1.7 eV, with a maximum at 1.35 eV. PETE is more efficientat higher solar concentrations, as expected from equation (4),with maximum efficiencies of 32% for ×100 concentrationand 47% for ×3,000. Impressively, PETE efficiency exceeds theShockley–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 oversingle-junction PV devices is that it successfully uses the heatproduced by thermalization and sub-bandgap photon absorptionto increase the output voltage, as was observed in the GaNexperiments. Figure 4a (inset) shows that photon and thermalcontributions (Eg and χ) are comparable at ×1,000 concentrationand roughly correspond to the relative amounts of the solarspectrum absorbed as photons and heat for a given Eg.

The temperature-dependent power output for a number ofelectron affinities is shown in Fig. 4b. Larger χ values producehigher output voltages yet require higher temperature to producesignificant current. Although a device with χ = 0.4 eV reaches

a maximum efficiency of ∼25% at 200 ◦C, for χ = 1.0 eV themaximum efficiency is 40% but requires a temperature of 800 ◦C.The low temperatures necessary are also quite appealing comparedwith thermionic devices.

The potential of PETE devices to improve solar-energy conver-sion is not just a more efficient single stage, but the opportunityto create a tandem cycle with a thermal engine. The high oper-ating temperature in a PETE device matches well with thermalsystems, such as a steam turbine or Stirling engine, enabling thewaste heat from the PETE stage to drive a second thermal stage.A diagram of the energy flow in a PETE/solar-thermal tandemarchitecture is shown in Fig. 5a. Light is absorbed by the PETEcathode, which emits electrons and blackbody radiation that deliverheat energy to the anode. The anode is coupled to a thermalcycle, which removes the excess heat and uses it to generateelectrical power. Tandem-PETE/thermal-engine efficiency for aconcentration of ×1,000 suns is shown in Fig. 5b, assuming ananode temperature of 285 ◦C and a thermal-to-electricity efficiencyof 31.5% (refs 21,22). Total conversion efficiencies exceeding 53%are possible even at these low anode temperatures, constituting a70% increase over the thermal cycle alone. The optimal bandgapshifts to a slightly lower value, ∼1.15 eV, favouring more heatproduction than in a stand-alone PETE device. These calculationscompare well with a previous report2 that found that an idealizedphotovoltaic/Carnot-engine tandem cycle at 500K could reach 62%efficiency, provided that the PV cell could operate at arbitrarytemperatures. In this context, the PETE device can be thought of asa high-temperature photovoltaic that can be used in combinationwith a thermal cycle.

By using both thermal energy and photon energy, PETE canpotentially achieve device efficiencies that exceed the fundamentallimits on single-junction cells and rival those of complex mul-tijunction cells, the best of which are around 40% efficient23.PETE’s straightforward design could lead to inexpensive man-ufacturing, using processes derived from microelectromechani-cal systems (MEMS) technology, such as vacuum encapsulationby wafer-to-wafer bonding. In addition, high solar concentra-tions could potentially reduce material costs by scaling the de-vice area. PETE devices are naturally synergistic with thermalengines and could be implemented as modular attachments to

766 NATURE MATERIALS | VOL 9 | SEPTEMBER 2010 | www.nature.com/naturematerials

NATURE MATERIALS DOI: 10.1038/NMAT2814 ARTICLESexisting solar-thermal infrastructure. Even a modestly efficientPETE module in tandem with a thermal engine could achieve atotal system efficiency exceeding what is at present possible in asolely thermal or photovoltaic system, motivating research intocombined quantum/thermal processes. Further efficiency improve-ments may be possible through new materials, nanostructures andplasmonic processes24 that can increase light absorption, carrierconcentrations and emission probability. From the calculations anddata shown here, the concept of harvesting photon and thermalenergy together through PETE is a highly attractive mechanismfor improving the efficiency of solar-energy collection that meritsserious investigation.

MethodsEnergy-resolved electron-emission measurements in Fig. 3a,b were made atbeamline 8-1 at the Stanford Synchrotron Radiation Lightsource (SSRL),maintained by Y.S. Yield measurements in Fig. 3c were made at a system onStanford’s campus maintained by J.W.S., D.C.R. and F.S. Most experimental detailsare similar between the two set-ups, with differences noted below.

Sample preparation. The 100 nm GaN samples were grown on sapphire substratesby SVT Associates and were Mg doped to a hole density of 5.3× 1018 cm−3(measured by SVT Associates, dopant concentration of approximately1× 1020 cm−3). The samples were cleaned in 98% sulphuric acid at 70 ◦Cfor 5min. A piece of tantalum foil was placed between the sample and amolybdenum sample holder to improve thermal contact, and the sample wasaffixed using molybdenum clips. The sample holder was put in a load lock, whichreached a pressure in the 10−8 torr range. The sample was then transferred into themain chamber, whose base pressure was in the low-10−10 torr range. The samplewas heat cleaned in vacuum at approximately 400 ◦C.

Caesium deposition and sample heating. The caesium evaporator was fromAlvatec at Stanford and from SAES at SSRL. Caesium was incrementally depositedat the maximum sample temperature (220 ◦C at Stanford and 400 ◦C at SSRL) untilmeasurements 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 30–60min to ensurereliable temperature readings, and sample measurements were made at each step.Following this temperature sweep, the sample temperature was increased to checkfor degradation of the Cs coating. The temperature was read by a thermocouple onthe heater assembly, which had been previously correlated to sample temperature.At Stanford, temperature calibration had been carried out with a thermocouple ona GaN reference. This calibration is expected to be accurate to±20%. Temperaturecalibration at SSRL had been carried out using a silicon reference, and temperaturesreported here are only approximate.

Measurement. The light source for QE measurements was a monochromatized150WXe lamp. After passing through a fibre bundle and an order-sorting filter, themonochromatized light was collimated, and a fraction was split off to a calibratedsilicon photodiode to measure intensity for yield measurements. The remainderwas focused through a viewport to make a spot of approximately 2mm diameteron the sample surface at Stanford and approximately 4mm at SSRL. The split-offbeam and beam through the viewport, which was fused silica at Stanford and Pyrexat SSRL, had been previously calibrated, and this measurement is expected to beaccurate to±10%. The fibre bundle and optics were all fused silica.

In the yield measurements at Stanford, a copper disc, which was locatedapproximately 75mm from the sample surface, was biased to 400 V to accelerateelectrons away from the sample, which was near ground potential. Currentsreported here were measured from the sample.

At SSRL, the low-energy cutoff of the emitted electrons was measured usinga PHI 10-360 hemispherical analyser at 5.85 eV pass energy, resulting in ananalyser resolution estimated to be around 100meV, consistent with manufacturerspecifications. To overcome the 4.40 eV analyser work function, the samplewas biased to 9.90V. The energy-distribution curves shown in this report arecorrected for this bias as well as for the calculated Fermi-level position relativeto the valence-band maximum assuming a 170meV activation energy for Mg, asdetailed in the Supplementary Information. Cs coverage and the valence-bandposition at the surface were monitored with synchrotron radiation at 120 eV butare not reported here.

Received 9 October 2009; accepted 24 June 2010;published online 1 August 2010

References1. Würfel, P. Physics of Solar Cells: From Basic Principles to Advanced Concepts

2nd edn (Wiley-VCH, 2009).

2. Luque, A. & Marti, A. Limiting efficiency of coupled thermal and photovoltaicconverters. Sol. Energy Mater. Sol. Cells 58, 147–165 (1999).

3. Green, M. A. General temperature dependence of solar cell performanceand implications for device modelling. Prog. Photovolt. Res. Appl. 11,333–340 (2003).

4. Kribus, A. & Mittelman, G. Potential of polygeneration with solar thermal andphotovoltaic systems. J. Sol. Energy Eng. 130, 011001 (2008).

5. Hatsopoulos, G. N. & Gyftopoulos, E. P. Thermionic Energy Conversion Vol. I(MIT Press, 1973).

6. Hatsopoulos, G. N. & Kaye, J. Measured thermal efficiencies of a diodeconfiguration of a thermo electron engine. J. Appl. Phys. 29, 1124–1125 (1958).

7. National Research Council Committee on Thermionic Research andTechnology. Thermionics Quo Vadis? An Assessment of the DTRA’s AdvancedThermionics Research and Development Program (National Academy 2001).

8. Adams, S. F. Solar thermionic space power technology testing: A historicalperspective. AIP Conf. Proc. 813, 590–597 (2006).

9. Sze, S. M. Physics of Semiconductor Devices 2nd edn (Wiley, 1981).10. Bell, R. L., James, L. W., Antypas, G. A., Edgecumbe, J. & Moon, R. L.

Interfacial barrier effects in III–V photoemitters. Appl. Phys. Lett. 19,513–515 (1971).

11. Fisher, D. G., Enstrom, R. E., Escher, J. S. & Williams, B. F. Photoelectronsurface escape probability of (Ga, In)As : Cs–O in the 0.9 to ∼1.6 µm range.J. Appl. Phys. 43, 3815–3823 (1972).

12. Smestad, G. P. Conversion of heat and light simultaneously using a vacuumphotodiode and the thermionic and photoelectric effects. Sol. Energy Mater.Sol. Cells 82, 227–240 (2004).

13. Martinelli, R. U. Thermionic emission from Si/Cs/O(100) surface. J. Appl. Phys.45, 1183–1190 (1974).

14. Machuca, F. et al. Prospect for high brightness III-nitride electron emitter.J. Vac. Sci. Technol. B 18, 3042–3046 (2000).

15. Guichard, A. R., Barsic, D. N., Sharma, S., Kamins, T. I. & Brongersma, M. L.Tunable light emission from quantum-confined excitons in TiSi2-catalyzedsilicon nanowires. Nano Lett. 6, 2140–2144 (2006).

16. Zhu, J. et al. Optical absorption enhancement in amorphous silicon nanowireand nanocone arrays. Nano Lett. 9, 279–282 (2009).

17. Fomenko, V. S. Handbook of Thermionic Properties (Plenum, 1966).18. Madey, T. E. & Yates, J. T. Jr Electron-stimulated desorption and work

function studies of clean and cesiated (110) GaAs. J. Vac. Sci. Technol. 8,39–44 (1971).

19. Koeck, F. A. M., Nemanich, R. J., Lazea, A. & Haenen, K. Thermionicelectron emission from low work-function phosphorus doped diamond films.Diamond Relat. Mater. 18, 789–791 (2009).

20. Shockley, W. & Queisser, H. J. Detailed balance limit of efficiency of p–njunction solar cells. J. Appl. Phys. 32, 510–519 (1961).

21. Mills, D. R., Le Lievre, P. & Morrison, G. L. Solar 2004 ANZSES Conf. Proc.,Perth (ANZSES, 2004).

22. Mills, D. R., Morrison, G. L. & Le Lievre, P. EuroSun 2004 Conf.Proc., Freiburg (DGS, 2004).

23. Green, M. A., Emery, K., Hishikawa, Y. & Warta, W. Solar cell efficiency tables(Version 34). Prog. Photovolt. Res. Appl. 17, 320–326 (2009).

24. Nakayama, K., Tanabe, K. & Atwater, H. A. Plasmonic nanoparticleenhanced light absorption in GaAs solar cells. Appl. Phys. Lett. 93,121904 (2008).

AcknowledgementsJ.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 ofMaterials Sciences, under Award DE-AC02-76SF00515. I.B. was partially supportedby Robert Bosch Palo Alto Research and Technology Center and DARPA throughthe Center on Interfacial Engineering in Microelectromechanical Systems. Portionsof this research were carried out at the SSRL, a national user facility operated byStanford University on behalf of the US Department of Energy, Office of Basic EnergySciences. The authors would like to thank Z. Hussain, J. Pepper, V. K. Narasimhan andK. Sahasrabuddhe for discussions.

Author contributionsJ.W.S., D.C.R., Z-X.S. and N.A.M. designed experiments. Sample preparation was carriedout by J.W.S. and Y.S. J.W.S., D.C.R. and Y.S. made energy-resolved measurements, andJ.W.S. and D.C.R. made yield measurements with the help of F.S. All authors discussedthe 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.andN.A.M. wrote the paper with editing fromD.C.R., S.J.R. and B.E.H.

Additional informationThe authors declare no competing financial interests. Supplementary informationaccompanies this paper on www.nature.com/naturematerials. Reprints and permissionsinformation is available online at http://npg.nature.com/reprintsandpermissions.Correspondence and requests formaterials should be addressed toN.A.M.

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