Engineered nanomaterials for solar energy conversion

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Nanotechnology 24 (2013) 042001 (11pp) doi:10.1088/0957-4484/24/4/042001

TOPICAL REVIEW

Engineered nanomaterials for solarenergy conversion

Vladan Mlinar

School of Engineering, Brown University, Providence, RI 02912, USA

E-mail: vladan mlinar@brown.edu

Received 7 November 2012, in final form 7 December 2012Published 8 January 2013Online at stacks.iop.org/Nano/24/042001

AbstractUnderstanding how to engineer nanomaterials for targeted solar-cell applications is the key toimproving their efficiency and could lead to breakthroughs in their design. Proposedmechanisms for the conversion of solar energy to electricity are those exploiting the particlenature of light in conventional photovoltaic cells, and those using the collectiveelectromagnetic nature, where light is captured by antennas and rectified. In both cases,engineered nanomaterials form the crucial components. Examples include arrays ofsemiconductor nanostructures as an intermediate band (so called intermediate band solarcells), semiconductor nanocrystals for multiple exciton generation, or, in antenna–rectifiercells, nanomaterials for effective optical frequency rectification. Here, we discuss the state ofthe art in p–n junction, intermediate band, multiple exciton generation, and antenna–rectifiersolar cells. We provide a summary of how engineered nanomaterials have been used in thesesystems and a discussion of the open questions.

(Some figures may appear in colour only in the online journal)

1. Introduction

The proposed mechanisms for the conversion of solar energyto electricity include those exploiting the particle natureof light in conventional photovoltaic cells, where absorbedphotons generate electron–hole pairs, and those using thecollective electromagnetic nature of the light, where sunlightis captured by antennas and rectified. In recent years, therehas been immense progress in solar-cell technologies and adramatic decrease in their cost. For example, the efficiencyof solid-state photovoltaic (PV) cells started with valuesof ∼5% [1], but now there are routinely achievable valuesof >20% in Si-based systems and >30% in GaAs-basedsystems [2].

Perhaps the best way to track the technological progressis by examining the three generations of PV, defined by theincrease of efficiency versus the reduction in cost [2]. Firstgeneration PV includes solar cells made of semiconductingp–n junctions, such as single crystal Si and poly-grainSi. Second generation PV reduced cost by introducing the

thin-film technologies. Examples include amorphous Si, thin-film Si, CuInSe2, CdTe, and dye-sensitized photochemicalcells. Current, third generation, PV should lead to anincrease in efficiency. Proposed improved solar cells includee.g., high efficiency multi-gap tandem cells, multiple excitongeneration solar cells, intermediate band solar cells (IBSCs),hot carrier converters, thermophotovoltaics/thermophotonics,etc. Furthermore, it has been proposed that sunlight could becaptured by (nano)antennas and rectified using a diode byexploiting the wave nature of the light [3–5, 2].

Engineered nanomaterials are the key building blocksof the current generation solar cells. For example, the ideabehind the IBSCs is to introduce one or more energy levelswithin the bandgap so that they absorb photons in parallel withthe normal operation of a single-bandgap cell [6]. The searchfor optimal sub-bandgap absorbers has been focused on highlymismatched semiconductor alloys that naturally exhibit anintermediate band (IB) [7, 8, 6], and on nanostructures, inparticular arrays of quantum dots that form an IB [9–11, 8,6].

10957-4484/13/042001+11$33.00 c© 2013 IOP Publishing Ltd Printed in the UK & the USA

Nanotechnology 24 (2013) 042001 Topical Review

Other examples include the potential usage of semi-conducting nanocrystals in multiple exciton generation solarcells, where excitation of a semiconductor nanocrystal by asingle, high-energy photon may result in a few electron–holepairs [2, 12–19], or nanomaterials for the design of opticalantennas with a typical dimension of ∼100–1000 nm,supporting modes which exhibit extremely short wavelengthsand strong confinement of the electromagnetic field on thenanometer scale [5, 2, 20].

A new playground has opened for engineered nanoma-terials, and at this point it is simply not sufficient to focusonly on technological improvements. Further technologicalbreakthroughs depend strongly on an improved fundamentalunderstanding of electronic, optical, and transport propertiesof nanomaterials and finding an efficient way to transfertechnology from research laboratories to industry. Recentadvances in computational nanoscience, combined withstate-of-the-art experiments, could potentially enable suchbreakthroughs.

Quantum mechanical models have become sophisticatedenough to handle nanosystems of a few tens or a fewthousands up to hundreds of thousands of atoms, includingexcitations and many-body effects. They are able to handlerealistic structural information obtained from the structuralcharacterization measurements and take into account all therelevant effects, including the strain and piezoelectric effects,and external magnetic and electric fields [21]. Using thesemodels we can, at least in principle, connect structure andphysical properties of a nanomaterial.

Furthermore, combining the quantum methods withmachine learning algorithms has opened new pathways forthe design and engineering of nanomaterials with targetedproperties [21]. Once a targeted physical property has beendefined, the quantum mechanical models and search/machinelearning algorithms are employed to deduce one or a fewbest candidate nanomaterials. It was suggested that, fortechnological applications, the same method could be usedto optimize the nanomaterials with respect to the targetedphysical property, avoiding a long and costly process thatincludes nanomaterials’ fabrication and characterization [21].However, before even considering the application of thepredictive-theory-guided design to solar cells, we need tounderstand the current fundamental and practical problemswith the solar cells. Only then can we discuss how realisticand potentially useful the predictive-theory-guided designcould be.

Here, we discuss the state of the art in p–n junction,IB, multiple exciton generation, and antenna–rectifiersolar cells. We provide a summary of how engineerednanomaterials have been used in these systems and adiscussion of the open questions. For example, we addressrecent findings on how to exceed the thermodynamical limiton light trapping [22], or very recently reported multipleexciton generation enhancement of photocurrent in PbSenanocrystal-based solar cells [19]. Understanding how toengineer nanomaterials for targeted solar-cell applicationsis the key to improving their efficiency and could lead tobreakthroughs in the design.

2. p–n junction solar cells

The solar spectrum contains photons with energies rangingfrom about 0.5 eV to 3.5 eV. Conventional solar-celltechnology is based on a single p–n junction, benefiting fromone electron–hole pair for each absorbed photon, as shownin figure 1(a). When light quanta are absorbed, electron–holepairs are generated, and if their recombination is preventedthey can reach the junction, where they are separated by anelectric field.

Current photovoltaic technologies utilize semiconduc-tors, such as large crystals of silicon, or thin films ofamorphous silicon, cadmium telluride (CdTe), or copperindium gallium selenide (CIS). The semiconductor materialhas to be able to absorb a large part of the solar spectrum,which is determined by its bandgap, as illustrated by examplesin figure 1(b). For example, amorphous silicon has a higherbandgap (1.7 eV) than crystalline silicon (1.1 eV), whichmeans that it absorbs the visible part of the solar spectrummore strongly than the infrared portion of the spectrum.

The p–n junction solar cells based on crystallinesilicon now routinely achieve an efficiency of ∼22% [23,2]. The maximum thermodynamic efficiency for single-bandgap devices, assuming detailed balance, is 31%, theShockley–Queisser limit [24]. It is obvious from figure 1(b)that by layering materials with different bandgaps one canimprove the efficiency. This is the underlying idea of themulti-layer (‘tandem’) cells, which are highly efficient, butalso expensive [2].

The energy conversion efficiency of solar cells basedon thin-film silicon is typically lower than that of bulksilicon [23]. These limitations have been overcome byemploying light-trapping schemes. The incoming light isobliquely coupled into the silicon and the light traverses thefilm several times, enhancing the absorption in the films [23].The minimum thickness of the material is defined by thethermodynamical limit on light trapping [25]. However, recentfindings demonstrate that, in principle, any semiconductormaterial can exceed the light-trapping limit when the localdensity of optical states (LDOS) of its absorbing layer exceedsthe LDOS of the bulk semiconductor material [22]. This couldpotentially allow for the design of novel solar cells that canabsorb light from the entire solar spectrum, but are ∼10 nmthick [22].

Another way of creating the p–n junctions in semicon-ductors is by utilizing the electric field effect, where theconcentration of charge carriers in a semiconductor is alteredby the application of an electric field. Very recently, it hasbeen proposed to exploit this effect to induce a p–n junction,enabling, at least in principle, a high quality p–n junction to bemade of basically any arbitrary semiconductor [26]. The ideais to carefully design the top electrode so the gate electric fieldcan sufficiently penetrate the electrode and more uniformlymodulate the semiconductor carrier concentration and type.The method is illustrated on the example of silicon and copperoxide, where in the case of silicon, the top contact is made ofa single layer of graphene across the surface [26].

The major factors limiting the conversion efficiency arethe inability to absorb photons with energy less than the

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Figure 1. (a) Schematic diagram of a conventional single-junction semiconductor solar cell (CSC). Absorbed light with photon energiesgreater than the bandgap produces carriers, electrons and holes. Loss processes are nonabsorption of below-bandgap photons, heat losses,and radiative recombination. (b) Different materials absorb different parts of the solar spectrum depending on their bandgaps.

Figure 2. (a) Band diagram of an intermediate band solar cell (IBSC). Simultaneous with normal operation of the cell, below-bandgapphotons get absorbed by the two transitions to and from the intermediate level contributing to the photocurrent. (b) Limiting efficiency forIBSC and conventional SC (CSC) as a function of E1 (intermediate band–valence bandgap). We used data from Laque and Marti [27].

bandgap, thermalization of photon energies exceeding thebandgap, and radiative recombination losses [23, 2]; seefigure 1(a). When a photon is absorbed with energy greaterthan the bandgap of a semiconductor, the resultant carrierundergoes fast cooling via phonon scattering and emission.

Three approaches have been put forward to addressthis loss of efficiency [2]: (i) increasing the number ofenergy levels, typically by using a stack of multiple p–njunctions in different semiconductor materials (figure 1(b));in this way higher-energy photons are absorbed in thehigher-bandgap semiconductors and lower-energy photonsin the lower-bandgap semiconductor; (ii) capturing carriersbefore thermalization, yielding a higher photovoltage; and(iii) multiple-carrier-pair generation per high-energy photonor single-carrier-pair generation with multiple low-energyphotons, leading to the enhancement of the photocurrent.

3. Intermediate band solar cells

The main idea behind IBSCs is to introduce one ormore energy levels within the bandgap such that theyabsorb photons in parallel with the normal operation of asingle-bandgap cell [6, 8, 2, 27, 28]. A band diagram of anIBSC is shown in figure 2(a). Sub-bandgap energy photons areabsorbed through transitions from the valence band (VB) tothe intermediate band (IB) and from the IB to the conduction

band (CB), enabling, at least in principle, IBSCs to achieveboth high current and high voltage.

The IB has to be partially occupied to enable absorptionfrom the VB into the empty states of the IB, and fromoccupied states of the IB to the CB. Splitting the Fermilevel into three separate quasi-Fermi levels preserves the highoutput voltage of the cell [6]. Of course, VB to IB and IBto CB transitions must be optically allowed and strong, andthe IB needs to be electronically isolated from both the CBand the VB, so VB to IB and IB to CB absorption spectrado not have spectral overlaps with each other [8, 11, 27]. Thetheoretical limiting efficiency of IBSC is 63% [27], derivedat isotropic sunlight illumination and assuming the Sun andEarth temperatures to be 6000 K and 300 K, respectively.Under the same conditions, the maximum efficiency of asingle-gap solar cell was 41%. Variation of the efficiency withthe IB–VB gap E1 is shown in figure 2(b), where we used datafrom Laque and Marti [27].

The quest for finding optimal sub-bandgap absorbers hasbeen focused on (i) alloys that naturally exhibit an IB [7, 8, 6]and (ii) nanostructures, in particular arrays of quantum dots(QDs) that form an IB [9–11, 8, 6].

Bulk IBSCs. The electronic band structure of highlymismatched semiconductor alloys can be tuned bothexperimentally and theoretically to exhibit three electronicallyisolated energy bands [8]. In highly mismatched alloys this

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can be achieved by the substitution of a relatively smallfraction of host atoms with an element of very differentelectronegativity. Examples include III–V and II–VI alloys, inwhich group V and VI anions are replaced with the isovalentN and O, respectively, see e.g., [29, 30]. The electronicstructure of such alloys is determined by the interactionbetween localized states associated with N or O atoms andthe extended states of the host semiconductor matrix. Asa result the conduction band splits into two subbands withdistinctly nonparabolic dispersion relations [29], affecting theoptical and electrical properties of these alloys. A narrowlower band can be formed only if the localized stateslie well below the conduction band edge. Consequently,the absorption spectrum is modified by adding two newabsorption edges, which can be tuned, at least in principle,to fall within the solar energy spectrum [30]. Experimentalexamples include the formation of an IB within thebandgap of highly mismatched semiconductor alloys suchas Zn1−yMnyOxTe1−x and GaNxAs1−x−yPy [29, 30]. The IBwas detected by spectral photoreflectance measurements, andits formation was attributed to band anticrossing. In orderto obstruct electron tunneling between the IB and CB, andconsequently maintain a high open-circuit voltage, blockinglayers were introduced. This was successfully demonstratedon an example of GaN0.024As0.976 [28, 8].

From theoretical and computational viewpoints, numer-ous ab initio calculations have been performed in the quest foroptimal IB materials. The most promising of these has beenV0.25In1.75S3, which has strong sub-bandgap absorption andan inherent partially filled IB [7]. This is important because itmeans that the IB is already partially filled without having torely on impurity doping, which reduces densities and thereforelowers absorption levels.

Bulk IBSCs have so far exhibited efficiencies far belowtheir potential, and the issue of finding the best candidatematerials for this technology is essential if IBSC research isto succeed.

Quantum dot IBSCs. An IB can also be formed fromthe confined states of QDs situated within the bandgapof a host semiconductor. QDs should be closely spacedand with high quality interfaces, which would enable thestrong wavefunction overlap and the formation of minibands.To achieve strong absorption to and from the IB, a highconcentration of QDs is required. By engineering theparameters such as QD geometry (size and shape), inter-dotseparation, and dot arrangement, one can optimize IB positionand width to achieve the maximum efficiency [31, 32].Typically, self-assembled (In, Ga)As QDs embedded in aGaAs matrix have been used as an IB (see, e.g., [6]).Other examples include InAs QDs in a GaAs/(Al, Ga)Asmatrix [33], or GaSb QDs in GaAs [34]. Interestingly, some ofthese devices have demonstrated features of IBSC operation,and achieved efficiencies over 18% [10, 6].

Self-assembled QDs consist of 104–106 atoms of asemiconductor such as (In, Ga)As embedded in anothersemiconductor matrix, e.g., GaAs. They are fabricated bythe Stranski–Krastanov (SK) growth mode, which uses thenatural lattice mismatch between the substrate and the

deposited material [35, 36]. The shape and average sizeof these QD islands depend mainly on factors such as thestrain intensity in the layer as related to the misfit of thelattice constants, the temperature at which the growth occurs,and the growth rate. The islands evolve to the state ofquasi-equilibrium in which they assume the shape of pyramidsor lenses formed on a thin wetting layer, that are then cappedby the barrier material. The main advantages of the SKgrowth mode are fabrication of defect-free QDs of small sizes,homogeneity in sizes and shapes of QDs, formation of orderedarrays of 3D coherent islands, and fairly convenient growthprocesses [35, 36]. Indeed, their structural perfectness (noimpurities, dislocations, and defects), the excellent isolationfrom the environment, and the ability to charge the systemwith a few electrons or holes (multiexcitons), have madethem essential in studying many-particle physics in confinedspaces [37, 38]. Unlike colloidal QDs, where nonradiativedecay channels rapidly destroy multiexcitons and, e.g., causeblinking in photoluminescence (commonly interpreted asbeing caused by the presence of extra charges that enhancenonradiative decay rate) [39, 40], in self-assembled QDsthe multiexcitons ‘survive’ (and decay radiatively). Also,the photocorrosion and photostability [41] of colloidal QDs,where QDs stability depends on the solution (e.g., it wasfound that CdS QDs in nonpolar solvent were remarkablystable even under UV light irradiation) [41], do not influenceself-assembled QDs.

In order to create a mini-band, some measure ofhomogeneity must exist between the successive quantum dotlayers. However, the strain may accumulate so that layers ofcoherent quantum dots may no longer be formed, thus limitingthe number of QD layers [42–44]. The strain-induced limit ofthe number of QD layers can be lifted by employing systemswith the strain symmetrization within the structure, such as the(In, Ga)As/Ga(As, P) system [11]. It was found that, whereasthe number of QD layers was indeed increased, the intensityof absorption between QD-confined electron states and thehost CB was weak (because of their localized-to-delocalizedcharacter) and the position of the IB within the matrixbandgap did not satisfy suitable energetic locations for theIB [11].

Furthermore, one of the challenges in the QD IBSCdesign has been the loss of output voltage at room temperaturecompared to reference solar cells without an IB [6]. The lossof voltage at room temperature is caused by the thermal escapeof electrons from the IB to the CB (in addition to tunneling ofelectrons from the IB to the CB) [6, 8].

Thus, from a fundamental viewpoint, there is a needfor better understanding of the nature of the IB (localizedversus extended), and carrier relaxation processes. Froma purely technological viewpoint, the quest for improvedfabrication techniques and more suitable materials (strainsymmetrization and strong absorption between the IB andCB) has only just begun. As an illustration of the sensitivityof the problem, careful fabrication of InAs/GaAs IBSCs ledto a significant elimination of output-voltage reduction [45],potentially opening pathways for room temperature IBSCs.

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Figure 3. The single photon generation of multiple excitons (electron–hole pairs). (a) Bulk and (b) nanocrystal.

Figure 4. (a) The ideal profiles for carrier multiplication efficiency η, the number of excitons generated by absorption of a photon, for bulkPbSe (green), nanocrystals NC1 (blue) and NC2 (red). The shaded region represents the AM1.5G solar spectrum [49]. (b) Quantum yieldversus photon energy for PbSe [13, 50, 15, 47] and PbS [13, 17, 47] nanocrystals (NCs) and bulk; data from various groups illustrate widevariations of reported MEG QYs. The quantum yield represents the averaged number of excitons per absorbed photon. QY = 200% meansall dots have two excitons.

4. Multiple exciton generation solar cells

Multiple exciton generation (MEG), or carrier multiplication,is the generation of more than one electron–hole pair(exciton) by absorption of one photon [46–48]. High-energyphotons, at least twice the bandgap energy, absorbed in abulk semiconductor can generate one or more additionalelectron–hole pairs close to the bandgap energy through ascattering process, known as impact ionization (the inverseof Auger recombination) (figure 3(a)) [2, 47, 48, 46]. Theimpact ionization was previously observed in bulk Si, PbS,PbSe, Ge, InSb, etc. This effect is inefficient in bulk becausethe rate of impact ionization is much slower than the rate ofradiative recombination at low electron energies (in visibleand near IR spectrum) and the need to conserve momentum. Inaddition, the impact ionization in bulk is not useful for energyconversion purposes because the required photon energies lieoutside the solar spectrum (3.5 eV); e.g., it requires ∼7 eVphotons to produce one extra carrier in silicon [19, 46, 2].

Thus, it was proposed that MEG can be more efficientin semiconducting nanocrystals [12, 15]. Given the uniqueelectronic structure properties of nanocrystals–atomic-likeelectronic structure and size-dependent bandgap energies [15,38], it was suggested that the relaxation dynamics of

photogenerated carriers may be affected by quantizationeffects, and lead to more efficient solar cells (figure 3(b)). Forexample, hot carrier cooling rates of impact ionization couldbecome competitive with the rate of carrier cooling [2, 13].

Numerous experiments have confirmed the existenceof MEG in nanocrystals (although not without controversy,as discussed below) by showing that excitation of asemiconductor nanocrystal by a single, high-energy photonmay result in a few electron–hole pairs (figure 3(b)) [2,12–19]. The single photon generation of multiple excitonsoccurs on a very short time scale following photon absorption,where the efficiency increases with the energy of the photon.

Figure 4(a) shows the ideal profiles for multiple excitongeneration efficiency η [48, 46] in bulk PbSe Eg = 0.27 eV(green), nanocrystal NC1 with Eg = 0.72 eV (1722.2 nm)(blue) and nanocrystal NC2 with Eg = 1.3 eV (954 nm)(red). The efficiency η is defined as the number of excitonsgenerated by absorption of a photon. It was calculated usingthe detailed balance model under the assumptions that allphotons with energies above the bandgap were absorbed andthose with energies less than the bandgap were not, thatthe only loss is the radiative recombination, and that allphotogenerated carriers are collected [48]. The calculationsalso give the maximum efficiency depending on the bandgap,

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defined as ηmax(Eg) = 4/Eg [48]. In our case this gives, e.g.,ηmax(Eg = 0.72) = 5 and ηmax(Eg = 1.3) = 3.

Figure 4(b) shows quantum yield (QY) versus photonenergy for PbSe [13, 50, 15, 47] and PbS [13, 17, 47]nanocrystals and bulk. The quantum yield represents theaveraged number of excitons per absorbed photon. Data fromvarious groups illustrate wide variations of reported MEGQYs [13–19, 50]. This caused controversies, especially at thebeginning, because the reported experimental probes of MEGhave relied only on indirect evidence of the existence andefficiency of MEG (signature of Auger recombination withinthe exciton population decay traces) [16, 46, 18, 2].

In a typical MEG experiment, ultrafast transientabsorption spectroscopy is used to infer the number ofelectron–hole pairs produced per absorbed photon. Samplesare illuminated with a low-intensity beam of high-energyphotons, and the ensuing dynamics of multiexciton decayversus single exciton decay are measured. If a fast componentwith a lifetime similar to multiexciton lifetimes is observedin addition to exciton decay, it is attributed to multiexcitons.However, MEG artifacts exist and can give ‘false positive’signatures of MEG. For example, the single exciton decaycan acquire a fast component due to opening of nonradiativechannels, e.g., electron or hole traps in a nanocrystalsurface [46]. Detailed discussion of the measurement ofMEG versus its artifacts, and the proposed ways to minimizechances of overestimating MEG QY, is given in [46].

Furthermore, disagreements have arisen over the roleof quantum confinement for MEG. Interpretations rangefrom those showing that the MEG efficiency of the PbSenanocrystal is about twice the efficiency observed inbulk PbSe [19, 48] to those stating that the advantageof nanocrystal MEG is merely due to a possibly largerphotovoltage owing to quantum confinement [46]. Finally,there is the issue of the impact the MEG can have on solarenergy conversion, demonstrating that MEG can occur in aworking solar cell.

Very recently, MEG-induced enhancement of photocur-rent in PbSe nanocrystal-based solar cells was demon-strated [19]. For the best device measured, the externalquantum efficiency, defined as the spectrally resolved ratio ofcollected charge carriers to incident photons, peaked at 114±1%. The associated internal quantum efficiency, correctedfor reflection and absorption losses, was 130% [19]. Thesolar-cell architecture incorporated arrays of QD layers inp–n planar heterojunctions. Special attention was paid tothe chemistry of PbSe QD surfaces, including removinglong-chain organic ligands (such as oleic acid) while con-trolling electrical properties, and using four distinct chemicaltreatments (1,2-ethanedithiol, which showed reduced MEG,and hydrazine, methylamine, and ethanol, which preservedMEG). Furthermore, the beneficial aging effect on the solarcell performance was observed under oxygen and water-freenitrogen storage conditions [19].

Theoretical studies regarding the basic mechanisms ofMEG give confusing results. Models offering explanations ofMEG range from those that consider a coherent superpositionof single and multiple exciton states; to excitations of a

virtual multiexciton state that is strongly coupled to a realmultiexciton state; to incoherent impact ionization, analogousto bulk impact ionization with appropriate modifications ofthe electronic states [16, 51, 2]. In order to distinguishbetween different interpretations, one would need additionalconstraints on the set of initial parameters. The set of initialparameters includes the coupling strength between excitonsand multiexcitons, decay rates, and/or density of states. Thisis still an open issue.

Theoretical/computational models should link structure(typically extracted from structural characterization measure-ments) and predict or explain experiment. They should alsopredict any size dependence, explain how MEG is influencedby the coupling of the nanocrystal to its environment,and provide understanding of how MEG is influenced bycoupling of nanocrystals. However, structural informationabout nanocrystal systems is not complete. For example,it is difficult to extract information about the surface ofa nanocrystal, so it is not clear whether a charge carriercan reside at the nanocrystal surface in deep-trap energystates or not. One could, e.g., analyze different nonradiativedecay channels for an assumed nanocrystal structure and thendiscuss the plausibility of the constructed scenarios.

From a more pragmatic (but not necessarily recom-mended) viewpoint, whereas understanding of the underlyingphysics is unquestionably important, the primary interestshould lie in demonstrating that MEG can occur in a workingsolar cell. MEG-induced enhancement of photocurrent inPbSe nanocrystal-based solar cells has been very recentlyachieved [19], so the practical challenge is how to improve theMEG-enhanced quantum efficiency and search for different ornew candidate nanomaterials for MEG, e.g., PbSe nanorods,carbon-based nanostructures, etc [19, 21]. Usage of simpleempirical models that heavily rely on experiment can be moreuseful than employment of detailed many-body atomisticmethods. Also, although not the most elegant approach, it isnot uncommon in materials science to use linear regressionor neural networks to interpret experimental data whenphysical models do not exist or are difficult to implement;see, e.g., [52]. The underlying equations do not have to bephysically justified and the parameter set is determined byfitting the equations to a large set of experimental data [21,52].

5. Antenna–rectifier system for solar energyconversion

Solar energy can be converted to electricity by exploiting thewave nature of light instead of its particle nature: sunlightis captured by (nano)antennas and then rectified [3–5, 2].The fact that this approach had been previously successfullyapplied at longer wavelengths in radio and microwavefrequency bands [53] opened the possibility, at least initially,for high efficiency conversion of solar energy. The uses ofrectennas in the microwave region have been investigated overthe past half century for power transmission and detection.Applications have included long-distance power beaming,signal detection, and wireless control systems [53, 4].

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Figure 5. (a) Block diagram of antenna and rectifier system and load; (b) proposed realization of rectenna system using nanowires.Nanowires behave as antennas and the tip of the nanowires and surface create rectifying tunneling junctions. It was suggested that thenanowire’s asymmetrical, nonplanar geometry in conjunction with the flat anode is an essential requirement for increasing the cut-offfrequency of the diode (for more details see [5]).

Conventional rectennas consist of two distinct elements [53,4, 5], a dipole antenna plus a separate rectifying diode such asan MIM or Schottky diode, as illustrated in figure 5(a).

In the case of solar energy conversion to electricity, arectenna device should collect and rectify electromagneticradiation distributed over a wide range of submicronwavelengths (from the infrared (IR) through the visibleportion of the spectrum, extending the range to 1014 Hzand higher), which, in contrast to monochromatic microwaveradiation, is also incoherent and unpolarized. Schottky diodesare generally limited to frequencies less than 5 THz [54] andconventional MIM diodes have been used up to frequenciesof about 100 THz [54–56, 5]. So, it is not obvious if anantenna–rectifier system, as used for monochromatic radioand microwave radiation, can be simply applied for solarenergy conversion, for example, how to design an antenna tocollect sunlight, or how to obtain efficient optical frequencyrectification.

The conversion efficiency for the rectenna system in thecase of monochromatic radio and microwave radiation ismore than 80% [53]. Estimates for the theoretical limitingconversion efficiency of the antenna–rectifier solar cells rangefrom 48% [2, 57, 58] to 95% [58], depending on how theantenna–rectifier solar cells were modeled.

In one model [2, 4, 57, 58], electrical noise powerreceived through an antenna is replaced by a resistor at atemperature TR, whose resistance is equal to the radiationresistance of the antenna. If the antenna can be replaced bythe resistor at a given temperature, the rectification occursonly if the diode is at a lower temperature TD (TD < TR).There is no rectification for TR = TD, otherwise the secondlaw of thermodynamics is violated, the so called Brillouinparadox [59]. Note that the equivalent arguments can befound in Feynman analysis of the ratchet as an engine [60],where it was shown that the engine cannot work if thevanes and the ratchet are at the same temperature. In bothcases the efficiency is less than the Carnot efficiency becauseof the unavoidable heat exchange between the two thermalreservoirs [61]. It was shown that, if the antenna was replacedby a resistor at the temperature TR = 6000 K, the maximumefficiency was ∼48% [57, 58, 2, 4]. Obviously, this is adisappointingly low value and casts doubt on the usefulnessof the approach.

Other reported values of the theoretical limitingconversion efficiency of the rectenna system are higher than

85%, and are based on rather elementary considerations. Forexample, the model Sun–space–absorber–solar cell gives theefficiency of ∼85% [4], whereas the model Sun–space–solarcell, which included entropy losses, led to the value of∼93% [62, 4].

Unfortunately, it is not clear which one of these methodsapplies to the rectenna system. Whereas the simple models,which give overly optimistic values of efficiency, do notinclude specific features of the antenna–rectifier solar cells,the model based on replacing the antenna by a resistor is asgood as the initial assumption that the antenna can be replacedby a resistor at the temperature TR. This assumption is validfor lower frequencies (up to the near IR) [4, 53], but it is notclear to what degree the resistor replacement can be used inthe optical frequency range. Thus, the question of determiningthe theoretical limiting conversion efficiency of the rectennasolar cell (that includes all the characteristics of the system) isstill open.

From a (more important) practical viewpoint, the designof antennas and rectifiers operating at optical frequenciesrepresents a significant challenge due to the required size andfrequency of operation (see, e.g., [5, 20]). We are in a situationin which we need to, on one hand, improve our understandingof the behavior of materials used for antennas, e.g. metals,in the optical regime, which differs from that at frequenciesbelow the IR, and on the other hand improve the ability tofabricate optical antennas with nanometer dimensions. Forexample, the common requirement for an antenna structureis that its size is comparable to the wavelength of thecollected light. For optical antennas this gives a typicaldimension of ∼100–1000 nm. Such (nano)antennas supportlocalized plasmon polaritons, which exhibit extremely shortwavelengths and strong confinement of the electromagneticfield on the nanometer scale [20]. In addition to the sizerequirements, to produce an effective output signal, theantenna must be coupled to a device that can respond in a timet ∼ 1/f , which for optical frequencies corresponds to times of10−15–10−13 s [5].

So far, optical antennas have been produced in a varietyof sizes and shapes [63, 5], including, e.g., thin wire orwhisker, dipole, bow-tie, etc. For example, figure 5(b) showsa thin wire antenna consisting of arrays of vertically alignednanowires, where the tips of the nanowires and surface createrectifying tunneling junctions [5, 64, 55]. For a review and

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recent developments on antenna issues in rectenna solar cellssee, e.g., [5, 20, 65, 66].

In order to get an efficient rectification at opticalfrequencies, the diode will have to respond fast enoughto operate at optical frequencies, and have a relativelylow turn-on voltage. It will also require sufficiently smallcapacitance to minimize its time constant [5].

Quantum point-contact (QPC) devices, e.g. whiskerdiodes, have been used in measurements of absolutefrequencies up to the green portion of the visiblespectrum, demonstrating a response time of the order offemtoseconds [5].

One way to realize QPCs is in a break junction bypulling apart a piece of conductor until broken, or, in a morecontrolled way, in a two-dimensional electron gas (2DEG),e.g. in GaAs/AlGaAs heterostructures [67]. Rectification ofthe terahertz field has been discussed both experimentallyand theoretically, in terms of its coupling to the source–drainbias, or in terms of modulating the QPC gate voltage [68].Theoretically, one can model, e.g., current fluctuations in aballistic QPC biased by applied voltage and irradiated byexternal field, where the external field could be consideredto be either coherent (e.g. microwave radiation) or incoherent(e.g. representing the environment at high enough temperatureor a heat phonon pulse) [69].

QPCs can also be created by positioning the tip of ascanning tunneling microscope close to the surface of aconductor [70, 71]. The tunneling phenomenon in these QPCdevices is such that the current passes predominantly throughthe sharp protrusion closest to the planar sample surface. Therectification properties of tunneling junctions at fixed gapwidth originate from material, geometrical, and/or thermalasymmetry, and photo-stimulated changes in the electron fluxdistribution [5, 72, 64, 55].

Material asymmetry is expected when the electrodeshave different work functions: the barrier shape will beasymmetric at zero bias. Thermal asymmetry will occurwhen there is a temperature difference between the twoelectrodes causing different electron occupations of the statesinvolved in tunneling. Geometrical asymmetry representsasymmetry of the electrodes comprising the tunnel junctions.Examples include the geometrical asymmetry effect inSTM [70], or optical rectification caused by the nonlineartunneling conduction between gold electrodes separated bya subnanometer gap [71]. The asymmetrical, nonplanargeometry of the pointed whisker in conjunction with the flatanode is an essential requirement for increasing the cut-offfrequency of the diode, but inconsistent with the planargeometry [5].

There have been many innovative proposals on how toachieve efficient optical frequency rectification. For example,very recently, Sabou et al [73] theoretically investigatedidealized junctions between oppositely doped Mott insulators,modeling them as one-dimensional chains of interactingspin-polarized fermions. They predicted efficient rectificationat very high frequencies. For practical realizations, Sabouet al [73] recommended transition metal oxides, which,although often predicted to be conductors by band theory, can

be found to be Mott insulators. Also, such oxides can showinteresting behavior when driven by high frequency fields.

To summarize, whereas the entire rectenna concept forsolar energy conversion may be very difficult to realize inpractice, the problems such as understanding the materialsbehavior at optical frequencies, design and fabrication ofantennas with a typical dimension of ∼100–1000 nm, or theissue of efficient optical frequency rectification and how toengineer nanomaterials to rectify on such high frequencies,represent challenges that need to be addressed. As to thesolar energy conversion using rectennas, at this point onlya proof-of-concept device will provide convincing evidenceregarding this approach.

6. Discussion and summary

Engineered nanomaterials are the key building blocks ofsolar cells, irrespective of the mechanisms for the conversionof solar energy to electricity—those exploiting the particlenature of light and those using the collective electromagneticnature, where light is captured by antennas and rectified.Understanding how to engineer nanomaterials for targetedsolar-cell applications is the key to improving their efficiencyand could lead to breakthroughs in the design.

The design of nanomaterial-based solar cells is farfrom being straightforward. Traditional approaches for theimprovement of the design of solar cells, or the design of solarcells based on new mechanisms, have relied on the intuition ofresearchers, focusing on trial-and-error search and accidentaldiscovery.

Alternatively, predictive-theory-guided design combinesquantum mechanical methods and search/machine learningalgorithms, such as genetic algorithms, data mining, orneural networks, to design optimized nanomaterials withtargeted physical properties [21]: we define a targeted physicalproperty and then employ the quantum mechanical andsearch/machine learning algorithms to deduce the structure.Of course, this sounds very appealing, especially because thecomputer-generated nanomaterials could be counterintuitiveand difficult to discover otherwise, and the actual fabricationof a large number of structures and their processing could beavoided. The main premise behind this approach is that theoryis able to correctly link the structure and the property.

The real test for all those predictive methods wouldbe to fabricate nanomaterials using information from thetheoretically predicted structure, and then check how theirmeasured physical properties correspond to the targetedones. Let us analyze and discuss the solar-cell design fromthe viewpoints of traditional versus predictive-theory-guideddesign.

In the ‘simplest case’ where the underlying physicalprocesses are well understood, solar-cell design includes asearch for optimal constituent nanomaterials and geometries.For example, a thermodynamical limit on the lighttrapping within a semiconductor can be overcome by usingsubwavelength nanomaterial-based solar absorbers, suchas nanowires that have elevated local density of opticalstates [22]. Thus, the design reduces to the search for optimal

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Nanotechnology 24 (2013) 042001 Topical Review

materials, ideally those that could absorb light from the entiresolar spectrum.

The design is more complicated for IBSCs. The questfor finding optimal sub-bandgap absorbers has been focusedon (i) alloys that naturally exhibit an IB [7, 8, 6] and (ii)nanostructures, in particular arrays of quantum dots (QDs),that form an IB [9–11, 8, 6]. The problem is twofoldhere—from a fundamental viewpoint, there is a need forbetter understanding of the nature of the IB (localized versusextended), and carrier relaxation processes; however, froma more practical viewpoint, bulk- and QD-based IBSCshave been fabricated already, but they have so far exhibitedefficiencies far below their potential. For example, to lift thestrain-induced limit of the number of QD layers in the IB, itwas intuitively clear that it could be achieved by employingsystems with the strain symmetrization within the structure,such as the (In, Ga)As/Ga(As, P) system [11]. However,whereas it was found that the number of QD layers wasincreased, the intensity of absorption between QD-confinedelectron states and the host CB was weak and the positionof the IB within the matrix bandgap did not satisfy suitableenergetic locations for the IB [11]. A careful implementationof the predictive-theory design could have led to differentresults, especially given that electronic and optical propertiesof QDs are very well understood and the design rules for a QDIBSC known [32]. Thus, the issue of finding the best candidatematerials for the current technology is still open.

Although intuitively clear, it is important to stress thatthe problem is not only to design solar-cell devices based onwell understood physical principles, but also to control subtledetails such as tricks in fabrication which can play a relevantrole. Perhaps this statement is best illustrated by the exampleof fabrication of InAs/GaAs IBSCs. One of the challengesin QD IBSC design has been a loss of the output voltage atroom temperature compared to reference solar cells withoutan IB [6]. The loss of voltage at room temperature is causedby thermal escape of electrons from the IB to the CB (inaddition to tunneling of electrons from the IB to the CB).However, ‘careful fabrication’ led to a significant eliminationof output-voltage reduction [45].

The issues with the design of MEG solar cells arerather complex. From an experimental viewpoint, the issuesinclude indirect evidence of the existence and efficiency ofMEG [46], and the role of quantum confinement for MEG,where interpretations range from those showing that theMEG efficiency of the PbSe nanocrystal is about twice theefficiency observed in bulk PbSe [19, 48] to those stating thatthe advantage of nanocrystal MEG is merely in a possiblylarger photovoltage owing to quantum confinement [46].Furthermore, theoretical studies disagree on the basicmechanisms of MEG [16, 51, 2]. Theoretical/computationalmodels should link structure (typically extracted fromstructural characterization measurements) and predict orexplain experiment. They should also predict any sizedependence, explain how MEG is influenced by thecoupling of the nanocrystal to its environment, and impartunderstanding of how MEG is influenced by couplingof nanocrystals. However, structural information about

nanocrystal systems is not complete. For example, it isdifficult to extract information about the surface of ananocrystal, so it is not clear whether a charge carriercan reside at the nanocrystal surface in deep-trap energystates or not. One could, e.g., analyze different nonradiativedecay channels for an assumed nanocrystal structure andthen discuss the plausibility of the constructed scenarios.From a more pragmatic viewpoint, whereas understandingof the underlying physics is unquestionably important, theprimary interest lies in demonstrating that MEG can occurin a working solar cell. This has been very recentlyachieved [19], so the practical challenge is how to improve theMEG-enhanced quantum efficiency and search for differentor new candidate materials for MEG, e.g., PbSe nanorods,carbon-based nanostructures, etc. The recent advances incomputational design could enable such a search for optimalmaterials and geometries, as discussed in [21].

Application of the rectenna system for energy conversionhas been present in the literature for quite some time [3–5, 2],discussing theoretical efficiency [4, 2] and proposing variousantenna–rectifier realizations [3–5, 65, 66, 71, 2]. At thispoint only a proof-of-concept device will provide convincingevidence regarding this approach. However, regardless ofhow difficult it may be to realize the whole rectennaconcept for solar energy in practice, the problems such asunderstanding the materials behavior at optical frequencies,design and fabrication of antennas with a typical dimensionof ∼100–1000 nm, or the issue of efficient optical frequencyrectification and how to engineer nanomaterials to rectify atsuch high frequencies represent challenges that need to beaddressed.

Acknowledgment

This work was supported by NASA EPSCoR.

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