Halide Perovskites for Tandem Solar CellsJin-Wook Lee,† Yao-Tsung Hsieh,† Nicholas De Marco,† Sang-Hoon Bae,† Qifeng Han, and Yang Yang*

Department of Materials Science and Engineering and California NanoSystems Institute, University of California, Los Angeles,California 90095, United States

ABSTRACT: Perovskite solar cells have become one of the strongest candidates for next-generation solar energy technologies. A myriad of beneficial optoelectronic properties ofthe perovskite materials have enabled superb power conversion efficiencies (PCE)exceeding 22% for a single-junction device. The high PCE achievable via low processingcosts and relatively high variability in optical properties have opened new possibilities forperovskites in tandem solar cells. In this Perspective, we will discuss current research trendsin fabricating tandem perovskite-based solar cells in combination with a variety of maturephotovoltaic devices such as organic, silicon, and Cu(In,Ga)(S,Se)2 (CIGS) solar cells.Characteristic features and present limitations of each tandem cell will be discussed andelaborated upon. Finally, key issues for further improvement and the future outlook will bediscussed.

Photovoltaic technologies began attracting remarkableattention when William Shockley and Hans J. Queisser

calculated the theoretical efficiency limit of the single p−njunction solar cell, coined the Shockley−Queisser limit ordetailed balance limit.1 Assuming the sun as a blackbody (6000K) and the absence of nonradiative recombination, a maximumpower conversion efficiency (PCE) was calculated to beapproximately 33% based on a single p−n junction withbandgap (Eg) of 1.1−1.4 eV. This indicated that ca. 77% of theenergy coming from the sun cannot be utilized. The PCE is acombination of current (short-circuit current) and voltage(open-circuit voltage) from a cell; both of them are correlatedwith the bandgap of the material. A major part of the loss wasattributed to spectral losses,1 which is caused by fundamentaloptical responses of semiconducting absorbers. Photons withlower energy than that of the absorber bandgap (Eg) cannot beabsorbed, while photons with higher energy than Eg ultimatelyproduce charge carriers having the same energy as the Eg.Persistent research efforts have been devoted to surpassing theShockley−Queisser limit, from which several advancedconcepts have been devised to reduce spectral losses, includinghot carriers,2 multiple exciton generation (MEG)3 and tandemdesigns.4 So far, however, only the tandem solar cells haveshown practical efficiencies higher than the Shockley−Queisserlimit among them.5

Tandem solar cells were devised to minimize spectral losses.As seen in Figure 1a, in single-junction devices, photons withenergy lower than Eg will not be absorbed by the absorber,whereas photons with energy higher than Eg will produce hotcarriers, which will be thermalized to band edge by phononinteraction while emitting excessive energy as a heat. As a result,more than 50% of the energy losses arise by the spectral losses.1

To reduce the spectral losses, tandem solar cells incorporatemultiple junctions (Figure 1b). The tandem devices consist oftwo junctions having one relatively larger and one smaller Eg,such that the higher energy photon will be absorbed by the top

absorber with higher Eg, and the lower-energy photons will passthrough the high Eg cell and become absorbed by the bottomlower Eg cell. This will utilize a broader range of the solarspectrum to maximize absorption with minimized energy losses(Figure 1b). For tandem solar cells based on two junctionsunder standard light intensity (1 sun), the optimal combinationof bandgaps was calculated to be ca. 1.9 and 1.0 eV, which can

Received: February 15, 2017Accepted: April 19, 2017Published: April 19, 2017

Figure 1. (a) Schematic illustration showing light absorption in singleand multijunction solar cells. (b) Typical spectral response of top(high Eg ∼ 1.9 eV) and bottom (low Eg ∼ 1.0 eV) devices.

Perspective

pubs.acs.org/JPCL

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produce a maximum efficiency of 42% based on the detailedbalance limit.4

Tandem solar cells can also incorporate more than twoelectrically coupled junctions, in which each junction iscomposed of light absorbers with different Eg so that theycan better respond to corresponding spectral ranges of the solarspectrum (Figure 2). Tandem solar cells are mainly classified

according to how the junctions are electrically coupled to eachother. With two junctions, for example, four terminal (orexternal) tandem solar cells consist of two devices having theirown anode and cathode, in which the device with high Eg issuperimposed on the device with low Eg (Figure 2a). Whenusing a spectral splitting dichromatic mirror, the devices are notnecessarily stacked since the mirror can guide the light withdesired wavelength to each device.6 The devices are fabricatedseparately and electrically connected through external circuiteither by series or parallel connections. In two terminal (ormonolithic) tandem solar cells, the whole device is fabricatedsequentially onto a single substrate, which are connectedthrough a interlayer deposited between the two subcells. This isthe site at which charge carriers from the top and bottomsubcells recombine, to maintain charge neutrality, (Figure 2b)either by a band-to-band tunneling junction or a metallicrecombination layer.7 In general, fabrication of internal tandemsolar cells is much more challenging than that of externaltandem solar cells because of the limitation in the fabricationprocess and manipulation of electrical coupling. The bottomdevices should be durable during the fabrication processes ofthe top devices, while the current or voltage should be well-matched with use of an appropriate interlayer. However, sincethis design requires fewer electrodes compared to externaltandem devices, which impede the transmission of the light toabsorbing layer, higher efficiencies can be achievable inprinciple. Furthermore, in practical applications, a monolithictandem device could avoid additional manufacturing costs dueto the necessity for multiple transparent conducting layers andexternal wiring for interconnection of the two independentdevices.Perovskite (PVSK) solar cells recently have attracted great

attention due to their unprecedentedly rapid progress inPCE.8−10 Because of the underlying superior optoelectronicproperties of the PVSK materials,11−13 the PCE has enhancedfrom around 10% to 22.1% during the last five years.6,8 Withthe remarkable progress of single-junction devices, severaloptical and processing features of the PVSK materials haveopened up the possibility for its use as a top cell in tandem solarcells. PVSK materials have relatively higher Eg (>1.5 eV)compared to typical inorganic light absorbers such as silicon(1.1 eV) and CuInGaSe2 (1.02−1.68 eV).14 The Eg of thePVSK materials can be easily tuned by controlling halidecomposition over the whole visible wavelength region, and it

has shown high VOC with small potential loss (∼0.39 V).10,15

Furthermore, it can be processed via low temperature solutionprocesses (<150 °C).16,17 Due to such beneficial features,researchers have tried to use PVSK as a top cell in tandem solarcells in combination with various bottom cells. Feasibleefficiency limits of tandem solar cells incorporating PVSK canbe derived by considering several optical parameters originatingfrom materials themselves, such as reflective index andabsorption coefficient, in which an efficiency of 28% to 32%was shown to be achievable.18,19

In this Perspective, we will discuss current research trends infabricating tandem solar cells utilizing PVSK solar cells incombination with a variety of other devices such as organic,silicon, and Cu(In,Ga)(S,Se)2 (CIGS) solar cells. Based onrecent progress, future directions for improvements will bediscussed.Organic/PVSK Tandem Solar Cells: Further Understanding

Properties of Organic Materials. Organic solar cells (OSCs) arebased on organic semiconductors that have carbon-basedconjugated systems comprised of alternating C−C single andCC double bonds. The delocalized electrons along theconjugated backbone of organic semiconductors play animportant role in their electrical properties.20 Moreover,organic materials have unique properties that differ frominorganic materials. Thus, an understanding of organic materialproperties is a necessary first step in designing OSC/PVSKtandem cells. There are three main characteristics of organicsemiconductors necessary for OSC/PVSK tandem cells: (i)long-wavelength absorption beyond 800 nm, which can beachieved by modifying chemical structures in ways that directlychange the properties of the organic materials;21 (ii) attractionby intermolecular forces (instead of covalent or ionic bonds),which allows for a low activation energy in utilizing organicmaterials as a solar absorber and ensures low temperatureprocessing of OSC/PVSK tandem cells;22 and (iii) a lowdielectric constant (εr ≈ 2−4) that induces tightly boundexcitons (electron−hole pairs), which prevents excitondissociation by lower potential.14 This also results in a lowermobility of organic semiconductors, which ultimately limits theperformance of OSC/PVSK tandem cells. These three uniquefeatures must be considered for the design of high performanceOPV/PVSK tandem cells.

The absorption range of halide PVSK materials ranges fromapproximately 300 to 800 nm, depending on the compositionof the PVSK material.23−25 The synthetic variability of organicmaterials makes them strong candidates as a supplementaryabsorber layer to PVSK.21 Since the electrical properties oforganic materials depend on the electronic structure ofmolecular and polymeric materials, introducing small changesinto the molecular structure or composition remarkablychanges the electrical properties and enables Eg engineeringof organic materials. Thus, we can design organic moleculeswith an optimal absorption spectrum for light harvesting withhalide PVSK materials. In general, the electron-donating groupelevates the HOMO energy level, whereas the electron-withdrawing group lowers the LUMO energy level. Also, the

Figure 2. Tandem solar cells with different configurations: (a) Fourterminal and (b) two terminal tandem solar cells.

An understanding of organic ma-terial properties is a necessaryfirst step in designing OSC/PVSK

tandem cells.

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energy difference between the HOMO and LUMO increases asa result of the decrease of the length of conjugation.27 Forexample, the so-called push−pull effect stabilizes the quinoidresonance structure and can enable the design of a polymerhaving a Eg as low as 1 eV.26 (Figure 3)The formation energy of PVSK is low compared to other

inorganic solar absorbers, where most inorganic solar materialsrequire high energy to form a suitable phase for photovoltaics.14

The OSC is an appealing choice in terms of its low temperatureprocessing requirements, since organic materials need similarlevels of formation energy as halide PVSK materials. Organicmaterials are bound by intermolecular forces, such as hydrogenbonding, dipole−dipole interactions, and dispersion forces,which are not strong compared to materials with ionic orcovalent bonding.28 Therefore, we do not need high energies to

deposit or facilitate bonding between organic materials. Instead,the molecules and polymers can be easily dissolved in solvents,per their polarity, and form into a solid state thin film.However, due to such a low formation energy, stability issuescan arise since the lower activation energy leads to the organicmaterials being more susceptible to their bonding beinginterrupted. This can accelerate degradation of the activelayer during processing and under device operation.There is another limitation with OSC/PVSK tandems due to

the tightly bound electron−hole pair, or Frenkel exciton, oforganic semiconductors. The exciton is a molecular excitedstate that can hop from molecule to molecule or from chain tochain, which is the same mechanism of charge carrier transportin organic materials. Thus, the excitonic state determines theoptoelectronic properties of organic semiconductors. The

Figure 3. Approaches to make low Eg polymers. (a) Aromatic and quinoid resonance structure. (b) Stabilized quinoid resonance structure. (c)Donor−acceptor copolymer by Yamamoto. (d) Donor−acceptor copolymer by Havinga. (e) Eg lowering by donor−acceptor interaction. (f)Approach to combine the electron-accepting and stabilizing of the quinoid resonance structure. Reprinted with permission from ref 26. Copyright2015 American Chemical Society.

Figure 4. OPV/PVSK monolithic tandem solar cells (a) The solid lines indicate the external quantum efficiency of the OPV and the PVSK cells inthe tandem cells. Dashed lines are for the single-junction reference devices. (b) J−V characteristics of tandem devices using different conditions. (c)The band alignment of OPV/PVSK tandem cells. (d) The structure of low Eg polymer, PBSeDTEG8. Reprinted with permission from ref 31.Copyright 2015 Royal Society of Chemistry.

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Frenkel exciton is the primary species of organic semi-conductors with a binding energy of ∼1 eV. This is a resultof a low dielectric constant (εr = 2−4), since the Coulombicinteraction between the electron and hole is strong.29

Accordingly, charge carrier transport is quite slow comparedwith other inorganic semiconductors due to the stronginteraction. In general, while the mobility of inorganic materialsranges from 102 to 104 cm2/(V s) at room temperature, organicmaterials show ∼1 cm2/(V s), which eventually limits theperformance of organic based solar cells.30 Thus, tandem cellswith OSCs are always accompanied by slow charge carriertransport from organic materials. It is critical that we findanswers to these issues generated by the tightly boundelectron−hole pair to remove restrictions on the potential oforganic materials as tandem solar cells with PVSK solar cells.Chen et al. demonstrated a good example of organic/PVSK

monolithic tandem cells31 utilizing CH3NH3PbI3 (MAPbI3), anIR-sensitive block copolymer, and PBSeDTEG8, to increase theabsorption range up to 950 nm (Figure 4). They designed aninterconnecting layer to facilitate recombination between cellsconsisting of PFN/TiO2/PEDOT:PSS PH500/PEDOT:PSS AI4083 double hole and double electron transporting layers.PCEs of 9.08% for the MAPbI3 single junction and 6.62% forthe PBSeDTEG8 single junction were obtained, while a PCE of10.23% was demonstrated for a two terminal OSC/PVSKtandem solar cell. However, the PCE demonstrated is lowerthan that of recently reported single PVSK cells, which was dueto limitation in process temperature and solvents.The Organic/PVSK Bilayer System: Toward an Enhanced

Absorption Range. While conventional tandem cells consist oftwo or more subcells, the bilayer system is essentially one cellwith two stacked absorber materials (organic and PVSK). In2014, Y. Liu et al. first reported the concept of a PVSK/bulk-heterojunction (BHJ) integration to extend the absorptionrange.32 They utilized MAPbI3 and the small moleculeDOR3T-TBDT as a donor in the BHJ (Figure 5a). Thiscontributed the overall device photocurrent by converting

additional near-infrared (NIR) light to current, which lead to animprovement in short-circuit current density (JSC) from 19.3mA/cm2 to 21.2 mA/cm2 (Figure 5b). They claimed that theBHJ layer can function as an absorption layer as well as a chargetransporting layer. In 2016, J. Kim et al. reported a similarconcept work based on the integration of PVSK materials andBHJ to harvest the long wavelength region.33 They integrated adiketopyrrolopyrrole (DPP)-based low Eg polymer (LBP) DT-PDPP2T-TT (TT) and [6,6]-phenyl C71 butyric acid methylester (PC71BM) as the BHJ layer with MAPbI3. They claimedthat high electron transport from the BHJ can play animportant role for high FF and VOC. Later, M. Cheng et al.also showed an integrated structure by using other smallmolecules based on benzo[1,2b:4,5b′]-dithiophene (BDT)flanked by phenoxaz ine (POZ) un i t s . 3 4 (FAP-bI3)0.85(MAPbBr3)0.15, was used for more optimal bandalignment (Figure 5c), and the integration helped to extendthe long wavelength light harvesting up to 900 nm (Figure 5d).The BHJ was composed of small molecules and PC70BM,which enables exciton dissociation in organic materials. ThePCE was enhanced from 15.0% to 16.2% by utilizing a PVSK/BHJ system with improved JSC from 20 mA/cm2 to 24 mA/cm.2 Considering the limitation of single-junction OSC devices,the PVSK/BHJ system might be a promising approach toenhance the efficiency of PVSK solar cells.Silicon/PVSK Tandem Cells: A Promising Approach to Reduce

the Cost-per-Kilowatt of Silicon-Based Solar Cells. Silicon, thecurrent photovoltaic material of choice due to its well-established industry and relatively high efficiencies (∼25.6%PCE), is the current standard for terrestrial photovoltaicapplications. However, its efficiency has largely plateaued overthe past several years. Thus, reducing the cost-per-kilowatt ofsilicon-based solar relies majorly on manufacturing rather thandevice performance improvements. One promising approach toovercome these limitations is to construct a tandem devicecomposed of a silicon and another material with comple-mentary absorption, which is tandem solar cells. Silicon has a Eg

Figure 5. Integration of PVSK and BHJ. (a) Schematic energy level diagrams of the integrated PVSK/(DOR3T-TBDT:PC71BM) device and (b)External quantum efficiency (EQE) curves of corresponding devices. (c) Schematic energy level diagrams of the integrated PVSK/M3 or M4 deviceand (d) EQE curves of corresponding devices. Reprinted with permission from refs 32 (Copyright 2015 American Chemical Society) and 34(Copyright 2016 American Chemical Society).

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of ∼1.1 eV, absorbing lower energy photons, which means thatthe second absorber material ought to have a higher Eg toefficiently collect higher energy photons. Because of the well-established silicon industries, relatively active research workshave been done for the development of silicon/PVSK tandemsolar cells.

For monolithic two-terminal tandem cells, there is a requiredcurrent matching between the subcells for the device to operateeffectively. In addition, the processing temperature of the PVSKsubcell atop silicon must be <200 °C so as not to damage the a-Si:H passivation layer of the silicon subcell,35 which posesproblems with the conventional mesoporous architectures thatrequire temperatures >500 °C. This monolithic integrationprovides the challenge of producing a mechanism of electricalcoupling between subcells that is simultaneously opticallytransparent to long wavelength (infrared) light to the bottomcell. Mailoa et al. were the first to demonstrate a two-terminalsilicon/PVSK tandem device using a silicon tunnel junction.36

Using silicon, with an indirect Eg, allows for electrical couplingof the subcells with minimal parasitic absorption loss.Moreover, the band alignment of the PVSK subcell TiO2selective contact and silicon conduction band alleviates thenecessity for use of a transparent conducting oxide as arecombination layer (e.g., ITO). Charge neutrality isestablished via tunneling of the electrons and holes throughthe tunnel junction to n-type silicon base and p-type emitter,where recombination can readily occur. The device and bandstructures are shown in Figure 6a. The MAPbI3-based silicon-PVSK tandem could achieve an efficiency of 13.7% with anopen-circuit voltage of 1.65 V using the silicon tunnel junctionmonolithic integration (Figure 6b). The authors claim that thelower efficiency is due to use of materials that are not of thehighest quality, both for PVSK and silicon subcells, and that byusing higher quality materials the device has the potential toachieve efficiencies up to 29%. Moreover, Albrecht et al.introduced low-temperature monolithic devices employing aSnO2 layer deposited via atomic layer deposition (ALD) toachieve a stabilized efficiency of 18% (Figure 6c,d).35 Theauthors claim this low-temperature process to be compatiblewith the low-temperature requirements of the highest perform-ing crystalline silicon single-junction devices.Werner and co-workers have recently shown higher

efficiency monolithic tandem cells using a low-temperatureprocess consisting of a sputtered indium−zinc-oxide (IZO)recombination layer and inorganic PC61BM/PEIE and Spiro-OMeTAD selective contacts.37 These devices yielded efficien-cies up to 21.2 and 19.2% for 0.17 and 1.22 cm2 device areas,respectively, with no hysteresis, for an architecture of IZO/PEIE/PCBM/MAPbI3/Spiro-OMeTAD/MoOx/IO:H/ITO.Werner et al. later built upon this work by introducing rear sidetexturing to the silicon bottom cell to increase light harvestingcapability in the NIR region.38 This was accomplished via astandard double-sided texturization in a KOH-based solution.

Furthermore, the electron selective contact of the PVSKsubcell was improved upon through use of sputtered SnO2between the PVSK and PCBM/PEIE layers to enhanceuniformity and further prevent shunting pathways. Ultimately,a higher quality PVSK subcell was achieved with a steady-stateefficiency of 16.4% (compared to 14.5% in the previous work).Along with the rear-side texturization, an efficiency for themonolithic tandem device of 20.5% was achieved, compared toa previous 19.2% for polished surfaces and unoptimized topcell. Recently, McGehee’s group at Stanford has announced amonolithic two-terminal silicon-PVSK tandem reaching anefficiency of 23.6% for 1 cm2 active area.39 The device consistsof a c-Si bottom cell from Holman group at ASU, a NiO holecontact, ITO/LiF transparent top contact, and PVSK film withcomposition FA0.83Cs0.17Pb(I0.83Br0.17)3. The authors claim thatthis device to be very stable, and we are awaiting formalpublication of this work.Bailie and co-workers demonstrated mechanically stacked

silicon-PVSK tandem devices (four terminal) using lowerquality multicrystalline silicon (mc-Si) as the bottom cell.40 Thelower quality mc-Si was used in an effort to reduce costs of theexpensive single-crystalline silicon (sc-Si), and supplementingthe poor efficiency with use of the PVSK addition in tandemcells. Constructing a mc-Si-PVSK tandem device improved theperformance of the stand-alone mc-Si device from 11.4% to17% PCE for the tandem cell. The PVSK top cell consisted ofmesoporous (mp)-TiO2/MAPbI3/Spiro-OMeTAD/AgNW,where a silver nanowire (AgNW) mesh was used as thetransparent top electrode. The AgNW mesh provided a lowsheet resistance of 12.4 Ω-cm2 with 90% transmission betweenthe 530−730 nm range of the spectrum, and falls to 87% up to1000 nm. In addition, the electrode must be applied withoutdamaging the sensitive PVSK and Spiro-OMeTAD layers,

Reducing the cost-per-kilowatt ofsilicon-based solar relies majorlyon manufacturing rather thandevice performance improve-

ments.

Figure 6. (a) The device structure of a two-terminal monolithicallygrown PVSK/Si multijunction solar cell with an n-type Si base. Thepolished SEM image (500 nm scale bar) and corresponding banddiagram of the PVSK/silicon cell interface. (b) J−V curve of the two-terminal PVSK/silicon multijunction solar cell under AM1.5Gillumination. (c) J−V curves of single-junction and monolithic tandemsolar cells. Inset shows cross-sectional SEM image of the tandemdevice. (d) External quantum efficiency of the individual subcell in themonolithic tandem device with AR coating. Reprinted with permissionfrom refs 36 (Copyright 2015 AIP Publishing LLC) and 35(Copyright 2015 Royal Society of Chemistry).

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which was achieved by a spray deposition technique. Later,Chen et al. demonstrated the potential of obtaining anefficiency of 23% for a silicon-PVSK four-terminal tandem byfiltering light through a PVSK top cell onto a silicon bottomcell (Figure 7a−c).41 The PVSK subcell used a thinsemitransparent 1 nm Cu/7 nm Au transparent electrode,providing a sheet resistance of 23 Ω-cm2. A 40 nm-thick layerof BCP was also added to improve transmittance (by ∼10%) inthe NIR region. The PVSK subcell achieved a single-junctionefficiency of 16.5% with a device area of 0.075 cm2 andarchitecture of ITO/PTAA/MAPbI3/PCBM/C60/BCP/Cu/Au. The silicon subcell was enhanced by applying a double-layer antireflection coating at the front side, a MgF2 backreflector layer at the rear side, and replacing ITO with thehigher carrier mobility IZO. The authors ultimately demon-strated a summed 23% efficiency for a silicon-PVSK and a 6.5%efficient silicon cell after filtering light using the PVSK cell ontosilicon. Werner and collaborators achieved efficiencies of 23%and 25.2% for 4-terminal PVSK/SHJ tandem cells with deviceareas of 1.015 cm2 and 0.25 cm2 PVSK top cell aperture areas,respectively, using the same SnO2-based low temperaturesemitransparent PVSK subcell (Figure 7d-f).38 Because thesame top cell was used for both the monolithic andmechanically stacked tandem cells, a direct comparisonbetween tandem cell architectures could be made in terms ofparasitic absorption and light management requirements. Theauthors note that for the monolithic tandem cell, a larger Eg topcell is necessary to achieve optimal performance, as it is current-limited by the bottom cell. Another promising approach hasbeen demonstrated using an optical splitting system. Uzu et al.used a dichroic mirror to split and guide the light to twoseparate solar cells responding to corresponding wavelengthregions.42 They combined a monocrystalline silicon hetero-junction solar cell and MAPbI3 PVSK solar cell, in which shortwavelength light (<550 nm) was incident to the PVSK solar cellwhile long wavelength light (>550 nm) was incident to thesilicon solar cell. They achieved total PCE of 28%, which is thehighest PCE reported for four terminal tandem solar cellincorporating PVSK. Takumi et al. used a similar approach,where an infrared dye-sensitized solar cell was used instead ofthe silicon solar cell and achieved PCE of 21.5%.43 However,

application of the approach in the commercial field is still underdebate due to use of the expensive dichroic mirror.The optimal Eg of the PVSK subcell ought to be around 1.8

eV for optimal efficiency.40 Surprisingly, most the PVSKcompositions discussed in the above tandem devices utilize thetraditional MAPbI3 PVSK composition, which possesses an Egof ∼1.55−1.6 eV. This is likely due to photosegregation ofmixed halide PVSK that occurs readily in mixed I and BrPVSKs.44 Several studies have been conducted to obtain a moreoptimal PVSK Eg for tandem cells. Beal et al. demonstratedPVSKs with composition CsPbBrI2 with an Eg of 1.9 eV andenhanced photo- and thermal stability against phase separa-tion.45 However, this material was only able to achieve astabilized efficiency of 6.5%, which requires further work toboost efficiency while stabilizing the large Eg PVSK. McMeekinand co-workers demonstrated the potential of mixedcompositions for tandem cells using a composition ofFA0.83Cs0.17Pb(I0.6Br0.4)3 with an optical Eg of approximately1.74 eV,46 which is close to the ideal top-cell Eg of 1.8 eV. Solarcells employing this PVSK absorber composition achieved opencircuit voltages up to 1.2 V and a PCE of 17% on small areas.By considering the individual efficiencies of the subcells, theauthors suggest that by combining the 17% PVSK cell with a19% efficient silicon cell, a tandem device has the potential toachieve >25% PCE in an ideal four-terminal configuration. Asimilar composition was recently demonstrated by McGeheegroup, as discussed in the previous section, consisting of thePVSK absorber composition FA0.83Cs0.17Pb(I0.83Br0.17)3. It willbe of paramount importance to develop a stable PVSKcomposition with a near-optimal Eg to achieve high perform-ance tandem devices.CIGS/PVSK Tandem Cells: Another Promising Branch of

Tandem Solar Cells. Chalcopyrite (CIGS) compounds haveproven to be a promising material for photovoltaics. Currently,the highest efficiency of CIGS solar cells has reached 22.6%.6

CIGS is still one of the photovoltaic technologies providingcommercialized high-efficiency products that can compete withthe prevalent silicon wafer-based photovoltaics.6 CIGScompounds are stable inorganic quaternary alloys with directEg. To achieve superior photovoltaic performance requires theratio of Ga/(Ga+In) to be finely controlled between 0.25 and

Figure 7. Device structure and corresponding J−V curves and external quantum efficiency spectra of four terminal tandem solar cells reported by(a−c) Chen et al.41 and (d−f) Wener et al.37 Reprinted with permission from refs 41 (Copyright 2016 John Wiley and Sons) and 37 (Copyright2016 American Chemical Society).

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0.35, corresponding to a Eg of 1.1 to 1.24 eV. With its excellentabsorption coefficient, only approximately 2 μm of the CIGSthin film is needed to absorb most of the incident sunlight,which significantly decreases the demand of absorbingmaterials. Another promising feature of CIGS is that it canbe integrated onto flexible substrates without a significantefficiency loss.47 This capability can theoretically lowerproduction costs by using techniques such as roll-to-rollmanufacturing, thus offering the possibility for commercializedlarge-scale applications.In past years, many efforts have been devoted to improving

the efficiency of CIGS solar cells, especially CIGS absorbermaterials development. However, the progress in enhancingdevice efficiency has not been significant.6 In order to boost theefficiency of CIGS solar cells beyond their practical limit, onepromising approach is to combine CIGS solar cells withsuitable absorbers to form a tandem device. According tocalculations, the optimum Eg for bottom cells in a doublejunction is 0.9−1.2 eV.4,48 With the capability to adjust the Egby tuning Ga/(Ga+In) and S/(S+Se) ratios, CIGS becomes anideal candidate to work as the bottom cell in tandem structure.By operating with PVSK solar cells, a CIGS/PVSK tandemdevice can extend the absorption range further into thespectrum for more light harvesting. The advantage ofcombining CIGS and PVSK photovoltaic technologies hasbeen realized for many years. Nonetheless, in contrast to severalencouraging results of silicon/PVSK tandem devices, theCIGS/PVSK tandem solar cells still have not demonstratedtheir superiority over single-junction solar cells.

A typical tandem structure of the CIGS/PVSK solar cell isthe same as for the silicon/PVSK tandem devices. It consists ofone wide-Eg PVSK solar cell upon a low-Eg CIGS solar cell, andthese two single-junction devices are connected either bymonolithic integration (two-terminal) or mechanically stacking(four-terminal). The incident solar light first passes through thePVSK top cell and then reaches the bottom CIGS cell.Regarding the realization of high efficiency CIGS/PVSKtandem solar cells, the top PVSK cell plays an essential role.The key aspect of this subject is to achieve the highperformance near-infrared transparent PVSK solar cells.Reducing the thickness of the metal electrode is a simple andstraightforward route to increase optical transmission, even if ithas to compensate for higher resistance. The first monolithicCIGS/PVSK tandem solar cell with a 10.9% efficiency waspublished by an IBM research group in 2015.49 A Ca-based topelectrode was employed, composed of thermally evaporated Ca(10−15 nm) and bathocuproine (5 nm), that contributed theserious parasitic optical losses. The authors claimed that thedevice efficiency could be augmented to 25% once state-of-artCIGS and PVSK technologies are integrated together perfectly.Later, Yang and co-workers first exhibited the dielectric/metal/dielectric (MoOx/Ag/MoOx) structure (DMD structure) intransparent electrode for PVSK solar cells (Figure 8).50 Basedon the thermal evaporation technique for DMD electrodefabrication, they demonstrated a four-terminal CIGS/PVSKtandem device, showing a device efficiency of 15.5%.

On the other hand, the high-performance transparentconducting oxides (ITO, AZO, and In2O3:H) depositedthrough sputtering processes have been introduced andcommonly applied on semitransparent PVSK solar cells.51−54

In order to adopt this approach, it is inevitable to depositadditional buffer layers (e.g., zinc oxide nanoparticles orMoO3), which serve as sacrificial layers to prevent mechanicaldestruction during sputtering. Optimization of the buffer layerbecomes necessary to minimize optical and electrical losses. Todate, the highest efficiency of 4-terminal CIGS/PVSK tandemsolar cells is 22.1%, which was achieved in 2016.53 In the sameyear, McGehee and co-workers proposed an alternativeapproach to laminate a silver nanowire mesh as the topelectrode, as applied to a silicon-PVSK tandem cell describedabove.40 This advanced process can be conducted in roomtemperature without any solvents involved. The auuthorsreported an efficiency of 18.6% for the four-terminal CIGS/PVSK tandem device. However, the sophisticated transferringprocess would affect the reproducibility, resulting in a variationof device efficiency.To date, the development of the monolithic CIGS/PVSK

tandem structure has been retarded for some time. Comparedwith the mechanically stacking architecture, the monolithicdesign on a single substrate would be gifted with better deviceefficiency because of the minimum number of ancillary layersfor optical and parasitic resistance losses. Yet, the lack ofappropriate recombination layers and a fully compatiblefabrication sequence for all layers becomes the major hindrancein realizing high performance monolithic CIGS/PVSK tandemsolar cells. In the work done by the IBM research group, whichis the only published work successfully demonstrating amonolithic CIGS/PVSK tandem device, the intrinsic ZnOlayer was removed from the CIGS solar cell since it can cause achemical instability of PVSK materials at processing temper-atures above 60 °C.49 It is understandable that the ZnO-free

A CIGS/PVSK tandem device canextend the absorption rangefurther into the spectrum for

more light harvesting.

Figure 8. (a) Schematic device structure and SEM cross-sectionalimage of the photovoltaic device. (b) J−V curve and (c) externalquantum efficiency of top illuminated PVSK, CIGS, and CIGS cellunder the PVSK device. Reprinted with permission from ref 50.Copyright 2015 American Chemical Society.

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CIGS structure would ensure the tandem device from damage;however, it also ruined the entirety of the CIGS solar cell,which is a large trade-off with the high efficiency of CIGS. As aresult, while the top PVSK performance is noteworthy, it is alsocrucial to preserve the merits of CIGS solar cells within thetandem structure. Especially for the monolithic devicearchitecture, the overall device performance might be limitedby the reduced efficiency of the bottom cells for currentmatching. To prevent this condition, the low temperatureprocessing for PVSK solar cell fabrication and the careful designfor chemically stable recombination layers are essential. Oncehigh-quality transparent top electrodes, suitable recombinationlayers, and compatible fabrication sequences become reachable,all achievements from the state-of-the-art PVSK and CIGS solarcells, such as Eg engineering, materials stability, and efficiencyenhancement, can be transferred to the CIGS/PVSKmonolithic tandem solar cells.All-PVSK Tandem Solar Cells: An Emerging Technology. To

date, the high-efficiencies of single-junction PVSK devicesmainly stem from methylammonium lead iodide and itsrelatives, with substitution of formamidium, cesium, and/orbromide. As this group of PVSK, with a Eg range between 1.5and 1.7 eV, exhibits excellent optoelectronic properties, it isinstinctive to pair them with low-Eg solar cells for tandemdevices, as we have discussed in previous sections. Recently, therange of PVSK Eg has been extended due to noteworthyprogress on compositional engineering and advanced deposi-tion techniques.46,55−58 These developments have opened upan opportunity for researchers to explore all-PVSK tandemsolar cells. Recently, considerable research works have beenconducted for low-Eg as well as wide-Eg PVSK materials. With

rewards of facile solution processability and low materials cost,all-PVSK tandem solar cells are considered to possess

enormous potential for large-scale commercialization overother PVSK-based tandem technologies.In late 2015, researchers were able to demonstrate all-PVSK

tandem solar cells with high open circuit voltage (>1.8 V).59,60

At that early stage, however, the device efficiency was limited bythe inferior current density because two subcells can only useanalogous absorbers. A major challenge to deliver highefficiency all-PVSK tandem devices comes from the difficultyof synthesizing stable low-Eg PVSKs for highly efficient photon-to-electron conversion. Pb-based PVSKs are relatively stablewith halide atoms, but the corresponding Eg can merely beadjusted downward to ∼1.48 eV. The theoretical Eg’s arelocated between 1.57 and 2.29 eV for MAPbX3, and 1.48−2.23eV for FAPbX3 (X = Cl−, Br−, and I−). So far, the most effectiveand widely adopted approach to lower PVSK Eg is to replace Pbwith Sn in PVSK compounds. This method is rationallyaccessible since Sn and Pb are both from IVA group and theyhave the similar ionic radii (Sn2+ 1.35 Å and Pb2+ 1.49 Å),which allows for easy substitution without large latticedistortion.Several works have been published on Sn-based PVSK solar

cells. In 2014, Snaith and co-workers first demonstrated a lead-free organic−inorganic tin halide PVSK (MASnI3).

61 Theirresults confirmed that a pure tin-based PVSK with a Eg of 1.23eV was able to deliver an efficiency over 6% on a mesoporousTiO2 scaffold. After that, Kanatzidis and co-workers reported asystematic investment for the anomalous Eg behavior in mixedSn and Pb PVSKs (Figure 9).62 The authors claimed that thePVSK Eg could be successfully reduced to 1.17 eV with a deviceefficiency over 7% by varying the Pb-to-Sn ratio in MA-(Pb,Sn)I3. Later, Jen and co-workers improved the PCE to10.1% based on Pb/Sn alloy PVSKs (MAPb1−aSnaI3−‑xClx) withan Eg of 1.38 eV, which was grown on the planar heterojunctionarchitecture.63 The superior efficiency was credited to a goodfilm quality and better coverage of PVSKs.In 2016, Jen’s group demonstrated higher efficiency and

stable Pb−Sn binary PVSK solar cells, and further realized high-performance all-PVSK tandem solar cells in a four-terminalstructure.64 By incorporating formamidium cations, the stablemixed cation Sn-based PVSK (MA0.5FA0.5Pb0.75Sn0.25I3) pre-sented a stabilized PCE of 14.19% with an Eg of 1.33 eV. ThePCE of a four-terminal all-PVSK tandem solar cell was pushedto 19.08%, which consisted of a 1.33 eV low-Eg PVSK with asemitransparent MAPbI3 solar cell. Very recently, Snaith andco-workers revealed a notable result by accomplishing a

With rewards of facile solutionprocessability and low materialscost, all-PVSK tandem solar cellsare considered to possess enor-mous potential for large-scalecommercialization over otherPVSK-based tandem technolo-

gies.

Figure 9. Absorption spectra and schematic energy level diagram of the MASn1−xPbxI3 solid solution PVSKs. (a) Absorption spectra and (b)schematic energy level diagram of the MASn1−xPbxI3 solid solution PVSKs. Reprinted with permission from ref 62. Copyright 2014 AmericanChemical Society.

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monolithic all-PVSK tandem solar cell.65 They successfullydeveloped a FA0.75Cs0.25Pb0.5Sn0.5I3 absorber with an Eg of 1.2eV. This PVSK device alone showed a PCE of 14.8% withexcellent stability. By applying this infrared−absorbing PVSKwith a 1.8 eV FA0.83Cs0.17Pb(I0.5Br0.5)3 film, they eventuallyestablished a current-matched monolithic all-PVSK tandemsolar cell. The monolithic and four-terminal tandem devicesupgraded the PCE to 17% and 20.3%, respectively (Figure 10).

While the performance of low-Eg Sn-based PVSK devices isprogressing, there is still a discernible gap compared with thePb-based PVSK devices. The nature of the stable Sn oxidationstate is the root of the problem. When Sn exists within thePVSK compounds as Sn2+ cation, it can be easily oxidized toSn4+, as that is its most stable state. This proclivity to oxidizewould induce a thermodynamic instability of crystal, andconsequently device degradation becomes inevitable. As aresult, it is critical to overcome the stability issue brought by theSn incorporation. It has been confirmed that by hybridizingwith Cs and formamidium cations, degradation from photo andmoisture effects can be alleviated.66,67 In another work, by usinghydrazine to create a reducing atmosphere, researchers havesuccessfully suppressed the formation of Sn4+ species during thepreparation of a Sn-based PVSK device.68 Recently, anantioxidant, ascorbic acid, has also been introduced as anadditive to increase the stability and efficiency of Sn-basedPVSK solar cells in which the antioxidant can impede theoxidation of a Sn-containing precursor solution.69

Besides the stability issue, the charge recombination layersmight limit further progress of tandem device performance. Asuitable design for band alignment and compatible fabricationsequences is essential. High optical transparent conductingoxides (such as ITO) are commonly used as the chargerecombination layer in tandem solar cells;65 however, peoplehave to pay more attention to the compromise between thedeposition processes and the underlying layers since thematerials for PVSK solar cell are not as rigid as materials forinorganic subcells. An alternative strategy has been proposed

using doped organic semiconductors.70 The main advantage ofusing organic semiconductors is that it can be deposited by asimple vacuum technique at low fabrication temperature, whichprevents chemical and physical interactions with the underlyinglayers. By using the doped organic semiconductors as chargedrecombination layers, the high efficiency all-PVSK monolithictandem device composed of Cs0.15FA0.85Pb(I0.3Br0.7)3 andMAPbI3 has been achieved with average PCE of 15%.Considering the high production cost of conventional

inorganic solar cells, the all-PVSK tandem solar cells mightbe a promising approach for development of low cost andsuperhigh efficient tandem solar cells. However, as mentionedabove, stabilization of low Eg PVSK and design of proper devicearchitecture and process might be prerequisite for thedevelopment of high efficiency all-PVSK tandem solar cells.We expect that incremental research works on all-PVSKtandem solar cells will deliver another striking breakthrough fortandem solar cells in the near future.Breaking the Barrier: Achieving Market Competitive PVSK-

Based Tandem Solar Cells. The PCE of a PVSK-based tandemdevice is still lower than the highest reported PCE of a single-junction PVSK solar cell. We believe this is a result of devicearchitecture and the constituent materials of PVSK solar cellsthat have been optimized for single junction use, but not fortandem application. So far, most of the PVSK-based tandemsolar cells incorporate similar device architecture and materialsused for single-junction PVSK solar cells. For the case oftandem application, however, one should consider differentdesign rules, which require development of new materials andprocesses specialized for tandem application. In this section, wedescribe the key issues in device design and material propertiesfor PVSK-based tandem solar cells. The keys to reaching highefficiencies rely on

(i) reducing parasitic absorption,(ii) optical management,(iii) using electrode(s) with high transparency in the NIR that

can be processed without damaging the underlying PVSKlayers, and

(iv) improving PVSK single-junction performances for largerdevice areas with optimal Eg’s.

Reducing Parasitic Absorption: Parasitic absorption from thenecessary selective contacts of the PVSK subcell poses the firstissue for obtaining high tandem cell efficiencies. The topselective contact must possess an Eg as large as possible so asnot to absorb any light before entering the PVSK film. Thebottom selective contact would ideally have an Eg identical tothat of PVSK, and may be larger but not smaller, so as not toabsorb any light passing through the PVSK cell that is to becollected by the bottom subcell. Common selective contactsinclude TiO2 (Eg = 3.2 eV), Spiro-OMeTAD (Eg = 3.1 eV),PCBM (Eg = 1.9 eV), and PEDOT:PSS. Of these, TiO2 andSpiro-OMeTAD both have Eg’s large enough to preventparasitic absorption; however, Spiro-OMeTAD is commonlydoped with Li-based salts, which allows it to absorb largelythroughout the UV to IR regions of the spectrum. For the caseof a two-terminal device, according to the optical simulation byFilipic et al., in which light was incident to spiro-MeOTAD ontop of a PVSK layer, 2.4 mA/cm2 of JSC loss was found to occurby the spiro-MeOTAD layer.18 Albrecht et al. also pointed outthat not only the optimization of thickness and Eg of PVSKlayer but also the elimination of parasitic absorption by spiro-MeOTAD are key to achieve efficiency higher than 30%.19 For

Figure 10. (a) Schematics showing two-terminal tandem PVSK solarcell concepts. (b) Scanning electron micrograph of the two-terminalPVSK−PVSK tandem. (c) Scanned current−voltage characteristicsunder AM 1.5G illumination of the two-terminal PVSK−PVSKtandem, of the 1.2 eV solar cell, and the ITO-capped 1.8 eV solar cell.(d) External quantum efficiency spectra for the subcells. Reprintedwith permission from ref 65. Copyright 2016 American Association forthe Advancement of Science.

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this reason, similarly PCBMs, which are typical top selectivecontacts in inverted PVSK solar cells, are poor candidates fortop selective contacts in tandem architectures. Ideally thesematerials ought to be minimized or replaced altogether withmore appropriate Eg materials to dispose of all parasiticabsorption. Potential candidates may include CuSCN, SnO2,and NiO.71−73 However, careful attention must be paid to theprocessing techniques employed for these materials so as not todamage the underlying layers.Optical Management: Light management is another critical

component to achieving high efficiency tandem devices. Theabsorption depth of a material provides the distance that lightmay penetrate the material for which its intensity drops by 1/e(∼36%) of its original intensity. Typically, the thickness of theoptimized PVSK film is lower than that of its absorption depth,especially in the long wavelength region. As such, not all thelight can be effectively absorbed. For instance, MAPbI3 has anabsorption depth of 398 nm for λ = 750 nm, but increases to855 nm for a wavelength increase of only 20 nm to λ = 770nm.7 In single-junction PVSK devices, metallic counter-electrodes such as Ag act as rear reflectors to reflect andrecycle the light through the material a second time to enhanceabsorption. However, these metals cannot be incorporated onthe bottom of the PVSK subcell, as light must still be able topass through toward the bottom silicon subcell. Furthermore,with a flat top PVSK subcell, JSC of around 4−7 mA/cm2 istypically lost by light reflection.19,74,75 Several computationalsimulation results demonstrated that the absolute efficiency of2−4% can be enhanced with improved light reflection bytexturing the front surface.71,74,75 The surface texturing of thesilicon subcell would be an effective technique to create light-trapping capabilities within the device. In general, highefficiency inorganic bottom cells incorporate a textured surfaceto enhance the light trapping, which, however, can causedifficulty in forming a uniform and compact layer on it using asolution process (typically spin-coating process). Opticalmodeling with consideration of practical process should beperformed to solve the light management issue.Electrode Transparency: In traditional single-junction PVSK

solar cells, the absorber grows on the transparent FTO (orITO) glass substrate with an opaque metal back contact(considered as the superstrate configuration). For application intandem solar cells, it becomes a primary requirement for topPVSK cells that the opaque metal back contact has to bereplaced with the transparent conducting electrode. Suchtransparent electrodes with low sheet resistance and hightransmittance are designated to allow the penetration of longwavelength photons (typically 700−1200 nm) as much aspossible. Moreover, it has to be designed carefully so that thefabrication process for the top electrode would not impairfunctional layers within the PVSK cell, as underlying PVSKmaterials and adjacent charge transporting layers usuallycontain organic components that are not as concrete asinorganic layers. Implementing electrodes with high trans-parency and high mobility that do not damage the underlyinglayers during processing is a large challenge for obtaining highefficiencies. For example, sputtering of the common ITOtransparent electrode can damage the underlying hole-trans-porting and PVSK layer, and its high annealing temperatureswould further damage the device. AgNWs, also discussed above,have been shown to be effective, but present the potential issueof forming silver halide complexes, such as AgI, by reacting withions migrated from the PVSK layer. In general, a MoOx layer is

used to protect the underlying layers as mentioned above.37 Itwill be of great importance to develop techniques to utilizematerials with high transparency and high mobility that do notcompromise the Jsc, Voc, or FF of a PVSK device.PVSK Single Junction: Improving the PVSK single-junction

cell efficiency, with favorable Egs near 1.8 eV, over larger wafer-sized device areas will be an important factor for furtherdevelopment of PVSK-based tandem solar cells. So far, the Egtuning has mainly been done for single-junction use, which,however, will need more delicate tuning for tandem use.Furthermore, stability of the large (mixed halide) and low Eg(Sn-containg) PVSK is a crucial issue for realistic commerci-alization of PVSK-based tandem solar cells. Currently, thehighest single-junction PVSK devices are based on mixed-composition PVSKs and mesoporous titania scaffolds.Ultimately, mixed-compositions must be fine-tuned in termsof efficiency, Eg, and processing considerations. The hightemperatures of mesoporous scaffolds will prevent their use intandem devices. Therefore, new low temperature processingtechniques, potentially utilizing different materials, must bedeveloped. Larger device areas must also be developed toreduce complexity in module design, and may be accomplishedusing alternative solution-processing techniques such asprinting, doctor-blading, and more. Finally, incorporation ofstate-of-the-art technologies for management of crystal growthand charge carrier manipulation in single-junction PVSK solarcells will enable higher quality of PVSK top cells.25,76−78

Regardless of the remarkable progresses in PVSK single-junction devices in recent years, relatively less attention hasbeen paid to their application in tandem solar cells. Althoughthe PVSK single-junction solar cell itself has showncompetitiveness against other presenting photovoltaics, itscombination with well-established industries will open up newbusinesses that can penetrate into the market over a shortperiod to provide highly efficient and cost-effective energysources. Recent progress on PVSK-based tandem solar cells hasshown noteworthy potential in terms of both PCE andmanufacturing costs. With consideration of the aforementionedissues and incorporation of state-of-the-art single-junctionPVSK technologies, we believe that a PCE of 30% is a realisticgoal for the near future.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: yangy@ucla.edu.

ORCIDYang Yang: 0000-0001-8833-7641Author Contributions†These authors contributed equally to this work.

NotesThe authors declare no competing financial interest.Biographies

Jin-Wook Lee is a postdoctoral researcher in Prof. Yang Yang’s groupat the University of California Los Angeles (UCLA). He got his Ph.D.in Energy Science from Sungkyunkwan University (SKKU), Korea, in2016 under the supervision of Prof. Nam-Gyu Park. His research hasbeen focused on the development of highly efficient and stableperovskite solar cells by materials and process engineering.

Yao-Tsung Hsieh is a Ph.D. candidate at the University of CaliforniaLos Angeles (UCLA) in Prof. Yang Yang’s group. He received his B.S.degree in materials science and engineering from National Cheng

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Kung University, Tainan, Taiwan. His research focuses on solution-processed thin-film solar cells.

Nicholas De Marco is a Ph.D. candidate in Materials Science &Engineering at the University of California, Los Angeles (UCLA)under Prof. Yang Yang. He received his B.S. in MechanicalEngineering from the University of California, Merced (UCM) in2013. His research focuses on hybrid perovskite thin film growth forhighly efficient solar cells. His overall interests lie in energy harvesting,storage, and other optoelectronic applications.

Sang-Hoon Bae is a Ph.D. candidate in Materials Science andEngineering at the University of California, Los Angeles (UCLA)under the supervision of Prof. Yang Yang. He received his B.S. degreefrom Sungkyunkwan University (SKKU), Korea, in 2011, and his M.S.from Sungkyunkwan University, Korea, in 2013 under the supervisionof Prof. Jong-Hyun Ahn, both in Materials Science and Engineering.

Qifeng Han received his Ph.D. in Condensed Matter Physics from theInstitute of Solid Physics, Chinese Academy of Sciences in 2008. Nowhe is an associate professor of Shanghai Normal University and avisiting associate researcher in Prof. Yang Yang’s group at theUniversity of California Los Angeles (UCLA). His research focus onsolution-processed thin-film solar cells and single crystal growth.

Yang Yang received his M.S. and Ph.D. in Physics and Applied Physicsfrom the University of Massachusetts, Lowell, in 1988 and 1992,respectively. Before he joined UCLA in 1997, he served as a researchstaff member at UNIAX (now DuPont Display) from 1992 to 1996.Yang is now the Carol and Lawrence E. Tannas Jr. Endowed ChairProfessor of Materials Science at UCLA. He is also the Fellow of MRS,SPIE, RSC and the Electromagnetic (EM) Academy. He is an expert inthe fields of organic, inorganic, and organic/inorganic hybridelectronics and the development and fabrication of related devices,such as photovoltaic cells, LEDs, transistors, and memory devices.

■ ACKNOWLEDGMENTS

This work is supported by the Air Force Office of ScientificResearch (AFOSR, Grant No. FA9550-15-1-0610), the Officeof Naval Research (ONR, Grant No. N00014-04-1-0434), andthe National Science Foundation (NSF, Grant Nos. DMR-1210893 and ECCS-EPMD-1509955).

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2011