Toward Tandem Photovoltaic Devices Employing NanoarrayGraphene-Based SheetsYongfu Zhu, Ning Zhao, Jianshe Lian, and Qing Jiang*

Key Laboratory of Automobile Materials (Jilin University), Ministry of Education, and School of Materials Science and Engineering,Jilin University, Changchun, 130022, China

*S Supporting Information

ABSTRACT: Graphene quantum dots (GQDs) are promisingphotonic materials for light harvesting. However, only low photo-electron conversion efficiency can be generated in single-junctiongraphene-based solar cells when isolated GQDs with the edge bondingdefects are used as semiconductors. To address this issue, a four-junction GQD-based tandem solar cell with high theoreticalconversion efficiency was proposed in this paper. Instead of isolatedGQDs, nanoarray GQDs embedded in hexagonal host materials, suchas graphane or boron nitride, was adopted as the photoactive layer.Utilizing our universal thermodynamic approach to the gap openingsin low-dimensional graphene, nanoarray armchair-interfaced GQDsembedded in graphane to achieve the maximal diameter of confinedGQDs are found preferential for fabricating tandem solar cell devices.Besides these, the separation between GQDs and the thickness of GQD-based sheets were determined. This contribution is ofbenefit to the application of graphene for solar cell devices.

■ INTRODUCTION

Because of the limited supply of today’s main energy sources(i.e., oil, coal, and uranium) and their detrimental long-termeffects on the environment, scientists and engineers havedevoted considerable efforts to converting the energy ofsunlight directly into electricity using solar cells.1−5 Amongthem, some semiconductors, such as Si, TiO2, CdS, CdSe,CdTe, or PbTe, have been proven to be excellent solar energymaterials.6−12 Because of its low cost, low toxicity, andecofriendly nature with high surface area, electrical con-ductivity, and mechanical stability,12−14 much attention isnow being directed to graphene as a future material in nano-/microelectronics.15−18 Although bulk graphene has a zero bandgap [Eg(∞) = 0 eV, where Eg denotes the band gap and ∞ thebulk size in two dimensions (2D)],19 the band gap openings(BOs) can be realized in graphene quantum dots (GQDs) viathe edge effect. Since the BOs enable the spectral response ofGQD-based photovoltaic devices,20 GQDs are therefore nowregarded as a candidate for photonic applications.As solar energy materials, GQDs own high optical

absorptivity in the visible and near-infrared (IR) region,21−23

slow carrier cooling,24 and excellent electron donors andacceptors with large mobilities compared to those of Si.25,26

Single-junction GQD-based solar cell has been fabricated usingisolated GQDs spin-coated on an indium tin oxide substrate.25

However, its conversion efficiency is limited because thephotocurrent generated by it is low. To solve it, GQDs werefunctionalized with some polymer molecules,25,26 such aspolyethylene glycol or aniline. With this means, the conversion

capability is somewhat enhanced, but still needs to be furtherimproved. Because of this, we herein report on the designationof a high efficiency GQD-based photovoltaic device for solarcell applications.

■ THEORETICAL APPROACH

In our previous works, inspired by Lindemann’s criterion forsolid melting and Mott’s expression for vibrational meltingentropy,43−46 the authors have developed a thermodynamicway to elucidate the BOs in disordered GQDs based on thenearly free-electron approach.38,47 In view of this theoreticalmethod, one sees that the change in cohesive energy of edge-Catoms has played an essential role in the openings in graphene,and an analytical Eg(D) equation has been established fordisordered GQDs. In fact, this thermodynamic approachconcerning the role of cohesive energy is universal for theopenings in 2D flakes or sheets regarding the edge or interfaceeffect. Here, we will investigate the openings in GQDs/M usingthe universal thermodynamic theory.Compared to isolated disordered and naked GQDs, although

GQDs/M have different geometrical structures at boundaries,they have the same crystalline structure. With this means, thedistinct physicochemical nature of C atoms at the edge orinterface should decide the BOs in isolated GQDs or GQDs/M. Hence, the openings in GQDs/M can also be explored

Received: December 15, 2013Revised: January 14, 2014Published: January 27, 2014

Article

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based on the nearly free-electron approach,47 which can beprincipally given using what we developed for disorderedGQDs.38 In light of this, Eg(D) of GQDs/M is shown as

= − ∞E D E D E E( ) [1 ( ) / ( )]g c 2D c h (1.1)

α∞ = − − −E D E D D( ) / ( ) exp[ ( 1)/( / 1)]c 2D c 2D 2D0

(1.2)

where Ec denotes the cohesive energy and Eh is the hopping ortransfer integral between neighboring atoms with Eh = 2.96 eV.In eq 1.2, two amounts of D2D

0 and α2D should be developed.D2D

0 denotes the critical diameter of a nanocrystal where all theatoms are located at boundaries (edge or interface), related tothe dimensionality or the geometrical shape of graphene flakes.According to it, D2D

0 can be principally given using D/D2D0 = s/

lh, where s/l is the area/edge ratio of low-dimensional grapheneflakes.38 D2D

0 can be directly given with D2D0 = 4h for GQDs.38

On the other hand, α2D is a physicochemical amount decidedby the edge or interface nature relative to the bulk case. Thus,α2D of GQDs/M, α2D

M , should be explored using α2DM = σin(D)

2/σb(D)

2, where σ2 denotes the mean square displacement ofthermal vibration at the melting temperature, and the subscripts“in” and “b” mean the respective atoms at the interface and inthe bulk. In contrast to the disordered case, the impact from theinterface geometrical structure should be considered. Since σ isrelated to the atomic nature at the edge or interface, α2D

M can beresolved through α2D

0 for naked GQDs, which can be givenusing α2D

0 = σedge0 (D)2/σb(D)

2 with the subscript “edge”denoting the atoms at the naked edge.38 Dividing α2D

M by α2D0 ,

α2DM /α2D

0 = σin(D)2/σedge

0 (D)2. Since Ec ∝ σ−2, one gets α2DM =

[Ec0(D)/Ec

M(D)]α2D0 , where Ec

0(D) and EcM(D) are the respective

atomic cohesive energies of C atoms from the edge of nakedGQDs and the interface of GQDs/M. Provided that Ec

0(D) andEcM(D) have the same D-dependencies, the amount of Ec

0(D)/EcM(D) should be D-independent, and thus α2D

M can be modifiedas

α α= E E[ / ]2DM

c0

cM

2D0

(1.3)

Note that the way to determine α2D0 in eq 1.3 has been

discussed previously, and it can be given with α2D0 =

9[2Svib(∞)/3R + 1]/8,38 where Svib(∞) is the vibrationentropy. As to Ec

0, it can be shown with Ec0 = ECC for ZZ

and AC-GNRs.48 In this work, EcM of GQDs/M is given as Ec

M =ECC + EC−M/2, where ECC and EC−M are the bond energiesof C atoms at the GQDs/M interface, and “M” in the subscriptmeans the atom from the host material. ECC and EC−M will becalculated with the simulation methods. Compared to isolatedand disordered GQDs,38 as will be seen, since the edge stabilitychanges with the AC or ZZ geometry, α2D

M varies accordinglywith the interface structure, leading to the different openingbehaviors.To evaluate the effect of the crystalline field interaction

existing between neighboring GQDs, Eg(D) as a function of Lis investigated for GQDs/M by the DMol3 code. Thegeneralized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) is chosen as the exchange correlationfunctional. All electron core treatment and double numeric pluspolarization (DNP) basis set are adopted. The Brillouin zone issampled by 8 × 8 × 1 k-points and the global cutoff radius is setto 4.5 Å. In addition, the periodic boundary conditions areemployed for all calculations, and a uniform vacuum of 15 Å isapplied perpendicular to the slab to avoid the interactionsbetween neighboring cells. During geometry optimization, all

atoms are allowed to relax until the convergence tolerances ofenergy, maximum force, and displacement of 1 × 10−5 Ha,0.002 Ha/Å, and 0.005 Å are reached, respectively. Consideredthat the GGA-PBE method might underestimate the band gapvalues,49 the hybrid sX-LDA functional with CA-PZ in theCASTEP code has also been performed in this work, which ismore accurate compared to those experiment results.50,51 Wetested the precision of the hybrid sX-LDA functional with theexample of the h-BN sheet, whose band gap is calculated to be5.68 eV, in good agreement with the experimental result of 5.69eV.52 During electronic calculations by the hybrid sX-LDAfunctional, Norm-conserving pseudopotential is used, and theBrillouin zone is sampled by 2 × 2 × 1 k-points with the energycutoff of 500 eV.

■ RESULTS AND DISCUSSIONDevice Structure. In the 1960s, a Shockley-Queisser limit

theory was developed to predict the maximal theoreticalefficiency of a solar cell using a p−n junction to collect powerunder sunlight.27 In light of it, the Eg size plays an importantrole in absorbing visible and infrared lights with the photonenergy ranging from 0.7 to 3.2 eV. Carrying out the analysis forthe AM1.5 solar spectrum, the perfect balance is reached atabout 1.1 eV for Si or 1.5 eV for CdTe. The maximal theoreticalefficiency for a traditional Si-based single-junction cell is 34%,while the best lab examples have efficiencies around 25%.28 Onthe basis of this theory,27 the conversion efficiency can befurther improved by reducing the energy waste relative tosingle-junction solar cells via forming tandem or multijunctioncells made using semiconductors with band gaps decreasing in agradient way.29,30 As examples, the conversion efficiency oftandem solar cells increases with the number of junctions, up to50% with 1.6/0.9 eV, 56% with 1.8/1.2/0.7 eV, and 62% with2.5/1.7/1.1/0.6 eV.29 As the junction number is increasedfurther, the enhancements become less obvious as more thanfour junctions are added.29 Utilizing a structure with four III−Vsemiconductor subcells, strikingly, a new world record wasreported recently for the conversion of sunlight into electricitywith a solar cell efficiency of 44.7% (www.helmholtz-berlin.de).Stimulated by these, high-performance GQD-based photo-voltaic devices can be achieved using such a tandem structure.Since increasing the number of junctions will make themanufacturing process more complicated, an optimum four-junction structure with 2.5/1.7/1.1/0.6 eV plotted in Figure1A,B is adopted in this work.In the tandem structure, we will adopt ITO (100 nm) as the

top anode and Al (100 nm) as the bottom cathode, while theneighboring cells will be connected utilizing an Al(2 nm)/ITO(2 nm) structure (see Figure 1B). The work functions aredifferent for Al and ITO, which are close to the lowestunoccupied molecular orbital and the highest occupiedmolecular orbital of GQD-based materials, respectively.25,26

Thus, each subcell will work under the Schottky tunnelingmode. This mode ensures the electron−hole separation inGQD-based materials under sunlight illumination, whileelectrons and holes will then move to and accumulate at theAl and ITO electrodes, respectively. According to Kirchoff’slaw,6 the voltage across the whole device is equal to the sum ofthe voltages across each subdevice. As a result, the photocurrentcan be generated along the external circuits driven by such aninternal electrical field.

Photoactive GQD-Based Materials. To have theaforementioned tandem photovoltaic devices with excellent

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light harvesting, high-quality photoactive GQD-based materialswith suitable band gaps are necessary. At the present time,however, isolated GQDs are usually fabricated with the imprintor sol−gel technique, and their edges are usually kept nakedwith one dangling bond for each C atom. Such an electronicnature will lead to the localization of charge or Coulombblockade effects at the edges especially when the diameter D islower than 40 nm,31,32 having a detrimental effect on the chargeinjection. To stabilize the edge nature, as usual, dangling bondsof edge-C atoms for isolated GQDs can be chemically saturatedwith some radicals (R) beneficial for the BOs, such as R =H.33,34 Alternatively, they can be eliminated by embeddingGQDs in hexagonal host materials to form large-area graphene-based sheets consisting of periodic nanoarrays of GQDs,denoted with GQDs/M as shown in Figure 1C. Asreported,35,36 if M = graphane (GA) or boron nitride (BN),the gap openings in GQDs were realized successfully. However,no further investigation has been made on adopting edge-saturated GQDs or GQDs/M as semiconducting materials forsolar cells.Some contribution has been made to investigating the gap

openings in isolated GQDs, where Eg(D) rises as D of GQDsdeclines.21,37,38 On this basis,38 if GQDs saturated by H areused, the corresponding diameters should be 0.78/0.86/1.53/2.2 nm for the above tandem structure. According to previousstudies,39,40 however, there exists a critical size Dc = 1.6 nm,below which isolated GQDs will suffer from serious edgeirregularity and mechanical delicacy, posing a problem forhandling and assembly. When Eg(D) rises up to 1.1 and 2.5 eV,the respective D values decline from 1.53 to 0.78 nm, so lowerthan Dc.

38 This infers that isolated GQDs are not suitable forsuch a tandem structure. Instead, since the mechanical problemdoes not exist for GQDs embedded in the host materials,35

nanoarray GQDs/M in Figure 1D will thus be considered forfabricating tandem solar cells.Several Essential Parameters of Photoactive Nano-

array GQD/M Sheets. To ensure the absorption of sunlight

for high conversion efficiency, GQDs/M with suitable bandgaps should be provided, which can be controlled by D ofGQDs. Moreover, the area fraction of GQDs over the wholesheet should be as high as possible. On account of this, therequired D values of GQDs should be large, while theseparation L between neighboring GQDs should be small.The former depends on the BO ability of GQD/M regardingthe interfacial nature involving the host materials and theinterface geometrical structure, while the latter is influenced bythe crystalline interaction between neighboring GQDs. Inaddition, the thickness t of graphene-based sheets should belarge enough to ensure full light absorption. All these materialparameters will be clarified as follows.Utilizing our universal thermodynamic approach, the Eg(D)

curves as a function of D are plotted in Figure 2 using eqs 1.1

and 1.2 with (A) M = GA and (B) M = BN. The BOs inGQDs/GA and GQDs/BN are observed, which rise onlowering of D. Eg(D) of AC-GQDs are noticeably larger thanthat of ZZ-GQDs. As D → D0, Eg(D) approaches to 2.96 eV.Such BO behaviors are rooted from the variation in chemicalbonding of interfacial C atoms, which leads to the inequivalenceof A and B sublattices. Our predicted curves are in agreementwith those simulation results denoted by symbols, confirmingthe validity of our predictions. Considering that Eg(D) ofGQDs/M can be modulated within 0−2.96 eV, the band gaprequirement of 2.5/1.7/1.1/0.6 eV can be met for itsapplication in tandem solar cells.Figure 3 shows the plot of ΔEg(D) as a function of D with

(A) ΔEg(D) = Eg(D)AC − Eg(D)ZZ concerning the edgegeometrical structure and (B) ΔEg(D) = Eg(D)GA − Eg(D)BNrelating to the host material. For the former in (A), ΔEg(D) areboth positive for M = GA and BN, increasing from 0 to 0.8 eVon lowering D. This suggests that Eg(D) of the AC structure is

Figure 1. Schematic figure of GQD-based tandem photovoltaicdevices for solar cells.

Figure 2. Eg(D) curves in solid as the function of D for (A) GQDs/GA and (B) GQDs/BN using eqs 1.1 and 1.2. The symbols denoteavailable simulation results with ●35 for AC-GQDs/GA and (reddiamond)35 for ZZ-GQDs/GA in (A) and ■53 for AC-GQDs/BN and(red circle)53 and (red diamond)54 for ZZ-GQDs/BN in (B). To haveα2DM , α2D

0 = 2.54,38 and the respective ECC values are 4.68 and 5.81 eVfor ZZ and AC structured interfaces.48 Ec

M for M = GA can be directlycited as Ec

M = 7.51 eV,35 while that for M = BN are given with EC−M =5.44 eV and ECC = 5.34 eV calculated using the simulation methodselucidated in Supporting Information.

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larger than that in the ZZ case, in agreement with Figure 2.This difference is relevant to the lower stability of C atoms atthe AC edge relative to the ZZ case because of thehomogeneous/inhomogeneous repulsion along the ZZ/ACedges.41,42 In the latter case in (B), ΔEg(D) are also positive,rising from 0 to 0.3 eV as D declines. This indicates that GAowns the strong confinement role in opening the band gap ofGQDs.Furthermore, Figure 4 shows the respective sizes D of AC

and ZZ-GQDs/M required to achieve the respective Eg(D)

values of 2.5, 1.7, 1.1, and 0.6 eV for the first, second, third, andfourth nanoarray GQDs/M sheets with M = GA or BN. It canbe seen that D is lowered as Eg is increased. Among the D−Eg(D) curves, the one for AC-GQDs/GA is located on the top,while that of ZZ-GQDs/BN is at the bottom. This resultsuggests that the armchair edge and the GA host material own

the strongest opening capability resulting in large D of GQDs.In contrast, the capability from the zigzag edge and the BN hostmaterial is the weakest, leading to small D. All these areconsistent with Figures 2 and 3. Figure S1 exhibits Eg(D) ofGQDs/M as a function of the physicochemical amount α2D

M ,which reflects that the prominent confinement roles from theAC geometrical structure and the graphane host materialoriginated from the strong atomic activity at the GQD/Minterface. Owing to the above discussion, one sees that AC-GQDs/GA can be adopted for fabricating tandem photovoltaicdevices with high efficiency. In light of Figure 4, their respectiveD values of GQDs for the first, second, third, and fourthnanoarray sheets in Figure 1 should be given as 3.07/1.79/1.23/0.87 nm.To ensure the sunlight absorption, as aforementioned, the

separation L between neighboring GQDs should be kept smallas possible. However, when the separation L is too small, theconfinement role of the host material in the BOs will bepossibly weakened in relation to a crystalline field coupleexisting between neighboring GQDs.35 To keep the BOsstrong, an optimum separation L should be selected. To assessEg(D) of GQDs/M as a function of L, we performed thesimulation using the generalized gradient approximation(GGA) with Perdew-Burke-Ernzerhof (PBE). As depictedand discussed in the Supporting Information, however, theGGA-PBE method indeed underestimates the band gap valuesas claimed previously. Because of this, instead, the results fromthe hybrid sX-LDA functional was provided here, as shown inFigure 5. In view of it, the Eg(D) size depends largely on the

host materials and the interface structure, decreasing in theorder of AC-GQDs/GA, AC-GQDs/BN, ZZ-GQDs/GA, andZZ-GQDs/BN. An increase in Eg(D) from 2.61 to 2.68 eV isobserved for AC-GQDs/GA when L rises from 0.42 to 0.55nm, while the change is hardly observed when L > 0.55 nm. Asfor ZZ-GQDs/GA, Eg(D) changes little at 2.08−2.12 eV whenL rises from 0.42 to 0.90 nm. In contrast, when L rises, anobvious change in Eg(D) is observed from 2.32 to 2.52 for AC-GQDs/BN and from 1.90 to 2.06 eV for ZZ-GQDs/BN. Thissuggests that, as the host material, graphane has the ability toweaken the crystalline field couple between GQDs relative toBN. If AC-GQDs/GA is adopted for fabricating the tandemstructure of solar cells as mentioned above, a minimal

Figure 3. ΔEg(D) as the function of D with (A) ΔEg(D) = Eg(D)AC −Eg(D)ZZ concerning the edge geometrical structure and (B) ΔEg(D) =Eg(D)GA − Eg(D)BN relating to the host material.

Figure 4. Plot of D necessary to achieve Eg(D) for different nanoarrayGQDs/M sheets shown in Figure 1 with M = GA and BN. See thecaption of Figure 2 for necessary parameters.

Figure 5. Simulation on Eg(D) as a function of L using the hybrid sX-LDA functional for GQDs/M with the AC-structured interface at D =0.92 nm or the ZZ-structured interface at D = 1.04 nm.

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separation should be designed at L = 0.55 nm to ensure themaximal GQD density for high efficiency.In addition, the thickness t of GQD-based sheets is decided.

The sunlight absorption through GQDs can be given with I =I0e

−αt, where I is the light intensity at the thickness t, I0 theinitial light intensity, and α the absorption coefficient. As aresult, the absorption fraction is increased as t rises.Conventionally, α of semiconductors ranges from 10−5 to10−6 cm−1. Since small aromatic compounds have a large lightabsorption ability,21 α of GQDs on the order of 10−6 cm−1 canbe achieved for GQDs. Thus, as the absorption fractionrequired is 95%, t should be 3.4 nm or so. No obvious increasein the absorption can be obtained as t is even increased. Onaccount of this, the optimum thickness t of 3.4 nm for GQD-based sheets should be taken.

■ CONCLUSIONSA tandem GQDs-based structure with 2.5/1.7/1.1/0.6 eVjunctions has been designed for solar cells. On the basis of ourthermodynamic theory, we have clarified how the interfaceinteraction will induce the BOs in GQDs/M. It is predicted thatthe D-dependencies of Eg(D) for GQDs/M are differentlyassociated with the interface geometrical structure and the hostmaterials. The separation L can also influence the BOs becauseof the crystalline interaction. According to our predictions, AC-interfaced GQDs embedded in the graphane host materials canbe selected for light harvesting in photovoltaic devices.Correspondingly, the D values of AC-GQDs should be 3.07/1.79/1.23/0.87 nm with an optimum value of L = 0.55 nm andthe thickness t of 3.4 nm.

■ ASSOCIATED CONTENT*S Supporting InformationThe way to explore Ec

M. Eg(D) as a function of thephysiochemical amount α2D

M (Figure S1). Difference in Eg(D)as the function of L assessed between the GGA-PBE methodand the hybrid sX-LDA functional (Figures S2 and S3). Thismaterial is available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*Fax: 86-431-85095371. E-mail: jiangq@jlu.edu.cn.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSFinancial support from the National Key Basic ResearchDevelopment Program (Grant No. 2010CB631001) isacknowledged.

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The Journal of Physical Chemistry C Article

dx.doi.org/10.1021/jp412257g | J. Phys. Chem. C 2014, 118, 2385−23902390