Toward Tandem Photovoltaic Devices Employing Nanoarray

Article pubs.acs.org/JPCC

Toward Tandem Photovoltaic Devices Employing Nanoarray Graphene-Based Sheets Yongfu 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 promising photonic materials for light harvesting. However, only low photoelectron conversion efficiency can be generated in single-junction graphene-based solar cells when isolated GQDs with the edge bonding defects are used as semiconductors. To address this issue, a fourjunction GQD-based tandem solar cell with high theoretical conversion efficiency was proposed in this paper. Instead of isolated GQDs, nanoarray GQDs embedded in hexagonal host materials, such as graphane or boron nitride, was adopted as the photoactive layer. Utilizing our universal thermodynamic approach to the gap openings in low-dimensional graphene, nanoarray armchair-interfaced GQDs embedded in graphane to achieve the maximal diameter of confined GQDs 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 of benefit to the application of graphene for solar cell devices.

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INTRODUCTION Because of the limited supply of today’s main energy sources (i.e., oil, coal, and uranium) and their detrimental long-term effects on the environment, scientists and engineers have devoted considerable efforts to converting the energy of sunlight directly into electricity using solar cells.1−5 Among them, some semiconductors, such as Si, TiO2, CdS, CdSe, CdTe, or PbTe, have been proven to be excellent solar energy materials.6−12 Because of its low cost, low toxicity, and ecofriendly nature with high surface area, electrical conductivity, and mechanical stability,12−14 much attention is now being directed to graphene as a future material in nano-/ microelectronics.15−18 Although bulk graphene has a zero band gap [Eg(∞) = 0 eV, where Eg denotes the band gap and ∞ the bulk size in two dimensions (2D)],19 the band gap openings (BOs) can be realized in graphene quantum dots (GQDs) via the edge effect. Since the BOs enable the spectral response of GQD-based photovoltaic devices,20 GQDs are therefore now regarded 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 and acceptors with large mobilities compared to those of Si.25,26 Single-junction GQD-based solar cell has been fabricated using isolated GQDs spin-coated on an indium tin oxide substrate.25 However, its conversion efficiency is limited because the photocurrent generated by it is low. To solve it, GQDs were functionalized with some polymer molecules,25,26 such as polyethylene glycol or aniline. With this means, the conversion © 2014 American Chemical Society

capability is somewhat enhanced, but still needs to be further improved. Because of this, we herein report on the designation of a high efficiency GQD-based photovoltaic device for solar cell applications.

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THEORETICAL APPROACH In our previous works, inspired by Lindemann’s criterion for solid melting and Mott’s expression for vibrational melting entropy,43−46 the authors have developed a thermodynamic way to elucidate the BOs in disordered GQDs based on the nearly free-electron approach.38,47 In view of this theoretical method, one sees that the change in cohesive energy of edge-C atoms has played an essential role in the openings in graphene, and an analytical Eg(D) equation has been established for disordered GQDs. In fact, this thermodynamic approach concerning the role of cohesive energy is universal for the openings in 2D flakes or sheets regarding the edge or interface effect. Here, we will investigate the openings in GQDs/M using the 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, the distinct physicochemical nature of C atoms at the edge or interface should decide the BOs in isolated GQDs or GQDs/ M. Hence, the openings in GQDs/M can also be explored Received: December 15, 2013 Revised: January 14, 2014 Published: January 27, 2014 2385

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based on the nearly free-electron approach,47 which can be principally given using what we developed for disordered GQDs.38 In light of this, Eg(D) of GQDs/M is shown as Eg (D) = [1 − Ec(D)2D /Ec(∞)]E h

atoms are allowed to relax until the convergence tolerances of energy, maximum force, and displacement of 1 × 10−5 Ha, 0.002 Ha/Å, and 0.005 Å are reached, respectively. Considered that the GGA-PBE method might underestimate the band gap values,49 the hybrid sX-LDA functional with CA-PZ in the CASTEP code has also been performed in this work, which is more accurate compared to those experiment results.50,51 We tested the precision of the hybrid sX-LDA functional with the example of the h-BN sheet, whose band gap is calculated to be 5.68 eV, in good agreement with the experimental result of 5.69 eV.52 During electronic calculations by the hybrid sX-LDA functional, Norm-conserving pseudopotential is used, and the Brillouin zone is sampled by 2 × 2 × 1 k-points with the energy cutoff of 500 eV.

(1.1)

0 Ec(D)2D /Ec(∞) = exp[−(α2D − 1)/(D/D2D − 1)]

(1.2)

where Ec denotes the cohesive energy and Eh is the hopping or transfer integral between neighboring atoms with Eh = 2.96 eV. In eq 1.2, two amounts of D02D and α2D should be developed. D02D denotes the critical diameter of a nanocrystal where all the atoms are located at boundaries (edge or interface), related to the dimensionality or the geometrical shape of graphene flakes. According to it, D02D can be principally given using D/D02D = s/ lh, where s/l is the area/edge ratio of low-dimensional graphene flakes.38 D02D can be directly given with D02D = 4h for GQDs.38 On the other hand, α2D is a physicochemical amount decided by the edge or interface nature relative to the bulk case. Thus, M 2 α2D of GQDs/M, αM 2D, should be explored using α2D = σin(D) / 2 2 σb(D) , where σ denotes the mean square displacement of thermal vibration at the melting temperature, and the subscripts “in” and “b” mean the respective atoms at the interface and in the bulk. In contrast to the disordered case, the impact from the interface geometrical structure should be considered. Since σ is related to the atomic nature at the edge or interface, αM 2D can be resolved through α02D for naked GQDs, which can be given 0 0 using α2D = σedge (D)2/σb(D)2 with the subscript “edge” 0 denoting the atoms at the naked edge.38 Dividing αM 2D by α2D, 2 0 2 −2 0 M αM /α = σ (D) /σ (D) . Since E ∝ σ , one gets α 2D 2D in edge c 2D = 0 0 M [E0c (D)/EM (D)]α , where E (D) and E (D) are the respective c 2D c c atomic cohesive energies of C atoms from the edge of naked GQDs and the interface of GQDs/M. Provided that E0c (D) and 0 EM c (D) have the same D-dependencies, the amount of Ec (D)/ M M Ec (D) should be D-independent, and thus α2D can be modified as M 0 α2D = [Ec0 /EcM]α2D

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RESULTS AND DISCUSSION Device Structure. In the 1960s, a Shockley-Queisser limit theory was developed to predict the maximal theoretical efficiency of a solar cell using a p−n junction to collect power under sunlight.27 In light of it, the Eg size plays an important role in absorbing visible and infrared lights with the photon energy ranging from 0.7 to 3.2 eV. Carrying out the analysis for the AM1.5 solar spectrum, the perfect balance is reached at about 1.1 eV for Si or 1.5 eV for CdTe. The maximal theoretical efficiency for a traditional Si-based single-junction cell is 34%, while the best lab examples have efficiencies around 25%.28 On the basis of this theory,27 the conversion efficiency can be further improved by reducing the energy waste relative to single-junction solar cells via forming tandem or multijunction cells made using semiconductors with band gaps decreasing in a gradient way.29,30 As examples, the conversion efficiency of tandem solar cells increases with the number of junctions, up to 50% with 1.6/0.9 eV, 56% with 1.8/1.2/0.7 eV, and 62% with 2.5/1.7/1.1/0.6 eV.29 As the junction number is increased further, the enhancements become less obvious as more than four junctions are added.29 Utilizing a structure with four III−V semiconductor subcells, strikingly, a new world record was reported recently for the conversion of sunlight into electricity with a solar cell efficiency of 44.7% (www.helmholtz-berlin.de). Stimulated by these, high-performance GQD-based photovoltaic devices can be achieved using such a tandem structure. Since increasing the number of junctions will make the manufacturing process more complicated, an optimum fourjunction structure with 2.5/1.7/1.1/0.6 eV plotted in Figure 1A,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 the neighboring cells will be connected utilizing an Al(2 nm)/ ITO(2 nm) structure (see Figure 1B). The work functions are different for Al and ITO, which are close to the lowest unoccupied molecular orbital and the highest occupied molecular orbital of GQD-based materials, respectively.25,26 Thus, each subcell will work under the Schottky tunneling mode. This mode ensures the electron−hole separation in GQD-based materials under sunlight illumination, while electrons and holes will then move to and accumulate at the Al and ITO electrodes, respectively. According to Kirchoff’s law,6 the voltage across the whole device is equal to the sum of the voltages across each subdevice. As a result, the photocurrent can be generated along the external circuits driven by such an internal electrical field. Photoactive GQD-Based Materials. To have the aforementioned tandem photovoltaic devices with excellent

(1.3)

Note that the way to determine α02D in eq 1.3 has been 0 discussed previously, and it can be given with α2D = 38 9[2Svib(∞)/3R + 1]/8, where Svib(∞) is the vibration entropy. As to E0c , it can be shown with E0c = ECC for ZZ M and AC-GNRs.48 In this work, EM c of GQDs/M is given as Ec = ECC + EC−M/2, where ECC and EC−M are the bond energies of C atoms at the GQDs/M interface, and “M” in the subscript means the atom from the host material. ECC and EC−M will be calculated with the simulation methods. Compared to isolated and disordered GQDs,38 as will be seen, since the edge stability changes with the AC or ZZ geometry, αM 2D varies accordingly with the interface structure, leading to the different opening behaviors. To evaluate the effect of the crystalline field interaction existing between neighboring GQDs, Eg(D) as a function of L is investigated for GQDs/M by the DMol3 code. The generalized gradient approximation (GGA) with PerdewBurke-Ernzerhof (PBE) is chosen as the exchange correlation functional. All electron core treatment and double numeric plus polarization (DNP) basis set are adopted. The Brillouin zone is sampled by 8 × 8 × 1 k-points and the global cutoff radius is set to 4.5 Å. In addition, the periodic boundary conditions are employed for all calculations, and a uniform vacuum of 15 Å is applied perpendicular to the slab to avoid the interactions between neighboring cells. During geometry optimization, all 2386

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for high conversion efficiency, GQDs/M with suitable band gaps should be provided, which can be controlled by D of GQDs. Moreover, the area fraction of GQDs over the whole sheet should be as high as possible. On account of this, the required D values of GQDs should be large, while the separation L between neighboring GQDs should be small. The former depends on the BO ability of GQD/M regarding the interfacial nature involving the host materials and the interface geometrical structure, while the latter is influenced by the crystalline interaction between neighboring GQDs. In addition, the thickness t of graphene-based sheets should be large enough to ensure full light absorption. All these material parameters 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

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

light harvesting, high-quality photoactive GQD-based materials with suitable band gaps are necessary. At the present time, however, isolated GQDs are usually fabricated with the imprint or sol−gel technique, and their edges are usually kept naked with one dangling bond for each C atom. Such an electronic nature will lead to the localization of charge or Coulomb blockade effects at the edges especially when the diameter D is lower than 40 nm,31,32 having a detrimental effect on the charge injection. To stabilize the edge nature, as usual, dangling bonds of edge-C atoms for isolated GQDs can be chemically saturated with some radicals (R) beneficial for the BOs, such as R = H.33,34 Alternatively, they can be eliminated by embedding GQDs in hexagonal host materials to form large-area graphenebased sheets consisting of periodic nanoarrays of GQDs, denoted with GQDs/M as shown in Figure 1C. As reported,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 edgesaturated GQDs or GQDs/M as semiconducting materials for solar cells. Some contribution has been made to investigating the gap openings in isolated GQDs, where Eg(D) rises as D of GQDs declines.21,37,38 On this basis,38 if GQDs saturated by H are used, the corresponding diameters should be 0.78/0.86/1.53/ 2.2 nm for the above tandem structure. According to previous studies,39,40 however, there exists a critical size Dc = 1.6 nm, below which isolated GQDs will suffer from serious edge irregularity and mechanical delicacy, posing a problem for handling 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 lower than Dc.38 This infers that isolated GQDs are not suitable for such a tandem structure. Instead, since the mechanical problem does not exist for GQDs embedded in the host materials,35 nanoarray GQDs/M in Figure 1D will thus be considered for fabricating tandem solar cells. Several Essential Parameters of Photoactive Nanoarray GQD/M Sheets. To ensure the absorption of sunlight

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 denote available simulation results with ●35 for AC-GQDs/GA and (red diamond)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 have 38 0 αM 2D, α2D = 2.54, and the respective ECC values are 4.68 and 5.81 eV for ZZ and AC structured interfaces.48 EM c for M = GA can be directly 35 cited as EM c = 7.51 eV, while that for M = BN are given with EC−M = 5.44 eV and ECC = 5.34 eV calculated using the simulation methods elucidated in Supporting Information.

and 1.2 with (A) M = GA and (B) M = BN. The BOs in GQDs/GA and GQDs/BN are observed, which rise on lowering of D. Eg(D) of AC-GQDs are noticeably larger than that of ZZ-GQDs. As D → D0, Eg(D) approaches to 2.96 eV. Such BO behaviors are rooted from the variation in chemical bonding of interfacial C atoms, which leads to the inequivalence of A and B sublattices. Our predicted curves are in agreement with those simulation results denoted by symbols, confirming the validity of our predictions. Considering that Eg(D) of GQDs/M can be modulated within 0−2.96 eV, the band gap requirement of 2.5/1.7/1.1/0.6 eV can be met for its application 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 edge geometrical structure and (B) ΔEg(D) = Eg(D)GA − Eg(D)BN relating to the host material. For the former in (A), ΔEg(D) are both positive for M = GA and BN, increasing from 0 to 0.8 eV on lowering D. This suggests that Eg(D) of the AC structure is 2387

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the strongest opening capability resulting in large D of GQDs. In contrast, the capability from the zigzag edge and the BN host material is the weakest, leading to small D. All these are consistent with Figures 2 and 3. Figure S1 exhibits Eg(D) of GQDs/M as a function of the physicochemical amount αM 2D, which reflects that the prominent confinement roles from the AC geometrical structure and the graphane host material originated from the strong atomic activity at the GQD/M interface. Owing to the above discussion, one sees that ACGQDs/GA can be adopted for fabricating tandem photovoltaic devices with high efficiency. In light of Figure 4, their respective D values of GQDs for the first, second, third, and fourth nanoarray 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 small as possible. However, when the separation L is too small, the confinement role of the host material in the BOs will be possibly weakened in relation to a crystalline field couple existing between neighboring GQDs.35 To keep the BOs strong, an optimum separation L should be selected. To assess Eg(D) of GQDs/M as a function of L, we performed the simulation using the generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE). As depicted and discussed in the Supporting Information, however, the GGA-PBE method indeed underestimates the band gap values as claimed previously. Because of this, instead, the results from the hybrid sX-LDA functional was provided here, as shown in Figure 5. In view of it, the Eg(D) size depends largely on the

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.

larger than that in the ZZ case, in agreement with Figure 2. This difference is relevant to the lower stability of C atoms at the AC edge relative to the ZZ case because of the homogeneous/inhomogeneous repulsion along the ZZ/AC edges.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 GA owns the strong confinement role in opening the band gap of GQDs. Furthermore, Figure 4 shows the respective sizes D of AC and ZZ-GQDs/M required to achieve the respective Eg(D)

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

host materials and the interface structure, decreasing in the order of AC-GQDs/GA, AC-GQDs/BN, ZZ-GQDs/GA, and ZZ-GQDs/BN. An increase in Eg(D) from 2.61 to 2.68 eV is observed for AC-GQDs/GA when L rises from 0.42 to 0.55 nm, while the change is hardly observed when L > 0.55 nm. As for ZZ-GQDs/GA, Eg(D) changes little at 2.08−2.12 eV when L rises from 0.42 to 0.90 nm. In contrast, when L rises, an obvious change in Eg(D) is observed from 2.32 to 2.52 for ACGQDs/BN and from 1.90 to 2.06 eV for ZZ-GQDs/BN. This suggests that, as the host material, graphane has the ability to weaken the crystalline field couple between GQDs relative to BN. If AC-GQDs/GA is adopted for fabricating the tandem structure of solar cells as mentioned above, a minimal

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

values of 2.5, 1.7, 1.1, and 0.6 eV for the first, second, third, and fourth nanoarray GQDs/M sheets with M = GA or BN. It can be 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 result suggests that the armchair edge and the GA host material own 2388

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Absorption and Modulate Charge Recombination in Mesoscopic Solar Cells. Adv. Funct. Mater. 2013, 23, 1846−1854. (4) Garcia-Iglesias, M.; Cid, J.-J.; Yum, J.-H.; Forneli, A.; Vazquez, P.; Nazeeruddin, M. K.; Palomares, E.; Gratzel, M.; Torres, T. Increasing the Efficiency of Zinc-Phthalocyanine Based Solar Cells through Modification of the Anchoring Ligand. Energy Environ. Sci. 2011, 4, 189−194. (5) Snaith, H. J. The Perils of Solar Cell Efficiency Measurements. Nat. Photon. 2012, 6, 337−340. (6) Swanson, R. M. A Vision for Crystalline Silicon Photovoltaics. Prog. Photovoltaics 2006, 14, 443−453. (7) de la Fuente, M. S.; Sánchez, R. S.; González-Pedro, V.; Boix, P. P.; Mhaisalkar, S. G.; Rincón, M. E.; Bisquert, J.; Mora-Seró, I. Effect of Organic and Inorganic Passivation in Quantum-Dot-Sensitized Solar Cells. J. Phys. Chem. Lett. 2013, 4, 1519−1525. (8) Ruland, A.; Schulz-Drost, C.; Sgobba, V.; Guldi, D. M. Enhancing Photocurrent Efficiencies by Resonance Energy Transfer in Cdte Quantum Dot Multilayers: Towards Rainbow Solar Cells. Adv. Mater. 2011, 23, 4573−4577. (9) Zewdu, T.; Clifford, J. N.; Hernandez, J. P.; Palomares, E. PhotoInduced Charge Transfer Dynamics in Efficient Tio2/Cds/Cdse Sensitized Solar Cells. Energy Environ. Sci. 2011, 4, 4633−4638. (10) Zhang, X.; Thavasi, V.; Mhaisalkar, S. G.; Ramakrishna, S. Novel Hollow Mesoporous 1d Tio2 Nanofibers as Photovoltaic and Photocatalytic Materials. Nanoscale 2012, 4, 1707−1716. (11) Docampo, P.; Guldin, S.; Steiner, U.; Snaith, H. J. Charge Transport Limitations in Self-Assembled Tio2 Photoanodes for DyeSensitized Solar Cells. J. Phys. Chem. Lett. 2013, 4, 698−703. (12) Chen, D.; Zhang, H.; Liu, Y.; Li, J. Graphene and Its Derivatives for the Development of Solar Cells, Photoelectrochemical, and Photocatalytic Applications. Energy Environ. Sci. 2013, 6, 1362−1387. (13) Dai, L. Layered Graphene/Quantum Dots: Nanoassemblies for Highly Efficient Solar Cells. ChemSusChem 2010, 3, 797−799. (14) Brennan, L. J.; Byrne, M. T.; Bari, M.; Gun’ko, Y. K. Carbon Nanomaterials for Dye-Sensitized Solar Cell Applications: A Bright Future. Adv. Energy Mater. 2011, 1, 472−485. (15) Guo, C. X.; Guai, G. H.; Li, C. M. Graphene Based Materials: Enhancing Solar Energy Harvesting. Adv. Energy Mater. 2011, 1, 448− 452. (16) Kim, H.-i.; Moon, G.-h.; Monllor-Satoca, D.; Park, Y.; Choi, W. Solar Photoconversion Using Graphene/TiO2 Composites: Nanographene Shell on TiO2 Core Versus TiO2 Nanoparticles on Graphene Sheet. J. Phys. Chem. C 2011, 116, 1535−1543. (17) Guldi, D. M.; Sgobba, V. Carbon Nanostructures for Solar Energy Conversion Schemes. Chem. Commun. 2011, 47, 606−610. (18) Zhu, P.; Nair, A. S.; Peng, S.; Yang, S.; Ramakrishna, S. Facile Fabrication of TiO2−Graphene Composite with Enhanced Photovoltaic and Photocatalytic Properties by Electrospinning. ACS Appl. Mater. Interface 2012, 4, 581−585. (19) Ihn, T.; Güttinger, J.; Molitor, F.; Schnez, S.; Schurtenberger, E.; Jacobsen, A.; Hellmüller, S.; Frey, T.; Dröscher, S.; Stampfer, C.; et al. Graphene Single-Electron Transistors. Mater. Today 2010, 13, 44−50. (20) Peng, J.; Gao, W.; Gupta, B. K.; Liu, Z.; Romero-Aburto, R.; Ge, L. H.; Song, L.; Alemany, L. B.; Zhan, X. B.; Gao, G. H.; et al. Graphene Quantum Dots Derived from Carbon Fibers. Nano Lett. 2012, 12, 844−849. (21) Yan, X.; Cui, X.; Li, B. S.; Li, L. S. Large, Solution-Processable Graphene Quantum Dots as Light Absorbers for Photovoltaics. Nano Lett. 2010, 10, 1869−1873. (22) Durantini, J.; Boix, P. P.; Gervaldo, M.; Morales, G. M.; Otero, L.; Bisquert, J.; Barea, E. M. Photocurrent Enhancement in DyeSensitized Photovoltaic Devices with Titania−Graphene Composite Electrodes. J. Electroanal. Chem. 2012, 683, 43−46. (23) Thongrattanasiri, S.; Koppens, F. H. L.; García de Abajo, F. J. Complete Optical Absorption in Periodically Patterned Graphene. Phys. Rev. Lett. 2012, 108, 047401. (24) Mueller, M. L.; Yan, X.; Dragnea, B.; Li, L.-S. Slow Hot-Carrier Relaxation in Colloidal Graphene Quantum Dots. Nano Lett. 2010, 11, 56−60.

separation should be designed at L = 0.55 nm to ensure the maximal 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 the initial light intensity, and α the absorption coefficient. As a result, the absorption fraction is increased as t rises. Conventionally, α of semiconductors ranges from 10−5 to 10−6 cm−1. Since small aromatic compounds have a large light absorption ability,21 α of GQDs on the order of 10−6 cm−1 can be achieved for GQDs. Thus, as the absorption fraction required is 95%, t should be 3.4 nm or so. No obvious increase in the absorption can be obtained as t is even increased. On account of this, the optimum thickness t of 3.4 nm for GQDbased sheets should be taken.

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CONCLUSIONS A tandem GQDs-based structure with 2.5/1.7/1.1/0.6 eV junctions has been designed for solar cells. On the basis of our thermodynamic theory, we have clarified how the interface interaction will induce the BOs in GQDs/M. It is predicted that the D-dependencies of Eg(D) for GQDs/M are differently associated with the interface geometrical structure and the host materials. The separation L can also influence the BOs because of the crystalline interaction. According to our predictions, ACinterfaced GQDs embedded in the graphane host materials can be 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 and the thickness t of 3.4 nm.

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ASSOCIATED CONTENT

S Supporting Information *

The way to explore EcM. Eg(D) as a function of the physiochemical amount αM 2D (Figure S1). Difference in Eg(D) as the function of L assessed between the GGA-PBE method and the hybrid sX-LDA functional (Figures S2 and S3). This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Fax: 86-431-85095371. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the National Key Basic Research Development Program (Grant No. 2010CB631001) is acknowledged.

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REFERENCES

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dx.doi.org/10.1021/jp412257g | J. Phys. Chem. C 2014, 118, 2385−2390