Low-Temperature Solution-Processed Solar Cells Based on PbS

Feb 13, 2013 - PbS colloidal quantum dot heterojunction solar cells have shown significant improvements in performance, mostly based on devices that u...
0 downloads 0 Views 2MB Size
Letter pubs.acs.org/NanoLett

Low-Temperature Solution-Processed Solar Cells Based on PbS Colloidal Quantum Dot/CdS Heterojunctions Liang-Yi Chang,† Richard R. Lunt,‡ Patrick R. Brown,§ Vladimir Bulović,∥ and Moungi G. Bawendi*,⊥ †

Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States ‡ Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, Michigan 48824, United States § Department of Physics, ∥Department of Electrical Engineering and Computer Science, and ⊥Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States S Supporting Information *

ABSTRACT: PbS colloidal quantum dot heterojunction solar cells have shown significant improvements in performance, mostly based on devices that use high-temperature annealed transition metal oxides to create rectifying junctions with quantum dot thin films. Here, we demonstrate a solar cell based on the heterojunction formed between PbS colloidal quantum dot layers and CdS thin films that are deposited via a solution process at 80 °C. The resultant device, employing a 1,2ethanedithiol ligand exchange scheme, exhibits an average power conversion efficiency of 3.5%. Through a combination of thicknessdependent current density−voltage characteristics, optical modeling, and capacitance measurements, the combined diffusion length and depletion width in the PbS quantum dot layer is found to be approximately 170 nm. KEYWORDS: PbS, CdS, quantum dot, chemical bath deposition, heterojunction, solar cell

L

Our fabrication process utilizes the chemical bath deposition technique, which has been shown to be a low-temperature, solution-phase, and scalable method for the fabrication of numerous inorganic semiconductors.14,15 For example, chemical bath deposition is used to fabricate CdS thin films as n-type window layers for conventional CdTe and CIGS solar cells with efficiencies as high as 15.8%.16,17 It has been shown that the superior performance of CdTe solar cells coated with CdS is due to field quenching, attributed to the excitation of trapped holes and recombination of electron−hole pairs in the CdS.18 Analogous to this work, in the present study we chose chemical-bath-deposited CdS to form a rectifying heterojunction with PbS QDs, enabling us to assess the compatibility of this deposition process with PbS QDs. Figure 1a,b shows the device architecture and the band diagram of our PbS QD/CdS bilayer heterojunction solar cells. PbS QDs of a wide band gap (∼1.5 eV, as determined from the first absorption excitonic peak at λ = 850 nm shown in Supporting Information Figure S1) are used to ensure energetically favorable electron transfer from PbS QDs to CdS and to reduce the interfacial recombination current.19 Energy levels of the constituent materials are taken from the literature.20,21 Light is incident on the heterojunction from the

ow-temperature solution-processed solar cells incorporating organic semiconductors1,2 and colloidal quantum dots (QDs)3 are a potential alternative to conventional solar cells fabricated via vacuum or high-temperature sintering processes for large-area, high-throughput, and low-cost manufacturing. While there has been significant effort to synthesize low-band gap organic semiconducting molecules for photovoltaic applications,4 PbS and PbSe QDs can already be tuned across the near-infrared spectrum from λ = 2200 nm to λ = 600 nm wavelength,5−7 encompassing the range of ideal band gaps for optimum efficiency in both single- and multijunction solar cells.8,9 For example, tunable band structures facilitate implementation of cascaded band gaps in the multijunction stack geometry, which can optimize the light capture of the solar cell stack. Since the report of the first PbS QD Schottky junction solar cell in 200810 there have been steady improvements in the power conversion efficiency of QD photovoltaics. The highest currently reported efficiency of 7.0% was achieved through passivation of the PbS QDs with halide anions and organic thiols, incorporating TiO2 annealed at 520 °C.11 Recently, the low-temperature fabrication of PbS/Bi2S3 QD bulk heterojunction and PbS QD pn junction solar cells exhibiting efficiencies of 4.912 and 5.4%,13 respectively, were reported. Here, we explore an alternative heterojunction solar cell based on PbS QDs and a low-temperature solutionprocessed CdS n-type inorganic semiconductor window layer adapted from traditional CdTe photovoltaic technology. © 2013 American Chemical Society

Received: November 8, 2012 Revised: January 24, 2013 Published: February 13, 2013 994

dx.doi.org/10.1021/nl3041417 | Nano Lett. 2013, 13, 994−999

Nano Letters

Letter

Figure 1. (a) Schematic of the PbS QD/CdS heterojunction device fabricated in this study. (b) Energy band diagram showing band edges of isolated 1.5 eV PbS QDs and CdS along with electrode work functions. (c) Cross-sectional SEM image of the device. Platinum was deposited on top of the device before focused ion beam milling to protect the underlying layers. (d) XPS depth profile of a PbS QD/CdS device without Al electrodes.

minimize the Fermi-level pinning that frequently occurs at metal−semiconductor interfaces, which limits the Schottky barrier height and open-circuit voltage (Voc). In addition, wide band discontinuities at p−n heterojunctions can suppress the contribution of electron or hole injection to the dark current and benefit both the fill factor (FF) and the Voc. Figure 2

side of the PbS where excited states are mainly generated in the smaller-energy-band gap PbS QDs, and the larger gap CdS can act as an optical spacer. Aspects of optical design are subsequently explored with the use of optical simulations. Material synthesis and device fabrication are detailed in the Supporting Information and briefly summarized here. PbS QDs were prepared by a modified recipe reported by Hines et al.,5 then deposited onto ITO-coated glass substrates using a layerby-layer dip-coating method22 employing 1,2-ethanedithiol (EDT) ligand exchange to increase carrier mobility and insolubilize the QDs. The thickness of the PbS QD layer was determined by the number of dip-coating cycles and ranged from 40 to 280 nm as measured with a profilometer. CdS thin films were deposited onto PbS QDs at 80 °C in an aqueous solution. The scanning electron microscope (SEM) image in Supporting Information Figure S2 displays the polycrystalline nature of these chemical-bath-deposited CdS thin films with grain sizes around 200 nm. The electrical conductivity measurement provided in Supporting Information Figure S3 reveals that CdS thin films are 5 orders of magnitude more conductive than PbS QD thin films of similar thickness. The relatively high conductivity of as-synthesized CdS thin films guarantees that the series resistance added to the PbS QD devices is negligible, thus eliminating the need for further vacuum or annealing processes. The cross-sectional SEM image and depth-profile X-ray photoelectron spectrum (XPS) presented in Figure 1(c,d) confirm the layer structure of the PbS QD/CdS heterojunction devices. The advantages of utilizing p−n heterojunctions over Schottky junctions for photovoltaics have been discussed by Pattantyus-Abraham et al.23 In particular, heterojunctions can

Figure 2. J−V characteristics of typical PbS QD Schottky (red) and PbS QD/CdS heterojunction (blue) devices measured in the dark and under AM1.5G simulated solar illumination.

displays the representative dark and light current density− voltage (J−V) characteristics of PbS QD Schottky and PbS QD/CdS bilayer heterojunction devices under AM1.5G illumination. Both of these devices consist of a 200 nm thick layer of PbS QDs, prepared using the same EDT ligand exchange procedure and sandwiched between an ITO bottom anode and an Al top cathode. The Voc, short-circuit current 995

dx.doi.org/10.1021/nl3041417 | Nano Lett. 2013, 13, 994−999

Nano Letters

Letter

initially increases with PbS QD layer thickness to a maximum at 160 nm, then decreases with greater PbS QD layer thicknesses. With a 160 nm thick PbS QD layer, we achieved an average Jsc of 15.3 ± 1.1 mA/cm2, Voc of 0.54 ± 0.02 V, FF of 0.42 ± 0.01, and PCE of 3.5 ± 0.3%. The trend in PCE is primarily correlated with that of the Jsc as illustrated in Figure 3. We therefore investigated the origin of the dependence of Jsc on PbS QD thickness. The generation of photocurrent in a p−n junction solar cell can be described in terms of two fundamental processes.26 The first process involves the absorption of incident photons and the creation of electron−hole pairs. Since the constituent materials and fabrication processes are identical for the devices of different thickness, any variation in the generation efficiency of electron−hole pairs following photon absorption can be neglected. Consequently, the first process is determined only by the absorption of incident photons where it is well-known that the optical electric field (and correspondingly the generation rate) inside multilayered thin films with reflective metal contacts can be modulated dramatically as a result of optical interference between incident and reflected light.27−29 In order to understand the spatial distribution of generation rates, we employed an optical model as previously described by Pettersson et al.30 where the complex indices of refraction (reported in Supporting Information Figure S5) and layer thicknesses of the materials were determined by spectroscopic ellipsometry and profilometry. The model assumes smooth interfaces between each layer, which is justified in the Supporting Information. The simulated wavelength- and distance-dependent photon absorption rates under AM1.5G solar photon flux for the complete device with various PbS QD thicknesses are illustrated in Figure 4. For ease of visualization, we also integrate the absorption rate with respect to wavelength and plot the total distance-dependent exciton generation rate in the PbS QD layers in Figure 4f. It is found that the generation rate (or, correspondingly, the rate of photon absorption) does not follow a simple exponential decay with thickness; instead, a local maximum occurs near the interface between PbS QDs and CdS regardless of PbS QD thickness. To elucidate whether such a generation pattern would favor a particular thickness of PbS QDs and because carrier separation is expected to take place at the heterojunction interface, we integrate the fullspectrum generation rate displayed in Figure 4f with respect to the distance from the PbS QD/CdS interface to obtain the integrated exciton generation rate, as depicted in Figure 5. Integrated to a given distance from the interface, the generation rates are smaller for thicker PbS QD films since more of the light is absorbed near the incident interface close to the ITO. With this simulation result, we find that even though there is an optical cavity effect in our devices, the thinner devices still have more excited states generated close to the PbS QD/CdS interface depletion region than in the thicker devices. The second process involved in photocurrent production is the extraction of photogenerated carriers. As mentioned above, the carrier extraction efficiency is described by the sum of the exciton and carrier diffusion lengths and depletion width relative to the PbS QD thickness and can be estimated by comparing the device data in Figure 3 with the optical modeling results in Figure 5. The devices with 40 and 220 nm thick PbS QD layers exhibit similar Jsc as shown in Figure 3. Consequently, the amount of carriers extracted must be the same for the two devices. Since 40 nm is rather thin compared to the typical depletion width and diffusion length reported for

density (Jsc), and PCE of heterojunction devices unambiguously outperform those of Schottky devices, indicating the effectiveness of using chemical-bath-deposited CdS as the n-type semiconductor in heterojunction devices. The applicability of CdS as an n-type material in p−n heterojunctions is further demonstrated by the inverted solar cell shown in Supporting Information Figure S4. The inverted CdS/PbS QD solar cell with symmetric ITO top and bottom contacts displays inverted polarity compared with the normal PbS QD/CdS, PbS QD Schottky, or ITO/PbS/ITO solar cells and an apparent Voc of −0.32 V, indicating that the built-in potential of the CdS/PbS QD heterojunction is greater than the top Schottky barrier that has been reported in several paper.22,24,25 Because the performance of thin film solar cells is highly dependent on the active layer thickness due to a trade-off between light absorption and carrier extraction, we studied the effect of the PbS QD layer thickness on the J−V characteristics to optimize device performance. Representative J−V curves for PbS QD/CdS heterojunction solar cells with various PbS QD thicknesses (40, 100, 160, 220, and 280 nm) are plotted in Figure 3a, and the photovoltaic parameters are summarized in

Figure 3. (a) J−V characteristics of representative PbS QD/CdS heterojunction solar cells with varying PbS QD layer thicknesses. (b) Performance characteristics of the above devices. The error bars are evaluated from the standard deviation of 20 devices fabricated with the same condition for each thickness of the PbS QD film.

Figure 3b. A decrease of Voc with increasing thickness of PbS QD films is observed, which is attributed to a reverse Schottky contact (nonohmic contact) that emerges at the anode, impeding electrical conduction and acting as an opposing diode in series, thus reducing the voltage.24,25 When the thickness is small, the built-in potential from the depletion region is sufficient to assist carriers tunneling through this nonohmic contact. While when the thickness is large, this nonohmic contact becomes important. Nevertheless, the PCE 996

dx.doi.org/10.1021/nl3041417 | Nano Lett. 2013, 13, 994−999

Nano Letters

Letter

Figure 4. Modeled photon absorption rate (1/sec-cm3) for PbS QD/CdS heterojunction devices with varying PbS QD thicknesses: (a) 40, (b) 100, (c) 160, (d) 220, and (e) 280 nm. The x-axis (distance) is measured from the ITO surface where light is incident. The horizontal stripes seen in the simulation plots result from the use of AM1.5G solar spectrum as a light source for the calculated absorption/generation rate. There are multiple dips in the solar spectrum due to light absorption by O3, O2, H2O, and CO2. The modeled total generation rates in PbS QD layers of different thicknesses is plotted in (f) and offset for clarity.

PbS QDs,19,25 we can assume that all of the carriers generated in the device are extracted. This assumption is supported by the high internal quantum efficiency (IQE) of 93% calculated from the ratio of measured to modeled Jsc (determined from the modeled total generation rate and assuming 100% extraction efficiency) and the good agreement between the measured Jsc and the integrated product of the external quantum efficiency (EQE) spectrum (Figure S9 in the Supporting Information) with the AM1.5G solar spectrum at low PbS QD thickness. From Figure 5, the integrated rate of carrier collection of the 220 nm thick device is seen to match that of the 40 nm thick device at a distance roughly 170 nm into the PbS film from the PbS/CdS interface; this distance constitutes an estimate of the convolution of the diffusion lengths and the depletion width within the 220 nm thick PbS QD layer. The depletion width can also be determined from a measurement of the device

capacitance. In order to obtain the depletion width in the PbS QD layer in our full device, we measured the capacitance of PbS QD/CdS devices with various PbS QD thicknesses under zero-bias conditions31,32 rather than implementing Mott− Schottky analysis in which a Schottky junction or a pN junction with the carrier concentration of the N layer much higher than that of the p-type QD layer must be employed.33 The capacitance is expected to decrease with increasing thickness as long as the thickness is smaller than the depletion width, in which case the fully depleted diode resembles a parallel-plate capacitor with a dielectric thickness equal to the depletion width. However, when the thickness exceeds the depletion width, the capacitance should be insensitive to the change of thickness. The measured and modeled (Supporting Information) capacitances are plotted in Figure 6. The modeled lower bound is calculated with the assumption that both the 997

dx.doi.org/10.1021/nl3041417 | Nano Lett. 2013, 13, 994−999

Nano Letters

Letter

and depletion width in the PbS QD layer is ∼170 nm. The integration of colloidal QDs and low temperature-deposited inorganic semiconductors in this work demonstrates the applicability of QDs in a potentially scalable device fabrication process and also opens up the possibility of pairing PbS QDs with other chemical-bath-deposited semiconductors, which may lead to further performance improvement.



ASSOCIATED CONTENT

S Supporting Information *

PbS QD synthesis, device fabrication and characterization, capacitance modeling, and additional figures for PbS QDs, CdS thin films, and J−V characteristics. This material is available free of charge via the Internet at http://pubs.acs.org.



Figure 5. The integrated generation rate (1/sec-cm2) as a function of the distance from the PbS QD/CdS interface for the above PbS QD thicknesses.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS This work was supported in part by the U.S. Army through the Institute for Soldier Nanotechnologies (W911NF-07-D-0004). L.-Y.C. acknowledges support from the Chesonis Fellowship Fund. P.R.B. gratefully acknowledges support from the Fannie and John Hertz Foundation and the National Science Foundation. The authors also thank Carl Brozek for the help with reflectance measurement and Chia-Hao Chuang and Gyu Weon Hwang for helpful discussion.



Figure 6. Measured (black square) and modeled (red circle for the lower bounds; blue triangle for the upper bounds) device capacitance at zero-bias as a function of PbS QD thicknesses. The lower bounds were calculated assuming that both the PbS QD and CdS layer are fully depleted, while the upper bounds were calculated assuming that only the PbS QD layer is fully depleted and none of the CdS layer is depleted.

REFERENCES

(1) Brabec, C. J.; Gowrisanker, S.; Halls, J. J. M.; Laird, D.; Jia, S.; Williams, S. P. Polymer-Fullerene Bulk-Heterojunction Solar Cells. Adv. Mater. 2010, 22, 3839−3856. (2) Walker, B.; Kim, C.; Nguyen, T.-Q. Small Molecule SolutionProcessed Bulk Heterojunction Solar Cells. Chem. Mater. 2011, 23, 470−482. (3) Kramer, I. J.; Sargent, E. H. Colloidal Quantum Dot Photovoltaics: A Path Forward. ACS Nano 2011, 5, 8506−8514. (4) Boudreault, P.-L. T.; Najari, A.; Leclerc, M. Processable LowBandgap Polymers for Photovoltaic Applications. Chem. Mater. 2011, 23, 456−469. (5) Hines, M.; Scholes, G. Colloidal PbS Nanocrystals with SizeTunable Near-Infrared Emission: Observation of Post-Synthesis SelfNarrowing of the Particle Size Distribution. Adv. Mater. 2003, 15, 1844−1849. (6) Liu, T.-Y.; Li, M.; Ouyang, J.; Zaman, M. B.; Wang, R.; Wu, X.; Yeh, C.-S.; Lin, Q.; Yang, B.; Yu, K. Non-Injection and LowTemperature Approach to Colloidal Photoluminescent PbS Nanocrystals with Narrow Bandwidth. J. Phys. Chem. C 2009, 113, 2301− 2308. (7) Moreels, I.; Justo, Y.; De Geyter, B.; Haustraete, K.; Martins, J. C.; Hens, Z. Size-Tunable, Bright, and Stable PbS Quantum Dots: A Surface Chemistry Study. ACS Nano 2011, 5, 2004−2012. (8) Shockley, W.; Queisser, H. J. Detailed Balance Limit of Efficiency of p-n Junction Solar Cells. J. Appl. Phys. 1961, 32, 510−51. (9) De Vos, A. Detailed balance limit of the efficiency of tandem solar cells. J. Phys. D: Appl. Phys 1980, 13, 839−846. (10) Johnston, K. W.; Pattantyus-Abraham, A. G.; Clifford, J. P.; Myrskog, S. H.; MacNeil, D. D.; Levina, L.; Sargent, E. H. Schottkyquantum dot photovoltaics for efficient infrared power conversion. Appl. Phys. Lett. 2008, 92, 151115−151118. (11) Ip, A. H.; Thon, S. M.; Hoogland, S.; Voznyy, O.; Zhitomirsky, D.; Debnath, R.; Levina, L.; Rollny, L. R.; Carey, G. H.; Fischer, A.;

PbS QD and CdS layers are fully depleted, while the modeled upper bound assumes that the PbS QD layer is fully depleted but that the CdS layer is not depleted. However, the measured capacitance deviates from the modeled capacitance bounds and becomes relatively constant for PbS QD thicknesses greater than ∼150 nm, suggesting that the PbS QD layer is no longer fully depleted. The ∼150 nm depletion width implied from the capacitance measurement is consistent with the ∼170 nm combined diffusion length and depletion width estimated from the optical model. The fact that the highest Jsc was obtained with a 160 nm thick layer of PbS QDs also correlates with this characteristic length. When the PbS QD thickness is smaller than this length, the Jsc increases with the thickness owing to improved light absorption. However, when the PbS QD thickness exceeds this length, more photons are absorbed in the quasi-neutral region and fewer photons are absorbed in the combined diffusion length and depletion width region, causing inefficient carrier extraction and a lower Jsc. In conclusion, we demonstrated the fabrication of PbS QD/ CdS heterojunction devices based on a low-temperature solution process with an average PCE of 3.5%. Thicknessdependent J−V characteristics, optical modeling, and capacitance measurements suggest that the combined diffusion length 998

dx.doi.org/10.1021/nl3041417 | Nano Lett. 2013, 13, 994−999

Nano Letters

Letter

Kemp, K. W.; Kramer, I. J.; Ning, Z.; Labelle, A. J.; Chou, K. W.; Amassian, A.; Sargent, E. H. Hybrid passivated colloidal quantum dot solids. Nat. Nanotechnol. 2012, 7, 577−582. (12) Rath, A. K.; Bernechea, M.; Martinez, L.; de Arquer, F. P. G.; Osmond, J.; Konstantatos, G. Solution-processed inorganic bulk nanoheterojunctions and their application to solar cells. Nat. Photonics 2012, 6, 529−534. (13) Tang, J.; Liu, H.; Zhitomirsky, D.; Hoogland, S.; Wang, X.; Furukawa, M.; Levina, L.; Sargent, E. H. Quantum Junction Solar Cells. Nano Lett. 2012, 12, 4889−4894. (14) Oladeji, I. O.; Chow, L. Optimization of Chemical Bath Deposited Cadmium Sulfide Thin Films. J. Electrochem. Soc. 1997, 144, 2342−2346. (15) Mane, R.; Lokhande, C. Chemical deposition method for metal chalcogenide thin films. Mater. Chem. Phys. 2000, 65, 1−31. (16) Britt, J.; Ferekides, C. Thin-film CdS/CdTe solar cell with 15.8% efficiency. Appl. Phys. Lett. 1993, 62, 2851−2852. (17) Contreras, M. A.; Romero, M. J.; B.; Hasoon, F.; Noufi, R.; Ward, S.; Ramanathan, K. Optimization of CBD CdS process in highefficiency Cu(In,Ga)Se2-based solar cells. Thin Solid Films 2002, 403− 404, 204−211. (18) Böer, K. W. Cadmium sulfide enhances solar cell efficiency. Energy Convers. Manage. 2011, 52, 426−430. (19) Pattantyus-Abraham, A. G.; Kramer, I. J.; Barkhouse, A. R.; Wang, X.; Konstantatos, G.; Debnath, R.; Levina, L.; Raabe, I.; Nazeeruddin, M. K.; Grätzel, M.; Sargent, E. H. DepletedHeterojunction Colloidal Quantum Dot Solar Cells. ACS Nano 2010, 4, 3374−3380. (20) Hyun, B.-R.; Zhong, Y.-W.; Bartnik, A. C.; Sun, L.; Abruña, H. D.; Wise, F. W.; Goodreau, J. D.; Matthews, J. R.; Leslie, T. M.; Borrelli, N. F. Electron Injection from Colloidal PbS Quantum Dots into Titanium Dioxide Nanoparticles. ACS Nano 2008, 2, 2206−2212. (21) Mumford, P. D.; Cahay, M. Space-charge effects and current self-quenching in a metal/CdS/LaS cold cathode. J. Appl. Phys. 1998, 84, 2754−2767. (22) Luther, J. M.; Law, M.; Beard, M. C.; Song, Q.; Reese, M. O.; Ellingson, R. J.; Nozik, A. J. Schottky Solar Cells Based on Colloidal Nanocrystal Films. Nano Lett. 2008, 8, 3488−3492. (23) Pattantyus-Abraham, A. G.; Kramer, I. J.; Barkhouse, A. R.; Wang, X.; Konstantatos, G.; Debnath, R.; Levina, L.; Raabe, I.; Nazeeruddin, M. K.; Grätzel, M.; Sargent, E. H. DepletedHeterojunction Colloidal Quantum Dot Solar Cells. ACS Nano 2010, 4, 3374−3380. (24) Gao, J.; Luther, J. M.; Semonin, O. E.; Ellingson, R. J.; Nozik, A. J.; Beard, M. C. Quantum Dot Size Dependent J-V Characteristics in Heterojunction ZnO/PbS Quantum Dot Solar Cells. Nano Lett. 2011, 11, 1002−100. (25) Brown, P. R.; Lunt, R. R.; Zhao, N.; Osedach, T. P.; Wanger, D. D.; Chang, L.-Y.; Bawendi, M. G.; Bulović, V. Improved Current Extraction from ZnO/PbS Quantum Dot Heterojunction Photovoltaics Using a MoO3 Interfacial Layer. Nano Lett. 2011, 11, 2955− 2961. (26) Sze, S. M.; Ng, K. K. Physics of Semidconductor Devices; John Wiley & Sons: New York, 2010; pp 719−736. (27) Peumans, P.; Yakimov, A.; Forrest, S. R. Small molecular weight organic thin-film photodetectors and solar cells. J. Appl. Phys. 2003, 93, 3693−3723. (28) Law, M.; Beard, M. C.; Choi, S.; Luther, J. M.; Hanna, M. C.; Nozik, A. J. Determining the Internal Quantum Efficiency of PbSe Nanocrystal Solar Cells with the Aid of an Optical Model. Nano Lett. 2008, 8, 3904−3910. (29) Kim, J.; Kim, S.; Lee, H.-H.; Lee, K.; Ma, W.; Gong, X.; Heeger, A. New Architecture for High-Efficiency Polymer Photovoltaic Cells Using Solution-Based Titanium Oxide as an Optical Spacer. Adv. Mater. 2006, 18, 572−576. (30) Pettersson, L. A. A.; Roman, L. S.; Inganas, O. Modeling photocurrent action spectra of photovoltaic devices based on organic thin films. J. Appl. Phys. 1999, 86, 487−496.

(31) Tang, J.; Brzozowski, L.; Barkhouse, D. A. R.; Wang, X.; Debnath, R.; Wolowiec, R.; Palmiano, E.; Levina, L.; PattantyusAbraham, A. G.; Jamakosmanovic, D.; Sargent, E. H. Quantum Dot Photovoltaics in the Extreme Quantum Confinement Regime: The Surface-Chemical Origins of Exceptional Air- and Light-Stability. ACS Nano 2010, 4, 869−878. (32) Rath, A. K.; Bernechea, M.; Martinez, L.; Konstantatos, G. Solution-Processed Heterojunction Solar Cells Based on p-type PbS Quantum Dots and n-type Bi2S3 Nanocrystals. Adv. Mater. 2011, 23, 3712−3717. (33) Green, M. A. Solar Cells; Prentice-Hall: Englewood Cliffs, NJ, 1998; pp 67−68.

999

dx.doi.org/10.1021/nl3041417 | Nano Lett. 2013, 13, 994−999