Singlet fission, a process that converts a singlet exciton into two triplet excitons, has the potential to achieve a high-efficiency solar cell that exceeds the Shockley-Queisser limit ^[1] . Singlet fission has been previously employed to enhance the photovoltaic efficiency of organic nanostructured solar cells ^[2] , photodetectors ^[3] , and fission-sensitized quantum dot solar cells ^[4] . To obtain optimum efficiency from singlet fission, we need to understand the molecular factors that control its rate. Since singlet fission involves two neighboring chromophores, their intermolecular coupling is expected to play an essential role in determining the single fission rate. Here, we investigate how intermolecular interactions control singlet fission in pentacene, an archetypal molecule exhibiting singlet fission.

In this project, we examine the rate of singlet fission while modulating the intermolecular coupling by altering the side group of pentacene derivatives. We study unsubstituted pentacene and four other pentacene derivatives in thin-film states, 6,13-bis(triisopropyl-silylethynyl) pentacene (TIPS-pentacene), 6,13-diphenylpentacene (DP-pentacene), 6,13-di-biphenyl-4-yl-pentacene (DB-pentacene), and 6,13-di(2’-thienyl)pentacene (thienyl pentacene); see Figure 1 for their crystal structures. We characterize the intermolecular coupling by monitoring the ref shift and peak broadening in their absorption spectra when the molecules in solutions become solid-state thin films. Then, we compared the intermolecular coupling with the rate of singlet fission measured using femtosecond photoinduced absorption spectroscopy; see Figure 2. We also perform density-functional calculations to estimate the coupling between a singlet and two neighboring triplets. We expect our study to contribute to better understanding of the mechanism of singlet fission and rational designs of singlet-fission-based photovoltaic devices.

1. M. B. Smith and J. Michl, “Singlet fission,” Chemical Reviews, vol. 110, pp. 6891-6936, Nov. 2010.
2. P. J. Jadhav, A. Mohanty, J. Sussman, J. Lee, and M. A. Baldo, “Singlet exciton fission in nanostructured organic solar cells,” Nano Letters, vol. 11, pp. 1495-1498, Feb. 2011.
3. J. Lee, P. Jadhav, and M. A. Baldo, “High efficiency organic multilayer photodetectors based on singlet exciton fission,” Applied Physics Letters, vol. 95, p. 033301, 2009.
4. B. Ehrler, M. W. B. Wilson, A. Rao, R. H. Friend, and N. C. Greenham, “Singlet exciton fission-sensitized infrared quantum dot solar cells,” Nano Letters, vol. 12, pp. 1053-1057, Jan. 2012.

Organic solar cells and photodetectors that feature singlet exciton fission materials have two additional exciton processes that traditional organic solar cells do not: singlet fission and triplet doublet annihilation. To maximize the usable power of the photovoltaic cell, we must understand how to optimize the gain from singlet fission and minimize the loss from doublet annihilation. We focus on the former here.

An organic photodetector is composed of thin layers of pentacene and PTCBI stacked repeatedly, as in Figure 1. This device structure is designed to enhance exciton dissociation at the donor/acceptor interface. The rapid dissociation of the singlet exciton in the photodetector competes with the singlet fission process, which is the formation of two triplet excitons from one singlet, and has been shown to be very fast and efficient ^{[1] [2]} . Modulation of the singlet fission rate by application of an external magnetic field changes the photocurrent by reducing the singlet fission rate relative to the rate of singlet dissociation into a charge.  The high field asymptotic value of the change in photocurrent is proportional to the fission yield ^[2] .

We built photodetectors that utilize variably thick layers of pentacene to modulate the rate competing with singlet fission. The maximum the internal quantum efficiency (IQE) of 130% occurs for an 8-nm-thick pentacene layer. The trend in IQE is matched by the trend of an increasing change in photocurrent with applied magnetic field, as Figure 2 shows. We conclude that there is less competition between the singlet for performing fission and dissociating at the donor/acceptor interface.

The gain in IQE from the singlet fission process is largest for pentacene layers of 8 nm. The change in photocurrent suggests that the fission efficiency is even larger for thicker layers; however, we observe loss in IQE, which could be due to exciton diffusion.

1. M. W. B. Wilson, A. Rao, J. Clark, R. S. S. Kumar, D. Brida, G. Cerullo, and R. H. Friend, “Ultrafast dynamics of exciton fission in polycrystalline pentacene,” Journal of the American Chemical Society, vol. 133, no. 31, pp. 11830–11833, 2011
2. J. Lee, P. Jadhav, and M. A. Baldo, “High efficiency organic multilayer photodetectors based on singlet exciton fission,” Applied Physics Letters, vol. 95, p. 033301, 2009.

Solar cells based on lead sulfide quantum dots (PbS QDs) represent a promising new class of solution-processable photovoltaics. The highly tunable bandgap of PbS QDs (0.5-2.1 eV) makes them ideally suited for incorporation into multijunction architectures, and their resistance to oxidation and photobleaching represent further advantages over typical solution-processed photovoltaic materials such as organic small molecules and polymers ^{[1] [2]} .

The electronic properties of QD films are determined not only by the size and composition of the QDs themselves but also by the properties of the organic ligands used to passivate the QD surfaces. As-synthesized PbS QDs are stabilized in solution by long, insulating oleic acid ligands, which are unsuitable for use in photovoltaics, where efficient electron transport is required. Therefore, a ligand-exchange treatment is typically performed, replacing the oleic acid ligands with short, bidentate molecules such as 1,2-ethanedithiol (EDT). Our research demonstrates that the power conversion efficiency of ZnO/PbS QD heterojunction photovoltaics ^[3] may be enhanced through ligand exchange with 1,3-benzenedithiol (BDT) rather than the more common EDT, despite the fact that BDT-treated films demonstrate a lower charge carrier mobility than EDT-treated films. Treatment with BDT simultaneously increases the fill factor (FF) and open-circuit voltage (V_OC) relative to treatment with EDT, thereby increasing the power conversion efficiency by a factor of 1.6, from 2.1% to 3.4%. Measurement of the transient photovoltage response of the devices indicates that this increase in FF and V_OC results from a decrease in the rate of bimolecular recombination and the concomitant increase in carrier lifetime within the QD film. This increase in carrier lifetime more than compensates for the lower mobility of BDT-treated films, emphasizing the importance of designing ligands that simultaneously decrease the inter-QD spacing and effectively passivate surface recombination sites.

1. J. Gao, J. M. Luther, O. E. Semonin, R. J. Ellingson, A. J. Nozik, and M. C. Beard, “Quantum dot size dependent J-V characteristics in heterojunction ZnO/PbS quantum dot solar cells,” Nano Letters, vol. 11, pp. 1002-1008, Feb. 2011.
2. X. Wang, G. I. Koleilat, J. Tang, H. Liu, I. J. Kramer, R. Debnath, L. Brzozowski, D. A. R. Barkhouse, L. Levina, S. Hoogland, and E. H. Sargent, “Tandem colloidal quantum dot solar cells employing a graded recombination layer,” Nature Photonics, vol. 5, pp. 480-484, Aug. 2011.
3. P. R. Brown, R. R. Lunt, N. Zhao, T. P. Osedach, D. D. Wanger, L.-Y. Chang, M. G. Bawendi, and V. Bulovic, “Improved current extraction from ZnO/PbS quantum dot heterojunction photovoltaics using a MoO3 interfacial layer,” Nano Letters, vol. 11, pp. 2955-2961, June 2011.

Water oxidation is the thermodynamically demanding step of the water-splitting reaction. Efficient sunlight-driven water splitting into molecular oxygen and hydrogen is a challenging prerequisite for solar-fuels production ^[1] . For this prerequisite to be achieved, two major requirements are necessary: (1) efficient photon-to-charge conversion, with efficient utilization of the solar spectrum, and (2) a lowering of the energetic barriers for the four-proton, four-electron proton-coupled electron transfer (PCET) reaction of water splitting. The first requirement can be addressed by using semiconducting materials that absorb well into the visible range, such as cadmium chalcogenides. However, many of these materials including CdSe are unstable and oxidize rapidly under the aqueous conditions for water oxidation, rendering them unusable for water splitting purposes. The second requirement of lowering energetic barriers to water oxidation has been researched extensively in the last several decades to yield different forms of catalysts. One such catalyst is the cobalt-based water oxidation catalyst (CoPi) ^[2] . CoPi can be formed either via electrochemical deposition from Co²⁺ ions in aqueous solutions containing potassium phosphate (KPi) or by processing of supported thin-film (800 nm thick) cobalt metal anodes in KPi at pH 7 ^[3] .

We demonstrate the dual benefit gained by using thin-film cobalt metal as the precursor in the preparation of CoPi on CdSe photoanodes. First, the cobalt layer protects the underlying semiconductor from oxidation and degradation in the aqueous solution. This process is followed by the advantageous incorporation of the CdSe layer into the CoPi layer during continued processing of the electrode. The resulting hybrid material forms a stable photoactive anode for light-assisted water oxidation. Figure 1 shows the high stability and reproducibility of currents through the hybrid material under demanding conditions. The benefits of the photoactive CdSe component are demonstrated in Figure 2, which presents the shift in catalytic onset under illumination.

1. N. S. Lewis and D. G. Nocera, “Powering the planet: Chemical challenges in solar energy utilization,” Proc. Nat’l. Acad. Sci. USA, , vol. 103, pp. 15729-15735, Oct. 2006.
2. M. W. Kanan and D. G. Nocera, “In situ formation of an oxygen-evolving catalyst in neutral water containing phosphate and Co2+,” Science, vol. 321, pp. 1072-1075, Aug. 2008.
3. E. R. Young, D. G. Nocera and V. Bulović, “Direct formation of a water oxidation catalyst from thin-film cobalt,” Energy Environ. Sci., vol. 3, pp. 1726-1728, Nov. 2010.

Thin-film solar cells incorporating colloidal quantum dot active layers have recently emerged as a notable third-generation photovoltaic (PV) technology, largely due to the strong absorption, tunable infrared bandgap, and ambient-atmosphere stability of lead sulfide quantum dots (PbS QDs). Photoactive PbS QDs can be solution-deposited on a transparent zinc oxide (ZnO) film to form a depleted np-heterojunction device (Figure 1a,b). However, this standard planar architecture incurs a fundamental trade-off between light absorption and carrier collection: to absorb most incident light, we need a ~1-µm-thick QD film ^[1] , but to collect most photocarriers, we need absorption to occur within a minority carrier diffusion length (~100 nm) of the ~150-nm-thick depletion region ^[2] . By introducing 1-D nanostructures (Figure 1c), we can decouple these parallel requirements and optimize for each independently. A vertical, QD-infiltrated array of ZnO nanowires orthogonalizes the mechanistic length scales of absorption and collection. Absorption is maximized as light traverses a thick QD film in the axial direction, while field-driven carrier collection is retained throughout the film as photogenerated electrons drift to nearby PbS/ZnO interfaces in the radial direction.

Our research demonstrates that moving from a planar ZnO film to a nanowire array can significantly improve QDPV performance, increasing short-circuit current density (J_SC) by ~40% and overall power conversion efficiency by ~15% ^[3] . We confirm the near-complete infiltration of PbS QDs into the ZnO nanowire array via cross-sectional scanning electron microscopy (Figure 1d) and elemental mapping with energy-dispersive x-ray spectroscopy. We further demonstrate a fast solution treatment to assist interfacial charge transfer using a bifunctional linker molecule, 3-mercaptopropionic acid (MPA). A simple MPA treatment increases both J_SC and open-circuit voltage (V_OC) of nanowire-QD devices (see Figure 2). Our work on ZnO nanowire-based QD solar cells—along with the recent demonstration of a 5.6%-efficient TiO₂nanopillar-based QDPV ^[4] —suggests that 1-D nanostructures may be the key to enhancing the efficiency and hence the economic viability of quantum dot photovoltaics.

1. A. G. Pattantyus-Abraham,I. J. Kramer, A. R. Barkhouse,X. Wang, G.Konstantatos, R. Debnath,L. Levina,I. Raabe,M. K. Nazeeruddin, M.Grätzel, and E. H. Sargent, “Depleted-heterojunction colloidal quantum dot solar cells,” ACS Nano, vol. 4, no. 6, pp. 3374-3380, May 2010.
2. K. W. Johnston, A. G. Pattantyus-Abraham, J. P. Clifford, S. H. Myrskog, S. Hoogland, S. Sjoerd, H. Shukla, E. J. D. Klem, L. Levina, and E. H. Sargent, “Efficient Schottky-quantum-dot photovoltaics: The roles of depletion, drift, and diffusion,” Applied Physics Letters, vol. 92, no. 12, pp. 122111, Mar. 2008.
3. P. R. Brown, R. R. Lunt, N. Zhao, T. P. Osedach,D. D. Wanger, L.-Y.Chang, M. G.Bawendi, and V. Bulović, “Improved current extraction from ZnO/PbS quantum dot heterojunction photovoltaics using a MoO₃ interfacial layer,” Nano Letters, vol. 11, no. 7, pp. 2955-2961, June 2011.
4. I. J. Kramer, D. Zhitomirsky, J. D. Bass, P. M. Rice, T. Topuria, L. Krupp, S. M. Thon, A. H. Ip, R. Debnath, H.-C. Kim, and E. H. Sargent, “Ordered nanopillar structured electrodes for depleted bulk heterojunction colloidal quantum dot solar cells,” Advanced Materials, vol. 24, no. 17, pp. 2315-2319, Mar. 2012.

Disordered semiconductors exhibit poor electronic transport properties due to their amorphous nature. Low carrier mobility and lifetime limits the diffusion length to 100 ~ 300 nm. Thus, conventional p-n junction photovoltaic design that is composed of a large quasi-neutral region and a small depletion region (Figure 1a) leads to poor charge extraction. To overcome this material limit, a p-i-n junction has been adopted in amorphous silicon solar cells. The internal electric field extends throughout the intrinsic absorber layer and assists carriers to be efficiently extracted to their respective electrodes (Figure 1b). Films composed of quantum dots (QD) show electronic transport properties similar to disordered semiconductors and may also benefit from the p-i-n “drift” device architecture, which has not been applied to QD solar cells to date.

This project aims to implement two major advantages of the p-i-n heterojunction using the QD as an intrinsic absorber layer. The first goal is to augment the width of the depletion region. This widening enhances the light absorbance of the device, allowing more photogenerated carriers and thereby increasing short-circuit current (J_sc). The second advantage to exploit is the ability to dope n- and p-type layers without having to affect the intrinsic absorber layer. Increasing the Fermi level difference by doping both window layers would increase the build-in electric field, enhancing open-circuit voltage (V_oc). Figure 1c and d show schematic illustrations of the device structure and energy diagram, respectively. Figure 2a and b show the device characteristic studied for each separate junction. Rectifying behavior is observed in both p-i, i-n and p-i-n junctions. Figure 2d and e show the JV curve under illumination with and without the intrinsic QD absorber layer. Future studies will focus on V_oc, J_sc, and fill factor (FF) as a function of p-type and n-type layer doping as well as intrinsic layer thickness.

1. M. Zeman, “Solar Cells,” TU Delft OpenCourseWare, Delft University of Technology, 2011. [Online]. Available: http://ocw.tudelft.nl/courses/microelectronics/solar-cells/readings/

Colloidal lead sulfide quantum dot (PbS QD) solar cells have recently shown attractive improvements in efficiency [1]. PbS QDs have been investigated in various device architectures—including Schottky junction, depleted planar heterojunction, and ordered bulk heterojunction photovoltaic (PV) architectures—with the aim of maximizing light absorption while maintaining efficient charge transport ^[1] . However, the thickness of the PbS QD layer in the aforementioned architectures remains limited by the relatively short exciton diffusion length characteristic of all QD films.  We developed a novel architecture in which PbS QDs and zinc oxide (ZnO) nanoparticles are co-deposited from solution to form a bulk heterojunction (BHJ). Much like a typical polymer BHJ solar cell, these PbS QD PV devices can decouple the light absorption, which is proportional to device thickness, from the exciton diffusion length ^[2] . We fabricated these BHJ PbS QD:ZnO solar cells in solution by layer-by-layer deposition in which each step is followed by ligand exchange as shown in Figure 1a. By conducting preliminary optimization of the processing condition, we obtained the current density as a function of the applied voltage graph shown in Figure 1b. Further studies aim at improving device performance while studying the morphological conformation of PbS and ZnO domains.

Figure 1: a) Schematic of the solution process for fabrication of bulk heterojunction lead sulfide quantum dots (PbS QD) and zinc oxide (ZnO) solar cells. The devices are fabricated by layer-by-layer deposition in which each step is followed by ligand exchange. b) JV characteristics under dark (squares) and AM 1.5 illumination (circles) for planar (control – red) and bulk heterojunction (blue) PbS QD:ZnO devices.

1. J. Tang and E. H. Sargent, “Infrared colloidal quantum dots for photovoltaics: Fundamentals and recent progress,” Advanced Materials, vol. 23, no. 1, pp. 12–29, Jan. 2011.
2. C. J. Brabec, S. Gowrisanker, J. J. M. Halls, D. Laird, S. J. Jia, and S. P. Williams, “Polymer-fullerene bulk-heterojunction solar cells,” Advanced Materials, vol. 22, pp. 3839–3856, Aug. 2010.

Nanostructured solar cells are attracting increasing attention as a promising photovoltaic (PV) technology ^[1] . Generation of free charge carriers in nanostructured PV devices occurs at the electron donor-acceptor interface, analogous to the pn-junction interface in traditional crystalline silicon solar cells. However, recombination at this interface constitutes one of the major charge carrier loss pathways. Thus characterizing and controlling recombination dynamics is critical for informing the design of novel device architectures. Recombination parameters also enable comparisons between different device architectures.

In this work, we employ the transient photovoltage (TPV) technique ^[2] to probe recombination mechanisms under standard operating conditions in three different solar cells, as shown in Figure 1: a poly(3-hexylthiophene) and phenyl-C₆₁-butyric acid methyl ester (P3HT:PCBM) bulk heterojunction; a chloroaluminium phthalocyanine and fullerene (ClAlPc:C₆₀) planar mixed heterojunction; and a lead sulfide quantum dot and zinc oxide (QD PbS:ZnO) pn-heterojunction. The normalized TPV data acquired at 0.5-sun illumination intensity are shown in Figure 2a, which compares the recombination lifetimes of charge carriers in these devices. The observed differences in carrier lifetimes may arise from variations in the respective interface morphologies: for example, the slower recombination transients observed in the ClAlPc:C₆₀ device may be attributed to the intrinsic planarity of this particular architecture.  We can also measure the charge carrier lifetime as a function of the light intensity, as shown in Figure 2b; this result confirms that recombination dynamics are faster in P3HT:PCBM and QD PbS:ZnO than in ClAlPc:C₆₀ PV devices.

1. Anonymous, “A sunny outlook,” Nature Photonics, vol. 6, no. 3, p. 129, Mar. 2012.
2. C. G. Shuttle, B. O’Regan, A. M. Ballantyne, J. Nelson, D. D. C. Bradley, J. de Mello, and J. R. Durrant, “Experimental determination of the rate law for charge carrier decay in a polythiophene: Fullerene solar cell,” Applied Physics Letters, vol. 92, p. 3, 2008.

Figure 1: The sample arm and probe arm on the cantilever are decoupled. The aim is to reduce the effective thermal conductance of the sample arm as much as possible by using a low conductivity material and avoid bending by using a single layer. The probe arm is attached to the sample arm and made up of a bi-material layer to enable temperature dependent deflection and allow for optical detection.

Microfabricated cantilever beams are used in microelectromechanical systems (MEMS) for a variety of sensor and actuator applications. Bimaterial cantilevers accurately measure temperature change and heat flux with resolutions several orders of magnitude higher than those of conventional sensors such as thermocouples, semiconductor diodes, as well as resistance and infrared thermometers and thus have allowed new applications to emerge where other techniques are unable to probe ^{[1] [2] [3] [4] [5]} . An important limitation in these systems, however, is the deflection of the measurement sample and sensitivity limitation due to inherent bimaterial design constraints ^{[4] [5] [6] [7] [8]} . To this end, a measurement platform based on the picowatt sensitivity of optomechanical microcantilever sensors was developed in which the probe- and sample section of the cantilever are separated ^[9] . The bending of a custom-designed bimorph cantilever accurately allows the absolute amount of transferred heat to be extracted and temperature to be determined based on the response from thermal inputs while the sample remains immobilized (Figure 1). Optimally tailoring the material properties for the different cantilever sections enhances the measurement sensitivity by over an order of magnitude with respect to current commercial systems. The rigid sample section offers measurement versatility ranging from thermal radiation and conduction measurements to the characterization of material thermal conductivities and absorptivities in nearly identical configurations. This measurement platform for fundamental heat transfer measurements will considerably improve the current understanding of nanoscale energy transport and conversion and material characterization. The platform will also lead to advanced design guidelines for energy capture and conversion devices, in particular thermophotovoltaic cells, (solar) thermoelectric generators, and waste heat recovery heat exchangers.

1. J. K. Gimzewski, C. Gerber, E. Meyer, and R. R. Schlittler, “Observation of a chemical reaction using a micromechanical sensor,” Chemical Physics Letters, vol. 217, pp. 589-594, Jan. 1994.
2. J. R. Barnes, R. J. Stephenson, M. E. Welland, C. Gerber, and J. K. Gimzewski, “Photothermal spectroscopy with femtojoule sensitivity using a micromechanical device,” Nature, vol. 372, pp. 79-81, Nov. 1994.
3. J. R. Barnes, R. J. Stephenson, C. N. Woodburn, S. J. O’Shea, M. E. Welland, T. Rayment, J. K. Gimzewski, and C. Gerber, “A femtojoule calorimeter using micromechanical sensors,” Review of Scientific Instruments, vol. 85, pp. 3793-3798, Dec. 1994.
4. J. Lai, T. Perazzo, Z. Shi, and A. Majumdar, “Optimization and performance of high-resolution micro-optomechanical thermal sensors,” Sensors and Actuators A:  Physical, vol. 58, pp. 113-119, Feb. 1997.
5. J. Varesi, J. Lai, T. Perazzo, Z. Shi, and A. Majumdar, “Photothermal measurements at picowatt resolution using uncooled micro-optomechanical sensors,” Applied Physics Letters, vol. 71, pp. 306-308, July 1997.
6. S. Shen, A. Narayanaswamy, and G. Chen, “Surface phonon polaritons mediated energy transfer between nanoscale gaps,” Nano Letters, vol. 9, pp. 2909-2913, Aug. 2009.
7. E. Rousseau, A. Siria, G. Jourdan, S. Volz, F. Comin, J. Chevrier, and J.-J. Greffet, “Radiative heat transfer at the nanoscale,” Nature Photonics, vol. 3, pp. 514-517, Sept. 2009.
8. S. Shen, A. Henry, J. Tong, R. T. Zheng, and G. Chen, “Polyethylene nanofibers with very high thermal conductivities,” Nature Nanotechnology, vol. 5, pp. 251-255, Mar. 2010.
9. B. R. Burg, J. Tong, W.-C. Hsu, P. Sambegoro, A. Mavrokefalos, and G. Chen, “Decoupled Cantilever Arms for Optomechanical Thermal Measurements,” U. S. Patent Application 61/599547, February 16, 2012.

The cost of silicon solar cells has fallen precipitously in recent years, primarily as a result of manufacturing improvements, increasing scale, and decreasing profit margin.  Further cost reductions will depend upon technical advances that increase cell efficiency and/or minimize the variable costs associated with module production.  One strategy to lower the cost of silicon photovoltaic modules is to dramatically reduce the amount of material required in a cell from the current 180-μm standard to 10 μm or less.  However, since the absorption length for longer-wavelength photons (red and infrared) is significantly larger than this thickness, thin cells must be designed to trap photons in the absorber layer very effectively to yield competitive efficiencies.  Light-trapping in conventional wafer-based photovoltaics is well understood ^[1] , and light-trapping structures are integrated into virtually all commercially available solar cells.  However, the physical basis associated with light-trapping in thin-film silicon cells is quite different than that for conventional silicon photovoltaics, both because the thinness of the material physically limits the dimensions of light-trapping features and because light-trapping based on geometric optics is less effective for very thin materials.  In this work, simulations based on the transfer matrix method were developed to identify optimal surface structures for light trapping.  As shown in Figure 1, a variety of potential geometries offer significant enhancement over a planar silicon surface.  Of the structures that are modeled in this work, the one offering the best combination of light-trapping effectiveness and manufacturability is a two-dimensional periodic array of inverted pyramids on a sub-micrometer pitch ^{[2] [3]} , as in Figure 2.  Theoretical calculations suggest that a 10 μm silicon film textured in this way can absorb as effectively as a flat film 300 μm thick.  Demonstration versions on SOI substrates are currently being fabricated in the Microsystems Technology Laboratories at MIT.

1. P. Campbell and M. A. Green, “Light-trapping of pyramidally textured surfaces,” Journal of Applied Physics, vol. 62, no. 1, pp. 243-249, July 1987.
2. S. E.  Han and G. Chen, “Toward the Lambertian limit of light-trapping in thin nanostructured silicon solar cells,” Nano Letters, vol. 10, pp. 4692-4696, Oct. 2010.
3. S. E. Han, A. Mavrokefalos, M. S. Branham, and G. Chen, “Efficient light-trapping nanostructures in thin silicon solar cells,” Proc. of  SPIE:  Micro- and Nanotechnology Sensors, Systems, and Applications III, 2011, vol. 8031, p. 80310T.