Hernan Míguez CSIC
Shanhui Fan Stanford University
Kylie Catchpole The Australian National University
Dim-Lee Kwong Institute of Microelectronics
J1: Exploring the Limits of Absorption Enhancement
Monday PM, November 28, 2011
Republic B (Sheraton)
9:30 AM - **J1.1
A Thermodynamic Approach to Artificial Photonic Materials for Solar Energy Conversion.
Harry Atwater 1 Show Abstract
1 Applied Physics and Materials Science, California Institute of Technology, Pasadena, California, United States
Artificial photonic materials can enhance light-trapping and absorption, as well as increase the open circuit voltage and enhance quantum efficiency in solar photovoltaic structures. We describe a thermodynamic approach to understanding the opportunities for artificial photonic materials to increase solar energy conversion efficiency. This approach focuses on the control of the increases in photon entropy in light-matter interactions, as a means of minimizing free energy losses in photovoltaics.From thermodynamic arguments, Yablonovitch and Cody in 1982 determined the maximum absorption enhancement in the ray optics limit for a bulk material to be 4n2, where n is the index of refraction of the absorbing layer . Stuart and Hall in 1997 expanded this approach to study a simple waveguide structure; however, for the waveguide structures they considered, the maximum absorption enhancement was <4n2 . Using a combination of analytical and numerical methods, we describe why these structures do not surpass the conventional ergodic limit, and show how to design structures that can. The conventional light trapping limit can be exceeded in waveguide-like structures when the active region has an elevated local density of optical states (LDOS) compared to that of the bulk, homogeneous material. Additionally, to practically achieve light trapping exceeding the ergodic limit, the modes of the structure must be appreciably populated via an appropriate incoupling mechanism. We find using full wave simulations that ultrathin solar cells incorporating a plasmonic back reflector can achieve spatially averaged LDOS enhancements of 1 to 3, and a metal-insulator-metal (MIM) structure can achieve enhancements over 50 at a wavelength of 1100 nm, near the the band edge of Si. Interestingly, incorporating the active solar cell material within a localized metallodielectric plasmonic or metamaterial resonator can lead to nearly spatially uniform LDOS enhancements above 1000 within the active material. Another opportunity for increased photovoltaic efficiency lies in the control of the angular distribution of absorbed and emitted light interacting with a solar cell. In particular, we illustrate how artificial structures placed on top of a thin solar cell that control the light emission angle can increase the open circuit voltage and cell efficiency.Overall, we find many opportunities for increasing photovoltaic efficiency by adopting a thermodynamic perspective on light-matter interactions. These results can guide future solar cell designs that incorporate dispersive dielectric, plasmonic and metamaterial artificial photonic structures. Yablonovitch and Cody. IEEE Trans. Elect. Dev. 29 300 (1982) Stuart and Hall J. Opt. Soc. Am A 14 3001 (1997)
10:00 AM - J1.2
Ergodicity of Light-Trapping in Nanocrystalline Silicon Solar Cells.
Hui Zhao 1 , Eric Schiff 1 , Baojie Yan 2 , Jeff Yang 2 , Subhendu Guha 2 Show Abstract
1 , Syracuse University, Syracuse, New York, United States, 2 , United Solar Ovonic. LLC, Troy, Michigan, United States
Nanocrystalline silicon solar cells (nc-Si:H) are thick enough that a simple "classical" estimate of the maximum photocurrent enhancement due to light-trapping is a useful guide. This maximum enhancement is 4n2, where n is the refractive index of nc-Si:H; this limit is based on an ergodic argument that all the electromagnetic modes in the cell at a given wavelength are equally excited by sunlight.We have prepared nc-Si:H solar cells using several different texturing and back reflector schemes, and analyzed their quantum efficiencies in terms of a simple enhancement metric Y that can be compared to this 4n2 result. We have also analyzed published nc-Si:H cell properties from other laboratories. While optical measurements have shown the full Y=4n2 effect, photocurrents in thin-film nc-Si:H cells do not. We find that the largest values for Y are 15 for 1.0 micron thick cells, and about 25 for 2.5 micron cells.Since enhancements of these magnitudes can be achieved using a variety of implementations, we suggest that this convergence indicates that the best light- trapping implementations for thin-film nc-Si:H cells are close to ergodicity, even though the Y-values are well below 4n2. We account for this difference by parasitic absorption in the cell (by doped layers, reflectance losses, etc.) and by imperfect anti-reflection coatings. We discuss three approaches to further increasing light-trapping: reducing parasitic absorption, improving anti-reflection coatings, and implementing true "supraclassical" designs involving evanescent electromagnetic excitations beyond the modes considered for the 4n2 limit [1,2]. Martin A. Green, Prog. Photovolt: Res. Appl (2010). Zongfu. Yu, Aaswath Raman, Shanhui Fan - Proc. Nat. Acad. Sci. (Oct 2010 Vol 107 #41).
10:15 AM - J1.3
Development of Photonic and Plasmonic Designs to Surpass the 4n2 Light Trapping Limit.
Jeremy Munday 1 , Dennis Callahan 1 , Harry Atwater 1 Show Abstract
1 Applied Physics, CALTECH, Pasadena, California, United States
Recently there has been great interest in the nanotexturing solar cells in an attempt to surpass the traditional light trapping limit as described by Yablonovitch. Because this limit is only valid for bulk absorbers, it does not apply to the new generation of subwavelength solar absorbers including wire-based, photonic crystal-based, or plamonic-based cells. Herein, we describe a methodology for designing solar cells that have intensity and absorption enhancements that exceed the ergodic light trapping limit by two methods: one based on the local density of optical states (LDOS) and one based on the density of waveguide modes. Using a combination of analytical and numerical methods, we show how structures can be designed to beat this limit over an arbitrarily large wavelength range using frequency sum rules. For thin film solar cells, incorporating a plasmonic back reflector can result in spatially averaged LDOS enhancements of >3, and a metal-insulator-metal (MIM) structure can result in enhancements of >200 near the bandedge of Si. We also find that placing the active material within a localized metallic resonator can lead to a nearly spatially uniform LDOS with enhancements > 1000. Purely dielectric structures can also lead to intensity enhancements exceeding the ergodic limit. For a low index active layer (n=1.5) clad by a high index layer (n=3), the LDOS enhancement is >10. Finally, we show that for thin film solar cells with dispersive dielectric structures such as photonic crystals the ergodic light-trapping limit can be exceeded with LDOS enhancements of 2 to 5 by placing a planar solar cell in close proximity to a photonic crystal. These results lead us to the design principles needed to construct optical structures with light trapping well beyond the 4n2 limit by elevating the local density of states above that of a similar bulk structure.
10:30 AM - **J1.4
Wave Domain Light Trapping Theory.
Zongfu Yu 1 Show Abstract
1 , Stanford University, Stanford, California, United States
Establishing the fundamental limit of nanophotonic light-trapping schemes is of paramount importance and is becoming increasingly urgent for current solar cell research. The standard theory of light trapping demonstrated that absorption enhancement in a medium cannot exceed a factor of 4n^2/sin(θ), where n is the refractive index of the active layer, and θ is the angle of the emission cone in the medium surrounding the cell. This theory, however, is not applicable in the nanophotonic regime. Here we develop a statistical temporal coupled-mode theory of light trapping based on a rigorous electromagnetic approach. Our theory reveals that the standard limit can be substantially surpassed when optical modes in the active layer are confined to deep-subwavelength scale, opening new avenues for highly efficient next-generation solar cells.
11:00 AM - J1:Limits
11:30 AM - **J1.5
Photonic and Plasmonic Solar Cells with Absorption Beyond the Classical 4n2 Limit.
Rana Biswas 1 2 Show Abstract
1 , Ames Laboratory, Ames, Iowa, United States, 2 Depts. of Physics & Astronomy; Electrical & Computer Engineering; Microelectronics Research Center, Iowa State University, Ames, Iowa, United States
Silicon based solar cells have very low absorption of long wavelength photons in the red and near-infrared regions of the solar spectrum. Light trapping and advanced photon management techniques are necessary to harvest such long wavelength photons. We describe recent advances in developing a photonic-plasmonic crystal back-reflector based conformal solar architecture in thin film nano-crystalline silicon. Simulations were performed with a rigorous scattering matrix approach  using experimental material properties. The simulated absorption and photo-current exceed the classical 4n2 limit expected for a randomly roughened Lambertian back-reflector, for commonly used thicknesses of the absorber layer (500-1000 nm). The conformal solar cells can exceed the classical limit over the entire range of solar wavelengths. This is a long-sought after goal since it provides fundamental limits under which periodically patterned solar cells may exceed the performance of traditional light-trapping approaches. The enhancement occurs through a combination of plasmonic light concentration and light-trapping through waveguide modes. Losses in these cells will be discussed. Collaborations with C. Xu and V. Dalal are gratefully acknowledged. R. Biswas, C. Xu, Optics Express 19, A664-A672 (2011).
12:00 PM - J1.6
Inverse Electromagnetic Design for Light Trapping in Solar Cells.
Vidya Ganapati 1 2 , Owen Miller 1 2 , Eli Yablonovitch 1 2 Show Abstract
1 Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, California, United States, 2 Material Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States
Light trapping in solar cell materials increases both the short circuit current and open circuit voltage, leading to increased efficiency. Additionally, light trapping allows for thinner materials, reducing cost. When material thickness is much larger than the wavelength of incoming light, the maximum absorption enhancement is 4n^2, where n is the index of refraction of the material. As material thicknesses become on the order of the wavelength of light, this limit does not necessarily hold, and the optimal surface texture geometry remains to be found. We propose the use of an inverse design algorithm with a commercial finite difference time domain solver to computationally find the surface texture for optimal light trapping under a maximum thickness constraint. We show solutions for broadband absorption in two-dimensional and three-dimensional Gallium Arsenide structures.
12:15 PM - J1.7
Limiting Solar Cell Acceptance Angle: A Path to Exceeding 40% Efficiency with a Single Junction.
Emily Kosten 1 , Harry Atwater 1 Show Abstract
1 , California Institute of Technology, Pasadena, California, United States
In a solar cell, increases in entropy are associated with reduced efficiency and open circuit voltage. A solar cell receiving light from the solid angle subtended by the disk of sun and emitting light into the upper hemisphere, suffers a large entropy increase, corresponding to an ~280 mV loss in open circuit voltage. Limiting the acceptance angle of the cell gives an increase in open circuit voltage because it is more difficult for emitted photons to leave the solar cell, which gives reduced dark current for materials with low non-radiative recombination rates, a phenomenon known as photon recycling. Limiting the acceptance angle of a solar cell to the disk of the sun avoids this entropy increase and allows the open circuit voltage to approach the bandgap of the semiconductor material. In addition, limiting the acceptance angle leads to improved light trapping within the solar cell, allowing for ultrathin cells. The few previous works in this area have not considered both the light trapping and photon recycling advantages, owing to the materials and geometries considered. In our work, we consider a system involving a high quality GaAs solar cell with a randomizing surface, which should give both photon recycling and light trapping effects. In addition, we move beyond the ray optics limit, accounting for mode cutoff, which allows us to accurately explore ultrathin cells. We find that for a 50 nm thick cell with an internal florescence yield (IFY) of 99%, an experimentally achievable figure in high quality GaAs systems , the detailed balance efficiency is 40.2% with angular restriction to the solar disk. In addition, the open circuit voltage is 1.41 V, very near the GaAs bandgap of 1.42 eV. For a more easily fabricated cell of 250nm with IFY of 90%, 37% efficiency is possible even if the angle of acceptance is relaxed to 1.8° for easier tracking. This is a 17% efficiency increase over a more traditional 3 um thick cell with no angular restriction and identical IFY. We will also show efficiency curves demonstrating more generally the effects of IFY, cell thickness and angular restriction. However, all these efficiency increases assume a low loss, broadband, angularly restrictive coupler. We have designed such a coupler and analyzed it using a ray-tracing approach. This coupler, based on a dielectric compound parabolic concentrator shape, with reflective surfaces, is low loss and broadband, owing to its reliance on total internal reflection and ray optics. Furthermore, it can be less than 1mm thick, depending on the degree of angular restriction desired. We will show transmission as a function of angle for various couplers based on this design, as well as the corresponding effect on detailed balance efficiency. Schnitzer et. al. Appl. Phys. Lett., 62(2), 1993.
12:30 PM - **J1.8
The Opto-Electronic Physics Required to Approach the Shockley-Queisser Efficiency Limit in Solar Cells.
Eli Yablonovitch 1 Show Abstract
1 Electrical Engineering & Computer Sciences, University of California, Berkeley, California, United States
Absorbed sunlight in a solar cell produces electrons and holes. But, at the open circuit condition, the carriers have no place to go. They build up in density and, ideally, they emit external fluorescence that exactly balances the incoming sunlight. Any additional non-radiative recombination impairs the carrier density buildup, limiting the open-circuit voltage. At open-circuit, efficient external fluorescence is an indicator of low internal optical losses. Thus efficient external fluorescence is, counter-intuitively, a necessity for approaching the Shockley-Queisser efficiency limit. A great Solar Cell also needs to be a great Light Emitting Diode.Owing to the narrow escape cone for light, efficient external emission requires repeated attempts, and demands an internal luminescence efficiency >>90%.We show here that maximizing the external emission of photons from the front surface of the solar cell proves to be the key to reaching the highest possible voltages. In the search for optimal solar cell candidates, then, materials that are good radiators, in addition to being good absorbers, are most likely to reach high efficiencies.As solar efficiency begins to approach the SQ limit, the internal physics of a solar cell transforms. Shockley and Queisser showed that high solar efficiency is accompanied by a high concentration of carriers, and by strong fluorescent emission of photons. In a good solar cell, the photons that are emitted internally are likely to be trapped, re-absorbed, and re-emitted, leading to “photon recycling” at open-circuit. The SQ limit assumes perfect external fluorescence yield at open-circuit. On the other hand, inefficient external fluorescence at open-circuit is an indicator of non-radiative recombination and optical losses. Owing to the narrow escape cone, efficient external emission requires repeated escape attempts, and demands an internal luminescence efficiency >>90%. We find that the failure to efficiently extract the recycled internal photons is an indicator of an accumulation of non-radiative losses, which are largely responsible for the failure to achieve the SQ limit in the best solar cells.In high efficiency solar cells it is important to engineer the photon dynamics. The SQ limit requires 100% external fluorescence to balance the incoming sunlight at open circuit. Indeed, the external fluorescence is a thermodynamic measure of the available open-circuit voltage. Owing to the narrow escape cone for internal photons, they find it hard to escape through the semiconductor surface. Thus external fluorescence efficiency is always significantly lower than internal fluorescence efficiency. Then the SQ limit is not achieved.The Shockley-Queisser limit cannot be achieved unless light extraction physics is designed into high performance solar cells, which requires that non-radiative losses be minimized, just as in LED’s.
J2: Novel Concepts for New Generation Photovoltaics I
Monday PM, November 28, 2011
Republic B (Sheraton)
2:30 PM - **J2.1
Trapping Light Fantastic.
Diederik Wiersma 1 , Filippo Pratesi 1 , Kevin Vynck 1 , Francesco Riboli 1 , Matteo Burresi 1 Show Abstract
1 micro and nano photonics, European laboratory for Non-linear Spectroscopy (LENS), University of Florence, and INFM-CNR BEC, sesto fiorentino (Florence), Florence, Italy
We will go into various strategies for trapping of light waves by multiple scattering of light, using random and hyper-uniform patterns. Enormous enhancement of absorption can be achieved in a broad frequency range, due to interference effects related to Anderson localization. The concepts explained in this contribution can also be used to make diffuse light sources of which the angular emission patterned can be tuned.
3:00 PM - **J2.2
Correlated Randomness for Broad-Band Light-Trapping in Semiconductor Systems.
Peter Bermel 1 2 , Michael Ghebrebrhan 1 2 , Claudia Lau 2 , Xing Sheng 3 , Jurgen Michel 4 , Lionel Kimerling 3 , Marin Soljacic 2 , Steven Johnson 5 Show Abstract
1 Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States, 2 Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States, 3 Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States, 4 Materials Processing Center, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States, 5 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States
All semiconductor-based devices used to capture broad-band light, such as selective solar absorbers and photovoltaic devices, are limited in their thickness and therefore their absorption. There are two strategies for addressing these limits, based on geometric and wave optics. Geometric optics-based light trapping relies on random scattering of incoming light into oblique angles to increase the average path length up to a factor of 4n^2 in a 3D medium of refractive index n. Wave optics-based light trapping uses resonant modes to enhance the dwell time of light at certain wavelengths. Here we consider a hybrid approach combining both geometric and wave-optics based light trapping strategies in the same framework. We define the key characteristics of correlated randomness necessary for this approach and report the results of our optimizations to date. Finally, we discuss potential strategies for experimental design and testing.
3:30 PM - J2.3
Temporal Coupled Mode Theory of the Microsphere Solar Cell.
Dennis Callahan 1 , Jonathan Grandidier 1 , Harry Atwater 1 Show Abstract
1 , Caltech, Pasadena, California, United States
Reducing the cost per watt of solar energy can be achieved by either utilizing cheaper materials and manufacturing methods or by increasing the efficiency of currently produced solar cells. We have recently introduced a simple, cheap and scalable method of increasing the efficiency of any planar solar cell by depositing a monolayer of dielectric nanospheres above the existing device. The spheres act as incoupling elements, utilizing both the diffractive nature of their arrangement and the coupled whispering gallery modes which exist in each individual sphere. Because the behavior of the sphere array is sensitive to many factors such as sphere diameter, sphere refractive index, inter-sphere spacing, lattice constant and spacing from the active layer, it is difficult to optimize the structure using methods such as finite difference time domain (FDTD) simulations. We thus utilize a different, faster method known as temporal coupled mode theory to optimize the incoupling structure for a given underlying device. This method has been used only a few times in the context of solar cells, and here we extend it to the new whispering gallery mode microsphere solar cell system.We find that, using this theory, the amount of light absorbed is sensitive to both the arrangement of the 2D array of nanospheres above the solar cell and the spacing of the array from the active layer. For example, when modeling power flow in both the nanosphere array and the underlying solar cell independently, we find that the decay rates from the sphere to the array and to the solar cell each need to be ½ the decay rate of the sphere back into free space. This can be achieved by keeping the sphere diameter the same while increasing the lattice constant while independently tuning the spacing of the sphere array from the active layer. Since the spacing of the active layer is usually the same as the anti-reflection coating thickness, this suggests that a tradeoff may be necessary between these two factors. We find optimal configurations for the nanosphere array using temporal coupled mode theory and compare with results from full wave FDTD simulations.
3:45 PM - J2.4
Visible Three Dimensional Photonic Crystals Using Silicon.
Ganapathi Subramania 1 , Arthur Fischer 1 Show Abstract
1 , Sandia National Laboratory, Albuquerque, New Mexico, United States
Silicon is an important material for solar cells and detectors. Achieving three dimensional light control as offered by three-dimensional (3D) photonic crystals (PC) can be quite useful in enhancing their performance especially in converting visible radiation. Silicon’s large refractive index (n~3.4) makes it ideal for obtaining large 3D photonic bandgap but its near-IR absorption edge (~1100nm) has discouraged its use for this purpose. Here, we experimentally demonstrate that the practical operational frequency range of a silicon based 3D photonic crystal can be extended nearly into the visible (~700nm), which is nearly 400nm above the absorption edge of silicon. To show this we fabricated a 9 layer logpile PC with lattice constants of 220nm, 250nm and 300nm composed of silicon rods obtained by electron beam evaporation of a silicon wafer. The optical response shows a strong bandgap for all three lattice constants with nearly 90% transmittance and negligible absorption past the lower band edge. By creating an ‘acceptor’ type defect cavities in the logpile PC we introduce an absorption peak within the photonic band gap whose wavelength can be tuned with lattice constant. This can be quite useful for controlled absorption localization. The absorption wavelength remains relatively stable up to an incidence angle range of 0- 23 degrees. This interesting and somewhat surprising behavior arises from the fact that silicon is an indirect bandgap semiconductor. As a result, the imaginary part of the refractive index (k) increases quite slowly with decreasing wavelength past the absorption edge. From the measured values of the extinction coefficient for our electron beam evaporated silicon samples, ‘k’ increases modestly from < 0.005 around 850nm to about 0.1 near 650nm thus indicating that a small amount absorption is indeed tolerable up to 9 layers. Silicon deposited using methods such as like as chemical vapour deposition or epitaxy is likely to offer better crystalline properties thus enabling operation further into the visible regime. Due to the mature nanofabrication technology this opens up new possibilities for large scale fabrication. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.References:G. Subramania, Y. J. Lee, A. J. Fischer, Advanced Materials 2010, 22, 4180.E. D. Palik, Ed. Handbook of Optical Constants of Solids, Academic Press, 1985.
4:00 PM - J2:Concepts 1
4:30 PM - J2.5
Intermediate Bands in Metallic Silicon: Design, Evolution, and Effectiveness for Sub-Band Gap Photon Management.
Mark Winkler 1 , Elif Ertekin 1 , Daniel Recht 2 , Joseph Sullivan 1 , Michael Aziz 2 , Jeffrey Grossman 1 , Tonio Buonassisi 1
1 , Massachusetts Institute of Technology, Cambridge, Massachusetts, United States, 2 School of Engineering and Applied Science, Harvard University, Cambridge, Massachusetts, United