Experimental demonstration of broadband solar absorption beyond the lambertian limit in certain thin silicon photonic crystals

Hsieh, Mei-Li; Kaiser, Alex; Bhattacharya, Sayak; John, Sajeev; Lin, Shawn-Yu

doi:10.1038/s41598-020-68704-w

Title: Experimental demonstration of broadband solar absorption beyond the lambertian limit in certain thin silicon photonic crystals

Abstract

The tantalizing possibility of 31% solar-to-electric power conversion efficiency in thin film crystalline silicon solar cell architectures relies essentially on solar absorption well beyond the Lambertian light trapping limit (Bhattacharya and John in Nat Sci Rep 9:12482, 2019). Up to now, no solar cell architecture has exhibited above-Lambertian solar absorption, integrated over the broad solar spectrum. In this work, we experimentally demonstrate two types of photonic crystal (PhC) solar cells architectures that exceed Lambertian light absorption, integrated over the entire 300–1,200 nm wavelength band. These measurements confirm theoretically predicted wave-interference-based optical resonances associated with long lifetime, slow-light modes and parallel-to-interface refraction. These phenomena are beyond the realm of ray optics. Using two types of 10-μm thick PhC’s, first an Inverted Pyramid PhC with lattice constant a= 2,500 nm and second a Teepee PhC with a = 1,200 nm, we observe solar absorption well beyond the Lambertian limit over λ = 950–1,200 nm. Our absorption measurements correspond to the maximum-achievable-photocurrent-density (MAPD), under AM1.5G illumination at 4-degree incident angle, 41.29 and 41.52 mA/cm2 for the Inverted Pyramid and Teepee PhC, respectively, in agreement with wave-optics, numerical simulations. Both of these values exceed the MAPD (= 39.63 mA/cm2) corresponding to the Lambertian limitmore »« less

Authors:

Hsieh, Mei-Li ^[1]; Kaiser, Alex ^[2]; Bhattacharya, Sayak ^[3]; John, Sajeev ^[4]; Lin, Shawn-Yu ^[1]

Rensselaer Polytechnic Inst., Troy, NY (United States). Center for Future Energy System (CFES); National Chiao-Tung Univ., Hsinchu (Taiwan)
Rensselaer Polytechnic Inst., Troy, NY (United States). Center for Future Energy System (CFES)
Univ. of Toronto, ON (Canada); Indraprastha Inst. of Information Technology, New Delhi (India)
Univ. of Toronto, ON (Canada)

Publication Date:: Thu Jul 16 00:00:00 EDT 2020

Research Org.:: Rensselaer Polytechnic Inst., Troy, NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES); Natural Science Foundation (NSF)

OSTI Identifier:: 1647330

Grant/Contract Number:: FG02-06ER46347; ECCS-1840673-NOA

Resource Type:: Accepted Manuscript

Journal Name:: Scientific Reports

Additional Journal Information:: Journal Volume: 10; Journal Issue: 1; Journal ID: ISSN 2045-2322

Publisher:: Nature Publishing Group

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; Energy science and technology; materials science; nanoscience and technology; optics and photonics

Citation Formats


                    Hsieh, Mei-Li, Kaiser, Alex, Bhattacharya, Sayak, John, Sajeev, and Lin, Shawn-Yu. Experimental demonstration of broadband solar absorption beyond the lambertian limit in certain thin silicon photonic crystals.  United States: N. p., 2020. 
Web.  doi:10.1038/s41598-020-68704-w.

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                    Hsieh, Mei-Li, Kaiser, Alex, Bhattacharya, Sayak, John, Sajeev, & Lin, Shawn-Yu. Experimental demonstration of broadband solar absorption beyond the lambertian limit in certain thin silicon photonic crystals.  United States.  https://doi.org/10.1038/s41598-020-68704-w

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                    Hsieh, Mei-Li, Kaiser, Alex, Bhattacharya, Sayak, John, Sajeev, and Lin, Shawn-Yu. Thu .  
"Experimental demonstration of broadband solar absorption beyond the lambertian limit in certain thin silicon photonic crystals".  United States.  https://doi.org/10.1038/s41598-020-68704-w.  https://www.osti.gov/servlets/purl/1647330.

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@article{osti_1647330,

  title        = {Experimental demonstration of broadband solar absorption beyond the lambertian limit in certain thin silicon photonic crystals},

  author       = {Hsieh, Mei-Li and Kaiser, Alex and Bhattacharya, Sayak and John, Sajeev and Lin, Shawn-Yu},

  abstractNote = {The tantalizing possibility of 31% solar-to-electric power conversion efficiency in thin film crystalline silicon solar cell architectures relies essentially on solar absorption well beyond the Lambertian light trapping limit (Bhattacharya and John in Nat Sci Rep 9:12482, 2019). Up to now, no solar cell architecture has exhibited above-Lambertian solar absorption, integrated over the broad solar spectrum. In this work, we experimentally demonstrate two types of photonic crystal (PhC) solar cells architectures that exceed Lambertian light absorption, integrated over the entire 300–1,200 nm wavelength band. These measurements confirm theoretically predicted wave-interference-based optical resonances associated with long lifetime, slow-light modes and parallel-to-interface refraction. These phenomena are beyond the realm of ray optics. Using two types of 10-μm thick PhC’s, first an Inverted Pyramid PhC with lattice constant a= 2,500 nm and second a Teepee PhC with a = 1,200 nm, we observe solar absorption well beyond the Lambertian limit over λ = 950–1,200 nm. Our absorption measurements correspond to the maximum-achievable-photocurrent-density (MAPD), under AM1.5G illumination at 4-degree incident angle, 41.29 and 41.52 mA/cm2 for the Inverted Pyramid and Teepee PhC, respectively, in agreement with wave-optics, numerical simulations. Both of these values exceed the MAPD (= 39.63 mA/cm2) corresponding to the Lambertian limit for a 10-μm thick silicon for solar absorption over the 300–1,200 nm band.},

  doi          = {10.1038/s41598-020-68704-w},

  journal      = {Scientific Reports},

  number       = 1,

  volume       = 10,

  place        = {United States},

  year         = {Thu Jul 16 00:00:00 EDT 2020},

  month        = {Thu Jul 16 00:00:00 EDT 2020}

}

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Works referenced in this record:

26.1%‐efficient POLO‐IBC cells: Quantification of electrical and optical loss mechanisms
journal, October 2018

Hollemann, Christina; Haase, Felix; Schäfer, Sören
Progress in Photovoltaics: Research and Applications, Vol. 27, Issue 11
DOI: 10.1002/pip.3098

Light trapping and absorption optimization in certain thin-film photonic crystal architectures
journal, August 2008

Chutinan, Alongkarn; John, Sajeev
Physical Review A, Vol. 78, Issue 2
DOI: 10.1103/PhysRevA.78.023825

Silicon heterojunction solar cell with interdigitated back contacts for a photoconversion efficiency over 26%
journal, March 2017

Yoshikawa, Kunta; Kawasaki, Hayato; Yoshida, Wataru
Nature Energy, Vol. 2, Issue 5
DOI: 10.1038/nenergy.2017.32

Thermodynamic limit to light trapping in thin planar structures
journal, January 1997

Stuart, Howard R.; Hall, Dennis G.
Journal of the Optical Society of America A, Vol. 14, Issue 11
DOI: 10.1364/JOSAA.14.003001

Limiting efficiency of silicon solar cells
journal, May 1984

Tiedje, T.; Yablonovitch, E.; Cody, G.D.
IEEE Transactions on Electron Devices, Vol. 31, Issue 5, p. 711-716
DOI: 10.1109/T-ED.1984.21594

Photonic crystal enhanced light-trapping in thin film solar cells
journal, May 2008

Zhou, Dayu; Biswas, Rana
Journal of Applied Physics, Vol. 103, Issue 9
DOI: 10.1063/1.2908212

15.7% Efficient 10-μm-Thick Crystalline Silicon Solar Cells Using Periodic Nanostructures
journal, February 2015

Branham, Matthew S.; Hsu, Wei-Chun; Yerci, Selcuk
Advanced Materials, Vol. 27, Issue 13
DOI: 10.1002/adma.201405511

Towards 30% Power Conversion Efficiency in Thin-Silicon Photonic-Crystal Solar Cells
journal, January 2019

Bhattacharya, Sayak; Baydoun, Ibrahim; Lin, Mi
Physical Review Applied, Vol. 11, Issue 1
DOI: 10.1103/PhysRevApplied.11.014005

Effectively infinite optical path-length created using a simple cubic photonic crystal for extreme light trapping
journal, June 2017

Frey, Brian J.; Kuang, Ping; Hsieh, Mei-Li
Scientific Reports, Vol. 7, Issue 1
DOI: 10.1038/s41598-017-03800-y

Beyond 30% Conversion Efficiency in Silicon Solar Cells: A Numerical Demonstration
journal, August 2019

Bhattacharya, Sayak; John, Sajeev
Scientific Reports, Vol. 9, Issue 1
DOI: 10.1038/s41598-019-48981-w

Designing High-Efficiency Thin Silicon Solar Cells Using Parabolic-Pore Photonic Crystals
journal, April 2018

Bhattacharya, Sayak; John, Sajeev
Physical Review Applied, Vol. 9, Issue 4
DOI: 10.1103/PhysRevApplied.9.044009

Efficient Light Trapping in Inverted Nanopyramid Thin Crystalline Silicon Membranes for Solar Cell Applications
journal, May 2012

Mavrokefalos, Anastassios; Han, Sang Eon; Yerci, Selcuk
Nano Letters, Vol. 12, Issue 6
DOI: 10.1021/nl2045777

Reassessment of the Limiting Efficiency for Crystalline Silicon Solar Cells
journal, October 2013

Richter, Armin; Hermle, Martin; Glunz, Stefan W.
IEEE Journal of Photovoltaics, Vol. 3, Issue 4
DOI: 10.1109/JPHOTOV.2013.2270351

Design of optical path for wide-angle gradient-index antireflection coatings
journal, January 2007

Chen, Minfeng; Chang, Hung-chun; Chang, Allan S. P.
Applied Optics, Vol. 46, Issue 26
DOI: 10.1364/AO.46.006533

Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection
journal, March 2007

Xi, J. -Q.; Schubert, Martin F.; Kim, Jong Kyu
Nature Photonics, Vol. 1, Issue 3
DOI: 10.1038/nphoton.2007.26

Light trapping and near-unity solar absorption in a three-dimensional photonic-crystal
journal, January 2013

Kuang, Ping; Deinega, Alexei; Hsieh, Mei-Li
Optics Letters, Vol. 38, Issue 20
DOI: 10.1364/OL.38.004200

Achieving an Accurate Surface Profile of a Photonic Crystal for Near-Unity Solar Absorption in a Super Thin-Film Architecture
journal, May 2016

Kuang, Ping; Eyderman, Sergey; Hsieh, Mei-Li
ACS Nano, Vol. 10, Issue 6
DOI: 10.1021/acsnano.6b01875

Laser contact openings for local poly-Si-metal contacts enabling 26.1%-efficient POLO-IBC solar cells
journal, November 2018

Haase, Felix; Hollemann, Christina; Schäfer, Sören
Solar Energy Materials and Solar Cells, Vol. 186
DOI: 10.1016/j.solmat.2018.06.020

Detailed Balance Limit of Efficiency of p‐n Junction Solar Cells
journal, March 1961

Shockley, William; Queisser, Hans J.
Journal of Applied Physics, Vol. 32, Issue 3, p. 510-519
DOI: 10.1063/1.1736034

Inhibited Spontaneous Emission in Solid-State Physics and Electronics
journal, May 1987

Yablonovitch, Eli
Physical Review Letters, Vol. 58, Issue 20, p. 2059-2062
DOI: 10.1103/PhysRevLett.58.2059

Solar cell efficiency tables (version 51)
journal, December 2017

Green, Martin A.; Hishikawa, Yoshihiro; Dunlop, Ewan D.
Progress in Photovoltaics: Research and Applications, Vol. 26, Issue 1
DOI: 10.1002/pip.2978

Experimental observation of extremely weak optical scattering from an interlocking carbon nanotube array
journal, January 2011

Yang, Zu-Po; Hsieh, Mei-Li; Bur, James A.
Applied Optics, Vol. 50, Issue 13
DOI: 10.1364/AO.50.001850

Experimental Demonstration of Guiding and Bending of Electromagnetic Waves in a Photonic Crystal
journal, October 1998

Lin, S.
Science, Vol. 282, Issue 5387
DOI: 10.1126/science.282.5387.274

Fundamental limit of nanophotonic light trapping in solar cells
journal, September 2010

Yu, Zongfu; Raman, Aaswath; Fan, Shanhui
Proceedings of the National Academy of Sciences, Vol. 107, Issue 41, p. 17491-17496
DOI: 10.1073/pnas.1008296107

Improved quantitative description of Auger recombination in crystalline silicon
journal, October 2012

Richter, Armin; Glunz, Stefan W.; Werner, Florian
Physical Review B, Vol. 86, Issue 16
DOI: 10.1103/PhysRevB.86.165202

Realization of a near-perfect antireflection coating for silicon solar energy utilization
journal, January 2008

Kuo, Mei-Ling; Poxson, David J.; Kim, Yong Sung
Optics Letters, Vol. 33, Issue 21
DOI: 10.1364/OL.33.002527

Experimental Observation of an Extremely Dark Material Made By a Low-Density Nanotube Array
journal, January 2008

Yang, Zu-Po; Ci, Lijie; Bur, James A.
Nano Letters, Vol. 8, Issue 2, p. 446-451
DOI: 10.1021/nl072369t

Light trapping beyond the 4 n ² limit in thin waveguides
journal, March 2012

Munday, Jeremy N.; Callahan, Dennis M.; Atwater, Harry A.
Applied Physics Letters, Vol. 100, Issue 12
DOI: 10.1063/1.3695156

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Title: Experimental demonstration of broadband solar absorption beyond the lambertian limit in certain thin silicon photonic crystals

Abstract

Citation Formats

26.1%‐efficient POLO‐IBC cells: Quantification of electrical and optical loss mechanisms journal, October 2018

Light trapping and absorption optimization in certain thin-film photonic crystal architectures journal, August 2008

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15.7% Efficient 10-μm-Thick Crystalline Silicon Solar Cells Using Periodic Nanostructures
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