light absorption (and optical losses) - mit … (mit) 2011 light absorption (and optical losses)...
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Buonassisi (MIT) 2011
Light Absorption (and Optical Losses)
Lecture 3 – 9/15/2011 MIT Fundamentals of Photovoltaics
2.626/2.627 – Fall 2011 Prof. Tonio Buonassisi
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2.626/2.627 Roadmap
You Are Here
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Absorption
2.626/2.627: Fundamentals Every photovoltaic device must obey:
Output EnergyConversion Efficiency
Input Energy
For most solar cells, this breaks down into: Inputs Outputs
Charge Excitation
Charge Drift/Diff usion
Charge Separation
Light Absorption
Charge CollectionSolar Spectrum
total absorption excitation drift/diffusion separation collection
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Liebig’s Law of the Minimum
S. Glunz, Advances in Optoelectronics 97370 (2007)
total absorption excitation drift/diffusion separation collection
Buonassisi (MIT) 2011
Image by S. W. Glunz. License: CC-BY. Source: "High-Efficiency Crystalline Silicon Solar Cells." Advances in OptoElectronics (2007).
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Learning Objectives: Light Absorption (Optical Losses)
• Calculate reflectance and non‐absorption optical losses of a solar cell
• Calculate reflection of an interface (semi‐infinite) • Calculate the absorption/transmittance through layer
• Describe the physical underpinnings and implementation of four advanced methods of reducing optical losses
• ARC/interference • Texturization • Reflective interfaces • Thickness • Plasmonics/photonics
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Light Management in Solar Cells: The Big Picture • Photons that aren’t absorbed can’t be used to create useful energy. (not absorbed means transmitted or reflected.)
• Only absorbed energy can make useful energy, thus we want to maximize this fraction!
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Photons – Quanta of Light
•Quantum theory describes the frequency dependence of photon energy.
Particle‐wave duality: Photons have discrete quanta of energy. Photons have momentum. Light can be polarized. Light can be diffracted. Light waves can destructively and
constructively interfere.
Relevant Equations:
Eph h hc
pph k h
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Photons – Quanta of Light
•Quantum theory describes the frequency dependence of photon energy.
•Visible photon wavelengths are in the hundreds of nanometers (nm) (solar spectrum peak ~ 550 nm).
•Visible photon energies are in the range of 0.6‐6 electron volts (eV) (solar spectrum peak ~2.3 eV)
Relevant Equations:
Eph h hc
pph k h
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Low‐Energy Photon‐Matter Interactions • At low energies (single eVs) typical for visible light, photons
interact primarily with valence electrons.
Courtesy of Humboldt Campus Center forAppropriate Technology. Used with permission.
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http://friends.ccathsu.com/bart/solarcooking/parabolic/parabolic_solar_cooker_pg_3_html.htm
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Interactions of Visible Light with Matter
Interactions of visible light with matter can be described by the index of refraction, which is a complex number:
n̂ c n̂ ik̂
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Interactions of Visible Light with Matter
Interactions of visible light with matter can be described by the index of refraction, which is a complex number:
ˆ n̂ ik̂ nc
Real Component
(indicates phase velocity)
Imaginary component, Extinction
coefficient(indicates attenuation)
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Interactions of Visible Light with Matter
Interactions of visible light with matter can be described by the index of refraction, which is a complex number:
n̂ c n̂ ik̂
Real and Imaginary components of the index of refraction are wavelength‐dependent, and are typically measured using a measurement technique called spectroscopic ellipsometry.
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Photons – Reflections off a Surface
At visible wavelengths, the fraction of reflected light depends most strongly on the real component of the index of refraction:
Air Semiconductor
I
T
R
Reflectance from air to a
solid.
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1 2
Mechanical Engineering Analogy
μ1 < μ2
μ1 > μ2
n1 n2Rlight Change in index of refraction (ignoring absorption) is
n1 1 n 2
2
z1 1 z2Rsimilar to reflection string z1 1 of string wave at interface! Replace n with z = μ*c.
z2 c
z
c T
T tension linear _ density
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Concept Question
Tinted window questions: •Why can’t you see inside? • If the glass pane was flipped, would this change anything?
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Bulk Absorption
Beer‐Lambert’s Law Demo
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Photons – Transmission Through a Medium
Io
ILight Inten
sity
Medium
I Io e l
Position
Simple Derivation of Beer‐Lambert’s Law:
dIz N dz Iz
ln Iz C N z
ln I0 N 0 C N l ln Il C N l l N I l I Io e o e Buonassisi (MIT) 2011
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Photons – Transmission Through a Medium
Light Inten
sity
Medium Io
I
Position
I Io e l
is a function of the wavelength of light, and property of the medium.
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Absorption Coefficient ( ) for different materials I Io e
l
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(0.62 eV) (6.2 eV)
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Methods to Improve Optical Absorption (Light Management Methods)
• Antireflection coatings (ARCs) • Snell’s Law • Texturization • Back surface reflection, total internal reflection • Plasmonics • Phase shifting
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1. Texturization
Multiple reflections on surface:
• Increase probability that light enters device.
• Increase effective path length of incoming light.
PV CDROM
Buonassisi (MIT) 2011
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Snell’s Law A change in refractive indices results in a “bending” of light.
A. Textured Front Surface B. Textured Back Surface 1
2 n̂1
n̂2
Snell’s Law:
n̂1 sin1 n̂2 sin2
Total internal reflection
To engineer front & back surface reflectance, carefully select refractive indices!
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Snell’s Law & Reflectance: Pool Example
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Pool filled with water n = 1.3 Pool filled with substance Pool filled with negative having n = 0.9 index material n = ‐1.3
Dominant Effect: Reflection Dominant Effect: Refraction
http://spie.org/x34206.xml?ArticleID=x34206 Buonassisi (MIT) 2011 23
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Lambertian Reflector
http://www.ecse.rpi.edu/~schubert/LightEmitting‐Diodes‐dot‐org/chap10/chap10.htm
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Specular reflector
θ θi r
Diffuse (lambertian) reflector
θ
Incident ray
Reflected ray
Image by MIT OpenCourseWare.
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Lambertian Reflector
http://www.pveducation.org/pvcdrom/design/lambertian‐rear‐reclectors
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Total Internal Reflection
A. Textured Busbar B. Textured Back Surface
Total internal reflection
Courtesy of 1366 Technologies. Used with permission.
White backskin, textured busbar on modules helps with light capture (via total internal reflection)!
Yablonovitch Limit: 4n2 = maximum increase in optical path length E. Yablonovitch & G.D. Cody, IEEE Trans. Electron Dev. 29, 300 (1982)
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Antireflection Coatings (ARCs)
For source and animation, see: http://pveducation.org/pvcdrom/design/anti‐reflection‐coatings Buonassisi (MIT) 2011
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Antireflection Coatings (ARCs)
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Antireflection Coatings (ARCs)
ARC
Absorber
Optimal ARC film thickness: ot 4n̂
where o is photon wavelength at the peak of the solar spectrum
Qualities of an optimized ARC: • Index of refraction between absorber and superstrate (air, glass) • Thickness on the order of a quarter wavelength (normalized for refractive index).
• Stable • Enhances electrical performance by passivating dangling bonds at the surface and repelling charges from the surface (e.g., through fixed charges).
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Photons – Reflections off a Surface
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1
2
3
4
5
6
00 200 400 600 800 1000 1200
7
Wavelength (nm)
Ref
ract
ive
inde
x an
d ex
tinct
ion
coef
ficie
nt
kSi3N4
kSi
nSi3N4
nSi
(n-1)2+k2
(n+1)2+k2R=
Image by MIT OpenCourseWare.
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Thin films require accounting of Phase information
• When EM waves (light) are interacting with matter that has interfaces that are spaced very close together, we need to account phase information when understanding how light moves through a medium.
• We do this to account for destructive and constructive interference.
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Importance of SiNx thickness
Note that minima appear at λ/(2n) intervals! Buonassisi (MIT) 2011
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Spectral Reflectivity for Optimized SiNx optimized at 550nm
When SiNx thickness is optimized for a specific wavelength, other wavelengths suffer! Buonassisi (MIT) 2011
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Equations Governing Thin Film R Reflectance
r012 r12
2 2r01r12 cos21R 2 21 2r01r12 cos21 r01r12
ni n jrij ni n j
2nidi
Buonassisi (MIT) 2011
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ARC: Impact on Reflectance
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Ray Tracing Software
RaySim (free!): http://www2.pv.unsw.edu.au/Links/RaySim6/Home OfRaySim6.htm
More sophisticated analysis (incl. non‐linear effects): Finite difference time domain (FDTD) method (good for large frequency ranges)
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Light Management • “Light Management” Ensures Absorptance is High. • Ensuring that light enters the absorber (minimize reflection). • Ensure good light trapping inside the absorber.
• Light trapping methods described on previous slide. • Change wavelength of incoming light to enhance optical absorption coefficient.
• Change optical absorption coefficient of material by manipulating band structure.
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Light Management is Necessary
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Light Management is Necessary
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“Bending Light” via Anomalous Refraction Yu, N., P. Genevet et al. “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction.” Science 334, no. 6054 (2011): 333‐337.
Photon Up/Down Conversion Jennifer Dionne (“Solar Cells That See More Light”), one of Technology Review’s Innovators Under 35.
Alombert‐Goget, G., D. Ristic et al. "Rare‐Earth Doped Materials Enhance Silicon Solar Cell Efficiency." SPIE Newsroom, 2011.
Buonassisi (MIT) 2011 © SPIE. All rights reserved. This content is excluded from our Creative Commons license. For more information, seehttp://ocw.mit.edu/fairuse. Source: Alombert-Goget, G., D. Ristic et al. "Rare-Earth Doped Materials Enhance SiliconSolar Cell Efficiency." SPIE Newsroom, 2011. DOI: 10.1117/2.1201105.003701.
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