Solar Energy-The Physics of Energy Devices-Lecture 8 Slides-Physics, Slides for Physics of Energy Devices. University of Toronto
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Solar Energy-The Physics of Energy Devices-Lecture 8 Slides-Physics, Slides for Physics of Energy Devices. University of Toronto

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Solar Energy, Thermal Emission, Solar Radiation Spectrum, Solar Endowment, Slanted Shelf Machine, Quantum Mechanics, The Physics of Energy Devices, Physics, Lecture Slides, Eric Switzer, University of Toronto, Canada.
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Overview of lectures in this series

1.  Introduction and Motors (Oct. 3) 2.  Motors and Generators (Oct. 10)3.  Distribution and use of Electricity (Oct. 17) 4.  The Wind (Oct. 24) 5.  Thermodynamics (Oct. 31) 6.  Heat Engines and Transportation (Nov. 7)7.  Nuclear Fission (Nov. 14) 8.   Solar Energy (Nov. 21) 9.   Special guest lecture (Dec. 5): “From the Freezer to

the Frying Pan: Trying to Understand the Wackier Climates of Ancient Earth.” – Dorian Abbot

10.  Summary; the future (Dec. 12)

C O M P T O N L E C T U R E 8 : N O V E M B E R 2 1 , 2 0 0 9 E R I C S W I T Z E R

Solar Energy

“I’d put my money on the sun and solar energy. What a source of power! I hope we don’t have to wait until oil and coal run out before we tackle that.” —Thomas Edison to Henry Ford and Harvey Firestone.

The sun

  Thermonuclear fusion in core out to ~¼ solar radius, there T ~ 14×106 K, density ~ 100x water.

  Power radiated: 3.8×1026 W.   Surface temperature 5,780 K.   Distance: 150 million kilometers.   1366 W/m2 in space.   ~1 kW/m2 on Earth (AM1.5,

~48 degrees off Zenith).   173,000 TW incident solar

power.   121,000 TW to the Earth’s

surface.   Energy used worldwide: ~16 TW

(all forms).   Electricity (world): ~2 TWe.   US ~ 3.4 TW, (~0.4 TWe).

Data: Fundamentals of Renewable Energy Processes (da Rosa) and EIA

Net release: 26.7 MeV Cf. uranium fission ~ 200 MeV

Image: wikipedia

Let’s face some facts

On the other hand, the 5 Gyr is a significant fraction of the age of the universe, 13.7 Gyr, and longer than our reserve of hydrocarbons.

Thermal emission


su nb

ur n


Images: wikipedia


Solar radiation spectrum

Data: NREL


Geometrical considerations

“Solar Collector Basics” J. Richter, J. of Ren. and Sus. Energy, Images: wikipedia

A horizontal collector at 35° latitude

Dashed is vacuum, next-lower is clear day, lowest is hazy day.

4.1, 5.7, and 5.7 h 2.12, 4.70, and 6.84 h

A tilted 35° collector at 35° latitude

Chicago: 41°52′55″N 87°37′40″W As a rule of thumb, a collector is optimized when its tilt is the latitude.

The Nellis AFB 14 MW (peak) plant –one axis

The solar endowment

Input 1kW/m2 peak

Covering Arizona in tilt=latitude concentrators: 74 TW

Illinois: 24 TW

Suppose ~10% efficiency to TWe, ~50% fill factor;

Arizona: ~4 TWe

Illinois: ~ 1 TWe

Image: NREL

1 kilowatt hour per day = 42 W

tilt=latitude collectors Facing: East to West

280 W/m2

150 W/m2

Game plan

  Solar energy is a very diverse field spanning physics, chemistry, biology, many areas of engineering.

  Restrict to solar electrical generation; photovoltaic and thermal.

  Restrict to basic physics.   Solar thermal insofar as it provides contrast and we

have talked about heat engines (Lec. 6)

Early history of photovoltaics

  1839: E. Becquerel discovers the photovoltaic effect.

  1877: Adams and Day, photoelectric response of selenium.

  1883: Fritts selenium cell (1% efficient).

  1950: Chapin, Fuller, Pearson et al. at Bell Labs; semiconductor cells (transistor: 1948).

  1958: satellite application.   Parallel to photoelectric


From: Selenium cells by Thomas William Benson, p. 17 (1919; google books scan)

“When selenium is vaporized by heat it gives off dark brown fumes having an odor similar to rotting cabbage”

The slanted shelf machine

Loss processes in the slanted shelf

Quantum mechanics and photon energy

  Atomic spectra: if your eyes could see colors as well as your ears hear chords.

  E = hυ : Photon energy is Planck’s constant (6.63×10−34 J s) times υ.

  Example: peak of solar spectrum ~ green light ~555 nm or υ=540 THz.

  E = 3.6 × 10−19 J.   E= 2.2 eV (in units from

Lec. 7).   Binding energy of hydrogen

is 13.6 eV.

Images: wikipedia (Bohr atom modified)

Sodium discharge lamp spectrum

Hydrogen Balmer (n=3-2, 4-2, etc.) spectrum

Energy and color

E = hυ

Rainbow image: wikipedia

Harvesting energy from little things

  Solar photon ~ 4 × 10−19 J or 2.5 × 1018 per J.

  Complete methane burning ~ 2 × 10−18 J or 5 × 1017 per J.

  Uranium fission ~ 3 × 10−11 J or 33 billion per J.

  Joule ~ lifting an apple one meter.

Image: wikipedia

Silicon and band structure

Silicon’s bandgap is 1.1 eV (1130 nm)

Exciting electrons to the conduction band

Relevant quantity for solar cells: rate of photon arrival above the bandgap. Silicon’s bandgap is 1.1 eV (1130 nm). Sunlight: 2.5 × 1021 photons with E > 1.1 eV per second per m2!

Rainbow image: wikipedia

Loss processes in the slanted shelf

The solar slanted shelf cell

Ingredients: 1.  Photogeneration 2.  Charge separation 3.  Charge transport

The slanted shelf machine

Design aspects

  AR: refractive index ~2: tantalum oxide, titania silicon nitride

  Point contacts and SiO2 passivation – minimize surface recombination

  Texturing increases optical depth (angle through cell), minimizes reflection (multiple bounce)

Image: derived from Wikipedia

Fundamental losses

  Case 1: recombination of the electron-hole pair.

  Case 2: photon energy in excess of the bandgap is thermalized.

  Case 3: a photon has insufficient energy and is unused.

  For AM1.5, want ~1.4 eV gap   Silicon is 1.1 eV (1130 nm), so

not so bad

Photon energy

U sa

bl e

A simple Heaviside engine model

Bang = buck? NO! Bang=$3 for any buck over $10. Would like to pay exactly $10, but nature provides too many $20 and $50 dollar bills that you can’t break

Enumerating the loss

  Absorption – 74% (need photons above the bandgap)   Thermalization – 67% (energy in excess of the bandgap is

wasted as heat)   Thermodynamic – 64% (not all of the exciton energy

converted to voltage)   Electrical – 89% (drawing current at the maximum-power

point)   Total = 28% (for a very efficiency cell)   Fundamental floor on this design: ~33% (41%

concentrator)   Plus: geometric factors that take 1000 W/m2 to 285 W/m2   In 2007, the average single crystal ~17% efficiency.   Thin films: ~8-16%.   What about those 40.7% efficiency cells that you hear about?

Example given in Würfel, efficiency data from “EIA Renewable Energy Annual 2007”

Improving on the basic design

  Multiple bandgaps (either multiple cells in a stack or following a frequency splitter, or a cell with multiple gaps) 69% limit.

  Hot carriers (avoid thermalization loss; cooling slower than transport; e.g. discrete energy levels > photon cooling steps; short transit times), 65% limit.

  Number of electron-hole pairs per photon (impact ionization) 55% limit.

Examples and limit at 1-sun radiation from Nelson

PV families

Image: NREL

Solar thermal overview

PS10 (Spain)

Image: Ps 10 from Wikipedia, parabolic trough derived from Wikipedia

Solar thermal efficiency (toy) argument

Carnot loss (absorber TH too low)

Re-radiative loss ~ T4 (absorber TH too high) Can improve significantly with selective absorber.

Image: PuO2 from Wikipedia

Steam lim


G as turbine lim


Peak efficiency in reality: 20% for trough, 23% for towers, 29% for dishes (Smil: Crossroads)

Energy payback

"What is the Energy Payback for PV?” National Renewable Energy Laboratory (NREL).

It is difficult to assess return on the cost of investment – consider energy instead. For 35 years sustained operation: energy returned on energy invested ~10.

Net energy flows 32% eff.

Solar: 0.01 Quad thermal, 0.08 Quad electrical


  Solar energy is a large, but diffuse resource   Can be exploited thermally – subject to usual losses

plus re-radiation   Discrete energy levels in atoms become wide energy

bands in solids; electrons can be excited from bands associated with bonding to bands where conduction is possible.

  Scheme: photogeneration, separation, transport, use   Solar photovoltaics have inherent limits from several

sources, but many aspects can be overcome.


  The Physics of Solar Cells –J. Nelson   Physics Of Solar Cells: From Basic Principles To

Advanced Concepts – P. Würfel   Fundamentals of Renewable Energy Processes – A.

V. da Rosa.   “Solar collector basics” – J. Richter in J. Ren. Sus.

Energy (043112, 2009).   “Renewable Energy Annual 2007” – EIA/DOE.

Extra slides (online version)

The silicon crystal structure

Image: EERE

Solar shipments Pe

ak k


EIA Renewable Energy Annual 2007

Growth in solar power


NREL: “Solar energy technologies program: Market Transformation”

Construction and operation costs

EIA Electricity Market Module 2008

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