A brief introduction to 3rd

generation photovoltaics:the road to high voltage

Noah BronsteinAlivisatos Group, UC Berkeley

PV Idea Lab, Sept. 2013

outline

• Thermodynamic assumptions and equations• Single junction photovoltaics• Multi-junction photovoltaics• Luminescent Solar Concentrators

Single Junction Solar Cell

ℎ𝜈𝜈 > 𝐸𝐸𝑔𝑔 ≡ 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 𝐵𝐵𝑙𝑙𝑙𝑙𝑙𝑙

ℎ𝜈𝜈 < 𝐸𝐸𝑔𝑔 ≡ 𝑅𝑅𝐵𝐵𝑅𝑅 𝐵𝐵𝑙𝑙𝑙𝑙𝑙𝑙

Bandgap around 1.4 eV is optimalMax Current = blue area = 33 mA/cm^2Max Voc ≈1.13 voltsMax Efficiency: 33%

Why is qVOC < EG?

For reference: this has beenachieved by Alta Devices with GaAs(Eg ≈ 1.41 eV, Voc ≈ 1.12 V, Eff=29%)

Photon entropy

𝑆𝑆 = 𝑘𝑘𝐵𝐵 lnΩ

Angular entropy:

Δ𝑆𝑆 = 𝑘𝑘𝐵𝐵 lnΩ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒Ω𝑆𝑆𝑆𝑆𝑆𝑆

= 0.925𝑚𝑚𝑚𝑚

𝐾𝐾𝐵𝐵𝐵𝐵𝐾𝐾𝐾𝐾𝐾𝐾 → 𝟐𝟐𝟐𝟐𝟐𝟐𝒎𝒎𝒎𝒎 @ 𝟑𝟑𝟑𝟑𝟑𝟑 𝑲𝑲

Ω𝑆𝑆𝑆𝑆𝑆𝑆 = 𝜋𝜋46000

sr

Ω𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 = 𝜋𝜋 sr

Non-ideal diodes

𝐽𝐽 = 𝐽𝐽𝑆𝑆𝑆𝑆 −𝐽𝐽0𝜂𝜂𝐵𝐵𝑞𝑞𝑞𝑞𝑘𝑘𝑘𝑘

η =photons outelectrons in ≡ External PLQY

𝐽𝐽0 = �Ω

�0

∞𝐵𝐵 𝜖𝜖 𝑎𝑎 𝜖𝜖,Ω 𝑅𝑅𝜖𝜖𝑅𝑅Ω

V

𝐽𝐽0𝐵𝐵𝑞𝑞𝑞𝑞𝑘𝑘𝐵𝐵𝑇𝑇

photons emitted

Under illumination:

𝐽𝐽 = 𝐽𝐽𝑆𝑆𝑆𝑆 −𝐽𝐽0𝜂𝜂𝐵𝐵𝑞𝑞𝑞𝑞𝑘𝑘𝐵𝐵𝑘𝑘

𝐽𝐽𝑆𝑆𝑆𝑆 photons absorbedfrom Sun

𝑚𝑚𝑂𝑂𝑆𝑆 =𝑘𝑘𝐵𝐵𝑇𝑇𝑞𝑞 ln

𝜂𝜂𝐽𝐽𝑆𝑆𝑆𝑆𝐽𝐽0

Luminescent recycling

(a)

e-

h+

hν hν hν

(b)hν hνg

Low-performing solar cellat open circuit

High-performing solar cellat open circuit

e-h+e-

h+

Slide credit: Eli Yablanovitch

η Depends on Refractive IndexIn a flat plate geometry:

Internal Luminescence Efficiency

Δ𝑚𝑚𝑂𝑂𝑆𝑆

n=1

n=4

Increase n by 0.5 per step

hν

hν

semi-conductor

only 1/4n2 = 1/50 = 2% of the light escapes.

Back Surface Reflectivity Effects η

0 0.2 0.4 0.6 0.8 1

1.16

Reflectivity

Voc

(Vol

ts) 1.14

1.12

1.10

1.08

1.06

Reflectivity0 0.2 0.4 0.6 0.8 1

Jsc

(mA/

cm2 )

32

32.21.104

1.115

1.145

32.4332.46

32.50

32.4

32.6

Slide credit: Eli Yablanovitch

Light trapping increases η and Voc

hν

hν

Solar Cell:

light trapping: path length increased by 4n2=50where n = refractive index

semi-conductor

semiconductor

single pass only

hν

hν

hν

Light Emitting Diode:

semi-conductor

semiconductor

only 1/4n2 = 1/50 = 2% of the light escapes.

all the light eventually escapes.

Slide credit: Eli Yablanovitch

Two Junctions in Series

ℎ𝜈𝜈 > 𝐸𝐸𝑔𝑔𝑔 ≡ 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 𝐵𝐵𝑙𝑙𝑙𝑙𝑙𝑙

ℎ𝜈𝜈 < 𝐸𝐸𝑔𝑔𝑔 ≡ 𝑅𝑅𝐵𝐵𝑅𝑅 𝐵𝐵𝑙𝑙𝑙𝑙𝑙𝑙

𝐸𝐸𝑔𝑔𝑔 < ℎ𝜈𝜈 < 𝐸𝐸𝑔𝑔𝑔𝐵𝐵𝐵𝐵𝑙𝑙𝑙𝑙 𝑟𝑟𝐵𝐵𝑅𝑅 𝐵𝐵𝑙𝑙𝑙𝑙𝑙𝑙, 𝐵𝐵𝐵𝐵𝑙𝑙𝑙𝑙 𝑏𝑏𝐵𝐵𝐵𝐵𝐵𝐵 𝐵𝐵𝑙𝑙𝑙𝑙𝑙𝑙

Bandgaps of 1.9 eV and 1.0 eV optimalMax Current = blue area = green areaMax Voc = sum of voltages ≈ 2.35 V

Max Efficiency = 44%

Best two-junction efficiency: 31%Best single-junction efficiency = 29%(both by Alta Devices)

Why are two junctions so far from ideal?

𝐸𝐸𝑔𝑔𝑔𝐸𝐸𝑔𝑔𝑔

Two Junctions in Series

𝑞𝑞𝑚𝑚𝑂𝑂𝑆𝑆 = 𝑘𝑘𝐵𝐵𝑘𝑘𝑞𝑞

ln 𝜂𝜂1𝐽𝐽𝑆𝑆𝑆𝑆𝐽𝐽0,1

+ 𝑘𝑘𝐵𝐵𝑘𝑘𝑞𝑞

ln 𝜂𝜂2𝐽𝐽𝑆𝑆𝑆𝑆𝐽𝐽0,2

We lose non-radiative voltage TWICE! Once at each junction!

Luminescence from large gap gets absorbed by low gap! Can’t get good voltage fromtop cell without electrically conductive, angle-insensitive, wavelength-selective mirror

Two Junctions, Electrically and Optically Isolated

• No current matching• Photon recycling allowshigh voltage in all cells

Spectral splitter

But: spectral splitter decreases photon entropy!Spectral information is traded for directional information. This is the opposite of concentration.

Two Junctions, Electrically and Optically Isolated

Example: a prism splits the spectrumFinal Illuminated area is bigger than initial illuminated areaVoltage loss from this is roughly 𝑘𝑘𝐵𝐵𝑇𝑇 ln

𝐴𝐴𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝐴𝐴𝑓𝑓𝑓𝑓𝑓𝑓𝑖𝑖𝑓𝑓𝑓𝑓𝑓𝑓

= 𝑘𝑘𝐵𝐵𝑇𝑇 ln 𝑁𝑁𝐵𝐵𝑚𝑚𝑏𝑏𝐵𝐵𝑟𝑟 𝑙𝑙𝑜𝑜 𝑆𝑆𝑙𝑙𝐵𝐵𝑎𝑎𝑟𝑟 𝐶𝐶𝐵𝐵𝐵𝐵𝐵𝐵𝑙𝑙

Polymerwaveguide

Escape cone

hν

High performance PV(Si, GaAs, etc…)

hν

Luminescent Solar Concentratora particularly bad case

Dye

𝐵𝐵 𝜈𝜈, 𝜇𝜇,𝑇𝑇 =2𝐾𝐾𝑔𝜈𝜈𝑔

𝑐𝑐𝑔 exp𝜇𝜇 − ℎ𝜈𝜈𝑘𝑘𝐵𝐵𝑇𝑇

𝑅𝑅Ω

𝜇𝜇 ≪ ℎ𝜈𝜈 due to angular entropy, so:

Principle of detailed balance:

𝐿𝐿 𝜈𝜈, 𝜇𝜇,𝑇𝑇 = 𝛼𝛼 𝜈𝜈, 𝜇𝜇,𝑇𝑇 𝐵𝐵 𝜈𝜈, 𝜇𝜇,𝑇𝑇

𝐿𝐿 𝜈𝜈, 𝜇𝜇,𝑇𝑇 = 𝛼𝛼 𝜈𝜈, 𝜇𝜇,𝑇𝑇2𝐾𝐾𝑔𝜈𝜈𝑔

𝑐𝑐𝑔 exp−ℎ𝜈𝜈𝑘𝑘𝐵𝐵𝑇𝑇

exp𝜇𝜇𝑘𝑘𝐵𝐵𝑇𝑇

𝑅𝑅Ω

Emissionspectrum

Excesscharge carriers

𝜇𝜇 = 𝑞𝑞𝑚𝑚

Emission Spectra ofSemiconductors and Dyes

𝐵𝐵 𝜈𝜈, 𝜇𝜇,𝑇𝑇 =2𝐾𝐾𝑔𝜈𝜈𝑔

𝑐𝑐𝑔1

exp ℎ𝜈𝜈 − 𝜇𝜇𝑘𝑘𝐵𝐵𝑇𝑇

− 1Blackbody coefficient:

Absorptionspectrum

BlackbodySpectrum

Emission Spectra ofSemiconductors and Dyes

Raman

ExcitonEmission

Upper band emission

Example: CdSe/CdS seeded nanorods

CdS arm CdSe core

Ener

gy

e-

h+

Luminescent Solar Concentratora particularly bad case

Now, both current and voltage dependon luminescent quantum yield of the dye.

𝑞𝑞𝑚𝑚𝑂𝑂𝑆𝑆 ≈ 𝐸𝐸𝑔𝑔 − 𝑘𝑘𝐵𝐵𝑇𝑇 lnΩ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒Ω𝑠𝑠𝑆𝑆𝑆𝑆

− ln1η𝑃𝑃𝑞𝑞

High performance PV(Si, GaAs, etc…)

Broadband mirror

𝐸𝐸𝑑𝑑𝑑𝑑𝑒𝑒 𝐸𝐸𝑔𝑔

Spectral splitting mirror

Luminescent Solar Concentratora particularly bad case

Now, both current and voltage dependon luminescent quantum yield of the dye.

𝑞𝑞𝑚𝑚𝑂𝑂𝑆𝑆 ≈ 𝐸𝐸𝑑𝑑𝑑𝑑𝑒𝑒 − 𝑘𝑘𝐵𝐵𝑇𝑇 lnΩ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒Ω𝑠𝑠𝑆𝑆𝑆𝑆

− ln1η𝑃𝑃𝑞𝑞

High performance PV(Si, GaAs, etc…)

Broadband mirror

𝐸𝐸𝑑𝑑𝑑𝑑𝑒𝑒 𝐸𝐸𝑔𝑔

Spectral splitting mirror

Acknowledgements

DOE Energy Frontier Research Center for Light-Matter Interactions

NSF GRFP for funding me

Prof. Paul Alivisatos Prof. Eli Yablonovitch Prof. Vivian Ferry