fundamental limits in “nano”...

Fundamental Limits in “nano” photovoltaics

Jenny Nelson

Department of Physics and Grantham Institute for Climate Change

Imperial College London

Thanks to: Ned Ekins-Daukes, UNSW

Thomas Kirchartz, FZ Juelich

Amsterdam,

18th June 2019

AMOLF International Nanophotonics Summer School

Solar energy conversion

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

100

200

300

400

500

600

Irra

dia

nce / W

m-2 e

V-1

Photon energy / eV

Energ

y

Heat

Light

Solar thermal

Light Dm Chemical

potential

energy

Solar chemical

Light Dm

Electric

work

Solar photovoltaic

Photons in, electrons out

eV

• Photovoltaic energy conversion requires:

– photon absorption across an energy gap

– separation of photogenerated charges

– asymmetric contacts to an external circuit

Photons in, electrons out

p type silicon

n t

yp

e

sil

ico

n

p type silicon

n t

yp

e

efficiency

~ 15-20%

power rating

~ 100-200 Wp

Applications

CIS Tower, Manchester

0.4 MWp

(Solar Century) Solar powered refrigeration

~100 Wp ~1 mWp

Blackfriars Bridge

~1.1 MWp

- +

Voltage

Eg Light

DEF = eVoc

scE

inc JdEEAbsEbeg

Voltage

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

100

200

300

400

500

600

Irra

dia

nce

/ W

m-2 e

V-1

Photon energy / eV

Power Conversion Efficiency =

Power converted into electrical work (J x V)

Radiant Power received from the Sun

Electrical work and efficiency

Efficiency from the Current density – Voltage (J-V) curve

• Short circuit current density Jsc,

• Open circuit voltage Voc

• Fill factor FF

7

200 400 600

-30

-20

-10

10

20

cu

rre

nt

de

nsity J

[m

Acm

-2]

voltage V [mV]

Jsc

Voc

po

we

r d

en

sity P

[m

Wcm

-2]

Pmpp

Jmpp, Vmpp

• J(V) measured under Standard Test Conditions (AM1.5, 1000 Wm-2, 25C)

• Approximately:

Power conversion efficiency:

http://upload.wikimedia.org/wikipedia/commons/3/35/Best_Research-Cell_Efficiencies.png

8

http://upload.wikimedia.org/wikipedia/commons/3/35/Best_Research-Cell_Efficiencies.png

9

Future directions in solar photovoltaics

Crystalline Silicon

“PV + X” Integrate solar panels with other functions

e.g. Electricity / heat

PV / fuels PV / storage

“Silicon + X” Add a layer to silicon to improve

performance

High efficiency designs Stack different solar cells together in

a multi-junction

Low cost, low energy manufacture Flexible, solution processible materials

Outline

• Photovoltaic energy conversion

• Limiting efficiency of solar cells

• Nanostructures in photovoltaics

• Routes to more work per photon

• Nanomaterials to approach the efficiency limit

• Nanomaterials to reduce costs

Detailed balance limit

(i) One electron hole pair per photon with h > Eg,

(ii) Carriers relax to form separate Fermi distributions at lattice temperature Tambient with quasi Fermi levels separated by Δm.

(iii) All electrons extracted with same electrochemical potential Δm = eV

(iv) Only loss process is spontaneous emission

Band gap

Solar cell absorbs visible light, emits IR light

0 1 2 3 4

1017

1018

1019

1020

1021

1022

5760 K

300 K

pho

ton

flu

x

bb [

cm

-2s

-1eV

-1]

energy E [eV]

5760 K

x 2.16 10-5

AM1.5G

AM1.5G spectrum sun

Ambient spectrum ambient

Co

nve

ntio

na

l so

lar

ce

ll

Ωemit >> Ωabs

Ts, Dm

Ts, 0

Dm N

Tsun,0

Ts, 0

Xb

1 - Xb

N

Particle flux

Calculation of limiting efficiency

0 1 2 3 4

10-1

100

101

p

ho

ton

flu

x

[1

01

8cm

-2s

-1]

energy E [eV]

AM1.5G

Emission of sun and solar cell at open circuit

The same integrated photon flux goes from the sun to the solar cell as back.

Graph: courtesy Thomas Kirchartz

Practical and limiting efficiencies

current

Radiative recombination

In the ideal (detailed balance) case: Energy is lost through transmission, relaxation and radiative recombination Limiting efficiency depends only on the band gap (and the concentration factor of the light)

0.00

0.10

0.20

0.30

0.40

0.50 1.00 1.50 2.00 2.50

Eff

icie

ncy

Band Gap / eV

current


Radiative recombination

Non-radiative recombination

In practice: Energy is lost through transmission, reflection, relaxation, radiative and non-radiative recombination

0.00

0.10

0.20

0.30

0.40

0.50 1.00 1.50 2.00 2.50

Eff

icie

ncy

Band Gap / eV

c-Si GaAs

perovskite

OPV


In the ideal (detailed balance) case: Energy is lost through radiative recombination. Part of the loss is due to the difference in angular range of absorbed and emitted light. Restricting the angular range of emission brings efficiency closer to the maximal concentration limit

Efficiency: 24.8 %

Spire Corp, IEEE Tr. Electron Dev. 37, 469 (1990)

Efficiency: 28.8 %

Alta Devices, Prog. Photovoltaics 20, 606 (2012)

Optical confinement in a thin-film

structure

Absorbing substrate

Hav

erko

rt e

t al

, Ap

pl.

Ph

ys. R

ev. (

20

18

)

How bad are the assumptions?

(i) One electron hole pair per photon with h > Eg,

(ii) Carriers relax to form separate Fermi distributions at lattice temperature Tambient with quasi Fermi levels separated by Δm.

(iii) All electrons extracted with same electrochemical potential Δm = qV

(iv) Only loss process is spontaneous emission

Overestimate current by 10-20%

~ OK

Overestimate eVoc by O(0.1 eV)

Overestimate qVoc by several 0.1 eV Overestimate fill factor

Assumptions in the Shockley Queisser limit

20 Slide: courtesy Thomas Kirchartz

Outline







Nanostructures in Photovoltaics

First International conference on “Nanostructures in Photovoltaics”

Max Planck institute for Complex Systems

Dresden, 2001

conjugated

polymer

1 nm

Photovoltaic “nano”-materials 10 n

m

quantum well

dye

conjugated molecule 1 n

m

5 nm

nanocrystal

2D transition metal

chalcogenide

Properties of nanomaterials for use in photovoltaics

1-10 nm

Energ

y

• Control of the electronic density of states

• Control of the phonon density of states

• Anisotropy in electronic and optical properties

• Access new spectral ranges

• Manipulate the optical response

How can nanomaterials help PV efficiency?

• Surpass the SQ efficiency limit (?)

• Approach the SQ efficiency limit with imperfect

materials

• Reduce the cost of reaching a given efficiency

Outline







Routes to more work per photon

0

200

400

600

800

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Photon Energy (eV)

Irra

dia

nc

e (

W m

-2 e

V-1

)

Optimum cell

converts 31% of power

Power spectrum from

black body sun at 5760K

Lost by thermalisation

Lost by

transmission

1. More band gaps

3. Slow carrier

cooling

2. Spectral

conversion

Band gap

L. H

irst

Pro

g. P

V (

20

11

)

Route 1. Higher efficiency via multiple band gaps

IR IR

red

red

blue blue

Single band gap Two band gaps

0

200

400

600

800

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Photon Energy (eV)

Irra

dia

nc

e (

W m

-2 e

V-1

)

Black body sunOne band gapTwo band gapsThree band gaps

• Multi-junction structures or spectral splitting

III-V Multi-Junction Solar Cells

1 2 3

This works, but multijunction III-V structures are expensive to grow

4

= 46.5% at 300 Suns

Tib

bit

s et

al,

29

th E

U P

VSE

C (

20

14

)

• Limiting efficiency around 46% for a monolithic four-junction cell under concentration

Using nanostructures to achieve multiple band gaps

• Strained layer quantum well solar cell: effectively a single junction device

Peak efficiency: 28.3%

• Quantum well structures could be used to achieve target band gaps for monolithic multi-junctions on selected substrates

N. J

. Eki

ns-

Dau

kes,

et.

al.,

Ap

pl.

Ph

ys. L

ett.

, 75

, p 4

19

5, (

19

99

)

Route 2. Reshaping the spectrum by up and down-conversion

E~Eg

E~Eg

E>2Eg

0

200

400

600

800

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Photon Energy (eV)

Irra

dia

nc

e (

W m

-2 e

V-1

)

Optimum cell


Power spectrum from



Lost by

transmission

Singlet fission (image: NREL)

Tim Schmidt, U. Sydney

Singlet fission as a downconversion strategy

• Singlet fission: high energy singlet excitons converted efficiently into triplet pairs in some molecular materials

– Separate triplets into e – h pairs OR

– Convert into IR luminescence by energy transfer to nanoparticles

• Goal of an optical coating on silicon

Ra

o a

nd

Fri

end

, Na

ture

Rev

iew

s M

ate

ria

ls (

20

17

);

Da

vis

et a

l. J.

Phy

s. C

hem

. Let

t. (

20

18

) 9

61

45

4-1

46

0

Reducing the photon entropy loss

• Approach the ‘ultimate’ efficiency by restricting the angular range of emission to match the range of absorption.

• May be possible by engineering the optical modes of semiconductor nanowires

Haverkort et al., Appl. Phys. Rev. 5, 031106 (2018)

Route 3: More work per photon by slowed cooling

generation equilibriation cooling recombination

3/2 kT h 3/2 kT

a

0

200

400

600

800

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Photon Energy (eV)

Irra

dia

nc

e (

W m

-2 e

V-1

)

Optimum cell


Power spectrum from



Lost by

transmission

Reduced thermalisation in solar cells

• Eliminating thermalisation of charge carriers with environment could increase efficiency to 85% but not physically achievable

• Approaches that have been studied:

– Multiple exciton generation

– Slow cooling via “phonon bottleneck”

Hardman et al., PCCP 2011 DOI: 10.1039/c1cp22330e; Schaller Phys. Rev. Lett 92, pp.186601 (2004)

ELO

Gre

en

an

d B

rem

ner

Nat

. Mat

er 2

01

7

Outline







Nanostructures to improve charge collection

B.Kayes et al. Journal of Applied Physics (2005) vol. 97 (11) pp. 114302

• Radial nanowire solar cells can outperform planar junctions only when diffusion length << absorption depth

• Helps to approach limiting efficiency in poor quality semiconductors

• Comparable to the use of ‘bulk heterojunctions’ in molecular photovoltaics

Nanostructures to reduce light reflection

Spinelli et al., Nat. Comm. 2012

• Array of low geometrical cross section nanowires results in low refractive index and weak refection

Ch

en

et a

l. A

pp

lied

Ph

ysic

s L

ett

ers

(2

00

9)

vo

l. 9

4 (

26

) p

p. 2

63

11

8

• Exploit forward Mie scattering into high index substrate to reduce reflection

Nanostructures to improve the radiative efficiency N

at. P

ho

ton

ics,

7, 3

06

–31

0 (

20

13

)

• Nanowires can show optical cross section > 10x geometrical

• If recombination is proportional to bulk volume can enhance generation relative to non-radiative recombination

Gre

en

an

d B

rem

ner

Nat

. Mat

er 2

01

7

Use of Plasmonics in Photovoltaics

Internal Scattering Field Enhancement Surface Plasmon

Polariton

Propagation

Use of Plasmonics in Photovoltaics

• Design of nanostructures for plasmonic enhancement depends strongly on accurate knowledge of the dielectric function of the metal used!

See poster by Phoebe Pearce at this meeting

P. P

ea

rce

et a

l., S

ola

r E

ne

rgy M

ate

ria

ls a

nd

So

lar

Ce

lls 1

91

(2

01

9)

13

3–140

Outline







Printable photovoltaics

contacts active layer

Current and

voltage output

flexible substrate

barrier coatingLight


Current and

voltage output

flexible substrate



Current and

voltage output

flexible substrate


Perovskite 2012-

~ 22%

Other new materials and new processes ...

2001- Organic (polymer:C60)

~ 16%

1990- Dye sensitised

~ 13%

e-

e-

e- e

-

e-

TiO2

Particle slurry CZTS 2010-

~ 13%

2007- Organic tandem

~ 17%

UC

LA

Summary

• Photovoltaic energy conversion efficiency is limited to 33% in unconcentrated sunlight

• To approach this efficiency need to maximise radiative efficiency; to surpass it we need to reduce losses to light transmission and charge carrier thermalisation

• Nanostructures have capability to modify the electronic and optical density of states

• Several approaches proposed to achieving more work per photon

– Upconversion, downconversion, multiple gaps, slowed cooling

– Only multi-junctions are currently practically useful

• Most effective uses of nanostructures to raise efficiency are in manipulating light absorption and emission to approach the theoretical limit

fundamental limits in “nano”...

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