nanophotonics: solar and thermal applications -...

Nanophotonics: solar and thermal applications

Shanhui Fan

Ginzton Laboratory and Department of Electrical Engineering

Stanford University

http://www.stanford.edu/~shanhui

Nanophotonic Structures

Photonic crystals Plasmonic Meta-materials

1 m

Au

2 m SOI

J. Pan et al, APL 97, 101102 (2010). L. Verslegers, Nano Letters 9, 235 (2009).

Photon as an important heat carrier

On earth From the sun

Improving Solar Cell Efficiency

P

N

V

Sun Semiconductor PN junction

1. Reduce cost for expensive materials

2. Facilitate carriers extraction to improve efficiency

Absorb sunlight using films

as thin as possible

Light management

Full absorption

depth ~ 1000nm

Carriers only travel

for 200-300nm

To facilitate carrier extraction, needs to absorb light with a layer

thinner than the absorption length

Challenges of light management for a-Si cell

TCO

a-Si

Ag

Flat Nanocone

11.4 mA/cm2

17.5

mA/cm2

Ph

oto

cu

rre

nt Total available: 20.5 mA/cm2

a-Si cell (~280nm thick)

Flat

Nanocone

Broadband anti-reflection and effective light trapping

Absorption spectra

ITO

a-Si

ITO Ag

air

a-Si

Broadband antireflection

l = 450nm

Flat

Nanocone


Absorption spectra

ITO

a-Si

ITO Ag

air

a-Si

Light trapping

l = 750nm

Flat Nanocone

J. Zhu, Z. Yu, G. Burkhard, C. Hsu, S. Connor, Y. Xu, Q. Wang, M. Mcgehee, S. Fan, and Y. Cui

Nano Letters 9,279 (2009).

Combine theory with experiment

Flat Nanocone

Jsc= 11.4mA/cm2 Jsc= 17.5mA/cm2

Efficiency 4.7% Efficiency: 5.9%

Most recent result: 9.7%

Significant efficiency enhancement

Flat

Nanocone


Absorption spectra

An important theoretical question

• What is the fundamental limit of absorption enhancement

using light trapping in solar cells?

A. Goetzberger IEEE Photovoltaic Specialists Conference (1981).

Optical confinement in thin Si-solar cells by diffuse back reflectors

E. Yablonovitch J. Opt. Soc. Am. A (1982).

Statistical ray optics

P. Campbell & M. Green J. Appl. Phys. (1986).

Light trapping properties of pyramidally textured surface

Classical Light Trapping Theory

50 m c-Si

Perfect AR

Perfect back mirror

0.2

0.4

0.6

0.8

1.0

0.0 400 600 800 1000

Wavelength (nm)

Ab

so

rptio

n

Weak absorption at semiconductor band edge

Si

Mirror

The Conventional Limit

Si

Mirror sin1 1

n

Maximum absorption enhancement factor

Derived with a ray tracing argument

4n2

E. Yablonovitch, J. Opt. Soc. Am. 72, 899 (1982); Goetzberger, IEEE Photovoltaic

Specialists Conference, p. 867 (1981); Campbell and Green, IEEE Trans. Electron.

Devices 33, 234 (1986).

Maximum absorption enhancement occurs in the

weak absorption limit

w/o light

trapping

with light

trapping

Wavelength (nm)

Ab

so

rptio

n

4n2

Nanocone

J. Zhu, Z. Yu, et al, Nano Letters 9, 279 (2009).

From conventional to nanoscale light trapping

~ 50 m

500 nm

Ray tracing Wave effect is important

M. Green (2001)

Light Trapping With Grating

mirror

Active layer

500nm

Absorption enhanced by guided resonance

• Guided resonance peak.

• Narrow spectral width for each peak.

• Requires aggregate contribution of large number of resonances.

Statistical Temporal Coupled Mode Theory

Instead of thinking about rays Think about many resonances

Zongfu Yu, Aaswath Raman, and Shanhui Fan Proceedings of the National Academy of Sciences 107,17491 (2010).

A single resonance

Resonant frequency

ab

so

rptio

n

Resonator

Intrinsic loss rate

External leakage rate

Incident plane wave

A simple model of a single resonance

i c

n

Assume no diffraction in free space

i

e

under-coupling

e

i

critical-coupling

e

i

over-coupling

e

i

Under, critical, and over coupling

100% 100% 100%

Traditional use of resonance for absorption enhancement, such as

resonance enhanced photodetectors, uses critical coupling

Spectral cross-section

Spectral cross-section

Contribution of a single resonance to the average absorption over the

bandwidth

A( )d

Incident spectral bandwidth

100% 100% 100%

Maximum spectral cross-section

MAX=2

i

A( )d

at the strong over-coupling limit, where the out-of-plane

scattering dominates over the intrinsic absorption

under-coupling

e

i

critical-coupling

e

i

over-coupling

e

i

Radio a

Radio b Radio c

88.5 MHz 97 MHz 106 MHz

Covering the broad solar spectrum with multiple

resonances

Sum over multiple resonances

M resonances

m

m

M resonances

N channels

Multiple plane channels in free space

max M

N2 i

Take into account diffraction in free space

=

M

N2

i

Theory for nanophotonic light trapping

Number of resonances in the structure: M

Number of plane wave channels in free

space: N

Maximum absorption over a particular

bandwidth

=

M

N2

i


Reproducing the conventional limit (the math)

Random texture can be

understood in terms of grating

with large periodicity

Conventional limit

Large Periodicity L >> l

Large Thickness d >> l

=

M

N2

i F

/ d =4n2

L

d

Maximum absorption Maximum enhancement factor

The intuition about the conventional limit from the

wave picture

F M

Nd

Number of resonance in the film

Thickness of the film

When the thickness

d l

Double the thickness doubles the number of the resonances

The key in overcoming the conventional limit

F M

Nd

Number of resonance in the film

Thickness of the film

Nanoscale modal confinement over broad-bandwidth

Light Scattering Layer e = 12.5, t = 80nm

Light Confining Layer e = 12.5, t = 60nm

Light Absorption Layer e = 2.5, = 400 cm-1, t = 5nm

Mirror

Light confinement in nanoscale layers

60n2

Light intensity distribution

5nm thick

15 times of the classical limit

Enhancement: 15 times the conventional limit


Red: 4n2 limit

Simulated Absorption Spectrum

4n2

Enhancement Factor Angular Response

Statistical Temporal Coupled Mode Theory

Instead of thinking about rays Think about many resonances


Guidance for grating design

Zongfu Yu, Aaswath Raman, and Shanhui Fan, Optics Express 18, A366 (2010).

2D 1D

Assuming isotropic emission (obtained when the grating period is much

larger than the wavelength)

4n2 n

~ l/2n

Maximum

enhancement

factor F

Grating with periodicity on the wavelength scale

L

x

y

z

Counting number of

channels in free space

2/L

kx

ky

2/l

Enhancement factor over 4n2

with grating

Zongfu Yu, Aaswath Raman,

and Shanhui Fan, Optics

Express 18, A366 (2010).

Angular sum rule of the enhancement factor

Uniform emissivity with the cone

Zero emissivity outside the cone

Zongfu Yu, Shanhui Fan, Applied Physics

Letters 98, 011106 (2011).

Fmax 4n2

sin2

Conventional case Arbitrary spatial emission pattern

d d F , cos sin 4n2

P. Campbell and M. A. Green, IEEE

Transactions on Electron Devices 33, 234

(1986).

Nanophotonics for solar cells

Z. Yu, A. Raman and S. Fan, Proceedings of the National Academy of Sciences 107,17491 (2010). Z. Yu, A. Raman and S. Fan, Optics Express 18,

A366 (2010). Z. Yu and S. Fan, Applied Physics Letters 98, 011106 (2011). A. Raman, Z. Yu, and S. Fan, Optics Express 19, 19015 (2011).

J. Zhu et al, Nano Letters 9, 279 (2009). J. Zhu, C. M. Hsu, Z. Yu, S. Fan, and Y. Cui, Nano Letters 10, 1979 (2010).

With Y. Cui’s group at Stanford Dr. Zongfu Yu, Aaswath Raman

Improving Solar Cell Efficiency

P

N

V

Sun Semiconductor PN junction

Basic Semiconductor Physics P

hoto

n E

nerg

y

Power

Solar Spectrum Semiconductor Bandstructure

Ele

ctr

on E

nerg

y

k

Valence band

Conductance band

Photons with energy below the band gap P

hoto

n E

nerg

y

Power


Ele

ctr

on E

nerg

y

k

Valence band

Conductance band

Eg

They do not contribute.

Eg

Photons with energy above the band gap P

hoto

n E

nerg

y

Power


Ele

ctr

on E

nerg

y

k

Valence band

Conductance band

Eg

•They do contribute, but only partially.

•After absorption, each photon contributes to approximately Eg

worth of the energy, the rest is lost due to thermalization.

Eg

Shockley-Queisser Limit P

hoto

n E

nerg

y

Power


Ele

ctr

on E

nerg

y

k

Valence band

Conductance band

Eg

A single-junction cell: maximal efficiency 41%.

Eg

“Detailed Balance Limit of Efficiency of p-n Junction Solar Cells”

William Shockley and Hans J .Queisser, J .Appl .Phys .32, 510 (1961)

What if the sun was a narrow-band emitter? P

hoto

n E

nerg

y

Power

Solar Spectrum (Ts=6000K) Semiconductor Bandstructure (Te=300K)

Ele

ctr

on E

ne

rgy

k

Valence band

Conductance band

Eg

Eg

Eg+dE

Approach Thermodynamic Limit

Solar Thermo-Photovoltaics (STPV)

Sun (Ts = 6000K)

P

N

Intermediate Absorber and

Emitter (Ti = 2544K)

Solar Cell (Te = 300K)

The sun to the

intermediate

The intermediate

to the cell

R. Swasnson, Proc. IEEE 67, 446 (1979); P. Harder and P. Wurfel, Semicond. Sci. Technol. 18, S151 (2003).

STPV: The Challenge

6000K

P

N

2544K 300K

Design requirement for the intermediate

• Broad-band wide-angle absorber

• Narrow-band emitter

Material requirement for the intermediate

• Need to have large optical loss.

• Need to withstand high temperature.

Tungsten is a natural choice of material.

Dielectric Function of Tungsten

Tungsten is a very lossy material in the solar wavelength range.

W

Absorptivity of a semi-infinite slab of Tungsten

Neither a good absorber or a good emitter.

Nanostructured Tungsten Photonic Crystals

Narrow-band Emitter Broad-band absorber

250nm

Tungsten Broad-Band Wide-Angle Absorber

E. Rephaeli and S. Fan, Applied Physics Letters 92, 211107 (2008).

Towards ideal solar thermal absorber

An ideal solar thermal absorber

• a near-unity absorption in the optical wavelength

• a near-zero absorption in the thermal wavelength range

Thermal Emitter

Vacuum Lamp:

1800 - 2700K

Gas Filled Lamp:

Up to 3200K

www.intl-lighttech.com/applications/appl-tungsten.pdf

Narrow-band Tungsten emitter tuned to band gap of 0.7eV

Energy (eV)

Em

issiv

ity

Blackbody 2100K

W Si SiO2

E. Rephaeli and S. Fan, Optics Express 17, 15145 (2009).

Schematic Incorporating both Absorber and Emitter

Beating Shockley-Queisser Limit

6000K

P

N

~2000K 0.7eV cell

E. Rephaeli and S. Fan, Optics Express 17, 15145 (2009).

Solar TPV (0.7eV cell)

Direct PV (1.1eV cell)

Direct PV (0.7eV cell)

# of Suns

Syste

m E

ffic

iency

Active control of thermal transport

http://www.aztex.biz/wp-

content/uploads/2009/01/ic-chip-

example.jpg

Can we provide more

active control of thermal

transport?

Electronic integrated circuit

Thermal Rectification (Thermal Diode)

Body 1 Body 2

Forward

Bias

Backward

Bias

TH TL

TH TL

TH >TL

S12

S21

• Rectification occurs when

• Previous experiments on phonon and electrons.

• Relies upon phonon-phonon or electron-electron interactions.

• Novel capability for thermal management

• Here, we aim to create thermal rectification for photons

S12 S21

SiC (6H)

• Photon mediated

• Heat conducting channel is linear (vacuum)

• The nonlinearity is in the dependency of the refractive index with

respect to temperature

Our construction

SiC (3C)

d=100nm

C. Otey, W. Lau, and S. Fan, Physical Review Letters 104, 153401 (2010).

Sharp thermal features in the near field

SiC (300K)

d

Greffet et al, PRL 85, 1548 (2000).

d = 1000m

d = 2m

d = 0.1m Narrow-band

resonance

Mechanism for thermal rectification

Body 1 Body 2

• Two different objects, both support narrowband resonances

• The resonant frequencies have different temperature dependence.

1 T 2 T

1 T

2 T

Forward bias

Body 1 Body 2

1 T 2 T

500K 300K

Resonances overlap, large thermal transfer

Body 1

Body 2

Backward bias

Body 1 Body 2

1 T 2 T

300K 500K

Body 1

Body 2

Resonances do not overlap, small thermal transfer

orward everse

Narrow-band electromagnetic resonances with temperature

dependent resonant frequency.

Our scheme


• Use surface phonon polaritons as our temperature

dependent resonances

• SiC has TO phonons that give clean dielectric resonances

in infrared that dominates the near field

• SiC-3C and SiC-6H have different TO phonon frequency

temperature dependence

3C

6H

A simple rectifier design

SiC (6H)

SiC (3C)

d=100nm

Forward Reverse

Spectral heat flux

SiC 3C SiC 6H SiC 3C SiC 6H

Rectification S12 S21

S21

Tl 300K

Overall heat flux


Summary

Nanophotonic light

trapping

Dr. Zongfu Yu

Aaswath Raman

SiC (6H)

SiC (3C)

Thermal Diode

Clayton Otey

Dr. Wah Tung Lau

Acknowledging support from GCEP, DOE, AFOSR

Eden Rephaeli

Solar

Thermophotovoltaic

nanophotonics: solar and thermal applications -...

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