applying sub-wavelength electromagnetics and...

Shanhui Fan

Department of Electrical Engineering

Stanford University

Stanford, CA 94305

Email: [email protected]

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

Applying sub-wavelength electromagnetics and

nanophotonics for energy conversion and transfer

Maxwell’s equations and large-scale computation

EB

t

HD

tJ

http://www.psc.edu/machines/sgi/uv/black

light_crpd.jpg

Outline

Nanophotonic light trapping Wireless energy transfer

TCO

a-Si

Ag

Si thickness

280nm

Nanodome a-Si Cell

With Y. Cui’s group at Stanford

Full absorption

depth ~ 1000nm

Carriers only travel

for 200-300nm

Nanophotonic light management:

• Absorb light efficiently in a layer that is as thin as possible.

• Reduce material cost.

• Facilitate carrier extraction.

Challenges of light management for a-Si cell

Simulated nanodome geometry

a-Si

Simultaneous Light Trapping and Anti-Reflection

= 450nm = 750nm

Anti-reflection Light trapping

Nanocone

J. Zhu, Z. Yu, G. Burkhard, C. Hsu, S. Connor, Y. Xu, Q. Wang, M. Mcgehee, S. Fan, Y. Cui, Nano Letters 9, 279 (2009).

Success in combining theory and experiments

TCO

a-Si

Ag

Si thickness

280nm

Nanodome a-Si Cell

J. Zhu, C.M. Hsu, Z. Yu, S. Fan, Y. Cui, Nano Letters 10,1979 (2010).

-0.2 0.0 0.2 0.4 0.6 0.8-20

-15

-10

-5

0

5

Cu

rren

t (m

A/c

m2)

Voltage (V)

-0.2 0.0 0.2 0.4 0.6 0.8-20

-15

-10

-5

0

5

Cu

rre

nt

(mA

/cm

2)

Voltage (V)

Thin Film Nanodome

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

Very significant improvement in short-circuit current

- Latest results, with simultaneous electronic and optical optimization, has pushed

efficiency to 9.7%.

Simultaneous Light Trapping and Anti-Reflection

= 450nm = 750nm

Anti-reflection Light trapping

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)

Absorp

tion

Weak absorption at semiconductor band edge

Si

Mirror

The Yablonovitch Limit

Si

Mirror sin 1 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).

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

absorp

tion

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 Yablonovitch Limit (the math)

Random texture can be

understood in terms of grating

with large periodicity

Conventional limit

Large Periodicity L >>

Large Thickness d >>

=

M

N2

i F / d =4n2

L

d

Maximum absorption Maximum enhancement factor

The intuition about the Yablonovitch limit from the

wave picture

FM

Nd

Number of resonance in the film

Thickness of the film

When the thickness d

Double the thickness doubles the number of the resonances

The key in overcoming the Yablonovitch limit

FM

Nd

Number of resonance in the film

Thickness of the film

Nanoscale modal confinement over broad-bandwidth

Light Scattering Layer = 12.5, t = 80nm

Light Confining Layer = 12.5, t = 60nm

Light Absorption Layer = 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 classical limit


Red: 4n2 limit

Simulated Absorption Spectrum

4n2

Enhancement Factor Angular Response

Application to organic solar cell structure

PCDTBT:PCBM PEDOT:PSS

TiOx

Al

ITO ITO

Increase the number of optical modes to enhance light absorption

Top layer

Side view

A. Raman, Z. Yu and S. Fan, Optics Express 19, 19015 (2011).

Outline


f = 10MHz, d = 2m, P = 60W, efficiency = 40%

A. Kurs et al. Science, vol. 317 (2007) pp 83-86

Previous Experiment

Wireless energy transfer into moving vehicles:

Complex EM environment (metallic car body).

High power (on the order of 10kW).

Moving (transfer distance might vary).

Challenges

Collaboration with

Dr. S. Beiker, Dr. R. Sassoon

2m

0.8m

Monitor point

Monitor point

Magnetic dipole

source

Wireless Energy Transfer in Free Space

Transfer efficiency:

Transfer time:

Source

Receiver

2m

0.8m

Metallic plane

Influence of the metal plate


Transfer time:

Source

Receiver

2m

0.8m

Optimized design incorporating metal plate


Transfer time:

Source

Receiver

Efficient transfer over 2 meter

Distance (m)

1 2 3

100

80

60

40

20

0

Eff

icie

ncy

97%

Summary


Z. Yu, A. Raman

Prof. Y. Cui

X. Yu, S. Sandhu

Dr. S. Beiker, Dr. R. Sassoon

Poster # 33

applying sub-wavelength electromagnetics and...

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