Surface plasmon-polaritons (SPP)

Surface plasmon-polaritons and LEDs

SPPs and light emission

송 석 호, 한양대학교 물리학과 http://optics.anyang.ac.kr/~shsong

1. What is surface plasmon (polaroton)?

2. What is the dispersion relation of SPs?

3. How can the SP modes be excited?

4. What can we play with SPPs for nanophotonics?

Key notes

Surface plasmon-polaritons (SPP)

1. How does the surface plamon resonance enhance the internal quantum efficiency of light source?

2. Understand the Fermi-Golden rule and Purcell enhancement factor in spontaneous emission 3. What are the practical difficulties in realizing SP-enhanced LEDs?

Key notes

SPP-enhanced LEDs

Light extraction

Light generation LED

RAY DESIGN ( d > λ )

WAVE DESIGN ( d ~ λ ) PHOTON DESIGN

( d < λ )

Three design regimes of LEDs

Let’s focus on photon design regime based on surface plasmon polaritons.

Light projection

Plasmonics: the next chip-scale technology

Plasmonics is an exciting new device technology that has recently emerged.

A tremendous synergy can be attained by integrating plasmonic, electronic, and conventional dielectric photonic devices on the same chipand taking advantage of the strengths of each technology.

Plasmonic devices,

therefore, might interface naturally with similar speed photonic devices and similar size electronic components. For these reasons, plasmonics may well serve as the missing link between the two device

technologies that currently have a difficult time communicating. By increasing the synergy between these technologies, plasmonics may be able to unleash the full potential of nanoscale functionality and become the next wave of chip-scale technology.

Plasmonics

λ

e-limit

Surface plasmon-polaritons (SPP)?

물방울

중력 표면장력

빛도 물방울처럼 표면을 흘러내릴 수 있을까?

전자기력

TM pol.

주파수/금속 용액/기판

Î SPP

Plasmons in the bulk oscillate at ω

determined by the free electron density and effective mass

Plasmons confined to surfaces that can interact with light to form propagating “surface plasmon polaritons (SPP)”

Confinement effects result in resonant SPP modes in nanoparticles

+ + +

- - -

+ - +

k

Plasmon = plasma wave = density fluctuation of free electrons

0 2

ω ε

m Ne

drude

p

=

0 2

3 1 ω ε

m Ne

drude

particle

=

Bulk plasmons

Surface plasmons

Localized (particle) plasmons

m d sp

m d

k c ω ε ε

ε ε

= +

Surface plasmons vs. Surface plasmon-polaritons

• 표면 플라즈몬 (Surface plasmon, SP)

– 금속표면의 전하(자유전자) 진동 → 표면 플라즈마 – 양자화된 표면 플라즈마 진동 → 표면 플라즈몬

6

TM pol.

• 표면 플라즈몬 폴라리톤 (Surface plasmon polariton, SPP)

– 표면 플라즈몬 (자유전자 진동)과 전자기파가 결합되어 있는 상태 Æ SPP

– 금속과 유전체의 경계면을 따라 진행 – 금속 표면에 수직한 TM 편광 특성 – 전송거리는 수십~수백 mm로 제한

metal air

L SP

1/e

1

D

Near-field profile of SPPs

λ

Local field intensity depends on wavelength

(small propagation constant, k) (large propagation constant, k)

Surface plasmons

0

2 _{m d}

x

m d

k n

c π ω ε ε

λ ε ε

⎧ ⎫ ⎧ ⎫

= ⎨ ⎩ ⎬ ⎭ = ⎨ ⎬ ⎩ ⎭ + ω

ω

d p

ε ω

+ 1

k _x

real k

real k

imaginary k

real k

real k

imaginary k

d

ck x

ε

Bound modes Radiative modes

Quasi-bound modes

Dielectric:

ε_d

Metal: ε_m = ε_m^'+ ε_m^"

x z

(ε'

> 0)

(−ε

< ε'

< 0)

(ε'

< −ε

)

2 2 2 2

p

c k

ω = ω +

Dispersion ( ω, k) relation of surface plasmons

surface plasmon plaritons

Cut-off frequency of SP

Very small SP wavelength

λ

=360 nm

X-ray wavelengths at optical frequencies

Ag SiO

surface plasmon plaritons

2 2 2 2 ' "

2 2 3 3

1

p p

m m

i

ω τ i ω τ

ε ε ε ε

ω τ ωτ ω τ

⎛ ⎞ ⎛ ⎞

= + = ⎜ ⎜ ⎝ − + ⎟ ⎟ ⎠ + ⎜ ⎜ ⎝ + ⎟ ⎟ ⎠

Ag/air, Ag/glass

surface plasmon plaritons

Silver(Ag) dispersion

0 10 20 30 40 50 60

1 2 3 4 5

light line air

E [eV]

kx [um-1]

SP Ag/air

SP Ag/glass light line glass

15001200 900 600 300

0.1 1 10 100

λ [nm]

L [um]

Gold(Au) dispersion

0 5 10 15 20 25 30 35 40

1 2 3 4 5

light line air

E [eV]

kx [um-1]

SP Au/air

SP Au/glass

light line glass

0.1 1 10 100

15001200 900 600 300

L [um]

λ [nm]

Copper(Cu) dispersion

0 10 20 30 40 50 60

1 2 3 4 5

E [eV]

SP Cu/glass light line glass

kx [_um^-1]

SP Cu/air light line air

0.1 1 10 100

15001200 900 600 300

0.1 1 10 100

15001200 900 600 300

L [um]

λ [nm]

L [um]

λ [nm]

For noble metals : J&C measured constants

Excitation of surface plasmons

n

//,d sp

k = k ± mG

ε d metal

//,_{d d}

sin

sin

k k

c

θ ε ω θ

= =

d d

c k ω ⁼ ε

sp //, d

k = k ± mG

//,_{d d}

sin k = k θ k

+ G

k

Localized surface plasmons (Particle plasmons)

(“Plasmons in metal nanostructures”, Dissertation, University of Munich by Carsten Sonnichsen, 2001)

Lycurgus cup, 4th century (now at the British Museum, London).

The colors originates from metal nanoparticles embedded in the glass.

At places, where light is transmitted through the glass it appears red, at places where light is scattered near the surface, the scattered light appears

greenish.

Focusing and guidance of light at nanometer length scales

Localized surface plasmons

For a 60 nm gold nanosphere embedded in a medium with refractive index n = 1.5.

(use of bulk dielectric functions (e.g. Johnson and Christy, 1972))

By the Rayleigh theory for ellipsoidal particles.

By the Mie theory for spherical particle By the Mie theory

for cross-sections

The red-shift observed for increasing size is partly due to increased damping and to retardation effects.

The broadening of the resonance is due to increasing radiation damping for larger nanospheres.

a/b = 1+3.6 (2.25 − E_res/ eV)

Influence of the refractive index of the embedding medium on the resonance position and linewidth of the particle plasmon resonance of a 20 nm gold nanosphere.

Calculated using the Mie theory.

Resonance energy for a 40 nm gold nanosphere embedded in water (n = 1.33) with increasing thickness dof a layer with refractive index n = 1.5.

Rayleigh theory & Mie theory for metal nanoparticle

using metal nanorods and nanotips

M. I. Stockman, “Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides,” Phys. Rev. Lett. 93, 137404 (2004)

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” PR B 76,035420 (2007)

Nanofocusing of surface plasmons

Nanofocusing of surface plasmons

Dispersion relation of metal nanotips

y x For a thin, nanoscale-radius wire Æ

k =nk0

ε

ε

For , the phase velocity v_p =c n z/ ( )→0 and the group velocity vg =c d n^/

[

]

Intensity Energy density

Nanofocusing of surface plasmons

In Summary

1/ 2 d m

SPP

d m

k c

ω ε ε

ε ε

⎛ ⎞

= ⎜ ⎝ + ⎟ ⎠

Dispersion relations

2 2

2 2 2 2

2 2

( ) 1

1 /

p p

m

p

ω i ω γ

ε ω ω γ ω γ ω

ω ω

= − + + + ⎛ ⎞ ⎜ ⎟ ⎝ ⎠

≈ −

Permittivity of a metal

0

Type-A

- Low frequency region (IR) - Weak field-confinement

- Most of energy is guided in clad - Low propagation loss

► clad sensitive applications

► SPP waveguides applications

Type-A : low k

H. Won, APL 88, 011110 (2006).

Type-B

- Visible-light frequency region - Coupling of localized field

and propagation field - Moderated field enhancement

►

Sensors, display applications

► Extraordinary transmission of light

Nano-hole

Type-B : middle k

Type-B : SPR sensors

Metal SPP waveguide

1.330 1.331 1.332 1.333 1.334 1.335 1.336 0

50 100 150 200 250 300 350

Intensity (uW)

Refractive index of water

Reference arm Sensing arm

Output signal

Type-C

- UV frequency region - Strong field confinement - Very-low group velocity

► Nano-focusing, Nano-lithography

► SP-enhanced LEDs

QW

2

0

1 1

( ) 2 ( )

R f i ρ ω

τ ω ε

= = p E ⋅

h SE Rate :

Electric field strength

of half photon (vacuum fluctuation)

Photon DOS

(Density of States)

Type-C : high k

Light emission

silver grating

Type-C : SP Nano Lithography

Ekmel Ozbay, Science, vol.311, pp.189-193 (13 Jan. 2006).

Some of the challenges that face plasmonics research in the coming years are

(i) demonstrate optical frequency subwavelength metallic wired circuits

with a propagation loss that is comparable to conventional optical waveguides;

(ii) develop highly efficient plasmonic organic and inorganic LEDs with tunable radiation properties;

(iii) achieve active control of plasmonic signals by implementing electro-optic, all-optical, and piezoelectric modulation and gain mechanisms to plasmonic structures;

(iv) demonstrate 2D plasmonic optical components, including lenses and grating couplers, that can couple single mode fiber directly to plasmonic circuits;

(v) develop deep subwavelength plasmonic nanolithography over large surfaces.

Challenges of SPs

1. What is the surface plasmon (polaroton)?

2. What is the dispersion relation of SPs?

3. How can the SP modes be excited?

4. What can we play with SPPs for nanophotonics?

Key notes

Final comments

SPP-enhanced LEDs

SPPs and light emission

1. How does the surface plamon resonance enhance the internal quantum efficiency of light source?

2. Understand the Fermi-Golden rule and Purcell enhancement factor in spontaneous emission 3. What are the practical difficulties in realizing SP-enhanced LEDs?

Key notes

silver grating

Light extraction

Light generation LED

RAY DESIGN ( d > λ )

WAVE DESIGN ( d ~ λ ) PHOTON DESIGN

( d < λ )

Remember!

Let’s focus on photon design regime based on surface plasmon polaritons.

Light projection

extraction

exter nal η η internal

η =

External efficiency of LEDs

extraction

exter nal η η internal

η =

^{[ ]}

2

1 1 ( ) sin

2 2

1 4( / )

4% for GaN(2.5)-air(1.0)

c

extraction s p

f g

R d

n n

θ

θ

η = ^{⎛ ⎞} ⎜ ⎟ ⎝ ⎠ − θ ^{⎛ ⎞} ⎜ ⎟ ⎝ ⎠ θ

≈

=

∑ ∫

Internal quantum efficiency

Î We need Wave Design tech.

Î We need Photon Design tech.

int

: nonradiative (loss) rate : spontaneous-emission rate

nr nr

η R

R R R

R

= +

Extraction efficiency

-. Geometric optics

-. Random scattering

in surface textured structure

APL 63, 2174 (1993)

Wave Design for efficient extraction of the guided light

extract external

nr ion

η R

η ⎛ R R ⎞

= ⎜ ⎝ + ⎟ ⎠

eMD Lab. Microoptics Lab –Hanyang University

32

What determines spontaneous emission rate of radiating source?

E i

E f

2

0

1 1

( ) 2 ( )

R f i ρ ω

τ ω ε

= = p E ⋅

SE Rate : h

Dipole moment of radiation source

Electric field strength

of half photon (vacuum fluctuation)

electron

Photon DOS (density of states)

( n 1/ 2) ω +

h

Energy of EM field

Number of photon

(Stimulated emission)

Vacuum fluctuation (Spontaneous emission)

Photon Design for increasing the emission rate

nr

η η

R R R

⎛ ⎞

= ⎜ ⎝ + ⎟ ⎠

Fermi’s Golden Rule

Atoms in microcavity

• High Q

• Narrow Δν

• F

~ 1 – 5

•

Photonic crystal cavity

• Moderate Q

• Wider Δν

• F

(Quantum wells) ~ 3

• F

(Quantum dots) ~ 5 –100

• Off-resonant and complicated fabrication

Surface plasmon coupling

• Low Q

• Narrow Δν

• F

~ 5 – 100

•

n-GaN

Quantum Well

p-GaN

Ag

www.phys.unt.edu/research/ photonic/website/Surf-Plasmon-OHPs-f.ppt

Photon Design for increasing the emission rate

external extraction

nr

η η

R R R

⎛ ⎞

= ⎜ ⎝ + ⎟ ⎠

2

2

)

1

( ) 1 (

R f i

τ ω ρ

ε ω

= = ⋅

h p E E, ρ increase

Photonic-crystal approach

Noda LumiLed

Baba

Limited by surface recombination

Good scheme!!!

100 um device size achievable.

Several layer of PC for extraction.

Good internal quantum efficiency Needed (>90%).

Multiple pass limits device size (~10um).

Small volume needed.

Not so good for lighting.

Surface recombination limited

Surface recombination limited.

Limited by surface recombination

Good scheme!

100 μm device size achievable.

Several layer of PC for extraction.

Good internal quantum efficiency Needed (>90%).

Multiple pass limits device size (~10um).

Small volume needed.

Not so good for lighting.

Surface recombination limited

Surface recombination limited.

external extraction

nr

η η

R R R

⎛ ⎞

= ⎜ ⎝ + ⎟ ⎠

2

2

)

1

( ) 1 (

R f i

τ ω ρ

ε ω

= = ⋅

h p E E, ρ increase

Good scheme!

Photonic-crystal assisted LEDs

2

2

)

1

( ) 1 (

R f i

τ ω ρ

ε ω

= = ⋅

h p E

Very small increase in E, ρ !

Look like an effect of wave design

rather than photon design!

Surface Plasmons

Surface-plasmon approach

external extraction

nr

η η

R R R

⎛ ⎞

= ⎜ ⎝ + ⎟ ⎠

2

2

)

1

( ) 1 (

R f i

τ ω ρ

ε ω

= = ⋅

h p E E, ρ increase

Requirements for enhancing SE rate -. slow group velocity

-. tight confinement of mode -. low ohmic loss

-. large field enhancement

slow group velocity, high loss

fast group velocity, low loss

A

B

eMD Lab. Microoptics Lab –Hanyang University

37

How does the surface-plasmon resonance contribute to emission rate?

2 0

1 1 ( )

( ) 2

R f i ρ

τ ω ω

= = ε p ⋅ E

h

Field enhancement near the emission layer

High DOS

due to decrease in group velocity

Emission layer

Surface Plasmons

( )

p

int p

p nr

R R R

R R

η = =

+

(

)

s p

p

p p nr

R R

R

R

R R R

η = ⁺ R = +

+ +

external extraction

nr

η η

R R R

⎛ ⎞

= ⎜ ⎝ + ⎟ ⎠

2

2

)

1

( ) 1 (

R f i

τ ω ρ

ε ω

= = ⋅

h p E E, ρ increase

The SP approach was started for organic LEDs

Cathode & Mirror ITO glass (anode) Organic molecules

SPP quenching (~40%)

( Λ > π / k

)

( Λ ~ π / k

)

Direct coupling SPP band gap

Nanostructures on metal mirror

SPP cross-coupling SPP1

SPP2

1 2

( Λ = π /[ k

− k

])

Metallic thin film Strongly coupled to SPPs

Main issue: SPP Î Radiation coupling

Effect of SPP band gap on PL

11411

1

and 2

order diffraction of SPPs

Angle resolved PL of dye molecule (DCM)

Tracing 1^storder peaks shows SPP band gap.

Modification of Spontaneous Emission Rate of Eu ³⁺

Main emission of Eu³⁺(614nm)

TRPL at 614nm

( spacer thickness )

τ

SPP quenching

42

p Metal interface

2 2

2

0 0

2

( / 2) ( / 2)

0

,

r

i ib t i ib t

r

d d e

p b p p E

dt m

dt

p p e

E E e

ω

− − − −

+ + =

= =

2

0 0

0 0

/ 1 e Im{ }

b b E

m p b ω

= +

2 2

0

0

0 0 0

Re{ }

8 4 2

bb

b e

m p E

ω ω ω ω

⎛ ⎞

Δ ≈ − −

⎜ ⎟

⎝ ⎠

2 unknowns and 2 equations d

Self-driven dipole (CPS) modeling

43

Dipole Decay Calculation Test : Metal Mirror Cavity

0.0 0.5 1.0 1.5 2.0

10^-4 10^-3 10^-2 10^-1 10⁰ 10¹ 10²

perpendicular dipole parallel dipole

dissipated power

k

/ k

10

10

J. A. E. Wasey and W. L. Barnes, J. Mod. Opt. 47, 725-741, 2000

44

0 50 100 150 200 250 300 350 400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

total emission rate air emission

emission to substrate guided modes emission to active layer guided modes

radiat ion rate ( R

)

active layer thickness (nm)

70nm 100nm 200nm 390nm

No guided mode TM₀ TM₀+TE₀ TM₀+TE₀+TM₁

CPS Model Calculation for Spontaneous Emission Rates of an OLED

Emission Spectrum

h

h

dipole active material (medium a)

substrate (medium s) cover (medium c)

( h

= h

+ h

)

45

100 200 300 400 500

60 70 80 90 100

PL Ef fi ciency (%)

Film Thickness (nm)

(measured) (calculated)

Comparison with an experiment

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0

10 20 30 40 50 60 70 80 90 100

P_air+P_sub+1.0P_guided P_air+P_sub+0.4P_guided P_air+P_sub+0.8P_guided P_air+P_sub+0.2P_guided P_air+P_sub+0.6P_guided P_air+P_sub+0.0P_guided

power ratio (%)

active layer thickness (

m)

Role of Preferred Orientation of the Dipole Source

Adv. Mater. 14 19 1393

Angle integrated EL

Enhanced PL by Coupled SPP

Cross-Coupled vs Coupled SPP

(1)

(2)

(3)

(4)

SPP Enhanced PL of InGaAs QW

Un-processed

Half-processed

Fully-processed

(a)

(b)

(c) 480nm period (2^ndorder coupling) (d) 250nm period (1^storder coupling) (160nm gap)

Most cited paper

Nature Materials, VOL 3, p.601-605, 2004

p external extractio

sp sp n

p nr

η η R

R R R

⎛ + R ⎞

= ⎜ ⎜ ⎝ + + ⎟ ⎟ ⎠

2

2

)

1

( ) 1 (

R f i

τ ω ρ

ε ω

= = ⋅

h p E E, ρ increase

1 ^st Result of SPP enhanced PL from InGaN QW

Nature Materials, VOL 3, p.601-605, 2004

1 ^st Result of SPP enhanced PL from InGaN QW

x2 x14

40x100nm

x28

133nm wide, 400nm period grating

(no enhancement for 200nm wide, 600nm period grating)

Nature Materials, VOL 3, p.601-605, 2004

Average internal quantum efficiency estimation

0.06 0.18 0.42

Purcell factor defining enhancement of the spontaneous emission

/

1 1 1

2 /

SP SP

p

p SP

R k k

F R L c

λ

π υ

= + = + ⎛ ⎞ ⎜ ⎟

⎝ ⎠

For a cavity mode:

2

2

( )

( ) ,

SP SP

at dipole

dz z

d L

dk

ω ωε ω

υ

∞

−∞

∂

= = ∫ ∂ ^E

E

We need a slow and confined mode!

3 2

mode_volume

3 ( / ) 4

cav c

p

free

R Q n

F R V

λ

= = π

For a SP mode :

original additional

1

original original

R R R

F R R

≡ + = +

( )

int

min max

int int

1

/

, 1

p p

p sp p

nr p sp nr p nr p

p

F

p nr F

R R F

η R

R R R R R F R R

η R η

R R

=

= = + =

+ + + +

⎡ ⎛ ⎞ ⎤

⎢ = ⎜ ⎜ ⎟ ⎟ = ⎥

⎢ ⎝ + ⎠ ⎥

⎣ ⎦

Factors influencing Purcell Enhancement F _p (ω)

GaN

Single Quantum Well

GaN ~ ζ

Ag ~ z

Variation with Ag thickness Variation with GaN thickness

Cover = 2.0 Cover = 1.0

Cover = 1.5

Purcell enhancement factor (F-1) Purcell factor: A numerical estimation

cover

Î Need a very thin p-GaN layer !!

2.68 10 1.75 300

p

at K

F at K

= ⎜ ⎛

⎝

“… the enhanced F

… can be attributed to an increase in the spontaneous emission rate due to SP-QW coupling.”

No improvement I-V curve

Improvement I-L curve

Why SP-LED hasn’t been successful yet?

Practical Barriers (especially for InGaN/GaN devices)

• Thin p-GaN leads to abrupt occurrence of leakage current under a certain thickness

• SP propagation length in blue wavelength along the Ag/GaN interface is extremely short

• Nanopatterning becomes a huge burden at short wavelength

• Damageless p-GaN patterning has been impossible

• SQW devices are prone to leakage current due to carrier overflow

• Silver is a nasty material with poor adhesion to GaN

and tends to agglomerate at an elevated temperature

SP propagation length

450 500 550 600 650 700 750 800

0 500 1000 1500 2000 2500 3000 3500 4000

Propagation Length of SPs [nm]

Wavelength of Photon [nm]

Surface Plasmon on the Ag/GaN Interface

PL

k

= ′′

2 1

2 2

3

) (

2

m d

m d m

k c

ε ε ε

ε ε ε ω

′

⎟⎟ ′′

⎠

⎜⎜ ⎞

⎝

⎛

′ +

= ′

′′

0.0 0.5 1.0 1.5 2.0 2.5

0 2 4 6 8 10 12 14

In-plane Wavevector (2

/

m)

Fr equenc y (2 π c/ μ m) 460nm

530nm

SP-dispersion on Ag/GaN

λsp~70 nm λsp~140 nm

2

order gratings (

might be readily fabricated by Holo litho at Green.

Λ = λsp, 2λsp, 3λsp, …

Nanopatterning

Green LEDs might be possible.

Schematic structure

Metal (Ag-based) p-GaN

n-GaN

Silicon submount Photon

Sapphire

c Exciton generation

dSurface plasmon excitation eRadiation

InGaN MQW e-h

High output directionality

by grating with non-even fill-factor

1

order grating, fill factor=0.1 1

order grating, fill factor=0.5

2

order grating, fill factor=0.1 2

order grating, fill factor=0.7

단일 원기둥 구조 계산

50 100 150 200 250 300 350 400 450 500 0.3

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

Normalized LifeTime

Internal Quantum Efficiency Upward Emitted Power

Diameter (nm)

N o rm a lize d LT / In te rna l Q E

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

Upw a rd em itt e d pow e r ( a .u.)

Λ = 250nm

Grating depth = 50nm Gap to QW = 30 nm

Two-dimensional silver-grating (2 ^nd order)

169 nm

Optimum gap distance between metal and QW

0 5 10 15 20 25 30

0.0 0.5 1.0 1.5 2.0 2.5

Upw a rd enh a n cement

Distance [nm]

6nm is a theoretical limit given by self-driven dipole (CPS) modeling coupling to surface plasmons

coupling to lossy surface wave

[W. L. Barens and P. T. Worthing, Optics Communications 162, 16 (1999)]

λ = 530 nm d = 20 nm

Grating on p-GaN

• Little damage to p-GaN

• Enlarged surface area for low contact resistance

Rotation stage

Linear stage

Aperture Mirro r L-Shape mount Substrate

mount Z

X

Y θ

Pinhole Objective

Lens

laser (λ = 266 nm)

Shutter

Mirror

Photoresist Aperture

x y

φ

Rotation

stage θ

θ

z

Mirror

Wafer holder with φ rotator

x y

z

θ rotator

Wafer-scale fabrication of ~ 100 nm patterns

NANO EGGBOX

6/10

EL Measurement

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045

0 0.1 0.2 0.3 0.4

C u r r e n t ( A )

Power(arb.)

r e f

250A _ 3 250B_ 2 250C _ 2 270A _ 4 270B_ 2 270C _ 3 290A _ 3 290B_ 2

Higher output power

up to 70 %

Sample images

400 500 600 700 800 0.0

0.2 0.4 0.6 0.8 1.0

Photons escaped

Wavelength (nm)

An Optimistic Estimation for SP-enhanced LEDs

At green (530 nm) with a 1^storder grating

(Bare-chip LED with 8 % extraction) Î (82 % / 8 %) x 2.3 ~ 24 times Brighter ( Optimized LED with 50 % extraction)

5 nm MQW

10 nm

60 nm

100 nm 180 nm

140 nm

grating depth

grating period 20 nm

2.3 times more Photons generated FDTD calculation

34.1% within 20^o after escape 82 %

1/(2n²) = 8 % Surface plasmon

Good directionality

Î (82 % / 50 %) x 2.3 ~ 4 times Brighter

Nanocavity lasers

Nanocavity lasers

Final comments

1. How does the surface plamon resonance enhance the internal quantum efficiency of light source?

2. Understand the Fermi-Golden rule and Purcell enhancement factor in spontaneous emission 3. What are the practical difficulties in realizing SP-enhanced LEDs?

Key notes

p p

nr p

E R

R R

η =

+

'

nr p SP

E R E R

R R R

η = ⁺

+ +

External Efficiencies

Conventional LED

SP LED

An Optimistic Estimation for SP-enhanced LEDs

At green (530 nm) with a 1^storder grating

5 nm MQW

10 nm

60 nm

100 nm 180 nm

140 nm

grating depth

grating period 20 nm

2.3 times more Photons generation FDTD calculation

Final comments

Summary

Nanophotonics needs SPPs based on Photon Design Tech.

1. cavity 도입에 따른 emission profile의 변화?

0 50 100 150 200 250 300 350 400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

total emission rate air emission

emission to substrate guided modes emission to active layer guided modes

radiat ion rate ( R

)

active layer thickness (nm) active layer

substrate air

( n = 1.73 2.27 10 + ×

i ) (quartz, 1.4612) n =

/ 2

0 0 ( ) sin 4

( ' ' for cover and ' ' for substrate emission)

R b q F d

c s

π

ν βν θ θν ν

ν

=

=

∫

Transmitted Emission Rate:

[ ] [ ]

2 2

2 2 2 2

3

, ,

( ) exp( ) exp( ) exp( )

1 exp(2 ) 1 exp(2 )

1 exp(2 ) and 1 exp(2 )

/ sin

TM a TE

TM

as ac s ac as c

s c

as ac a as ac a

x

k l T T

F i h k i h T i h

k

t r i h t r i h

T T

r r i h r r i h

k c and k

ν ν ν ν

ν ν ν ν ν ν

ν

ν ν ν ν

β β α ε α α

α ε α

α α

α α

ε ω β θ

⊥

⊥ ⊥

⎧ ⎛ ⎞

⎪ = ⎜⎜ + + ⎟⎟

⎪ ⎝ ⎠

⎪⎪ ± ±

⎨ = =

− −

⎪⎪

⎪⎪ = =

⎩

Q & A

2. Cathode와의 거리에 따른 SP에 의한 흡수?

0 10 20 30 40 50

0.0 0.2 0.4 0.6 0.8 1.0

Fraction

Distance [nm]

A

B

C

D A : Lossy surface wave mode

B : Surface plasmon mode C : Direct radiation mode D : Balance

h = 20 nm 에서의 비율은, A : 25.1 %

B : 55.9 % C : 19 %

Absorption loss due to metal

B

A

Q & A

3. cavity 최적화를 통한 SP 흡수 최소화?

0 50 100 150 200 250 300 350 400 0.0

0.5 1.0 1.5 2.0 2.5 3.0

total emission rate air emission

emission to substrate guided modes emission to active layer guided modes

radiation rate (R 0)

active layer thickness (nm)

70nm 100nm 200nm 390nm

No guided mode TM₀ TM₀+TE₀ TM₀+TE₀+TM₁

Assumptions

-Emitter:

uniformly distributed point-dipoles -Isotropic polarization

-No optical loss in the substrate -Optical constants

active layer:

substrate:

1.73 2.27 10

n = + ×

i quartz, 1.4612 n =

Emission Spectrum

Q & A

4. Excited dipole 혹은 oscillating dipole에 대한 구체적 설명

frequency

in-plane wavevector

Long-Range SP:

weak surface confinement, low loss

Short-Range SP:

strong surface confinement, high loss

Q & A

5. 만약 metal이 aluminum에서 Ag로 바뀐다면 OLED 소자에서 SP coupling에 미치는 영향은?

2 2 2

2 2 2 3 2

( ) 1

1

r

i

i

ω ω ω γ

ε ω ω ωγ ω γ ω ωγ

⎛ ⎞ ⎛ ⎞

= − + = − ⎜ ⎜ ⎝ + ⎟ ⎟ ⎠ + ⎜ ⎜ ⎝ + ⎟ ⎟ ⎠

Dielectric constant of free-electron plasma (Drude model)

0 10 20 30 40 50 60

1 2 3 4 5

light line air

E [eV]

kx [um-1]

SP Ag/air

SP Ag/glass light line glass

0 5 10 15 20 25 30 35 40

1 2 3 4 5

light line air

E [eV]

kx [um-1]

SP Au/air

SP Au/glass

light line glass

0 10 20 30 40 50 60

1 2 3 4 5

E [eV]

SP Cu/glass light line glass

kx [um-1]

SP Cu/air light line air

Silver(Ag) dispersion Gold(Au) dispersion Copper(Cu) dispersion

200 400 600 800 1000 1200 1400 1600 1800 2000 Ag (J & C) Au (J & C) Al (Palik) Pt (Palik) Pd (Palik) Cu (Palik)

wavelength (nm)

propagat ion lengt h (

m)

1 μm 10 μm 100 μm 1 mm

10 mm visible telecom.

Q & A

6. OLED decay time 과 SP coupling 관계?

Purcell Factor:

2 0

0

0

/ ( )

( ) / 1

/ '

SP SP

p SP p

SP SP

k k a

F R R R

V c k U ε

= + = + E

Green

Q & A