Coupling of InGaN quantum-well photoluminescence to silver surface plasmons

PRB, Vol 60, No 16, Pg 11564

Gontijo, M. Boroditsky, and E. Yablonovitch,UCLA Electrical Engineering Department, University of California, Los Angeles, California 90095

S. Keller, U. K. Mishra, and S. P. DenBaars Materials Science and Electrical Engineering Departments, University of California, Santa Barbara, California

Ashwin GopinathJournal Club

20th Nov 2006

Outline

• Optical properties of metals

• Surface Plasmons

• Dispersion

• Penetration depth

• Excitation

• Paper

• Motivation

• Device Sructure

• Results and discussion

• Conclusion

• Recent work

Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures, APL 98, Pg 011101, Stefan A. Maiera and Harry A. Atwater

Optical Properties of Metal

The Lycurgus cup, appears greenin reflection and appears red intransmission.

Colloidal gold Nanoparticles embedded in glass.

Optical response of metals is complex and fascinating.

Optical properties of metals

)}exp()(Re{)( tiEtE Consider a time varying field:

eEdt

xdm

2

2

The equation for motion of electron

)(.)( txetp Dipole moment of electron,

Harmonic time dependence )}exp()(Re{)( tiPtP

Substitution of P in equation of motion )()( 22 Eepm )(

1)(

2

2

Em

ep

The Dielectric Constant is2

2

20

2

0

11

1)(

)(1

p

r m

ne

E

np

The dielectric constant on metals can be calculated by treating itas free electron gas, using Drude model.

2

2

1

pr m

nep

0

22

ωp is defined as the bulk plasmon frequency

Dielectric function of Aluminium

The above is the expression for dielectric constant when only the conduction e’s contribute, and damping is neglected.

Typical shape of the dielectric function.

The bulk plasmon resonance of Ag (silver) occurs atћωp=3.76eV

Plane wave at metal-dielectric interface

Above Plasmon frequency

p

k

ck

222 kcp 2

22 2

,,r

tt

c

E r

E rt

, Re , expt i i t E r E r k r

2 2 2r c k

2

21 p

r

222

22 1 kcp

The wave equation is given by

Propagating wave is given by

Above two together gives

Dielectric constant is

Which yields the dispersion relation for bulk Plasmon

Its clearly seen that when ω is less than ωp there is no propagating solutions and the wave vector is imaginary

Bulk plasmon:Collective longitudinal oscillation of the conduction electron gas in a metal.

Below Plasmon frequency

))(exp(0 tzkxkiEE zx

2/1

21

21

ckx

The SP field is described by

pxk

2

pIn the above , where is the wavelength of SP

02

2

1

1

zz kk 222

zixi kkc

The boundary condition gives Together with

yields

22

2

1 1

p

21

psp

spThe SP condition is ε1 = -ε2, which occurs at high kx

Metal ħωsp wrt GaN (eV)

Au 2.2 (≈ 560nm)

Al 5 (≈ 250nm)

Ag 2.92 (≈ 410nm)

Surface Plasmon:Strongly localized electronic oscillation on the surface of metal.

Raether H 1988 Surface Plasmons (Berlin: Springer)

Penetration depthThe electromagnetic field of SPs is propagating on a surface in the x direction. The Hy is the magnetic field in the y direction of this P-Polarized wave.The exponential dependence of the field Ez is also shown (on the right).

Penetration depth:Depth at which value of Ez falls to 1/e ≈ 1/|Kz|=(λ/2π)(ε2-ε1/ε2

2)1/2

For Ag, Au and Al on GaN the penetration depths into GaN are,

Metal on GaN Peneration Depth (nm)Ag 40Au 33Al 77

"Near-field photonics: surface plasmon polaritons and localized surface plasmons",Anatoly V Zayats1,3 and Igor I Smolyaninov2, J. Opt. A: Pure Appl. Opt. 5 (2003) S16–S50

Surface Plasmons: Excitation

Surface Plasmon can be excited by:• Light (Photons)

•Excitation from high index medium (a,b) •Coupling using grating (c) •Coupling using sub wavelength scatter points (d)

•Electrons

(a)

(c)(b) (d)

H. F. Ghaemi, Tineke Thio, D. E. Grupp, T. W. Ebbesen, and H.J. Lezec, Phys. Rev. B 58, 6779 (1998) and 4H. R. Stuart and D. G. Hall, Appl. Phys. Lett. 69, 2327 (1996)

Motivation

• Fluorescence lifetime of molecules can be affected by metal surfaces in close proximity.• Optical transmission of thick metal films perforated with periodic array of subwavelength holes was enhanced due to plasmon coupling. (a) • Light absorption enhancement in thin silicon films by metal island. (b)

(a) (b)

:Si

Sapphire Substrate

Sample

• The excitation was by a continuous wave He-Cd laser operating at 326nm and focused to 150 W/cm2.

• The In0.04Ga0.96N:Si is a reference layer

• The SQW well is 12nm below the Ag, well within the penetration depth of the SP (40nm).

• The Ag was deposited only on one half of the structure so as to enable direct comparison of the PL spectrum.

• The sample was at room temperature during the experiment. The PL was collected by a lens, dispersed by a monochromator and detected by a silicon photodiode.

Results

Absorption/reflection correction, Tp x TPL(ω) ≈ 0.5Tp and TPL(ω) are obtained using Fresnel's equation.

• SQW PL peak at around 2.8eV• Second peak at around 3.17eV due, attributed to the reference layer.• The curve B was obtained using Fresnel's equation.• The curve C which is actual PL spectrum.• At 3.17eV, the curves C and B overlap.• At 2.8eV curve C is almost 2 orders less than B, due to Plasmon Coupling.• Above 3.4eV there is a very strong attenuation of the curve C, which is due to the bulk Plasmon excitation.

• Ratio of anticipated curve versus, actual curve is shown.• Surface-Plasmon resonance centered at 2.9eV with FWHM of 193meV. Q ≈ 15• Due to bulk Plasmon resonance at 3.76 there is a significant PL dip between 3.4-3.6eV

• Attenuation in external PL is not due to absorption or reflection.• Its due to competition between spontaneous emission into external electromagnetic modes and Plasmon modes.

)(

)(1

)()(

)()()()(

00

0

p

nr

nrp

InGaN

InGaNAgp PL

PLF

Г0 radiative recombination rateГp recombination rate of spontaneous emission into Plasmon modesГnr nonradiative recombination rate

Purcell Factor: A figure of merit for the cavity, which describes its ability to increase the coupling of an ideal emitter with the vacuum field.

Fp is a analogues to Purcell factor, as itdescribes the ability of the metal film toEnhance coupling of the emitter (SQW)with the Plasmon modes.

The nonradiative recombination rate is neglected, as the authors claim the quantum well is calibrated to have a quantum efficiency greater than 90%.

2)()(

2)( aEdp

• ρ(ħω), is the mode density of plasmons• d, local electron hole dipole moment• E(a), the local electric field of the plasmon mode

Fermi Golden Rule

)(

)(/)(8

2)( 2

020

22 aE

dzzEL

aE

E(a) is normalized

)(

)(

4)()2(

2)(

222

2

d

kdLL

d

dkk )(

)( 2

d

kd Can be obtained from the Dispersion curve of surface Plasmon.

)(

)(

)(/)(3

)(2)(

2

20

20

2

d

kd

dzzE

aEdp

The factor 1/3 comes due to polarizationaveraging.

3

32

0 3

4)(

c

nd

Spontaneous emission rate for bulk semiconductor.

L2 is the in-plane quantization area

represents the energy density in a highly dispersive media. 8/)(/)( 20 zE

)(

)(

)(/)(2

)(1)(

2

20

2

20

3

d

kd

dzzE

aEcFp

• Good agreement between experimental and theoretical Purcell factor.• Fp (Exp) = 56 ; Q (Exp) = 15• Fp (The) = 49 ; Q (The) = 60

• Differences were attributed to the adjustable parameter, Γnr that was dropped in theoretical calculations.

Conclusions

• Demonstrated direct coupling of electron and holes in SQW to the thin Ag film.• The Purcell factor into the Plasmon mode competes well with external spontaneous emission explaining the dip in PL spectra.• The Purcell factor could be further enhanced by the reducing the spacing between the quantum well and the Ag film.• If the Ag film is incorporated with some antenna structure, it would be possible to out-couple the SP. The result maybe a spontaneous emission which could be readily extracted, and this spontaneous emission could compete more effectively with nonradiative processes.

Surface-plasmon-enhanced light emitters based on InGaN quantum wells, K Okamoto, I Niki, A Shvartser, Y Narukawa - Nature Materials, 2004

Related works

• Showed that there is direct link between the Plasmon resonance and enhanced PL• When the surface is structured, there is more out-coupling of SP.