Transcript Coupling of InGaN quantum-well photoluminescence to silver

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 Gopinath
Journal 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
Optical Properties of Metal
The Lycurgus cup, appears green
in reflection and appears red in
transmission.
Colloidal gold Nanoparticles
embedded in glass.
Optical response of metals is
complex and fascinating.
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 metals
The dielectric constant on metals can be calculated by treating it
as free electron gas, using Drude model.
Consider a time varying field:
E (t )  Re{E () exp(it )}
d 2x
The equation for motion of m
 eE Dipole moment
2
dt
of electron,
electron
p(t )  e.x(t )
P(t )  Re{P( ) exp(it )}
Harmonic time dependence
Substitution of P in equation
of motion
 m 2 p()  e2 E()
e2 1
p( )  
E ( )
2
m
p
np()
ne2 1
 r  1
 1
 1 2
2
 0 E()
 0m 

2
The Dielectric Constant is
 p2
 r  1 2

ωp is defined as the bulk plasmon frequency
ne2
 
 0m
2
p
The above is the expression for dielectric constant when only the conduction e’s contribute, and
damping is neglected.
The bulk plasmon resonance of Ag (silver) occurs at
ћωp=3.76eV
Dielectric function of
Aluminium
Typical shape of the
dielectric function.
Plane wave at metal-dielectric interface
Above Plasmon frequency
Bulk plasmon:
Collective longitudinal oscillation of the conduction electron gas in a metal.

   p 2  c2k 2
  ck
The wave equation is given by
Propagating wave is given by
Above two together gives
p
Dielectric constant is
k
2
 r  E  r, t 
c
2
t
2
 2 E  r , t 
E  r , t   Re  E  r ,   exp  ik  r  it 
 2 r  c2 k 2
 p2
r  1 2

2


p
Which yields the dispersion relation for bulk Plasmon  2 1 
 2


  c2k 2


Its clearly seen that when ω is less than ωp there is no propagating solutions and the wave vector is imaginary
Below Plasmon frequency
Surface Plasmon:
Strongly localized electronic oscillation on the surface of metal.
E  E0 exp(i(kx x  kz z  t ))
In the above
kx 
2
p
, where
 p is the wavelength of SP
  2 2
 i    kx  kzi
c
2
k z1 k z 2

0
1  2
The boundary condition gives
sp
The SP field is described by
Together with
1/ 2
yields
  
k x   1 2 
c  1   2 
 p2
1  1  2   2

The SP condition is ε1 = -ε2, which occurs at high kx
 sp 
Metal
ħωsp wrt GaN (eV)
p
Au
2.2 (≈ 560nm)
1 2
Al
5 (≈ 250nm)
Ag
2.92 (≈ 410nm)
Penetration depth
The 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/ε22)1/2
For Ag, Au and Al on GaN the penetration depths into GaN are,
Metal on GaN
Ag
Au
Al
Peneration Depth (nm)
40
33
77
Raether H 1988 Surface Plasmons (Berlin: Springer)
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
(b)
(c)
(d)
"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
(a)
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)
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)
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
:Si
• 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.
Sapphire Substrate
• 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
• 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.
Absorption/reflection correction, Tp x TPL(ω) ≈ 0.5
Tp and TPL(ω) are obtained using Fresnel's equation.
• 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.
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 ( ) 
PLAg  InGaN
PLInGaN
Fp is a analogues to Purcell factor, as it
describes the ability of the metal film to
p ( )  0 ( )  nr ( )
p ( ) Enhance coupling of the emitter (SQW)

 1
0 ( )  nr ( )
0 ( ) with the Plasmon modes.
Г0 radiative recombination rate
Гp recombination rate of spontaneous emission into Plasmon modes
Гnr nonradiative recombination rate
The nonradiative recombination rate is neglected, as the authors claim the quantum well is
calibrated to have a quantum efficiency greater than 90%.
Fermi Golden Rule
p ( ) 
2
2
 ( )  d  E (a)

• ρ(ħω), is the mode density of plasmons
• d, local electron hole dipole moment
• E(a), the local electric field of the plasmon
mode
E 2 (a) 
 2
L2
8
 ( ) /  E


E02 (a )
2
0
E(a) is normalized
( z )dz
L2 is the in-plane quantization area
() / E02 ( z) / 8 represents the energy density in a highly dispersive media.
 ( ) 
p ( ) 
2k dk 2 L d (k )
L 
2
(2 ) d ( )
4 d ( )
2
3 


2d 2E02 (a)
2
d (k 2 )
( ) /  E02 ( z)dz d ( )
d (k 2 )
d ( ) Can be obtained from the
Dispersion curve of surface Plasmon.
The factor 1/3 comes due to polarization
averaging.
4nd 2 3
Spontaneous emission rate for bulk semiconductor.
0 ( ) 
3
3c
Fp ( )  1 
2 2 


c 3 E02 (a)
d (k 2 )
( ) /  E02 ( z)dz d ( )
•
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.
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.
Surface-plasmon-enhanced light emitters based on InGaN quantum wells,
K Okamoto, I Niki, A Shvartser, Y Narukawa - Nature Materials, 2004