, Handbook of Optical Constants of Solids The authors would ......Optical Properties of Silicon and...
1
Absorption Enhancement in Silicon Solar Cells due to Surface Plasmons of Nanotoroids Nathan Burford and Magda El-Shenawee Electrical Engineering Department, University of Arkansas, Fayetteville, AR 72701, USA 2012 IEEE International Symposium on Antennas and Propagation and USNC- URSI National Radio Science Meeting, July 8-14, 2012, Chicago IL Abstract Enhanced absorption in silicon is needed to improve the efficiency of solar cells. Analysis of Silver nanotoroids placed on top of a silicon substrate demonstrating larger absorption, will be presented. The method of moments model and Ansys ® HFSS are employed to compute the near electric fields absorbed in silicon substrate. The results show surface waves represented by large electric fields normal to the silicon surface and decayed as it gets deeper in the medium. Motivation Intensive research efforts are currently underway for using plasmonic nanoparticles to increase the light absorption in photovoltaic (PV) devices [1]-[3]. The reported results in the literature show the improved absorption in silicon when nearby nanoparticles were employed [3]. Although numerous works were published reporting the enhanced localized near fields due to these surface plasmon, work was focused on the red and blue shift of these plasmon in air. While the majority of published work focused on the assumption of infinite arrays of nanoparticles, less work was reported on characterizing the absorption in silicon due to finite number of nanoparticles [3]. Modeling is a necessary tool to help understand the interactions between the nanoparticles and the silicon. The goal of the current work is to use computational electromagnetics to investigate the effect of surface plasmon of nanotoroids on the absorption in solar cells. Statement of the Problem In this work, computational methods are used to investigate the plasmonic behavior of silver nanotoroids located on a layer of silicon. Two methods of analysis, the method of moments (MoM) surface integral equation and Ansys ® HFSS are used and compared. Effects of the silicon layer on the shift of the nanotoroid resonant frequency are investigated. In addition, a comparison is made between nanotoroid and disk-shaped nanoparticles tuned to the same resonant frequency. Background of Nanoantennas Antennas made of noble metals such as gold or silver have the ability to sustain surface plasmon polariton oscillations at the boundary between the metal and a dielectric, when excited at optical frequency. A combination of the antenna shape resonance and the surface Plasmon resonances will contribute to the antenna performance to exhibit strong enhanced local fields. From Literature 200 400 600 800 1000 1200 1400 200 400 600 800 1000 1200 1400 x (nm) y (nm) 700 720 740 760 700 720 740 760 10 20 30 x (nm) y (nm) z(nm) y-direction (nm) x-direction (nm) Top View Silicon X-Y direction: 140 nm x1440 nm & 2551 nm x2551nm infinite Z-direction Silver nanotoroid Side View Silver Nanotoroid 3D Method of Moments (MoM) Surface Integral Equation Model 3D MoM Model Equations 2 1 , 1 0 1 , r j I η r M , , k S r r j I r J n N n N n S k n N n n S k S k S k k S k tang. 2 2 2 2 1 1 2 1 tang. t t inc M η L η L J K K r H Surface Integral Equation: V I Z Linear system of equations: E inc H inc K inc m m m R , : tang. 2 1 2 1 tang. t t inc M K K J L L r E r J r M Electric and magnetic surface current density: Incident Gaussian Beam x y k k i i z s z inc inc K K K K W z ik r K i k K L W r 2 exp exp exp , 2 2 2 2 , ˆ sin sin ˆ cos sin y i i x i i o i a a k K y y x x a k a k K ˆ ˆ z a ˆ ˆ ˆ o y o z y x o z x v k k a k k k k a k k k k e y x x y v a k k a k k h ˆ ˆ y x x y h a k k a k k e ˆ ˆ For vertical polarization: ) ( , v v inc z inc h or e r k K For horizontal polarization: z a ˆ ˆ ˆ o y o z y x o z x h k k a k k k k a k k k k h Electric Field Magnetic Field ) ( , h h inc z inc h or e r k K Electric field on silicon surface @ 700 nm wavelength with single silver nanotoroid y-polarization z-component y-direction (nm) 500 600 700 800 900 1000 Gaussian beam excitation x-direction (nm) y-component x (nm) x-component 1000 900 800 700 600 500 500 600 700 800 900 1000 1000 900 800 700 600 500 y-direction (nm) x-direction (nm) 1000 900 800 700 600 500 2500 2000 1500 1000 500 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 Extinction Coefficient in Air 400 600 800 1000 1200 0 2 4 6 8 x 10 -4 Wavelength (nm) ~ ~ Img. 2 ˆ ˆ 0 E E C inc sca n n sca inc ext Plane wave excitation Rin= 10.5 nm Rout= 42 nm R = 48 nm H= 12 nm 2xRout 2xRin H 2xR Transmitted Electric Field in Silicon 400 600 800 1000 1200 0 0.1 0.2 0.3 0.4 0.5 0.6 Silicon Wavelength (nm) Disk: R = 48 nm, H= 12 nm Torus: Rin = 10.5 nm, Rout= 42 nm Torus: Rin = 6 nm, Rout= 42 nm Gaussian beam excitation Fields calculated at toroid center and z = -100 nm below the Air/Silicon Interface. Silicon size: 2551 x 2551nm Surface Plasmonic Enhancement of Magnetic Current Density on Silicon M 400 600 800 1000 1200 1.35 1.4 1.45 1.5 1.55 1.6 Wavelength (nm) Amplitude square of magnetic current density M| over Silicon surface Gaussian beam excitation patches surface Silicon Silicon patches surface Silicon Silicon on le nanopartic M M 2 2 | | | | Infinite Array of Nanotoroids on Silicon HFSS Simulation Parameters Infinite Array of Silver Toroids Center to center toroid spacing of 1440 nm and 2 nm spacing between toroids and silicon layer Incident plane wave excitation Wave propagation in -z direction Electric field polarized in x direction x z y Incident Plane Wave Nanotoroid Silicon Infinite Array of nanotoroids on Silicon Optical Properties of Silicon and Silver All nanoparticles in this work are made of Silver. 0.995 1 1.005 1.01 1.015 1.02 1.025 1.03 1.035 500 600 700 800 900 1000 Enhancement Factor Wavelength (nm) Enhancement Factor for Infinite Array of Nanotoroids Rin: 14.5 nm Rin: 13.5 nm Rin: 10.5 nm Rout: 42 nm Rout Rin z-direction (nm) Electric Field Magnitude of Infinite Array of Nanotoroids -500 x-direction (nm) |E| (V/m) |E| (V/m) Air Silicon 116.09 0.0110 1.1312 11.460 0.1117 6.9862 0.0011 3.0827 4.9317 1.8501 Linear Logarithmic 500 0 -720 720 500 0 -500 -720 720 100 -100 0 -100 100 100 -100 0 -100 100 Resonance at 817 nm Non-resonance at 895 nm Rin: 10.5 nm, Rout: 42 nm Comparison of Nanotoroids to Other Geometries In order to better understand the plasmonic behavior of toroid-shaped nanoparticles, comparisons with other geometries are needed. One of the interesting features of a toroid is the cavity at the center. As such, a disk geometry of the same outer radius is chosen for comparison, but with different height. Tuning of the disk resonant frequency is dependent on the height to radius ratio. Thus, fixing the outer radius (Rout) to 42 nm allows the height to be tuned such that the disk resonant frequency matches the toroid resonance when they are positioned on silicon (not in air). Enhancement Factor 0.995 1 1.005 1.01 1.015 1.02 1.025 1.03 750 800 850 900 950 1000 Enhancement Factor Wavelength (nm) Enhancement Factor Comparison of Silver Nanotoroid and Nanodisk Infinite Arrays Rmin: 10.5 nm Rout: 42 nm Height: 11 nm Radius: 42 nm z-direction (nm) Electric Field Magnitude of Infinite Array of Nanotoroids and Nanodisks x-direction (nm) Nanotoroid Resonance at 817 nm |E| (V/m) |E| (V/m) Air Silicon 116.09 0.0110 1.1312 11.460 0.1117 6.9862 0.0011 3.0827 4.9317 1.8501 Linear Logarithmic Rin: 10.5 nm, Rout: 42 nm 500 0 -500 -720 720 500 0 -500 -720 720 100 -100 0 -100 100 100 -100 0 -100 100 Nanodisk Resonance at 815 nm Height: 10.5 nm, Radius: 42 nm z-direction (nm) x-direction (nm) Phase Sweep Comparison of Infinite Array of Nanotoroids and Nanodisks at Resonance Conclusion In this work, two different computational methods were used in the analysis of plasmonic nanotoroids located atop a silicon substrate. In the HFSS analysis, a comparison of field enhancement was made between infinite arrays of nanotoroids and nanodisks tuned to have identical resonant wavelengths on silicon. The nanotoroid array shows slightly greater field enhancement over the nanodisk array. Future work investigating arrays with optimized array spacing is believed to provide more insight into the advantage of the nanotoroid structure. Since toroid structures have a smaller filling factor than disks, it is hypothesized that optimized array spacing of nanotoroids will allow more structures to be placed on the silicon surface than solid nanostructures, thus providing even greater advantages in field enhancement for the nanotoroids. REFERENCES [1] S. Mokkapati, F. J. Beck, R. de Waele, A. Polman, and K. R. Catchpole, “Resonant nano-antennas for light trapping in plasmonic solar cells,” J. Phys. D: Appl. Phys. 44, 185101, 2011 [2] F. Moreno, F. Gonzales, and J. M. Saiz, “Plasmon spectroscopy of metallic nanoparticles above flat dielectric substrates,” Optics Letters, Vol. 31, No. 12, pp. 1902 1904, June 15, 2006. [3] D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Applied Physics Letters 89, 093103, 2006. [4] M. El-Shenawee, “Polarization dependence of plasmonic nanotoroid,” IEEE Antennas Wireless Propagation Letters, vol. 9, pp. 463-466, 2010. [5] M. El-Shenawee, P. Blake, A. M. Hassan, and D. K. Roper, "Surface Plasmons of Finite Nanoring Arrays," Proc. of the IEEE International Symposium on Antennas and Propagation and USNC/URSI National Radio Science Meeting, pp. 1609-1612, 2011 [6] E. D. Palik, Handbook of Optical Constants of Solids. New York: Academic, 1985. [7] G.E. Jellison, Jr., S. P. Withrow, J.W. McCamy, J.D. Budai, D. Lubben, and M. J. Godbole "Optical functions of ion-implanted, laser-annealed heavily doped silicon” Physical Review B, vol. 52, no. 20, Nov. 15, 1995. [8] M. El-Shenawee, C. Rappaport, E. Miller and M. Silevitch, "Three-dimensional subsurface analysis of electromagnetic scattering from penetrable/PEC objects buried under rough surfaces: use of the steepest descent fast multipole method (SDFMM)," IEEE Trans. Geoscience Rem. Sensing, vol. 39, no. 6, pp. 1174-1182, 2001. ACKNOWLEDGEMENT This work is supported mainly through the NSF/ECCS award # 1006927 and in part through NSF Cyber infrastructure awards EP-0918970 and MRI # 072265. The authors would like to thank the staff of AHPCC at the University of Arkansas for their technical support. In addition, the authors would like to thank the IT staff at the University of Arkansas in Little Rock for facilitating the parallel computational resources for the MoM computer simulations. Nanotoroid Resonance at 817 nm Nanodisk Resonance at 815 nm -80 -60 -40 -20 0 200 700 1200 Wavelength (nm) Material Properties of Silver [4] Real Part of Permittivity Imaginary Part of Permittivity -30 -20 -10 0 10 20 30 40 50 200 400 600 800 1000 1200 Wavelength (nm) Material Properties of Silicon [4] Real Part of Permittivity |E| (V/m) |E| (V/m) Air Silicon 116.65 0.0038 0.8992 13.880 0.0583 6.9862 0.0039 3.7004 5.5487 1.8521 Linear Logarithmic Enhanced Transmitted Electric Field in Silicon with Nanotoroid on Top y-Polarized Gaussian beam excitation @ 610 nm wavelength Y-direction (nm) Y-direction (nm) 1100 1200 1300 1400 -500 -400 -300 -200 -100 0 0.1 0.2 0.3 0.4 1100 1200 1300 1400 -500 -400 -300 -200 -100 Z-direction (nm) Silicon alone Nanotoroid on Silicon 500 0 -500 -720 720 500 0 -500 -720 720 100 -100 0 -100 100 100 -100 0 -100 100 0° 30° Rin: 10.5 nm Rout: 42 nm 500 0 -500 -720 720 500 0 -500 -720 720 100 -100 0 -100 100 100 -100 0 -100 100 60° 90° 500 0 -500 -720 720 500 0 -500 -720 720 100 -100 0 -100 100 100 -100 0 -100 100 120° 150° 500 0 -500 -720 720 500 0 -500 -720 720 100 -100 0 -100 100 100 -100 0 -100 100 0° 30° Height: 11 nm Radius: 42 nm 500 0 -500 -720 720 500 0 -500 -720 720 100 -100 0 -100 100 100 -100 0 -100 100 60° 90° 500 0 -500 -720 720 500 0 -500 -720 720 100 -100 0 -100 100 100 -100 0 -100 100 120° 150° Rin:
Transcript of , Handbook of Optical Constants of Solids The authors would ......Optical Properties of Silicon and...
-
Absorption Enhancement in Silicon Solar Cells due to Surface Plasmons of Nanotoroids
Nathan Burford and Magda El-Shenawee
Electrical Engineering Department, University of Arkansas, Fayetteville, AR 72701, USA
2012 IEEE International Symposium on Antennas and Propagation and USNC-
URSI National Radio Science Meeting, July 8-14, 2012, Chicago IL
AbstractEnhanced absorption in silicon is
needed to improve the efficiency of
solar cells. Analysis of Silver
nanotoroids placed on top of a silicon
substrate demonstrating larger
absorption, will be presented. The
method of moments model and
Ansys® HFSS are employed to
compute the near electric fields
absorbed in silicon substrate. The
results show surface waves
represented by large electric fields
normal to the silicon surface and
decayed as it gets deeper in the
medium.
MotivationIntensive research efforts are
currently underway for using
plasmonic nanoparticles to increase
the light absorption in photovoltaic
(PV) devices [1]-[3]. The reported
results in the literature show the
improved absorption in silicon when
nearby nanoparticles were employed
[3]. Although numerous works were
published reporting the enhanced
localized near fields due to these
surface plasmon, work was focused
on the red and blue shift of these
plasmon in air. While the majority of
published work focused on the
assumption of infinite arrays of
nanoparticles, less work was reported
on characterizing the absorption in
silicon due to finite number of
nanoparticles [3]. Modeling is a
necessary tool to help understand the
interactions between the
nanoparticles and the silicon. The
goal of the current work is to use
computational electromagnetics to
investigate the effect of surface
plasmon of nanotoroids on the
absorption in solar cells.
Statement of the
ProblemIn this work, computational
methods are used to investigate the
plasmonic behavior of silver
nanotoroids located on a layer of
silicon. Two methods of analysis, the
method of moments (MoM) surface
integral equation and Ansys® HFSS
are used and compared. Effects of the
silicon layer on the shift of the
nanotoroid resonant frequency are
investigated. In addition, a
comparison is made between
nanotoroid and disk-shaped
nanoparticles tuned to the same
resonant frequency.
Background of NanoantennasAntennas made of noble metals such as gold or silver have
the ability to sustain surface plasmon polariton oscillations at the
boundary between the metal and a dielectric, when excited at
optical frequency. A combination of the antenna shape resonance
and the surface Plasmon resonances will contribute to the
antenna performance to exhibit strong enhanced local fields.
From Literature
200 400 600 800 1000 1200 1400
200
400
600
800
1000
1200
1400
x (nm)
y (
nm
)
700
720
740
760
700
720
740
760
10
20
30
x (nm)y (nm)
z(n
m)
y-d
irec
tio
n (
nm
)
x-direction (nm)
Top View
Silicon
X-Y direction:
140 nm x1440 nm &
2551 nm x2551nm
infinite Z-direction
Silver nanotoroid
Side View
Silver
Nanotoroid
3D Method of Moments (MoM) Surface
Integral Equation Model
3D MoM Model Equations
21,
1
0
1
,rjIηrM
, , kSr rjIrJ
n
N
n
NnS
kn
N
n
nS
kS
kSk
kS
k
tang.
22
221
121
tang.
tt
inc Mη
L
η
LJKKrH
Surface Integral Equation:
VIZ Linear system of equations:
Einc
Hinc
Kinc
mmmR , :
tang.2121tang.
tt
inc MKKJLLrE
rJ rM
Electric and magnetic surface current density:
Incident Gaussian Beam
x yk k
iizszincinc KKKK
WzikrKikK
L
Wr
2expexpexp,
2 2
2
2
,ˆsinsinˆcossin yiixiioi aakK yyxx akakK ˆˆ
z∈o
y
o
zy
x
o
zxv
k
ka
kk
kka
kk
kke
yx
x
y
v ak
ka
k
kh ˆˆ
yx
x
y
h ak
ka
k
ke ˆˆ
For vertical polarization: ) ( , vvinczinc horerkK
For horizontal polarization:
z∈o
y
o
zy
x
o
zxh
k
ka
kk
kka
kk
kkh
Electric Field Magnetic Field
) ( , hhinczinc horerkK
Electric field on silicon
surface @ 700 nm
wavelength with single
silver nanotoroid
y-polarization
500 600 700 800 900 1000
500
600
700
800
900
1000
x (nm)
y (
nm
)
500
1000
1500
2000
2500
z-component
y-d
irec
tion
(n
m)
x-direction (nm)
500 600 700 800 900 1000
Gaussian beam excitation
x-direction (nm)
500 600 700 800 900 1000
500
600
700
800
900
1000
x (nm)
y (
nm
)
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
y-component
500 600 700 800 900 1000
500
600
700
800
900
1000
x (nm)
y (
nm
)
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08x-component1000
900
800
700
600
500
500 600 700 800 900 1000
1000
900
800
700
600
500
y-d
irec
tion
(n
m)
x-direction (nm)
1000
900
800
700
600
500
2500
2000
1500
1000
500
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
Extinction Coefficient in Air
400 600 800 1000 12000
2
4
6
8x 10
-4
Wavelength (nm)
~~
Img.2ˆˆ
0 EECincsca nn
scaincext
Plane wave excitation
Rin= 10.5 nm
Rout= 42 nm
R = 48 nm
H= 12 nm
2xRout
2xRin
H
2xR
Transmitted Electric Field in Silicon
400 600 800 1000 12000
0.1
0.2
0.3
0.4
0.5
0.6
Silicon
Wavelength (nm)
Disk: R = 48 nm, H= 12 nm
Torus: Rin = 10.5 nm, Rout= 42 nm
Torus: Rin = 6 nm, Rout= 42 nm
Gaussian beam excitation
Fields
calculated
at toroid center
and z = -100
nm below the
Air/Silicon
Interface.
Silicon size:
2551 x 2551nm
Surface Plasmonic Enhancement of
Magnetic Current Density on SiliconM
400 600 800 1000 12001.35
1.4
1.45
1.5
1.55
1.6
Wavelength (nm)
A
mp
litu
de
squ
are
of
ma
gn
etic
curr
ent
den
sity
M
| o
ver
Sil
ico
n s
urf
ace
Gaussian beam excitation
patchessurfaceSilicon
Silicon
patchessurfaceSilicon Siliconon
lenanopartic
M
M
2
2
||
||
Infinite Array of Nanotoroids on Silicon
HFSS Simulation Parameters
Infinite Array of Silver Toroids
Center to center toroid spacing
of 1440 nm and 2 nm spacing
between toroids and silicon layer
Incident plane wave excitation
Wave propagation in -z direction
Electric field polarized in x
directionx
z
y
Incident Plane Wave
Nanotoroid
Silicon
Infinite Array of nanotoroids
on Silicon
Optical Properties of
Silicon and Silver
All nanoparticles in
this work are made of
Silver.
0.995
1
1.005
1.01
1.015
1.02
1.025
1.03
1.035
500 600 700 800 900 1000
En
ha
nce
men
t F
act
or
Wavelength (nm)
Enhancement Factor for Infinite
Array of Nanotoroids
Rin: 14.5 nm
Rin: 13.5 nm
Rin: 10.5 nm
Rout: 42 nmRout
Rin
z-d
irec
tio
n (
nm
)Electric Field Magnitude of Infinite
Array of Nanotoroids
-500
x-direction (nm)
|E| (V/m)
|E| (V/m)
Air
Silicon
116.09
0.0110
1.1312
11.460
0.1117
6.9862
0.0011
3.0827
4.9317
1.8501
Lin
ear
Lo
ga
rith
mic
500
0
-720 720
500
0
-500
-720 720
100
-100
0
-100 100
100
-100
0
-100 100
Resonance at 817 nm
Non-resonance at 895 nm
Rin: 10.5 nm, Rout: 42 nm
Comparison of Nanotoroids to Other GeometriesIn order to better understand the plasmonic behavior of toroid-shaped nanoparticles, comparisons with
other geometries are needed. One of the interesting features of a toroid is the cavity at the center. As such,
a disk geometry of the same outer radius is chosen for comparison, but with different height. Tuning of the
disk resonant frequency is dependent on the height to radius ratio. Thus, fixing the outer radius (Rout) to 42
nm allows the height to be tuned such that the disk resonant frequency matches the toroid resonance when
they are positioned on silicon (not in air).
Enhancement
Factor
0.995
1
1.005
1.01
1.015
1.02
1.025
1.03
750 800 850 900 950 1000
En
ha
nce
men
t F
act
or
Wavelength (nm)
Enhancement Factor
Comparison of Silver Nanotoroid
and Nanodisk Infinite Arrays
Rmin: 10.5 nm
Rout: 42 nm
Height: 11 nm
Radius: 42 nm
z-d
irec
tio
n (
nm
)
Electric Field Magnitude of Infinite
Array of Nanotoroids and Nanodisks
x-direction (nm)
Nanotoroid Resonance at 817 nm
|E| (V/m)
|E| (V/m)
Air
Silicon
116.09
0.0110
1.1312
11.460
0.1117
6.9862
0.0011
3.0827
4.9317
1.8501
Lin
ear
Lo
ga
rith
mic
Rin: 10.5 nm, Rout: 42 nm500
0
-500
-720 720
500
0
-500-720 720
100
-100
0
-100 100
100
-100
0
-100 100
Nanodisk Resonance at 815 nm Height: 10.5 nm,
Radius: 42 nm
z-d
irec
tio
n (
nm
)
x-direction (nm)
Phase Sweep Comparison of Infinite Array of Nanotoroids
and Nanodisks at Resonance
Conclusion
In this work, two different computational methods were used in the analysis of plasmonic nanotoroids
located atop a silicon substrate. In the HFSS analysis, a comparison of field enhancement was made
between infinite arrays of nanotoroids and nanodisks tuned to have identical resonant wavelengths on
silicon. The nanotoroid array shows slightly greater field enhancement over the nanodisk array. Future
work investigating arrays with optimized array spacing is believed to provide more insight into the
advantage of the nanotoroid structure. Since toroid structures have a smaller filling factor than disks, it is
hypothesized that optimized array spacing of nanotoroids will allow more structures to be placed on the
silicon surface than solid nanostructures, thus providing even greater advantages in field enhancement for
the nanotoroids.
REFERENCES[1] S. Mokkapati, F. J. Beck, R. de Waele, A. Polman, and K. R. Catchpole, “Resonant nano-antennas for light trapping in plasmonic solar cells,” J. Phys. D: Appl. Phys.
44, 185101, 2011
[2] F. Moreno, F. Gonzales, and J. M. Saiz, “Plasmon spectroscopy of metallic nanoparticles above flat dielectric substrates,” Optics Letters, Vol. 31, No. 12, pp. 1902
1904, June 15, 2006.
[3] D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in
nearby metallic nanoparticles,” Applied Physics Letters 89, 093103, 2006.
[4] M. El-Shenawee, “Polarization dependence of plasmonic nanotoroid,” IEEE Antennas Wireless Propagation Letters, vol. 9, pp. 463-466, 2010.
[5] M. El-Shenawee, P. Blake, A. M. Hassan, and D. K. Roper, "Surface Plasmons of Finite Nanoring Arrays," Proc. of the IEEE International Symposium on Antennas and
Propagation and USNC/URSI National Radio Science Meeting, pp. 1609-1612, 2011
[6] E. D. Palik, Handbook of Optical Constants of Solids. New York: Academic, 1985.
[7] G.E. Jellison, Jr., S. P. Withrow, J.W. McCamy, J.D. Budai, D. Lubben, and M. J. Godbole "Optical functions of ion-implanted, laser-annealed heavily doped silicon”
Physical Review B, vol. 52, no. 20, Nov. 15, 1995.
[8] M. El-Shenawee, C. Rappaport, E. Miller and M. Silevitch, "Three-dimensional subsurface analysis of electromagnetic scattering from penetrable/PEC objects buried
under rough surfaces: use of the steepest descent fast multipole method (SDFMM)," IEEE Trans. Geoscience Rem. Sensing, vol. 39, no. 6, pp. 1174-1182, 2001.
ACKNOWLEDGEMENT
This work is supported mainly through the NSF/ECCS award # 1006927 and in
part through NSF Cyber infrastructure awards EP-0918970 and MRI # 072265.
The authors would like to thank the staff of AHPCC at the University of Arkansas
for their technical support.
In addition, the authors would like to thank the IT staff at the University of
Arkansas in Little Rock for facilitating the parallel computational resources for the
MoM computer simulations.
Nanotoroid Resonance at 817 nm Nanodisk Resonance at 815 nm
-80
-60
-40
-20
0
200 700 1200Wavelength (nm)
Material Properties of Silver [4]
Real Part of
Permittivity
Imaginary Part of
Permittivity
-30
-20
-10
0
10
20
30
40
50
200 400 600 800 1000 1200
Wavelength (nm)
Material Properties of Silicon [4]
Real Part of
Permittivity
|E| (V/m)
|E| (V/m)
Air
Silicon
116.65
0.0038
0.8992
13.880
0.0583
6.9862
0.0039
3.7004
5.5487
1.8521
Lin
ear
Log
ari
thm
ic
Enhanced Transmitted Electric Field in
Silicon with Nanotoroid on Topy-Polarized Gaussian beam excitation
@ 610 nm wavelength
Y-direction (nm) Y-direction (nm)1100 1200 1300 1400
-500
-400
-300
-200
-100
0
0.1
0.2
0.3
0.4
1100 1200 1300 1400-500
-400
-300
-200
-100
Z-d
irec
tio
n (
nm
)
Silicon alone Nanotoroid on Silicon
500
0
-500
-720 720
500
0
-500
-720 720
100
-100
0
-100 100
100
-100
0
-100 100
0°
30°
Rin: 10.5 nm Rout: 42 nm
500
0
-500
-720 720
500
0
-500
-720 720
100
-100
0
-100 100
100
-100
0
-100 100
60°
90°
500
0
-500
-720 720
500
0
-500
-720 720
100
-100
0
-100 100
100
-100
0
-100 100
120°
150°
500
0
-500
-720 720
500
0
-500
-720 720
100
-100
0
-100 100
100
-100
0
-100 100
0°
30°
Height: 11 nm Radius: 42 nm
500
0
-500
-720 720
500
0
-500
-720 720
100
-100
0
-100 100
100
-100
0
-100 100
60°
90°
500
0
-500
-720 720
500
0
-500
-720 720
100
-100
0
-100 100
100
-100
0
-100 100
120°
150°
Rin:
