near-field radiative transferhelper.ipam.ucla.edu/publications/msews4/msews4_11524.pdf · 2013. 11....
TRANSCRIPT
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NEAR-FIELD RADIATIVE TRANSFER
For Energy Harvesting.... & Diagnostic+Manufacturing
MSEWS4: Energy Conservation and Waste Heat Recovery November 21, 2013
IPAM, UCLA, LA, CA, USA
M. Pınar Mengüç
Director, CEEE / EÇEM Center for Energy, Environment and Economy
& Head, Mechanical Engineering Ozyegin University
Istanbul, Turkey
Engineering Alumni Association Professor, Emeritus
Mechanical Engineering Department University of Kentucky
Lexington, KY, USA
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Workshop on NPNSNFC, Bremen, Germany, 11-12 March 2010. Solar-TR, April 29-30, ODTU/METU, Ankara, Turkey
OUTLINE OF PRESENTATION
The Big Picture
Overview of Far and Near-Field Radiative Transfer
Length Scales for Nano-regimes
Near Field Radiation
Near Field Radiation for Thermophotovoltaics (TPV) Applications
Analytical Analysis
Computational Analysis
Conclusions
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CEEE/EÇEM
Workshop on NPNSNFC, Bremen, Germany, 11-12 March 2010. Solar-TR, April 29-30, ODTU/METU, Ankara, Turkey
We are here…
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Nano-Scale
Energy
Fundamentals Radiative
Transfer and
Thermal
Sciences
Energy
Applications
and
Efficiency in
Buildings
Multi-Disciplinary
Industrial
Applications
EEE Solutions
for Districts
and Cities
Quantitative
Sustainability for
Businesses Nature &
Climate
Change
CEEE/EÇEM FOCI
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CLIMATE CHANGE? (IEA 2013)
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CLIMATE CHANGE? (IEA 2013)
2 Degrees by 2050?
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EVERY TON OF CO2 RELEASED TO THE ATMOSPHERE ...CORRESPONDS TO WASTED ENERGY ENDING UP SOMEWHERE! MINIMIZATION OF ENERGY USE HELPS DECREASING EMISSIONS OF CO2.
ENERGY LOSS
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ONE-YEAR CO2 EMISSION TRENDS CHANGE (IEA 2013)
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ENERGY RELATED CO2 EMISSIONS (IEA 2013)
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BIG PICTURE: WORLD ENERGY USE IS ABOUT 15 TW. CO2 EMISSIONS ARE RELATED TO FOSSIL ENERGY USE. ONLY A FRACTION OF ENERGY GENERATED IS FROM RENEWABLES.
ENERGY MODALITIES
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WORLD RENEWABLE ENERGY USE (IEA 2013)
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Quantitative
Sustainability for
Businesses Nature &
Climate
Change
America’s Energy Future, 2012, National Acedemy of Sciences, USA
Energy Production Modalities
ENERGY MODALITIES
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Quantitative
Sustainability for
Businesses Nature &
Climate
Change
America’s Energy Future, 2012, National Acedemy of Sciences, USA
REJECTED ENERGY
ENERGY MODALITIES
Wasted Energy should be used somehow!
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ENERGY MODALITIES
• Energy Generation
• Energy Conservation/Efficiency
• Energy Harvesting
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Energy Harvesting is to recover wasted energy from all sources to be used as auxiliarry energy source, for electricty generation or for storage. Carnot Efficiency:
ENERGY HARVESTING
HOT
COOL
Carnot Engine
Q-H
Q-L
Work
What to do with Q-L?
Aux Work
Q-L
h=W/Q
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CONVERGENCE
Solve Energy Challenge via Advanced Engineering on Fundamental Physics
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INSPIRATION: REACHING NANO-WORLD ... From 2005 ROCO!
2013 1999
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Size of WATER VAPOR
1 m
1 mm
1 mm
1 nm
Humans
Car
Butterfly
1 km
STEAM ENGINE
Laptop
Wavelength of Visible Light
Micromachines
Width of DNA
Smallest feature in microelectronic chips
Proteins
Biological cell
Nucleus of a cell
Aircraft Carrier
Size of a Microprocessor
Nanostructures & Quantum Devices Decreasing
Length scale
Resolving power of the eye ~ 0.2 mm
Human hair ~ 60-120 mm wide
PERSPECTIVE ON LENGTH SCALES
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Thermoelectric Devices (conduction/phonon based)
HOW TO RECOVER WASTE ENERGY?
Thermophotovoltaic Devices (Radiation/near-field radiation transfer based)
Nondimensional figure of merit:
ZT = σS2T/κ σ : the electrical conductivity S : the Seebeck coefficient T : the temperature κ : the thermal conductivity
Optical heat engine! (Figs from web sources!)
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POWER GENERATION EFFICIENCY
Zebarjadi, et al. Energy Environ. Sci., 2012, 5, 5147-5162.
h=W/Q
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THERMOELECTRIC DEVICES
Thermoelectric power generators are solid state devices which can directly convert heat into electricity. The device efficiency depends on the choice of material, configuration, and contacts. It requires new materials, dopants, and nanostructured geometries. MATERIAL PROBLEM!
Chen, et al., Progress in Natural Science: Materials International 2012;22(6):535–549
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TPV CELL
Schematic of the thermophotovoltaic cell proposed by Fan group. The idealized absorption spectrum (solar spectrum in yellow) and emission spectrum (the dotted line: PV cell bandgap energy level) are shown. http://gcep.stanford.edu/research/factsheets/ultrahigh_thermosolar.html
Schematic of the industrial thermophotovoltaic cell.
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Workshop on NPNSNFC, Bremen, Germany, 11-12 March 2010. Solar-TR, April 29-30, ODTU/METU, Ankara, Turkey
THERMOPHOTOVOLTAIC DEVICES
Potential Applications of TPVs:
• Power sources for Micro-electromechanical devices (MEMS).
• Energy sources in transportation.
• Co-generation of electricity and heat.
• Remote electricity generators.
• Aerospace and military power suppliers.
• And..
Waste-Energy harvesting purposes.
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Workshop on NPNSNFC, Bremen, Germany, 11-12 March 2010. Solar-TR, April 29-30, ODTU/METU, Ankara, Turkey
THERMOPHOTOVOLTAIC DEVICES
•How can we improve the efficiency of TPV Devices? • Materials? • Design and Geometry?
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TPV? Nano-TPV?
radiator
vacuum
T0 = 2000 K
Tcell(z)
thermal management system
tcell
dc
OBJECTIVE: RADIATE SELECTIVELY TO THE CELL ...
Nano Gaps!
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Workshop on NPNSNFC, Bremen, Germany, 11-12 March 2010. Solar-TR, April 29-30, ODTU/METU, Ankara, Turkey
THERMOPHOTOVOLTAIC DEVICES
Thermophotovoltaics (TPVs): energy-conversion systems generating an
electric current from the thermal photons radiated by a hot body.
TPVs
Far field TPVs
(Conventional TPVs) Near field TPVs
(Nano TPVs)
It is bounded by
Schockley-Queisser
limit.
Theory has shown
enhancement of power
transfer up to three orders of
magnitude.
DOI: 10.1038/srep01383
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THERMOPHOTOVOLTAIC DEVICES
Near-field PV Ability to control plasmon damping √ High power density√ Ability to operate in the intermediate (600−1200K) emitter temperature range √ Emitter plasmon frequencies optimally matches to the bandgap √
Far-field PV Ability to control plasmon damping X High power density X ability to operate in the intermediate (600−1200K) emitter temperature range X Emitter plasmon frequencies optimally matchesto the bandgap X
Ilic, Ognjen et al. “Overcoming the Black Body Limit in Plasmonic and Graphene Near-field Thermophotovoltaic Systems.” Optics Express 20.S3 (2012): A366. © 2012 OSA
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FAR AND NEAR FIELD RADIATIVE TRANSFER
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Near- Field Publications Statistics
Nano Thermophotovoltaic Published items in each year
Nano Thermophotovoltaic Citation in each year
Near-field thermal radiation Published items in each year
Near-field thermal radiation
Citation in each year
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Near Field Radiation Transfer @ Ozyegin Univ, Istanbul
Nano-Scale RADIATIVE TRANSFER
MEASUREMENTS
M.Pınar Mengüç/OzU Hakan Ertürk/BU
David Kurt Webb/OzU
Nano-Scale DEVICE
FABRICATION
M.Pınar Mengüç/OZU Tuba OKUTUCU/METU
Zafer ARTVİN /METU
NEAR-FIELD RADIATIVE TRANSFER
DEVICES and APPLICATIONS
M.Pınar MENGÜÇ /OzU
FLUCTUATIONAL ELECTRODYNAMICS
Mathieu Francoeur/UTAH M.Pınar Mengüç/OzU
Azedeh Didari/OzU
NEAR FIELD RADIATON
TRANSFER CALCULATIONS
COMSOL Multiphysics
Tuba Okutucu/METU
Hakan Ertürk/BU
Gazi Huda/UK Farhad Kazemi Khosroshahi/BU
M.Pınar Mengüç/OzU
Azadeh Didari/OzU Vincent Loke
Kürşat Şendur/SU Ali Koşar/SU M.Pınar Mengüç/OzU
S. Eren Yalcın/OzU
Erdem Ogut/SU
PLASMONIC EFFECTS
FOR NANO-SCALE COOLING
Todd Hastings/UK
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PLANCK’S BLACKBODY RADIATION: BROADBAND
0
0,2
0,4
0,6
0,8
1
0 2 4 6 8 10 12 14 16 18 20 22
En
erg
y/P
ea
k E
ne
rgy
Wavelength (mm)
5780 K
1600 K
300 K
(Francoeur, Mengüç)
T
“Throughout the
following discussion
it will be assumed
that the linear
dimensions of all
parts of space
considered, […], are
large compared with
the wavelengths of
the rays
considered.”
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RADIATIVE TRANSFER
Infrared Energy to be harvested
PV range
+From Andy Keller
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Workshop on NPNSNFC, Bremen, Germany, 11-12 March 2010. Solar-TR, April 29-30, ODTU/METU, Ankara, Turkey
Maxwells’s Equations fully describe the propagation of electromagnetic waves in all types of media. Since the late 1800’s, emission of radiation and radiation transfer were sufficiently explained bt Kirchhoff’s and Planck’s Laws at the far-field. Far-field radiation transfer is all about the microscopic space-time fluctuation of charge carriers. Temperature of the emitting body determines the spectral nature of thermal radiation.
RADIATION TRANSFER: via electromagnetic waves
1T
2T
propagating waves
photons!
2T
RADIATIVE TRANSFER
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RADIATIVE TRANSFER
Energy transfer by electromagnetic waves! Follows Planck’s Blackbody Law Long range ... No medium is required Scalable.... if the distance between objects more than wavelength of radiation
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RADIATIVE TRANSFER
• What happens if the objects are closer than the wavelength?
• What if the objects have structures on them?
• What if there are new materials to be used?
• Can we model and measure them?
• Can we come out with a device?
NANO-GAP THERMOHOTOVOLTAIC (n-TPV) CELL
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RADIATIVE TRANSFER
0
0,2
0,4
0,6
0,8
1
0 2 4 6 8 10
No
rmal
ized
En
erg
y
λ (μm)
5780 K
1600 K
About 400 K
About 3000 K Si Band Gap: 1.12 eV or 1.1 μm InSb Band Gap: 0.17 eV or 7.29 μm
InSb Indium Antimonide
PHOTONS RESULT i. at energy band voltage created ii. above energy band voltage + heat iii. below energy band heat
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Workshop on NPNSNFC, Bremen, Germany, 11-12 March 2010. Solar-TR, April 29-30, ODTU/METU, Ankara, Turkey
EVANESCENT WAVES: FRUSTRATED TIR
Evanescent waves on the surfaces (e.g., due to total internal reflection). Thermal near-fields and near-field spectral energy density are associated with the intrinsic electronic and vibrational excitations or extrinsic geometric resonances.
5.11 n
12 n
glass
air
cr 1
r
z
1 r
total internal reflection (TIR)
1n
air r
dipole oscillations
- + - - + -
+
+ [Jackson, 1999; Hecht, 2002]
z
+
(Francoeur, Mengüç)
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NEAR-FIELD REGIME OF THERMAL RADIATION
(Francoeur, Mengüç)
What happens if a structure interacts with an evanescent wave?
Two regimes of radiative transfer:
• Far-field regime: energy transfer via only propagating electromagnetic waves
• Near-field regime: energy transfer via both evanescent and propagating EM waves
1 1
2
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How to calculate and measure radiative energy transfer between two objects in close proximity to each other?
NEAR-FIELD RADIATION
1T2T
Wiend
+-
1T
(Francoeur, Mengüç)
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Workshop on NPNSNFC, Bremen, Germany, 11-12 March 2010. Solar-TR, April 29-30, ODTU/METU, Ankara, Turkey
Near field TPVs (Nano TPVs)
Near field TPVs (Nano TPVs) : By approaching a photovoltaic (PV) cell in
proximity of a thermal emitter, thermal energy can be extracted by photon tunneling
toward the cell…these devices are called Near-filed thermophotovoltaics (NTPVS).
Modeling NTPVS :
Analytical Techniques
Computational Techniques
Experimental Techniques
Lorenz-
Mie
Theory Finite Element
Method
Finite Difference Time
Domain Method (FDTD)
Discontinues Garlekin
Time Domain
Method(DGTD)
Discrete Dipole
Approximation
(DDA)
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NEAR-FIELD RADIATION ANALYTICAL ANALYSIS
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Workshop on NPNSNFC, Bremen, Germany, 11-12 March 2010. Solar-TR, April 29-30, ODTU/METU, Ankara, Turkey
NEAR-FIELD RADIATION TRANSFER
Maxwell’s equations are valid to describe the propagation of electromagnetic waves at all scales (until the definitions of dielectric constant and magnetic permeability fails...down to a few nanometers). However, thermal emission is not accounted for in the formulation of MEs. Temperature of the medium can be entered to the MEs as a source term using the fluctuation-dissipation theorem (FDT). FDT incorporates the statistical properties of the current-density distribution.
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Maxwell equations combined with fluctuational electrodynamics [Rytov, 1959; Francoeur and Mengüç, JQSRT, 2008; Francoeur et al., JQSRT, 2009]
)H(r,)B(r,)E(r, 0 m ii
),( rE)H(r, i
eρ ))E(r,)D(r, ˆ(
0))H(r,()B(r, 0 m
),( rJr
source of thermal radiation (stochastic current density)
Temperature of the medium correlated with Jr via the fluctuation-dissipation theorem
)(),()(
),(),( *rrrr
TJJ rvrr
isotropic media
locality of the dielectric constant mean energy of a Planck oscillator in thermal equilibrium
NEAR-FIELD REGIME OF THERMAL RADIATION
(Francoeur, Mengüç)
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0))H(r,()B(r, 0 m
NEAR-FIELD REGIME OF THERMAL RADIATION
Radiative heat flux (time-average Poynting vector):
S(r,w) = 2Re iwmv d ¢VV
ò d ¢¢VV
ò
x(GyaE Gzb
H* -GzaEGyb
H*)
+y(GzaEGxb
H* -GxaE Gzb
H*)
+z(GxaE Gyb
H* -GyaE Gxb
H*)
é
ë
êêêê
ù
û
úúúú
Ja
r( ¢r ,w)Jb
r*( ¢¢r ,w)
ì
íïï
îïï
ü
ýïï
þïï
Fluctuation-dissipation theorem:
Ja
r ( ¢r ,w)Jb
r*( ¢¢r ,w) =wevp
Im er (w){ }Q(w,T )dabd( ¢r - ¢¢r )
absorption/dissipation of thermal
radiation
locality of the dielectric
function
isotropic
media
General expression for the radiative heat flux:
S(r,w) =2kv
2Q(w,T )
pRe i ¢¢er (w) d ¢V
V
ò
x(GyaE Gzb
H* -GzaEGyb
H*)
+y(GzaEGxb
H* -GxaE Gzb
H*)
+z(GxaE Gyb
H* -GyaE Gxb
H*)
é
ë
êêêê
ù
û
úúúú
ì
íïï
îïï
ü
ýïï
þïï
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Near-field radiative heat flux between two thin films
TMTEdik
k
prop
abscz
v
eRR
TRTRdkk
Tq
,22
31
2
3
2
3
2
1
2
1
0
2
1,
21
11
4
),(
rr
TMTEdik
k
dkevan
abscz
v
cz
eRR
RRedkk
Tq
,22
31
312
2
1,
2
2
1
)Im()Im(),(
rr
r
z
SiC
vacuum
vacuum
t1
0
1
2
r1()
r2 = 1
r0 = 1
SiC3r3()
T3
t3
vacuum4 r4 = 1
z1
z2
z3
z4
T1
dc
Francoeur, Mengüç, Vaillon, J. Phys. D: Appl. Phys., 2010
NEAR-FIELD THERMAL RADIATION EMISSION
evan
abs
prop
absabs qqq ,,,
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0))H(r,()B(r, 0 m
NEAR-FIELD REGIME OF THERMAL RADIATION
Total net flux between medium 1 and control volume Dzj in medium 3:
qDz j
abs =w 2
2p 2cv2
dw Q(w,T1)-Q(w,Tj )éë ùûw=0
¥
ò
´Re i ¢¢er1(w)bdb
¢¢g1b=0
¥
ò
g13ra
E (b, z j,w)g13qa
H* (b, z j,w)
-g13qa
E (b, z j,w)g13ra
H* (b, z j,w)
æ
è
çç
ö
ø
÷÷
-g13ra
E (b, z j+1,w)g13qa
H* (b, z j+1,w)
-g13qa
E (b, z j+1,w)g13ra
H* (b, z j+1,w)
æ
è
çç
ö
ø
÷÷
é
ë
êêêêêêêê
ù
û
úúúúúúúú
ì
í
ïïïï
î
ïïïï
ü
ý
ïïïï
þ
ïïïï
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NEAR-FIELD THERMAL RADIATION BETWEEN TWO-FILMS
z
r
vacuum
T1 = 300 K T3 = 0 K
d
SiCSiC
[Mengüç and Francoeur, Thermal Radiation Heat Transfer, Chapter 16, 2010]
about 96-97% of the flux concentrated around res
res = 1.786 × 1014 rad/s
= 10.55 mm
T > 0 K
SiC
vacuum r
+
-
+
+
+
+
-
- -
kx
transverse optical (TO) phonon
1013
1014
1015
10-14
10-12
10-10
10-8
10-6
far-fieldblackbodies
d = 1 mm
d = 100 nm
q
,13 [
Wm
-2(r
ad/s
)-1]
[rad/s]
d = 10 nm
T1 = 300 K
T3 = 0 K
res
surface phonon-polaritons (SPhPs) supported by polar crystals (SiC, cBN,…)
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NEAR-FIELD THERMAL RADIATION BETWEEN TWO-FILMS
r
z
SiC
vacuum
vacuum
t1
0
1
2
r1()
r2 = 1
r0 = 1
SiC3r3()
T3
t3
vacuum4 r4 = 1
z1
z2
z3
z4
T1
dc
[Francoeur,Mengüc, Vaillon, J. Phys. D: Appl. Phys., 2010.
1.50x1014
1.60x1014
1.70x1014
1.80x1014
1.90x1014
10-17
10-15
10-13
10-11
10-9
10-7
10-5
LO
res
TO
dc = 500 nm
dc = 100 nm
dc = 50 nm
dc = 10 nm
q
,ab
stot [
Wm
-2(r
ad/s
)-1]
[rad/s]
dc = 1 nm
t1 = 10 nm
t3 = 10 nm
1.50x1014
1.60x1014
1.70x1014
1.80x1014
1.90x1014
10-14
10-13
10-12
10-11
10-10
10-9
t3 = 500 nm
t3 = 100 nm
t3 = 50 nm
t3 = 10 nm
LO
res
TO
q
,ab
stot
[Wm
-2(r
ad/s
)-1]
[rad/s]
dc = 100 nm
t1 = 10 nm
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Francoeur , Mengüç, Vaillon, Physical Review B., Vol. 84, Issue: 7, Aug. 2011.
COEXISTENCE OF MULTIPLE NEAR-FIELD RADIATION REGIMES
TMTEdik
k
dk
k
dik
r
czv
cz
v
cz eRR
RRedkk
eRR
TRTR
dkk
T
Tdh
,2
2
31
31)Im(2
0
22
31
2
3
2
3
2
1
2
1
0
2
2
2
2 1
)Im()Im(
14
11
),(1
rr
rr
r
z
film 1
vacuum
vacuum0
1
2
r1()
r2 = 1
r0 = 1
film 33r3()
t3 << w
vacuum4 r4 = 1
z1
z2
z3
z4
T
dc << w
T + T
t1 << w
RADIATIVE HEAT TRANSFER COEFFICIENT: kr is the wavevector parallel to the surfaces of the layers, kzj is the z-component of the wavevector in medium j, and kv is the magnitude of the wavevector in vacuum. T and R are the transmission and reflection coefficients of layer j , respectively, in polarization state .
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Francoeur , Mengüç, Vaillon, Physical Review B., Vol. 84, Issue: 7, Aug. 2011.
COEXISTENCE OF MULTIPLE NEAR-FIELD RADIATION REGIMES
2
3
2
011
2
01
22
0131
231
2
3
2
01
01
1
2
01
01
0 0
2
22
)]21()(1)][21()(1[
)(41
14
)21()(1Im
)21()(1Im
),(1
DrDr
erDDDD
Dr
r
Dr
rde
T
Td
dh
TMTM
TM
TM
TM
TM
TM
c
r
hh
hh
hhhh
h
h
2
3
2
011
2
01
22
0131
231
2
3
2
01
01
1
2
01
01
0 0
2
22
)]21()(1)][21()(1[
)(41
14
)21()(1Im
)21()(1Im
),(1
DrDr
erDDDD
Dr
r
Dr
rde
T
Td
dh
TMTM
TM
TM
TM
TM
TM
c
r
hh
hh
hhhh
h
h
22
31
31
0 0
2
22
1
)Im()Im(),(1
h
h hh
eRR
RRde
T
Td
dh
TMTM
TMTM
c
r
Approximate the Radiative Heat Transfer Coefficient
Then, consider the asymptotic cases: e.g., For D much smaller than 1 (t<<d)
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NEAR-FIELD THERMAL RADIATION EMISSION FROM A SINGLE FILM
z
r
vacuum
T1 = T T3 = T + T
d
SiCSiC
1 10 10010
0
101
102
103
104
105
106
far-field regime
blackbodies
Rad
iati
ve
hea
t tr
ansf
er
coef
fici
ent
hr [
Wm
-2K
-1]
Vacuum gap d [nm]
T = 300 K
near-field regime
(d -2 behavior)
d = 10 nm:
Near-field radiative transfer coefficient ~ 500 times
blackbodies
T
dq
hT
r
0
13,
0lim
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1 10 100
100
101
102
103
104
105
106
t1 = 1 nm
t1 = 10 nm
t1 = 50 nm
bulk
Rad
iati
ve h
eat
tran
sfe
r
co
eff
icie
nt
hr [
Wm
-2K
-1]
Vacuum gap d [nm]
T = 300 K
1 10 100
101
102
103
104
105
106
t1 = 10 nm
d -3
Vacuum gap d [nm]
Rad
iati
ve
hea
t tr
ansf
er
coef
fici
ent
hr [
Wm
-2K
-1]
d -2
transition region
Coexistence of two near-field thermal radiation regimes due to surface phonon-polariton coupling within the emitter
COEXISTENCE OF MULTIPLE NEAR-FIELD RADIATION REGIMES
Francoeur , Mengüç, Vaillon, Physical Review B., Vol. 84, Issue: 7, Aug. 2011.
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Francoeur , Mengüç, Vaillon, Physical Review B., Vol. 84, Issue: 7, Aug. 2011.
COEXISTENCE OF MULTIPLE NEAR-FIELD RADIATION REGIMES
r
z
film 1
vacuum
vacuum0
1
2
r1()
r2 = 1
r0 = 1
film 33r3()
t3 << w
vacuum4 r4 = 1
z1
z2
z3
z4
T
dc << w
T + T
t1 << w
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NEAR-FIELD RADIATION COMPUTATIONAL ANALYSIS
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FDTD (Finite Difference Time Domain Method) is a computational method
used to analyse electromagnetic wave propagation problems. It gives
solution to Maxwell’s equations. It is based on a computational grid.
• Two Silicon Carbide films, both supporting SPhP, each 10 nm thick, the
lower film has (T> 0 K) while the upper one (T=0 K ). They are separated
by vacuum gap of 100 nm thickness.
• Local Density of Electromagnetic States
(LDOS) is calculated. This allows
us to calculate thermal radiation
emission in the gap between
the SiC layers.
FDTD Analysis of Near Field Thermal Radiation Emission
Azadeh Didari, Mengüç, Ozyegin Univ, 2012
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Workshop on NPNSNFC, Bremen, Germany, 11-12 March 2010. Solar-TR, April 29-30, ODTU/METU, Ankara, Turkey
Computational Techniques : Finite Difference Time Domain Method (FDTD)
Finite Difference Time Domain Technique is a time domain technique
which has been chosen as our computational method of choice:
FDTD is a time domain based numerical method, hence it has the capability
to give us the solution of a very wide band frequency range within a
single run.
FDTD can model various arbitrary geometries having different shapes and
sizes whose analytical studies may not be available due to complexity of the
problem is possible
FDTD can incorporate the effects of reflection and radiation which are
commonly neglected by other methods
FDTD can model wave propagation in complex media, such as time-
varying, anisotropic, lossy, dispersive and non-linear media is possible.
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The 1D-FDTD Equations
We start by Maxwell equations:
D, H, and E are vectors in three dimensions. We will start with 1D case using Dx and Hy and denoting the plane wave in z direction.
In order to apply the PML ABC we use the following equations:
Where σ and σ* are respectively the electric conductivity and the magnetic conductivity of the PML medium with 𝜎/𝜀0=σ*/µ0 In order to produce a smooth transition from air cells to the PML cells, the conductivity is gradually increased from zero at the vacuum-layer interface to a maximum value of σ* for each layer.σ(ρ)=σm (ρ/δ)2
FDTD Analysis of Near Field Thermal Radiation Emission
Azadeh Didari, Mengüç, Ozyegin Univ, 2012
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Workshop on NPNSNFC, Bremen, Germany, 11-12 March 2010. Solar-TR, April 29-30, ODTU/METU, Ankara, Turkey
How does FDTD work?
Using Yee cells as discrete units, Maxwell's equations are converted to a set of central
difference equations which are to be solved in each Yee unit cell according to the following
flowchart:
Yee Cell
Computational Techniques : Finite Difference Time Domain Method (FDTD)
Didari, Mengüç, 2013
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FDTD Requirements :
• Boundary Conditions:
Mur’s first order ABC
Mei-Fang
superabsorption
Numerical Dispersion:
Cell size
Modelling of Near-field thermal radiation within nano-gaps via FDTD
λmin /10
Conventional Perfectly
Matched Layer(CPML)
Detailed modeling studies,
and accurate calculation of
near-field emission within
thin films are necessary in
order to calculate the local
density of electromagnetic
states (LDOS) which is a
key factor to obtain the
radiation heat flux in near
field thermal radiation
related problems.
Didari, Mengüç, 2013
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The fluctuation-dissipation theorem is a general result of statistical thermodynamics that quantifies the
relation between the fluctuations in a system at thermal equilibrium and the response of the system to applied
perturbations
TM evanescent component of monochromatic Local density of Electromagnetic state (LDOS)
FDT: Fluctuation dissipation theorem
2 2
2 2
LOr
TO
i
i
0, , ,
rr rJ J T
r r r r
Drude-Lorentz Model
2 2 2 2 2 2
2
2
0
r E E E E H H
v XX XZ ZX ZZ YX YZ
V V
k dV G G G G dV G Gc
r
r
Modelling of Near-field thermal radiation within nano-gaps via FDTD… Fluctuation Dissipation Theorem (FDTD)…
FDT Maxwell’s Equations Required Info. to study
near-field thermal
radiation & LDOS
Didari, Mengüç, 2013
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Medium specifications :
•Two Silicon Carbide films ,both supporting SPhP, each 10 nm thick, the lower film
has (T> 0 K) while the upper one (T=0 K ). They are initially separated by vacuum
gap of 100 nm thickness.
Modelling of Near-field thermal radiation within nano-gaps via FDTD…
Realistic model Considered model Future model
Didari, Mengüç, 2013
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Modelling of Near-field thermal radiation within via FDTD…
Bulk metamaterial
Single film of metamaterial
Thin films of metamaterial
Didari, Mengüç, 2013
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Methodology
A comparison has been made between Analytical results found
previously by Francoeur et al., and the FDTD calculations
developed. The results showed promising agreement between the
analytical and computational methods.
Modelling of Near-field thermal radiation within nano-gaps via FDTD…
ΔT small enough
AMR techniques
Intersections!
r Inverse Fourier
Transform
An equivalent recursive expression in the time domain:
2 2 2 2
0 / / 4LO TO TOA 2 2 / 4TO / 2
1 2 2 12 cos sinn t n t n t nS e t S e S Ae t E D D D D D
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Peak around :
Modelling of Near-field thermal radiation within nano-gaps via FDTD…
1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9
x 1014
100
102
104
106
108
1010
[rad/s]
r( D
) [m
-3 (
rad
/s)-1
]
Analytical LDOS at D=50(nm) , dc=100(nm) , t
1=100(nm) , t
3=10(nm)
FDTD Analysis of LDOS
Didari, Mengüç, 2013
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Modelling of Near-field thermal radiation within nano-gaps via FDTD…
1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9
x 1014
100
102
104
106
108
[rad/s]
r( D
) [m
-3 (
rad
/s)-1
]
FDTD Analy sis of LDOS at D=250(nm) , d
c=500(nm) , t
1=500(nm) , t
3=500(nm)
FDTD Analy sis of LDOS at D=50(nm) , dc=100(nm) , t
1=100(nm) , t
3=100(nm)
FDTD Analy sis of LDOS at D=500(nm) , dc=1000(nm) , t
1=1000(nm) , t
3=1000(nm)
FDTD Analy sis of LDOS at D=50(nm) , dc=100(nm) , t
1=100(nm) , t
3=10(nm)
Study of the effect of the gap size on LDOS profile…
An increase of three orders of
magnitude is observed when the
gap size is below 500 nm
Didari, Mengüç, 2013
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What about arbitrary Geometries?
When it comes it arbitrary
geometries e.g. A tip and a
plate… Use
DDA-SI
Test FDTD for the same geometries and compare the
results with DDA-SI results.
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Workshop on NPNSNFC, Bremen, Germany, 11-12 March 2010. Solar-TR, April 29-30, ODTU/METU, Ankara, Turkey
RADIATION ABSORPTION AND SCATTERING
BETWEEN CLOSE PARTICLES AND SURFACES
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Individual Absorptions
Integrated Poynting Vector
Geometries
Two Identical Spheres
Two Spheres with different sizes
Conical tip and a nanosphere
k
E, B
TWO PARTICLE INTERACTION
Donmezer, Okutucu, Mengüç
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DDA-SI: TO ACCOUNT FOR SURFACE EFFECTS RIGOROUSLY
Discrete Dipole Approximation – Surface Interaction
Based on DDSURF, unreleased code by Schmehl et al.
Prototype MATLAB implementation can be ported to C and Fortran if speed is required
MATLAB has a very efficient numerical linear system solver (gmres)
R. Schmehl, B. M. Nebeker and E. D. Hirleman, “Discrete-dipole approximation for scattering by features on surfaces by means of a two-dimensional fast Fourier transform technique”, J. Opt. Soc. Am. A. 14(11), 3026-3036 (1997).
V. L. Y. Loke and M. P. Mengüç. “Surface waves and afm probe-particle near-field coupling: Discrete dipole approximation with surface interaction”. to appear in J. Opt. Soc. Am. A, 2010.
Loke, Mengüç, 2010
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DDA-SI SYSTEM OF EQUATIONS
SI
,
1
N
jk k inc j
k
A P E jinc
N
k
kjkjk ,
1
EPRA
The interaction matrix now comprises the direct and reflected terms
Loke, Mengüç, 2011
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DECOMPOSING THE SPHERICAL WAVE
i
r
kre 0J kr r zik z
e
Spherical Cylindrical Planar
rr
rr dkeRkJ
k
ke jz zkTETM
zref
kri,
210
0
i
ir
(1)
0
1
2H kr ror
A. Sommerfled, “ ¨Uber die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Physik 28, 665–737 (1909). Loke, Mengüç, 2010
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M. A.Taubenblatt and T. K.Tran, “Calculation of light scattering from particles and structures on a surface by the coupled-dipole method”, J. Opt. Soc. Am. A, 10(5), (1993).
Testing the implementation
Loke, Mengüç, 2010
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TM incident TE incident
λ = 632nm
DDI-SI: TM VS TE COUPLING
Loke, Mengüç, 2010
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AFM PROBE SHAFT LENGTH
TM incident, λ = 632nm
• Field intensity of the 32 dipoles in the nanoparticle
Loke, Mengüç, 2010
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LATERAL DİSPLACEMENT
TM incident, λ = 632nm
Loke, Mengüç, 2010
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Wavelength
Loke, Mengüç, 2010
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DDA-SI is a useful tool for studying near-field coupling for systems comprising nano-objects on or in the vicinity of a subtrate
It currently does not account for emission
We can calculate optical forces
Half-space T-matrix for system can be formulated
Arbitriraly complex configurations are limited by available memory
Irregular local area for substrate possible
Conclusion
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Workshop on NPNSNFC, Bremen, Germany, 11-12 March 2010. Solar-TR, April 29-30, ODTU/METU, Ankara, Turkey
NUMERICAL MODELING OF
AFM-BASED
MANUFACTURING
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• Spherical simulation domain
• Symmetric plane
• Field defined analytically everywhere, except PML
• Setup checked with known solutions, and tested for convergence
Huda, Hastings, Menguc et al. IEEE JSTQE Nanoplasmonics 2013
Nano-Scale Patterning via AFM: (Gazi Huda)
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11/21/2013
As tip is brought closer to
particle:
• Absorption enhances.
• Resonant wavelengths get
red shifted.
• Quantum effects were not
taken into account.
x
y
z
k Huda, Hastings, Menguc et al. Opt. Express 2011
Effect of the Tip on Particle Absorption (TM)
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Preliminary results: Effect of Tip on Particle Absorption w.r.t. Lateral Separation (TM & TE)
82
• highest absorption when particle 5 nm
right of tip.
• Secondary peak might be because of
the interference between the particle
and tip.
k
x
y
z
Huda, Hastings, Mengüç, 2012
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At total internal reflection illumination • The field is strongly localized and enhanced under a nanoscale tip • The absorption is enhanced under a Si tip • The absorption is suppressed under a Au tip.
Huda et al. IEEE JSTQE Nanoplasmonics 2013
Absorption modification caused by a tip
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Effect of tip on different particle size
11/21/2013
10 15 20 25 30 35 40 45 500
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Diameter of the Au nano particle (nm)
Ab
sorp
tio
n e
ffic
ien
cy o
f A
uN
P
TM with tip
TM without tip
TE with tip
TE without tip
Efficiency=Cross section/geometrical cross sectional area Greatest enhancement is when radius of particle is smaller than the tip
Gazi M. Huda Master’s Thesis 114 University of Kentucky
Effect of tip on different particle size
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Workshop on NPNSNFC, Bremen, Germany, 11-12 March 2010. Solar-TR, April 29-30, ODTU/METU, Ankara, Turkey
THE STORY: NANO- & CASCADED PV & TPV
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At Ozyegin University
FP-7-PEOPLE-IRG-2008 (Grant No: 239382) TUBITAK 1001 Grant (No: 109M170)
At the University of Kentucky:
US National Science Foundation (NSF-CMMI-0403703)
Kentucky Science and Engineering Foundation (KSEF-1718-RDE-011) US Department of Energy (DE-FG02-07ER46375)
ACKNOWLEDGMENTS