Download Probing Near-Field Thermal Radiation between Parallel Plates

Probing Near-Field Thermal Radiation between
Parallel Plates using MEMS-based Platform
Mikyung Lim, Jaeman Song, Seung S Lee, and Bong Jae Lee
Department of Mechanical Engineering
Korea Advanced Institute of Science and Technology (KAIST)
WE-Heraeus-Seminar: Heat Transfer and Heat Conduction on the Nanoscale
Early Experiment on Near-Field Thermal Radiation
2
movoltage stays almost constant.
Ref. [19], and that for GaN by the ‘‘reststrahlen’’ formula
A theoretical discussion of the heat transfer between an
with parameters from Ref. [20], we obtain the dashed lines
idealized tip and a flat surface, which may serve as a
in Figs. 2 and 3, setting a ! 60 nm. This value is in
guideline for the analysis of our data, has been given by
accordance with scanning electron microscopy studies of
Mulet et al. [12]. These authors have modeled the tip by a
the tip and describes both experimental
week ending data sets for z *
DOI: 10.1038/NPHOTON.2009.144
P Hsphere
Y S I of
C radius
A L rRand
EV
I NATURE
E W theLincident
EPHOTONICS
TTERS
small dielectric
assumed
10 nm, as it should. The
fact also2005
indicates that the
25 latter
NOVEMBER
electric field to be uniform inside the sphere, so that it acts
use of Eq. (2), i.e., the neglect of the field’sNATURE
distortion PHOTONICS
by
10 dipole. If the temperature of the 20
102
as a pointlike
sample
tip, between
is justifiedthe
here.
neglected.
Theis totaltheflux
surface and the tip
significantly 8lower than that of the tip, as
in our
case, the entirely
In thebycase
of
GaN,directed
the theoretical
curve for !Pth
then
is determined
the
current
from the
Measurement
Monitor
&3
−6 mbar
18 can be
heat current flowing
back from the sample
to
the
tip
6
P ~ ∆T
10
diverges
as
z
for
sensor-sample
distances
below 10 nm.
= 21 K
tip to the sample, according to
In
contrast,
for
Au
this
familiar
behavior
would
becomeV0
Theory
4
PI
apparent
only
at
substantially
smaller
z
[3].
However,
the
16
Z
Z
Piezo
supply
1
1
2
experimental
data
clearly
show
a
different
trend,
leveling
!P
!
d!
d!""!##
"!;
!;
$;
z#;
(3)
E
-4
10 0
0 off to values
0
Piezo accessible distances are5 Hz
which for the smallest
14
actuator
0
5 10 15 20
significantly
lower than
!Pth . We interpret this finding
as
1
3 00
2
Challenges in Experimental Demonstrations (1)
Thermal conductance (nW K−1)
Thermal conductance (nW K−1)
LETTERS
thermopower VTh [µV]
PRL 95, 224301 (2005)
LETTER
DOI: 10.1038/NPHOTON.2009
Diameter 40 µm
10
where ""!# ! 2!"4%r #&tip =j&tip $ 2j describes the diOptical fibre
12
10
I-V
electric properties of the sphere, and the temperature
Photodiode
convertor
FIG. 1 (color online). (a) Cross section of the micropipette
-4
entering10 #E is that of the10tip. Taking this expression
G = 5 × 104 VA−1
Diameter 22 µm
glued into a tip holder. The thermoelectric voltage Vth builds up
fc = 100 kHz
at a representative frequency
!0 , one has !P
%
-8
d
Beamsplitter
between the inner platinum wire and 10
the outer gold film. The
2
""!0 #&08hE i=2, so that, within the scope of the model,
tunnel potential is applied between the sample and the grounded
-6
Stabilized
Heating
element be proportional to
10
the heat flux registered by the
tip should
laser source
gold film. (b) Dependence of the thermovoltage on the absorbed
the electrical
energy density of the flat sample, evaluated,
6
10-10
1
power !P of calibrating laser light for
two-9different sensors.
-6
10
10-8
10-7however,10
temperature
of-81,500
the tip.2,000 2,500
0at the 500
1,000
1
101
102
103
104
10
&8
z/m
Figure
1
|
Experimental
setup.
(Red
lines
are
used
for
the
optical
part
and
black
lines
for
the
electrical
part
of
the
setup.)
Reflection
of
the
laser
beam
on
Sphere–plane
separation
(nm)
Sphere–plane separation (nm)
For distances larger than about 10 m, our experimencantilever
produces
an
interference
pattern.
A
feedback
loop
keeps
the
bimorph–optical
fibre
distance
constant
by
applying
a
voltage
to
a
piezoelectric
ficient of the scanner. Results
of such measurements
are (in Watts)
tally observed
heat transfer is, to good accuracy, proporFIG. 2. Measured heat
current
!PPhys.
between
the
Figure
| Thermal
conductance
the sphere
withthe
diameter
40stabilized
mm
Figure
4Rousseau
| Thermal
conductance
between
the
sphere
andand
the
plate as
a
actuator
holding
the
optical fibre.between
The feedback
loop and
thermally
laser maintain
spurious
from
the laser
constant,
ensure
that
Kittel
et al.,
Rev. 3Lett.
(2005)
etheating
al., Nature
Photonics
(2009)
depicted in Fig. 2 for a sample
consisting
of
a
gold
layer,
tional
to
the
total
density
asblack
given
by
Eq. (2),
notfunction
to withofconstant
microscope tip and a gold layer (circles) vs tip-sample
-10
and
the plate
as
function
ofconductance
gap distance.
The
dots
represent
the
gap
for
two
sphere
diameters
(40
and
22
m
m).
The
blac
variations
aredistance
onlya due
toenergy
the
variations
as
the
separation
d
is
changed,
temperature
difference
DT
between
the
sphere
and
the
10
-9
-8
-6
and in Fig. 3 for a sample of
In both
the sensor
z. GaN.
The dashed
line, cases,
which coincides
with the the
solid
oneplate
fordata
larger
contribution
Since
the
constant
of
experimental
and
the
red mounted
line the theoretical
model.
The
temperature
represent
experimental
andfibre-actuator
the red line issupply.
the theoretical model
plate.electric
The
isfield
heated
and
on aalone.
piezoelectric
actuator.
The
measured
signal
is the10voltage
applieddata
to the
10
10
10-7dots
of
standard
fluctuating
z,
corresponds
to
the
prediction
!P
difference
between
the
plate
and
the
sphere
is
21
K.
The
distance
shift
used
The
dashed
blue
line is the asymptotic contribution varying as 1/d. This
/ m times
with Rth ! 54 K=mW has been employed. During theseth
proportionality, which carries the dimension ofz area
in the
comparison
is b ¼ 31.8 nm and the cantilever response coefficient
contribution is dominant for gaps smaller than 10 nm. For the 22-mmelectrodynamics, based on Eq. (2). The solid
line
is obtained
measurements, we have carefully
checked that the cross
velocity,
may
differ
substantially
""!
focus
on
21 from
0 #,Hwe
factorin the
can
be measured
independently.
found
to
be diameter
a
used
comparison
is HFIG.
¼ 2.162
nWAs
nmFig.
sphere,
the '
smallest separation is 150 nm owing to roughness.
. 2We
from Eq. (5) with the modified dielectric function
(4),
setting
3.
for
a
sample
of
GaN,
setting
L ! 1:0
Symmetry
axis
133106-2
Hu
et
al.
Appl. Phys. Lett. 92, 133106
2
21
:
talk
between
the
tunnel
current
signal
and
the
thermovoltthe
density
!P
chu"z#i,
where
c
is
!
%a
, 133106-2
with an
accuracy
of
2%.
The
conductance
is
the
2.30 scaled
nW nm energy
&10
&8
s is clearly shown in Figure 3B, L ! Ltip ! 1:2 ' 10&8 m.
th
etLal.
mHu
and
m.
10
tip ! 1:2 ' 10
and
the
near-field
contribution
sum
of
the
far-field
contribution
G
have
found
that
the
experimental
data
for
different
approach
curves
the
data
agree
with
the
theory
in
the
range 2.5 mm to 30 nm. T
remains
negligibly
small. The absence of interference
d age
radiation
is strongly
enhanced
ff
the velocity of light, and employ
the effective sensor area
d
(d)/DT
H
are
shifted.
A
microscope
image
of
the
sphere
shows
a
characteristic
agreement
with
theory
confirms
that
radiative heat transfer can
224301-3
2
ubstrate
are bothby
made
polar
is indicated
theoffact
that the tunnel current decreases
%a
as a fitting parameter. Modeling the dielectric function
roughness of !40 nm, which is consistent with the shifts observed significantly enhanced at distances in the nanometre regime. O
ared
to our previous
publication
strongly
in a range
of distances where the observed ther&"!#
fordifferent
Au bycurves.
a Drude
ansatzfor
with
H
between
To account
thisparameters
roughness, wetaken
intro- from
results strongly rsupport previous theoretical works and pave
G ðdÞ ¼ Gff þ
dðdÞ
ð1Þ
stem
to
precisely
control
the gap
movoltage stays almost
constant.
duce [19],
a shift and
b when
comparing
experimental
data of each
way to engineering radiative heat transfer in the mesosco
Ref.
thatexp
for GaN the
byDT
the ‘‘reststrahlen’’
formula
~
leads to much less scatter in the
approach
curve with from
the theoretical
conductance:
regime. Possible applications include
d (r) nano-electro-mechani
A theoretical discussion of the heat transfer between an
with
parameters
Ref. [20],
we obtain the dashed lines
d
o pushed the gap down to ∼30
systems,
heat-assisted magnetic recording29 or heat-assisted lith
The
theoretical
model
of
the
near-field
heat
transfer
is
now
disidealized tip and a flat surface, which may serve as a
in
Figs. 2 andbetween
3, setting
a ! 60 nm.
This value is graphy.
in Further aspects of radiative heat transfer at the nanosc
terials (metal and semiconductor)
cussed. The flux
the¼ sphere
the plate is locally
Gff þ Hand
dðdÞ=DT
ð3Þ
Gtheo ðd þ b; TÞ
3
guideline
for
the
analysis
of
our
data,
has
been
given
by
accordance
with
scanning
electron
microscopy
studies
of
remain
explored. For example, it has been predicted that
b to10be
described as a flux between two parallel plates separated by a disan be drawn on surface wave
flux
can be quasi-monochromatic21,30 and strongly depends
Mulet et al. [12]. These authors have modeled the tip by a
tancetip
d using
the heat transfer
coefficient
h(d,T ) derived
numerithe
and
describes
both
experimental
data
sets
for
z
*
Figure
aiscomparison
of the
with the model
for a par7,213. shows
22
the matching between the optical properties of both materi
This
knownThe
as
thedata
Derjaguin
approximation
callynm,
smallcalculation
dielectricfor
sphere
of radius r and assumed the incident
10
as
it should.
latter
fact
also
indicates
that"b! the
oretical
the nearticular
approach
curve.
Because
the
noise
on
the
cantilever
bending
FIG.
2.
"Color
online!
"a!
A
schematic
drawing
of
the
experiment
setup.
(Fig. 2a). We integrate over the whole area to obtain the theoretical The understanding of the role of non-local effects at distan
microsphere
and
atoplate
becausesetup.
field
beexperimental
uniform
inside
the sphere, so that it acts
measurements
was below
0.1 nm,
we prefer
tothe
consider
H as
a fitting smaller
use
Eq. (2),
i.e.,
the
neglect
field’s
distortion
by than 10 nm is also a subject under examination in
reelectric
2. Schematic
diagram
of
The thermal
Aof
scanning
electron
microscope
image
ofof
polystyrene
particles.
conductance:
or
isAa asimilar
silicon
nitride
AFM
cantilever
coated
a 70 nm
8,10,31
parameter
so
that
the
calculated
curve
shape
and
the
one
given
by
s.as
situation
occurs
inthe with
pointlike
dipole.
If
temperature
of
the
sample
is
, so further experiments are needed in this field.
literature
the tip, is justified here.
film. 20,21
A laser beam (650 nm wavelength, 3 mW output power)
102 setup. "b!
ðonline!
experimental data
can2.be"Color
best compared.
scaling factor
found
FIG.
"a!The
A schematic
drawing
of the experiment
R
ent.
So,
for
the
sphere-plate
cused
on the tip of thelower
cantilever
and reflected
a PSD.
significantly
than
that ofontothe
tip, as in our case, the
In thethiscase
ofðd;isGaN,
the
theoretical
curve
for
!Pthparticles.
FIG. 3. Measured radiative heat flux between the two optical fl
21
~gap
. This
value
following
method
H¼
2.162+0.005
nWdr
nm
TÞ
h½dðrÞ;
T&2pr
ð2Þthe Received
AGtheo
scanning
electron
microscope
image
of5polystyrene
= 24 ° C!, respectively.
As
the
decreases
below
!
m,
ication
of voltage
to the piezoelectric
translation
results
diation
is estimated
by the
so-fromstage
13 May 2009; accepted 25 July 2009;
&3
21
heat
current
flowing
back
the
sample
to
the
tip
can
be
diverges
as
z
for
sensor-sample
distances
below
10
nm.
0
is consistent
with coefficient
the calibration
value
H ¼ 2.30the
nW
nm found
e movement
of the substrate toward the sphere. In near-field,
22
heat transfer
starts
to exceed
blackbody
limit. published online 23 August 2009
rem
that
approximates
curved
Figure
4. Equivalent sphere-plate near-field
heat transfer
coefce phonon polaritons can tunnel through the gap and
they thus
for contrast,
another
cantilever
the
same
batch
but
with different
exact
pcontinues
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
In
for
Auof this
familiar
would
become
As
the
gap
shrinks
even
more,
coefficient
et al.,
Nano
(2009)
Hu et al.,
Appl.
Lett. (2008)
2 ' r 2 is to
~thebehavior
at
areas
and to
using
the known
ficantly
contribute
the radiative
heat transfer. Theficients
“cooling”
With the feedback
control,
thePhys.
temperature
the heatin
normalized to theShen
area 2πRd
versus
the
gap
for
where
RLett.
is distance
the
radius
ofathe
sphere
and dðrÞ
¼ d þ Ris'
Ryielding
dimensions.
Indeed,
the
cantilever
length
dispersion
10%,
FIG.
3. Measuredofradiative
he
apparent
only=sphere.
at
smaller
zthe
[3].
However,
the
t on the between
cantilever due
to the enhanced
radiation
grow,
owing
to substantially
enhanced
tunneling
of the
surface
waves.
24
°
C!,
respectively.
As
gap
decreases
below
5
!
m,
the
µm (blue circles) and a 50 µm (violet triangles)
diameter
iation
parallel
surfacesnear-field100
can
be
set
to
a
value
with
variations
within
1
° C. Th
References
the
local
distance
between
the
plane
and
the
sphere
surface
(Fig.
2a).
an H dispersion of 30%.
1
to the bending of the cantilever. Inset: A scanning electron
10 & Van Hove, M. Theory of radiative heat transfer between close
m,
coefficient
is more
than
50%
than
1in !
1. blackbody
Polder,
D.
experimental
data
clearly
show
asmaller
different
leveling
The flat line is the limit predicted by Planck’s
blackbody
radiation
ForItAround
two
infinite
planes
and
forsphere–plane
distances
than
dtrend,
¼higher
500 nm,
surfaces
of limit.
the optical flats are wrapped
with aluminu
near-field
conductance,
Far-field
heat
transfer
coefficient
starts
to
exceed
the
is seen
Fig.
3the
that
the
conductance
increases
oscope imageradiative
of a glass
mounted on an AFM cantilever.
3
-4 sphere
spaced bodies. Phys. Rev. B 4, 3303–3314 (1971).
2
-6
absorbed power ∆P [µW]
10
law. The dashed line is the near-field heat
transfer
coefficients
21
blackbody
which
is readily
measurable
in the short
distance
regime. If without
we retainthe
the the
flux
increases
aslimit,
1/d
Thermal conductance (nW K−1)
∆P / W
∆P / W
(b)
% " kz Þ( ';
(5)
" kz Þ( ';
(6)
completely consistent with thermal conduction through
theHeat
Macor
spacer
andthe
thevacuum
rest of the
for the hot
flow
over
gapsupport
is absorbed
by the cold
plate
in
parallel
with
radiation
from
the
rear
surface
of thethrough a
sample and sinks into the liquid helium bath
plate. The vacuum chamber is held at constant temperature
calibrated
thermal resistor, serving as a heat flow meter.
of 30:0 + C (303.2 K). The hot plate is brought close to the
nm thick layer of sputtered copper. These
space. mately
Wien’s200
displacement
law predicts that &max )
coatings have areas about 1 mm2 and serve as capacitor
9 'm atplates
T ¼that
310are
K. read by four 24-bit capacitance-to-digital
Figure
2 showscircuits
a sketch
of to
ourmeasure
apparatus.
is designed
converter
[15]
the Itseparation
and
3
around angular
two 50 *
50 * 5 mmofsapphire
plates.
haveis
misalignments
the plates.
The These
metal film
a specified
flatness
of &=8
nmofperthe
inch
on the to
largest
wrapped
around
to @
the633
sides
sapphire
allow
to that
the electrodes.
surfaceselectrical
and are contact
cut such
the c axis is perpendicular to
Challenges in Experimental Demonstrations (2)
$? come from
!
!
2
!
!
!
;
(7)
!
!
!
High temperature stability of the foot of the thermal resistor together with a resolution of 50 !K of the temperature
measurement enabled us to measure heat flows from
20 nW to 1 mW.
Keeping the cold sample at # 5 K, experimental results
were obtained at varying distances d between surfaces at
constant temperature T2 of the hot sample (Fig. 2), and vice
versa, with varying T2 at constant d. All measured data are
collected in Fig. 2 where the heat flux normalized to the
blackbody emissive power, q=qBB , qBB ¼ "B ðT24 ! T14 Þ, is
plotted as a function of T2 d. The inset of Fig. 2 shows
absolute values of measured heat fluxes obtained at
T2 ¼ 20 K.
The near-field values, theoretical and experimental,
follow approximately the same dependence (Fig. 2). We
can observe the onset of the near-field effect at T2 d0 #
1000 K !m. Comparing it to the wavelength #m from
Wien’s displacement law, T#m # 3000 K !m, we get
d0 # #m =3 (d0 # 50 !m at T2 ¼ 20 K, for example).
Calculations of theoretical values were doneOttens
for tunget al., Phys. Rev. Lett. (2011)
FIG. 3 (color online). Heat-transfer coefficient vs distance.
week
ending
2
sten
layers
150
nm
thick
characterized
by
permittivity
,
K
from
the
The
curves
are
each
offset
vertically
by
2
W=m
LETTERS
30 NOVEMBER 2012
q/qBB [%]
(5 mm by 5 mm) Sapphire plates
q [W/m2]
The cold plate is glued to a copper disk, which in turn is
attached to the experimental structure. The Macor spacer
on the back of the hot plate is attached to a modified
!
!
2
!
!
kinematic mirror mount which allows for z-axis linear
!
;
(8)
!
!
!
movement and tip and tilt angular adjustment by turning
the three adjustment screws in the back. Three stepper
for the medium and
motors turn screws on the kinematic mount via gear reduction boxes; each motor step translates to a linear movement
ffiffiffiffiffiffiffiffi
of the hot plate by 35 nm. The components are held
together by an ‘‘L’’ shaped backbone (not shown) to give
(9)
" #2 ;
rigidity. The assembly is located in a UHV chamber, with a
ffiffiffiffiffiffiffi
base pressure below 2 ! 10"7 Torr, making gas conduc2
tion
negligible. Signals to the stepper motors, capacitance
=c :
(10)
readouts, temperature readouts, and current and voltages to
maginary above the
the heater are all controlled and/or read by a LABVIEW
computer program.
oefficients T ev
and
k
Each pair of capacitor plates is calibrated by taking
eflection coefficients
capacitance readings as the plates are driven together
eory to calculate the
one step
of the stepper
motorsapparatus.
at a time. Stepper
A fit is motors
made to
FIG. 2 (color
online).
Experimental
pphire plates, using
C ¼ !0 a=d
Cstray
wheretip,
!0 and
is the
constant of
allow adjustment
ofþthe
spacing,
tiltdielectric
(read capacitively)
14].
sapphire
plates.
Thecapacitor
temperature
of part
the
hotisthe
is
the
vacuum,
aScheme
is the
and
Cstray
aplate
parallel
FIG.of1 two
(color
online).
of the area,
central
of
meathe model for z-cut
controlled
by
a
feedback
circuit,
and
the
power
required
to
contribution
independent
of
separation.
The
data
fit
the
H Y plane-parallelism
SICAL REVIEW
surement chamber
samples withP the
PRL 109, containing
224302 (2012)
2 heat transfer from
o media are Thot ¼
maintainequation
a temperature
gives
values ofgreater
than
above difference
very
well,
with
R
one below; their zeros are indicated by the horizontal lines
equalizer
(PPE).
Differential
screw
sets
the the
positions
the static
extending
from
the leftgap
axis.
The points
term dominates at
the hot plate
the cold
thermal
6 the
0.999.toThe
fittedplate
valueand
of toa the
equals
the bath.
metalized areaHeat flow
over
vacuum
is absorbed
by are
the the
colddata, with error
10
part of the PPE which is attached to the sample holder at the
Measured
Theoretical
determined
from
theThelium
scatter
in
the
heat-transfer
sample bars
and sinks
into the
liquid
bath
through
ad = 50 µmeasurewithin our knowledge of this area: Cstray % 0:4 pF. The
T2 = 20 K
m
Near field
2 = 10 K
end of the sample suspension. The static and movable parts of
ments
and
the
uncertainty
in
the
distance
calibration.
The
calibrated thermal resistor, servingT as
a heat Tflow
meter.d = 300 µm solid Far field
average capacitance gives the distance while the individual
2 = 12 K
2 = 30 K
PPE are coupled via three friction locks realized by three pairs of
lines are
the theoretical
predictions
for flat plates while the Total
014301-2
High temperature
stability
of the foot
the thermal
T2 = of
15 K
T2 = 40 Kresis-d = 500 µm
readings are used to correct the alignment by sending steps
105
dashed
are the of
theoretical
for slightly curved
tor together
withlines
a resolution
50 !K ofpredictions
the temperature
polished pins
pressed
against
each
other
with
a
spring.
When
the
T2=20 K (Data set 1)
to the motors controlling tip and tilt.
plates enabled
(see text).
Each
measured
measurement
us to
measure
heat
flows has
froma reproducible
T2=20 K (Data set 2)
100curve
sample suspension
is
shifted
downwards
until
the
contact
beTo obtain the heat-transfer coefficient we compute
addendum
due to other heat leaks which are not included
in the
Theoretical,
20 nW to
1 mW.
4
tween samples
is
achieved,
and
shifted
further,
the
friction
locks
T2=20 K,The
T1=5 K :
10cold
W ¼ P=½AðThot " Tcold Þ), where P is the power dissipatedKeeping
model
and sample
which athas
subtracted
from
the
# 5been
K, experimental
resultsthe data.
-1
10
Total
slip and plane
parallelism
samples
is set.
of
in the
heater, Abetween
is the plate
surface
area,Both
and parts
Thot and
temperatures
are distances
(top to bottom;
hot–cold):
327.0–308.0
K,
were obtained
at varying
d between
surfaces at
Near field
the PPE areTcold
thermally
by the
a soft
braid.
Far field
are theinterconnected
temperatures of
hotcopper
and cold
plates,
317.0–305.8
K, and
constant322.0–307.0
temperature K,
T2 of
the hot sample
(Fig.312.0–305.2
2), and viceK.
3
10
10-2
data are
versa, with varying
T2 at constant d. All measured
collected in Fig. 2 where the heat flux normalized to the
014301-3emissive power, q=q , q ¼ " -3ðT 4 ! T 4 Þ, is
The whole apparatus was immersed in liquid helium
blackbody
BB
BB
B 2
1
10
2
which cools the measurement chamber below 5 K. Vacuum
plotted as a 10
function
of T2 d. The inset of Fig. 2 shows
absolute values of measured heat fluxes -4obtained at
was maintained by cryopumping at a pressure lower than
10
T2 ¼ 20 K.
10!8 Pa, reducing thus the heat transfer by molecular flow
1
The near-field
values,
theoretical
and
experimental,
100
101
10
below measurable values.
follow approximately the same dependence (Fig. 2). We
can observe the onset of the near-field effect at T2 d0 #
After cooldown of the apparatus, the samples are set in
1000 K !m. Comparing
it to the wavelength #m from
plane-parallel position with zero gap (Fig. 1). Once plane
100
Wien’s displacement law, T#m # 3000 K !m, we get
parallelism was adjusted, the hot sample was moved up
¼ 220 K, for example).
d0 # #m =3 (d0 #
10150 !m at T2 10
103
Calculations
of
theoretical
values
were
done
for tunginto the starting
position
about
200
!m
above
the
cold
T
d
FIG. 1 (color online). Scheme of the central part of the mea2 [K µm]
sten layers 150 nm thick characterized by permittivity
surement
chamber
samples with
plane-parallelism
sample. The
zero
gap containing
was detected
bythedisappearance
of
equalizer (PPE). Differential screw sets the positions of the static
the electric
contact between samples. Preservation of the
part of the PPE which is attached to the sample holder at the
end of the
sample suspension.
The static
movable
parts of
plane-parallel
position
is ensured
by and
two
flexure
memPPE are coupled via three friction locks realized by three pairs of
branes, part
of hot sample suspension, that bear the sample
106
105
Corrected for
concavity 0.7 µm
d [µ m]
104
102
105
Kralik et al., Phys. Rev. Lett. (2012)
FIG. 2 (color online).
Experimental
and theoretical data on
Measured
Theoretical
T = 10
K
Tvacuum
= 20 K
d =gap
50 m d #Near
field
heat transfer
over
1–300
!m between samples
T = 12 K
T = 30 K
d = 300 m
Far field
with 150 nm
thick
tungsten
layers
on
polished
alumina substrate.
T = 15 K
T = 40 K
d = 500 m
Total
µ
2
2
2
2
µ
2
2
µ
4
its temperature (i.e., its electrical resistance). The
performed using a Fourier modal method basedmeasuring
on the
dimensions), we expect the heat transfer to be proportional to
Figure 1. (a) Schematic representation of the experiment. At small
19
fluctuational electrodynamics formalism,30,31 considering
beams of1/gap
inverse
the 2,slope
of thisplates.
temperature
vs value
electrical
power
as for parallel
The far-field
in Figure
1b is
gap, evanescent surface polariton resonances at the SiO2 surfaces
3 cross section
of
200
μm
length
and
500
nm
×
1.1
μm
a
b
10
measurement
yields
the
background
conduction,
in
units
of
MEMS
off
MEMS
on
the
total
far-field
emission,
integrated
over
all
directions
and
all
couple to enable near-field radiative heat transfer between the
(including a 100 nm thick SiO2 coating). The temperature frequencies, for a nanobeam maintained at 130 K above room
is
used
nanobeams. Si3N4 is used for mechanical purposes, whileVPt
Watt/K.
We
obtain
conduction
values
of
σ
=
237
nW/K
and
VMEMS
Simulation
fix
MEMS
Vsense (Vsensor.
102 K (as in our temperature.
S)
both as a resistive heater and a temperature
(b) Theoretical VS difference between the nanobeams is 130
This
value
is heated
calculated
by the
modal
σ
=
107
nW/K
for
the
fixed
beam
andFourier
the mobile
1.54
mob
experimental
results),
with
the
mobile
sensing
beam
maintained
1/d
fitfor a periodic array of nanobeams
prediction of the heat transfer between two nanobeams of 200 μm
analysis
method
with
sensing
respectively. Using these values and thea
at room temperature. Repeating the near-field
while beam,
101simulation
length and 500 nm × 1.1 μm cross-section. The SiO2 thickness in this
periodicity much larger than the size of nanobeams, such that
replacing the Si3N4 core with SiO2 shows that the Sitemperature
case is 100 nm.
Figurewith4, each
we other.
obtain the heat transfer
3N4 core theydata
do notofinteract
Heat transfer (nW K−1)
MEMS-based Measurements
(1
D
(3
T
h
LETTERS
0
200 400 600 800 1,000 1,200 1,400 1,600
(nm)
Enh
vers
translation
best fitsbetween
the experimental
data is +49 nm
10 µm
mechanical
stability at high
temperatures.
between two nanobeams as
a functionthat
of distance
them. The hot
200 nm
1 µm radiative heat transfer
Silicon
(to be removed)b, Simulated
6972
dx.doi.org/10.1021/nl503236k | Nano Lett. 2014, 14, 6971−6975
horizontally
and
+1.49
nW/K
vertically.
After
fitting,
the theory
Gap
(nm)
beam is set at T = 10 K above room temperature (293 K). The deep subwavelength regime occurs for beam separation below 200 nm, where the heat
is
found
to
correspond
closely
with
the
experimental
data.
1.54
transfer
to scaleelectrical
as 1/d heaters/temperature
(which appearssensors
linear are
on used
a logarithmic
scale).two
c, parallel
Simulated heat transfer spectrum between the nanobeams at two different
inciple.
MEMSbegins
with integrated
to bring together
Slight discrepancies between
theory
and
measurements
most
St-Gelais
et al.,
Nature
Nanotech.
(2016)
120
b a 120
separations.
For da,=Schematic
50 nm, the
heat
transfer
is concentrated
mainly
around
the SiC
surface
resonance (near ω = 937 cm−1). The
secondary
peaks
at lower
gth heat
transfer regime.
of the
MEMS
geometry
(not to scale) and
operation
principle.
Applying
likely
arise
from
deviation
of
the
beam
cross-section
from
the
Minimum
gapstructural release. e, SEM
caused
the presence
of Si3nm
N4initially
and SiO
scanning
electron micrographperfectly
(SEM)
ofrectangular
thenear-field
device shape
after
drivefrequencies
closes the gapare
between
theby
nanobeams,
from 1,500
(left)
to False-colour
sub-100 nm (right).
A Vheat
2. d,
considered
in
the
simulations
(see
100
Enhancement versus far-field
100
whilefalse-colour
the Vsens voltage
on the otherview
beamofallows
for temperature
sensing.
High tensile
stress allows for
cross-section
the nanobeams
before
structural
release.
Figure 2d). The 1.49 nW/K susbtrate conduction obtained
Simulated radiative heat transfer between two nanobeams as a function of distance between them. The hot
■
C
*
N
T
■
T
so
si
su
b
C
su
1
o
is
E
th
NAT
Heat transfer (nW K−1)
Power density (pW K−1 cm)
Heat transfer (nW K−1)
Power density (pW K−1 cm)
0
has a negligible effect on the heat transfer10compared
withlimit
a a function
Far-field
power
as
of the isnanobeam
(see Figure
5).
The structure
fabricatedseparation
using conventional
nanobeam that would be made entirely of SiO2. The insensitivity of fabrication processes, which consist of low pressure chemical
10−1the surface wave vapor deposition (LPCVD) of SiO and Si N , and electronheat transfer to the core material results from
Tensile
2
3 4
1 dominates102
nature of the SiO2 surface phonon-polariton 10
that
stress
Gap
103 of platinum
104resistors and aluminum electrical
beam evaporation
heat transfer at small gaps. In the gap range of Figure 1b, the contacts. The fabrication process begins with the successive
Gap (nm)
heat transfer
power approximately scales as 1/gap1.68. At much deposition
of 100 nm of SiO2, 300 nm of Si3N4, and 100 nm of
NATURE NANOTECHNOLOGY
DOI: 10.1038/NNANO.2016.20
smaller distances (i.e., distances much smaller than the beam SiO SiC
−1)
a virgin
wafer. The MEMS and nanobeams are
cmsilicon
2 on (937
c
dimensions), we expect the heat transfer to be proportional to then defined by deep ultraviolet lithography and etched in
8 in Figure 1b is
2, Siparallel
3N4, SiC
1/gap2,SiO
as for
plates.19 The far-field value
b
CHF3 + O2 chemistry using an inductively coupled plasma
103
50 nm gap
MEMS on
the total far-field emission, integrated over all directions and all reactive ion etching
÷ 50(ICP-RIE) reactor. Following this etch
1,500
nm
VMEMS
VMEMS
Simulationfor a nanobeam maintained at 130
6 K above room gap
frequencies,
102
VS
Platinum
step,
a
third
layer
of SiO2 is deposited, again by LPCVD, in
1/d1.54 fit This value is calculated by the Fourier modal
temperature.
order
to
conformally
cover the sidewalls of the etched
101
4
analysis method for a periodic array of nanobeams
with a structures. This layer is then anisotropically etched (using the
periodicity much larger than the size of nanobeams, such that same ICP-RIE chemistry) to clear the bottom of the trenches
100 Far-field limit
2
they do not interact with each other.
for subsequent isotropic release, while leaving some SiO2 on
The structure is fabricated using conventional nano- the sidewalls of the nanobeams (see the final nanobeams cross
10−1
0 of thechemical
2. (a)
(not
to scale)consist
and electrical
twofabrication
processes,
of lowcircuit
pressure
101
102Figure
103Schematic
104 which
section in Figure 2d). Platinum and aluminum are then
system
integrated
with theofMEMS
actuator.
(b)
Schematic
Vnanobeam
vapor
deposition
(LPCVD)
SiO
and
Si
N
,
and
electron200
400
600
800
1,000
1,400
2
3
4
H
Gap (nm)
Figure
5.
Heat
transfer
power1,200
between
thedefined
nanobeams
as a function
of
successively
deposited
over
the
structure
by
electron
(notbeam
to scale)
of the MEMS
displacement.
electron
St-Gelais
et al.,
Nano
Lett.
(2014)
Vheat (VH)
evaporation
of platinum
resistors(c)
andScanning
aluminum
electrical
−1
beam
evaporation
and
lift-off.
The
aluminum
layer
is
chosen
to
their
separation
distance.
Substrate
conduction
is
found
to
account
for
)
Frequency
(cm
VMEMS
VMEMS micrographs
−1
(SEM)
of
the
device.
(d)
False
color
SEM
of
the
SiC
(937 cmThe
) fabrication process begins with the successive
contacts.
c
be much
thicker
(250transfer
nm) than
the smallest
platinum gap.
layerNear-field
(60 nm),
less
than
15%
of
the
total
heat
at
the
nanobeam
cross
section
prior
to
substrate
removal.
SiO2, Si3N4, SiC
8
deposition of 100 nm of SiO2, 300 nm of Si3N4, and 100 nm of such that the resistance of the aluminum contacts is negligible
heat transfer is also found to be 7 times stronger than the far-field limit
50 nm gap
e a virgin
d
SiO2 on
÷ 50 silicon wafer. The MEMS and nanobeams are compared with the platinumSiO
2 for the
resistors.
Thecurrent
highergeometry
electrical
1,500 nm gap
(1.7
above the substrate conduction,
Platinum
heaters/
6
lithography and etchednW/K
in conductivity
Platinum
MEMS comb drive then defined by deep ultraviolet
of
aluminum,
relative
to
platinum,
also
contributes
and
temperatures).
temperature
sensors
CHF3 + O2 chemistry using
inductively
coupled plasma
actuator
4
aan reactor.
SiC
Si3N4
40
reactive ion etching (ICP-RIE)
Following this etch
6972
dx.doi.org/10.1021/nl503236k
| Nano Lett. 2014, 14, 6971−6975
Experiment
In Figure
step, a third layer of SiO2 is deposited, again by LPCVD,
in 5, the horizontal error bars correspond to the error
2
Tunable
gap of theonetched
order to conformally cover the
sidewalls
Simulation
the measurement of the MEMS
SiO2 displacement (see Figure
0
30 etched (using
structures. This layer is then anisotropically
the
3).
Vertical
error
bars
are
not
visible,
as they are determined by
VH
200 400 600 800
1,200
1,400
10
same1,000
ICP-RIE
chemistry)
to clear the bottom of the trenches
the very high resolution of the Agilent device parameter
−1)
VMEMS VMEMS
subsequent
isotropic release, while leaving some SiO2 on
10Frequency
µm for (cm
200 nm
1 µm
Silicon
(to
be
removed)
analyzer.
the sidewalls of the nanobeams (see the 20
final nanobeams
cross The theory curve is the same as in Figure 1, but is now
1
Figure 2. (a) Schematic
(not
to
scale)
and
electrical
circuit
of
the
twoFar-field
limit to best fit the experimental
e
and vertically
section in Figure 2d).
are then horizontally
SiO2 Platinum and aluminum translated
nanobeam system integrated with the Platinum
MEMS actuator.
heaters/(b) Schematic
successively
deposited
over
the
defined
structure
by
electron
data.
The
horizontal
translation
is included to account from our
comb
drive
(not
to scale) of the MEMS displacement.
(c)sensors
Scanning electron
temperature
Figure 1 | (SEM)
Deviceofoverview
and
operating
principle.
MEMS
with
integrated
electrical
heaters/temperature
sensors
are
used
to
bring
together
parallel
beam
evaporation
and
lift-off.
The
aluminum
layer
is
chosen
to
10
0.1
or micrographs
the device. (d) False color SEM of the
uncertainty on the initial distance (d0)two
between
the beams (see
SiC
Si3N4
be much
thicker
(250
nm) of
thanthe
theMEMS
platinum
layer (60
nm),
nanobeam
cross and
section
prior the
to substrate
removal.
100
1,000
nanobeams
reach
deep subwavelength
heat transfer
regime.
a, Schematic
geometry
(not
to
scale)
and
operation
principle.
Applying
a
discussion related to Figure 3 and the MEMS displacement
such that the resistance of the aluminum contacts is negligible
Tunable
gap
voltage (VMEMS) on the interdigitated comb drive closes the
gap betweenSiO
the2platinum
nanobeams,
from 1,500
nm
initially (left) to
sub-100
(right).translation
A Vheat
while
the nm
vertical
accounts for
compared with the
resistors. The
electrical
0 higher measurement),
spurious
conduction
of heat
the substrate. The
voltage is applied to heat one of the beams, while the Vsensconductivity
voltage on
other relative
beam allows
for temperature
sensing.
High tensile
stressthrough
allows for
of the
aluminum,
to platinum,
also contributes
5
■
(
(
18
(
(
10
(
12
(
93
(
J.
(
29
(
Jo
2
(
H
∆z
6
Gap
(
2.5 nm
20
MEMS-based
Measurements (2)
LETTERS
a
NATURE NANOTECHNOLOGY
150
100
Laser
SiO2 film receiver
Ta
Qrad,2f
Idc,out
t
Gap
Qrad,2f
0
Ta
Pt heater
Qcon,2f
+
Qjoule,2f
−
∆Trec (mK)
c
Contact
Au
V2f
−
50
45
I f,ou
Stiff
Si beam
Piezoelectric
actuation
Piezoelectric
actuation
t
d
200 µm
Contact
e
200 µm
30
Laser
100 µm
If,in
V−
If,out
50 µm
8
10
3 µm
2 µm
1 µm
100 nm
50 nm
Au
10
8
6
4
2
0
20
SiO2 film
1 min
6
12
Rib
15
V+
4
Gap (µm)
SiNx
+
60
c
2
Rib
n
I dc,i
Stiff ribbed
SiNx beam
V3f
0
b
PSD
If,in
4
DOI: 10.1038/NNANO.2015.6
Near-field conductance (nW K−1)
Optical signal (mV)
0
100
1,000
10,000
Gap (nm)
θy
Parallel
z-Piezo
b 25
eld conductance (nW K−1)
15
K−1)
–1
Deviation from flatness (nm)
Deviation from flatness (nm)
Height (nm)
Total heat transfer
efficient (W m−2 K−1)
a
Height (nm)
80
loop feedback control (Supplementary Fig. 6). The top panel of receivers coated with aθx 100-nm-thick SiO2 layer and measured
Fig. 2a shows the displacement, Δz , of the emitter towards the recei- GNF (Fig. 2c, green solid circles). Intriguingly, the near-field
Pt heater
ver, which begins with
coarse steps (∼5 nm) and continues in finer thermal conductance for these devices remains largely unchanged
60
steps (∼2.5 nm) close to contact. Throughout thee approach the when the gap
is reduced to well below 1 µm, and only begins to
f
50 µm
Emitter
25 300 nm. When the gap size
optical signal (middle panel) does not change until contact is estab- increase
25 noticeably with gaps below
40
increases rapidly and becomes
lished. Finally, thed bottom panel presents ΔTrec , which increases approaches the film thickness, GNFBulk
monotonically until contact
106 is made. Contact is heralded by a comparable to that obtained for 3-μm-thick SiO2 films at gaps
3 µmthe dependence of GNF20
on
sudden change in the optical deflection signal, which occurs con- less than 100 nm. To better understand
20 µm additional experiments for layer
Thin SiO
thickness, we performed
SiO2Au
currently (that is, within the same 2.5 nm displacement
step) with 20 µm
−30
−30
2
µm
50 2
50
a large jump in ΔTrec due to conduction of heat from0 the silica thicknesses of 500 nm, 1 µm and 2 µm (Fig. 2c, all data points refilm 0 10 20 present
0
sphere to the receiver. 50 µm
an average0 of ∼1010 independent
30d 40
20
301 µm
40 measurements). It is clear
75 µm
Scan lengthfrom
(µm) these experimentsScan
length
that
G(µm)
These experimental data
allowed
us
to
determine
the gapNF for each device depends on the
4
100
nm
10
SiO2of the coating and begins to increase rapidly only when
dependent, radiative thermal
conductance as Ggap = Gbeams × thickness
Figure 1 | Microdevices for probing near-field radiation between parallel-planar surfaces. a, Scanning electron microscope (SEM) image of the receiver
ΔTrec/(ΔT
the gap size becomes comparable to the
thickness. We also
emit–ΔTrec). We obtained the near-field thermal conducnmfilm
device, which features a 80 µm × 80 µm region coated with a desired dielectric/metallic film (false-coloured in blue). b, SEM image of 50
the emitter,
which
gap by subtracting the gap-dependent far-field performed a control experiment where the receiver had only a
tance (Gfeatures
NF) ata each
48 µm × 48 µm mesa-shaped region coated with SiO2 or Au (top of mesa false-coloured in red). Both emitter and receiver devices are suspended
Auof theThe
results of this expercontribution,
which
estimated
thethermal
thermal
conductance
100-nm-thick
Au filmshowing
and no
by long and
narrowwas
Si beams
to achievefrom
excellent
isolation
(Supplementary Sections
1 and 2). c, Schematic
theSiO
orientation
emitter
2 coating.
and receiver
devices with gap
respectsizes
to each(∼
other.
The relative
of the emitter and
receiver
(inset)
can be
controlled
custom-built
10 µm)
and alignment
the calculated
iment
(solid
olive
squares
inusing
Fig. a2c)
show that there is no measurable
at the largest
measured
c
22
nanopositioner
that factor
enables2lateral
(θz ) of the emitter
as well
control
the receiver about the x, y and z axes.
x, θy ) of
gap-dependent
view
(Fig.and2bangular
andcontrol
Supplementary
Fig.
7).as angular
increase
in(θG
NF as the gap size decreases. Taken together, our obser10the
d, Optical images showing
emitter and receiver devices. e, Line profile of the active region of the emitter showing the negligible deviation from planarity
for
the
3-µm-thick
layer
of
SiO
as
a
function
surfaces
vations
suggest
that
surface
phonon
polaritons
on
the
SiO
The estimated
G
NF
2
2
along the dashed line of the inset. Inset: topography obtained using atomic force microscopy. f, As in e, but for the receiver. Small deviations from planarity
of gap ofsize
is nm
shown
in µmFig.
(green
open
circles).
Clearly,
responsible
forthethe
observed,
gap-dependent GNF behaviour.
∼30–40
over a 40
× 40 2c
µm region
can be
seen (dashed
line aligned
with theare
centre
line parallel to
x axis
of the receiver).
Derjaguin approximation
20
15
10
100
1,000
d
10,000
Gap size (nm)
10−12
Bulk
−15
3 µm10
2 µm
1 µm
10−18
100 nm
0.0
50 nm
Au
0.5
Freq
Song et al., Nature Nanotech.
(2016)
d
10−9
Experimental data
Ideal parallel planes
Modelled plates
s)
Misaligned
Ta
1
Alignment
mark
2 Hz Joule heating
Total gap thermal conductance (nW K−1)
x
50 µm
Spectral conductance (nW K−1 rad−1 s)
NATURE NANOTECHNOLOGY DOI:Song
10.1038/NNANO.2016.17
et al., Nature Nanotech. (2015)
Figure 2LETTERS
| Gap-dependent near-field thermal conductance of thin films. a, Simultaneous recording of displacement, Δz, of the emitter towards the receiver
(top), optical contact signal (middle) and temperature increase in the receiver (bottom). During the final approach, piezo displacementb steps of ∼2.5 nm
d = 50 nm
were used. b, Contribution of far-field radiation to the radiative thermal conductance across the gap for a representative
film data
(100 nm). The solid red line
Experimental
d = 100 nm
−6
Ideal
parallel
planes
10 factor. d = 500 nm
describes the predicted far-field radiation, which increases weakly (<1 nW K ) with decreasing gap size due to the associated change in view
d = 1 µm
Modelled plates
As expected, the measured data (multiple runs, green symbols) agree well with the far-field prediction for gaps from
1 to 10
µm. c, Near-field thermal d = 10 µm
Blackbody
limit
Blackbody
48 μm x 48 μm
conductance
as
awithfunction
of film thicknesses. Data for each film thickness represent
an average of ∼10 different data
sets. See Supplementary
Fig. 7 for
towards the receiver
a piezoelectric actuator. Nanometre- GNF increases rapidly from ∼0 to 12 nW K−1 as the gap size
100is
10−9
b
Grey body
precise displacements
werethe
achieved
by monitoring
the movement
reduced
to ∼20 nm.
information
about
standard
deviation
of the
data.
48 μm x 48 μm
To investigate the effect of film thickness on NFRHT we used
of the actuator with integrated strain gauge sensors under closedFigure 1 | Experimental set-up and devices. a, Schematic of the experimental set-up. The emitter consists of a suspended silicon platform, with an attached
silica sphere and an integrated electrical heater–thermometer. The receiver is a stiff silicon nitride platform coated with gold and a silica film of suitably
chosen thickness. A laser (reflected off the receiver, see also e) and a position-sensitive
detector (PSD) enable optical
detection of emitter–receiver contact
NATURE NANOTECHNOLOGY
DOI: 10.1038/NNANO.2016.17
formation with nanometre resolution. A sinusoidal electrical current (If,in = If,out), at f = 1 Hz, is supplied to the emitter’s resistor, resulting in Joule heating
with amplitude Qjoule,2fa and frequency 2 Hz. This is partly conducted through the beams (Qcon,2f ) and partly radiated to the emitter (Qrad,2f). The emitter’s
c
Pt thermometer
a
Eucentric point
160
Ta
10-μm-thick
temperature oscillations are quantified by measuring the third harmonic
of the voltage
(V3f) across the resistor. The
receiver’s temperature oscillations are
of goniometer
Si beam
measured by supplying a dc current (Idc,in = Idc,out) through the receiver’s resistor and by monitoring the voltage output at 2f (V2f ) across it. Ta is the ambient
θy
temperature. b, Schematic cross-section of the planar receiver region and the spherical silica emitter. The gold layer is ∼100 nm thick, and the thickness140
t of
−1
the SiO2 film varies from 50 nm to 3 µm for different receiver devices. c, Scanning electronzmicroscope θ(SEM)
image of the suspended platform and optical
x
y
image (inset) of the spherical emitter. d, SEM images of the receiver show20-μm-tall
ribbed beams andθz suspended
regions. e, Optical image of the emitter and receiver
20-μm-thick
Receiver
120
Si mesa
during alignment. In this image the devices were laterally displaced to enable
simultaneous visualization.
Si beam
d = 50 nm
d = 100 nm
d = 500 nm
6
Motivation: Near-Field TPV Device
Space0charge
The Center of
Rotation
Gonio Stage
• x,y -rotation
Emitter
Photon
Heat
Emi$er
!
TPV Cell
or PV Cell
TPV*Cell
Cooling water
Piezo Actuator
• z-stage
z
Electrical0Output
Micro Stage
• z-rotation
• x, y, z-stage
y
x
Current Density (A/cm2)
Electric&Power
0.03
FIGURE 4. SCEMATIC DIAGRAM OF EACH STAGE SETUP
1000
0.3
FOR NANO-SCALE PARALLEL GAP POSITION
Dark
2000µm
500µm
36µm
10µm
0.02
0.01
0
-0.3
For realizing NF-TPV device,
we -0.1
need
0.1
0.3
-0.01
! source temperature to be as -0.02
high as possible
-0.03
! vacuum gap to be as small asVoltage
possible
(V)
FIGURE 6.
I-V CURVES FOR Si-PV CELL IN NEAR-FIELD
AND PROPAGATING
WAVE REGIMES
! surface area to be as wide
as possible
was only a small increase in the current density with decreasing
gap from 2000 m through 500 m to 36 m since the view
factor between the emitter surface area (5mm x 6mm) and the
cell area (15mm x 18mm) is close to unity. Those results were
also obtained in the regime of the conventional propagating
radiation. Similar to the case of GaSb-TPV cell, the conversion
Short-circuit current density
Jsc (A/cm2)
Waste&Heat&Energy&
(Infrared&radia2on)
0.25
0.2
Emitter temperature
800
Emitter temperature (K)
hole
electron
600
block mounted on piezo-actuator system which
was able to
0.15
positioning x-y-z- Jmicro-stages, while the400 emitter was
sc
mounted on 0.1
double axes
gonio-stage controlled by a computer.
Using the 0.05
gonio-stage, a parallel gap between200these surfaces
was made over the surface area of emitter. The minimum
0
incremental motion
of the piezo-actuator in the0direction of the
10
6
0
z-axis for controlling 8the gap
was 440nm.2
(µm) gap between the both
In order to make Distance
the parallel
surfaces,FIGURE
a following
procedure should be required using the
7. EMITTER TEMPERATURE AND SHORT
gonio-stage and the
piezo-actuator
beforeINthe
emitter was
CIRCUIT
CURRENT DENSITY
NEARgroup,
Tokyo
Tech
(AJTEC2011-44513)
REGIME
WHILE
USING
GaSb-TPV
heated.K.InHanamura’s
the first FIELD
step,
the
emitter
surface
was
rotated around
the x-axis, which was fixed onCELL
its surface. Just when the
surface contacted with the electrode, some electric current can
be conventional
detected. The
rotated angle
wasif recorded.
In the
second
propagating
radiation
the fill factor
is kept
at step,
theconstant.
emitter However,
surface was
rotated in
the opposite
direction
the conversion
efficiency
does notangle
change
only thewith
incident
energy
is enhanced
up so
tomuch
madebecause
on contact
the radiation
electrode
again.
Then, the half
effect. in
Asthe
a result,
energy
which the
is not
of by
the near-filed
rotated angle
secondthestep
becomes
first step
7
Proposed Device
Schematics
8
Fabricated Device
9
Measurement of Near-Field Thermal Radiation
(b)
M. Lim, S.S. Lee, and B.J. Lee, Physical Review B 91, 195136, 2015.
10
Advantage of the Proposed Device
Measured capacitance is related to the separation distance
Cm = ✏
Alternatively, C =
Thus, dm = L
"Z
Z
L
0
WL
dm
dA
✏
=
d(x)
dx
d(x)
#
Z
L
0
W dx
✏
= ✏W
d(x)
Z
L
0
dx
d(x)
1
= davg
According to Derjaguin approximation,
hR,avg ⇥ (W L) =
Z
A
hR {d(x)}dA
Since hR is predicted to be proportional to 1/d when the vacuum gap width varies from 200 nm to 1200 nm,
hR,avg
a
=
L
Z
L
0
dx
a
+b=
+b
d(x)
davg
The average radiative heat transfer coefficient is nothing but the radiative heat
transfer coefficient at the average gap distance.
11
Remaining Challenges
! Near-field enhancement of radiative heat transfer becomes significant
when the vacuum gap distance between parallel plates is less than
200 nm. But maintaining such a small gap distance between parallel
plates (with wide surface area) is extremely challenging.
! One of the most prominent applications of near-field radiation is a
thermophotovoltaic (TPV) energy conversion, which requires planar
geometry with wide surface area.
! We may also need to seek alternatives. For instance, we can modify
surface conditions using optical metamaterials including graphene in
order to further enhance the near-field thermal radiation at achievable
vacuum gap distance.
12
Spectral Control of Near-Field Radiation
Fig. 6. Contribution of graphene to the net heat transfer.
Fig. 1. Schematic of the near-field thermal radiatio
graphene separated by vacuum gap d (a) in three-dim
coordinate. A monolayer of graphene is modelled as
Fig. 5. Contour plot of S(β , ω ) with respect to the parallel wavevector component β normalized by plasma frequency (ω p = 2.90 × 1014 rad/s) of doped Si at 1019 cm−3 and 400
K. SPP dispersion curves are also overlaid. Source and receiver configurations for each
case are listed in Table 1.
to employ a monolayer of graphene with its chemical p
Graphene, a two-dimensional (2-D) lattice of carb
tal and electronic quality, draws enormous attention d
electronic and photonic devices [14, 15]. Because plasm
to near-infrared spectral region by modifying electron
focus on the role of graphene on the near-field radiativ
Fig. 7. Net heat transfer between graphene-coated Si plates at 1017 cm−3 with respe
Lim, S.S. Lee, and B.J. Lee, Optics Express 21, 22173–22185, 2013.
tiongap
onM.
near-field
thermophotovoltaic devices [21, 22].
the vacuum
width.
gated the effect of graphene on the near-field heat 13
tran
Graphene-Assisted NF-TPV System
d
Graphene
r
z
Fig. 3. Contour of Sβ ,λ (β , λ ) in logarithmic scale: (a)-(c) d = 10 nm and NSi = 1 × 1020
cm−3 ; (d)-(f) d = 10 nm and NSi = 5 × 1020 cm−3 ; and (g)-(i) d = 50 nm and NSi = 1 ×
1020 cm−3 . For simplicity, the parallel wavevector component β is normalized by bandgap
wavelength (λg = 7.29 µ m). Surface plasmon dispersion curves are also overlaid.
wever, the heat transfer enhancement is not as significant as in Fig. 3(c).
M. Lim, S.M. Jin, S.S. Lee, and B.J. Lee, Optics Express 23, A240-A253, 2015.
14
Extending Graphene’s Effects to Longer Distances
1
Doped Si Source (1×1020 cm-3) 500 K
.
Graphene
0
d
d
td
Dn
Figure 4. Spectral photocurrent densityDgenerated in the TPV cell when interf
r
SiO2 with thickness of
10
nm
(i.e.,
t
nm):
(a)
d
=
10
nm
(b)
d
= 50 nm (c
d = 10
p-doped
InSb
TPV
cell
300
K
r
200 nm. n-doped
2
··
Graphene
1
z
z
M. Lim, S.S. Lee, and B.J. Lee, 8th International Symposium on Radiative Transfer, RAD-16, June 6-10, 2016 .
Figure 5. Power output with respect to the vacuum gap width depending on t
15
HMM emitter is used from point of view of the effective medium theory. Figures 4(a) and 4(c)
show the contour of function S(β , ω ), defined in Eq. (1), for cases of the HMM emitter and pain
HMM-Assisted NF-TPV System
(a)
(b)
Tungsten substrate
SiO2
TPV cell
Vacuum
Receiver
Type Ⅱ
Hyperbolic Band
Tungsten
Type Ⅱ
Hyperbolic Band
2N
2N-1
r
z
}
Nth period
dd
dm
Tungsten
HMM
Source
SiO2
Tungsten
SiO2
2
1
}
0
d
1st period
p-region
Lp
Depletion region
Ldp
n-region
Ln
InAs
(c)
(d)
W substrate
Vacuum
InAs
Fig. 4. Contour plot of (a) S(β , ω ) and (b)
W substrate
Vacuum
InAs
S.M. Jin, M. Lim, S.S. Lee, and B.J. Lee, Optics Express 24, A635-A649, 2016.
p-polarization exchange function ξ p (β , ω ) with
16
3rd International Workshop on Nano-Micro Thermal Radiation (NanoRad)
(June 26-28 2017 at KAIST, South Korea)
Co-Chairs:
Bong Jae Lee, KAIST, South Korea
Mathieu Francoeur, University of Utah, USA
Long Shuai, Harbin Institute of Technology, China
17