1
Resonant
Thermoelectric Nanophotonics
Kelly
W. Mauser
1
, Slobodan
Mitrovic
2
, Seyoon
Kim
1
,
Dagny Fleischman
1
,
and
Harry
A.
Atwater
1,3
,
*
* haa@caltech.edu
1. Thomas J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA
9112
5, United States
2. Joint Center for Artificial Photosynthesis, California Institute of Technology, Pasadena, CA 91125,
United States
2
. Kavli Nanoscience Institute, California Institute of Technology, Pasadena, CA 91125, United States
Photodetectors are
typically
based on photocurrent generation from electron
-
hole pairs in
semiconductor
structure
s and on bolometry for wavelengths that are below ba
ndgap
absorption. In both cases, resonant
plasmon
ic and nanophotonic
structures have been
successfully used t
o enhance
performance. I
n this work, we
demonstrate sub
wavelength
thermoelectric
nanostructures
designed
for
resonant
spectrally selective absorption
,
which
create
s
large enough localized temperature gradients to generate
easily measureable
thermoelectric
voltage
s
. We show that such
structure
s are
tunable and are
capable of
highly
wavelength specific
detection
,
with
an
input power responsivity
of up to
1
19
V/W (referenced
to incident illumination),
and
response times of nearly 3 kHz,
by
combining
resonant
absorption
and thermoelectric
junctions
within a single structure
, yielding a
bandgap
-
independent
photodetection mechanism. We
report results for both
resonant nanophotonic
bismuth telluride
–
antimony
telluride
structures
and chromel
–
alumel
structures
a
s
examples of
a
broad class of nanophotonic thermoelectric
structures useful
for fast, low
-
cost
and robust optoelectronic applications such as non
-
bandgap
-
limited hyperspectral and
broad
-
band photodetectors.
2
Plasmon excitation
enable
s
extreme light confine
ment at the nanoscale, localizing energy
in subwavelength volumes and thus can enable increased absorption in photovoltaic or
photoconductive detectors
1
. Nonetheless, plasmon
decay
also
results in
energy
transfer
to the
lattice
as heat which
is det
rimental
to
photovoltaic detector
performance
2
.
H
owever
,
heat
generation
in resonant subwavelength nanostructures
also represents a power source for
energy
conversion, as we demonstrate here via design of resonant
thermoelectric
(TE
)
plasmonic
absorbers
for
optical detection. Though TEs have been used to
observe
resonantly coupled
surface plasmon polaritons
in
noble
-
metal thin films and microelectrode
s
3,4
and have been
explored theoretically
for
generation of ultrafast intense magnetic pulses
in
a dual
-
metal split
ring resonator
5
, they have
not been employed as resonant
absor
ber
s
in
functional
TE
nano
photonic
structures
.
Previously,
non
-
narrowband
photodetection
has been dem
onstrated
through
the
photothermoelectric effect in gated graphene
structure
s
6,7
and
the laser heating of
nanoantennas
and micropatterned
m
aterial
s
8
-
22
,
all
shown to be pro
mising fo
r infrared to teraherz
broadband detection.
Typical responsivities of the graphene
structure
s are around
10 V/W
for IR
and THz detectors, relative to incident (not absorbed) power
, with
a
time response ranging from
23 ms to nearly 10 ps.
Respons
ivities of non
-
graphene detectors
range from 10’s of V/W to
nearly
2,400 V/W
13
for thermopile
s made of many thermocouples. The response time of these
structures range from 10’s to 100’s of ms, though G
Hz response
times
have been
predicted
8
for
nanoantenna structures
.
High
-
figure
-
of
-
merit TE’s have been investigated as solar power
generators, but the light absorption process was entirely separate from the
TE
fun
ctionality and
relied on black carbon absorbers
23
or solar concentrators
24
.
W
e propose and demonstrate
here
nanostructures composed of
TE
thermocouple
junct
ions
using established
TE material
s
–
chromel
/
alumel and bismuth telluride
/
antimony
telluride
–
but patterned
so as to
support guided mode resonances
(GMRs)
with s
harp absorption
profiles, and
which thus
generate large thermal gradients upon optical excitation
and localized
heat generation
in the TE material.
Unlike the TE
absorbers described above
,
they feature
tunable
narrowband
absorption and
measured
single junc
tion
responsivities 10
times higher
than
the most similar graphene structures
6,22
, with potential for
much
higher responsivities
in
thermopil
e architectures
.
For bismuth telluride
–
antimony
telluride
structure
s
, w
e measure
thermoelectric
voltage
s
(TEV
s
)
up to
850 μV
with inciden
t optical power densities of 3.4
W/cm
2
.
The maximum responsivity
of a single thermocouple
structure
was measured at 1
19
V/W,
3
referenced
to incident
illumination
power. We also find that the
small heat capacity of optically
resonant
TE
nanowires enables a fast, 337 μs
temporal response
,
10
-
100 times faster than
conventional TE detectors
.
We note that TE
nanostructures have also been shown to display
improved performance
25
-
29
by increased phonon boundary scattering in high surface
-
to
-
volume
ratio geometries with dimensions comparable to phonon mean
-
free
-
paths; while we do not
believe that
our
structure
s at present exploit this phenomenon, this represen
ts an opportunity for
future nanophotonic
TE
structures.
We show
that
TE
nanophotonic structures are
tunab
le
from
the visible to the MIR,
with
small
structure
size
s
of 50
μm
x 100
μ
m
.
Our nanophotonic TE
structures
suspended on a thin membrane
s
to
reduce
substrate
heat losses
and improve thermal
isolation
between
TE
structure
s
arranged in arrays
suitable
for
imaging or spectro
scopy
. Whereas
photoconductive and photovoltaic detectors are
typically insensitive to sub
-
band
gap
radiation,
nanophotonic
TEs can b
e designed to be sensitive to any specific wavelength
dictated by
nanoscale
geometry
, without bandgap wavelength cutoff limitations
. From the point of view of
imaging and spectroscopy, they
enable
integrat
ion of
filter
and
photodetector function
s
into a
si
ngle
structure
.
POWER FLOWS IN T
HERMO
ELECTRIC PLASMONIC STRUCTURES
Fig
ure
1a depict
s
power flows in a
nanophotonic
TE
structure
, and Fig
s
. 1b
,c
shows a
schematic of our
experimental
structure
,
a
guided mode resonance (
GMR
)
wire array
,
in which
optical ra
diation is
coupled into a waveguide mode via
a
periodic
TE wire
array
that serves as
a
light absor
ber
.
O
ptical power is generated at the TE junction, while the ends of the TE wires are
at ambient temperature
,
resulting in
a
thermoelectric voltage (
TEV
)
.
Our
nano
photonic
TE
structures
on
membrane
substrate
s
have
dimensions large enough that bulk heat
transport
equations
can be used
(i.e. no ballistic
or quantized
thermal conductance).
T
he steady state
temperature of
the
illuminated region is found
by balan
cing light absorption
with
energy
loss
via
radiation, conduction through the interface,
conduction to the unilluminated
material, and
convection to the
surrounding gas ambient
:
푃
푎푏푠표푟푏푒푑
=
푃
푟푎푑푖푎푡푒푑
+
푃
푖푛푡푒푟푓푎푐푒
+
푃
푐표
푛
푑푢푐푡푒푑
+
푃
푐표푛푣푒푐푡푒푑
To characterize the
responsivity
, we
seek
to determine the
TEV
,
proportional to the
Seebeck coefficient
,
S
, and the
temperature
difference
ΔT
,
between cold and hot end
s
of the
material,
i.e.,
푇퐸푉
=
푆
∆
푇
.
4
At s
teady state, the
balance of absorbed
power
and dissipated power
is then
∫
1
2
휔
휀
′′
|
푬
|
2
푑푉
푉
푇퐸
=
∫
푒휎
(
푇
4
−
푇
0
4
)
푑퐴
퐴
푎푖푟
−
∫
휅
∇
푇푑퐴
퐴
푠푙푖푐푒
+
∫
ℎ
(
푇
−
푇
0
)
푑퐴
퐴
푎푖푟
+
∫
ℎ
푐
(
푇
−
푇
푠푢푏
)
푑퐴
퐴
푖푛푡푒푟푓푎푐푒
,
(
1
)
where
ω
is the incident light
frequency
,
ε’’
is the imaginary part of the
TE material
dielectric
function,
|
푬
|
is the
magnitude of the electric field within
the TE material,
V
TE
is the volume of
the illuminated TE material,
e
i
s the
TE material
e
missivity,
A
air
is the area of the TE exposed to
the air,
σ
is the Stefan
-
Boltzmann constan
t,
T
0
is the initial temperature
(also
cold end
temperature
/ambient air temperature
),
κ
is the
TE material
thermal conductivity,
A
slice
is the
TE
material
cross
-
sectional area separating the illuminated and unilluminated regions,
h
is the heat
transfer coefficient between the TE material and air,
h
c
is the thermal boundary conductance
between the T
E material and the substrate,
T
sub
is the temperatur
e of the substr
ate near the TE
material, and
A
interface
is the area of the intersection of the TE material with the substrate.
A
structure
optimized for
maximum responsivity (minimize power lost from the illuminated region
and maximize
power
absorbed into
the illuminated region)
would be
a
perfectly absorbing
structure
that is
non
-
emissive
in directions other than the light absorption direction
, suspended in
vacuum.
Our design is a compromise
among these factors
, with a temperature
increase over
ambient
ΔT
of approximately
1
K calculated
via
this simple
model
(see Supplementary
note 1
)
.
As an
example of a
TE
plasmonic nanostructure, we consider a periodic array of wires
composed o
f
TE
materials on a thin, suspended,
electrically insulating, low thermal cond
uctivity
substrate.
A wire
array/substrate heterostructure support
ing
GMRs
in
an n/p
-
type
TE
junction
is
shown
in
Fig.
1c
.
An
alumel
/
chromel
junction structure is shown in Fig. 1d, with
wires
100 nm
in width, 40 nm in height, and
470
nm
period
,
fabricated
on a 145
nm thick
freestanding
5
dielectric slab
waveguide
composed
of
45 nm
SiO
2
and
100 nm
SiN
x
layers
, and this structures
yields
the
resonant absorption spectrum depicted in
Fig.
1
e
.
T
he absorption
resonance
can be
shifted
by
several hundred nm
by varyi
ng the wire array period
.
Thus a
periodic til
ing of wire
array pixels
each with a different
period
and resonance frequency
could
function as a
TE
hyperspectral detector, shown conceptually in
Fig.
1
f
.
PHOTONIC DESIGN OF RESONANT THERMOELECTRIC STRUCTUR
ES: LINE
SHAPE AND PEAK POSITION
N
anophotonic
TE
structure
s
must concentrate the electric field in the
TE
material to
maximize absorption
.
Our GMR
st
ructure
s
acheive
this
via Fano
interference
30
of
a
waveguide
mode and
a
F
abry
-
P
erot
resonance
in the waveguide (
c.f.,
Supplement
ary Fig
s
. 1
-
3
,
Supplementary
equations (
S
2
-
S
7)
)
.
T
he location of this
waveguide
mode is predicted
quite well
by
the grating coupler equation for normal
ly
incident light, assuming infinitely narrow gratings,
2
휋
푑
=
훽
,
where
d
is the grating pitch and
β
is the
propagation
constant of
the
two
-
layer slab
waveguide
;
while interaction with the Fabry
-
Perot resonance shifts the waveguide resonance,
this a small correction
.
A wide range of
materials
with
varying Seebeck coefficients
including Al, Cr, antimony
t
elluride, and doped Si give rise to
GMRs
with
very similar
peak height
s
,
positions
, and width
s,
as shown in
Fig.
2a
(see Supplementary Fig.
6
for the dielectric function of antimony telluride)
.
Antimony telluride and Cr
exhibit
large
extinction
k
at the
wa
veguide
resonance
wavelength
and
are plasmonic
(
ε
’<0)
in this wavelength range
;
Al, which has a
larger magnitude
negative
ε
’
in
this region
has a narrower resonant linewidth, whereas
Au, Cu, and Ag have
resonances shifted
due to
interband transitions or pl
asmon
resonances
that couple to
the waveguide mode caus
ing a
Rabi splitting of the modes
31
.
Cross
-
sections of
bismuth
telluride wire
GMR structures
are
shown in Fig
s
.
2
b
-
g,
with
40
nm
height,
68
nm wid
th
and
48
8
nm
period
on top of a 50 nm
SiO
2
/
100
nm SiN
x
waveguide
layer
, all suspended in air.
Fi
gure
s
2
b,d,f,h
correspond to the absorpti
on maxima wavelength,
and Fig
s
.
2
c,e,
g
correspond to the absorption minima just to the
left of the maxima, as shown in
Fig
.
2
i
. Figure 2
b
shows the electric field
surrounding
the wires
at the maximum absorption
6
wav
elength
,
resulting from
a constructive interference of the waveguide mode and the Fabry
-
Perot resonance
.
The
large electric field magnitude
in
the wire correspond
s
to high
power
absorption
on resonance
, shown in Fig
.
2
d
(inset is enlarged wire
), whereas F
ig.
2
c
illustrates the
off
-
resonance electric field, at an
absorption
minimum
, shown in
Fig
.
2e
.
Fig
ures
2
f
and
g
are
two
-
dimensional
simulations
that
indicate
the
wire array
temperature distributions
on and off
resonance
,
also indicating
a large temperat
ure difference between these states
.
Figure
2
h
is a
three
-
dimensional thermal simulation
of
an
array of
antimony telluride
/
bismuth telluride wire
junction
s
under
Gaussian
illumination
with a
1 μm
beam
waist
.
This simulation indicates a
locally elevated te
mperature at the junction and small
temperature difference between
center
and
edge of
our
structure
, which
sustains a
temperature gradient in steady state.
For computational
reasons, t
h
e 3 μm x 5 μm
simulation
field
is smaller than
the
50
μm by 100 μm
field
in our
experimental structures
, which
are expected to sustain
a
larger
temperature gradient
between hot
and cold regions.
Figure 2
i
shows
the absorption and corresponding
wire
tempe
rature
spectral
distribution
obtained
from
the two
-
dimensional
simulation
s
.
We see that
the
temperature
spectral distribution
do
es
not exactly follow the absorption spectr
um
,
which we interpret as
nonlinear wire heat loss with temperature, since the
radia
tive power term (see e
quation
(
1
)
)
depends on the fourth power of temperature
.
TE
nanophotonic
structures
supporting
GMRs
exhibit
tunable
narrowband
absorption
over a
wide wavelength
range
by variation of
wire array geometrical
parameters.
We
can tune
the
absorption
resonance
over
the
entire
visible spectrum
at constant waveguide thickness (50
nm SiO
2
, 100 nm SiN
x
) by
vary
ing the wire
array period, as shown in in Fig. 3a, for the structure
depicted in Fig. 3c.
The peak
spectral position
is
thus
ma
inly dict
ated by
the
wire
array period as
well as
w
aveguide thickness
and material
indices
, and
only slightly
by wire material
.
Variation
of
w
ire
width
results in a small
peak
s
hift
, but primarily increase
s
the
peak absorption and
linewidth
FWHM
, as seen in
Fig
s
.
3
a,
b.
We find that increased wire
height increase
s
peak
absorption
up to
a height of 40 nm, where
as
absorption
asymptote
s for greater thicknesses
(
see
S
upplementary Fig. 7
). Figure 3
d
shows
the experimental extinction (black line),
simulated
absorption
(r
ed line), and simulated best
-
fit (blue dotted line)
for parameters listed in
Supplementary Table 2
.
A
bs
orption
(red line, dimensions extracted from sample SEM images)
was calculated using
full wave
simulations and
푃
푎푏푠
=
1
2
휔
휀
′′
|
퐄
|
2
,
normalized to the incident
7
power input
in the simulation
. The
measured
absorption
(black line)
was
determined from
absorption =
(
1
–
transmi
ttance
–
reflect
ance
)
(described in Methods)
.
The peak
positions
in our
experim
ent closely match those
predicted by simulations, including the minor peak to the
short
wavelength side
of the
main
absorption peak, which is
due
to
the
off
-
normal incidence
illumination and the
angle sensitivity of
GMR
structures (see
S
upplementa
ry
Fig.
7
)
.
The
incident illumination angle used in simulation, either 0.5 or 1 degree off normal incidence, was
chosen based on the best fit to the data.
The general predictability of these peak locations using
simulations makes fabrication
of
a hyperspectral pi
xel much simpler.
The
most noticeable
discrepancy between our simulation and experiment is the FWHM of the peaks.
Our experiment
performed better than simulation in creating narrow FWHM peaks for use in a hyperspectral
detector.
This points to potential
ly a
geometrical
cause, such as
not perfectly rectangular
wires
or surface roughness
.
The best
-
fit simulation (blue dotted line) was
achieved by fitting
the
experimental data
with
alter
ed
wire dimensions in
simulation
s
. Values for the simulation and
best
-
fit simulation can be found in Supplementary Table
2
. The best
-
fit simulation wire width
was thinner than the experimentally measured wire width by between 0
-
29 nm.
Fitting
experimental and simulat
ion spectra to a
F
ano shape
32
for one wire pitch
(described i
n
S
upplementa
ry
Fig
s
. 1
-
5,
Supplementary
Table 2
), we found that
the experiment
al spectra
exhibited larger damping caused by
loss
es
in
our
structure
, which altered the absorption spectra
shape
.
T
he
absorption
maxima can be tuned across several hundred
nanometers of wavelength
for a
gi
ven
waveguide thickness
. To access IR waveguide modes
which produce large
absorption peaks
,
the waveguide
thickness must be increased.
Figure 3
e
shows wavelength
versus
wire pitch for a 50/100 nm
SiO
x
/
SiN
x
waveguide thickness.
This
configuration is ideal
for sensing visible
to NIR
wavelengths.
Again, w
e can determine the
approximate
absorption
peak location
in our system
using
2
휋
푑
=
훽
.
As s
hown in Fig
.
3
f
, b
y
selecting a 300/500 nm thick
SiO
2
/SiN
x
layer, we can shift the
absorption
peaks
beyond
the detection limit of Si
photodetectors
, which is around 1100 nm
.
W
e can
create
absorption peaks in the MIR around
4
-
5
μm
if we ad
just the waveguide spacing to 500/500 nm SiO
2
/SiN
x
and increase the pitch to
several microns, as shown in Fig
.
3
g
.
In
principle
, the only limitation
in IR tun
ability for
these
8
detectors is
the phonon absorption band in
SiO
2
(and
SiN
x
) at around
8
-
11
μm
33,34
. Using
different materials as a waveg
uide layer could
further
extend
the range of these detectors.
SPECTRAL RESPONSE AND RESPONSIVITY
Figure 4 summarizes the measurements
for
our TE plasmonic GMR
structures
.
W
e
found the voltage to be linearly dependent on incident
power, as shown in Fig
.
4
g for a bismuth
telluride
–
antimony telluride
structure
with absorption spectra depicted by the red curve in Fig
.
4c.
We found
weighted
root mean squared error
values of
0.58 μV, 0.45 μV, 1.05 μV, 0.82 μV,
and 0.74 μV
for our
first order polynomial fit
for 700 nm, 675 nm, 650 nm, 625 nm, and 600 nm,
respectively, which strongly su
ggests
linear dependence of TEV on incident power.
F
or
each
wavelength
,
the
voltage
amplitude is proportional
to
power
absorbed
, i.e.
a wavelength
of
65
0
nm
yields
highe
r abso
rption and voltage than
60
0 nm
wavelength
for the same incident power.
The temperature scale in Fig
.
4
g
is based on an estimated Seebeck coefficient of 145 μV/K for
antimony telluride and
–
50 μV/K for bismuth telluride based on fabri
cation methods (see
Supplementary
note 6
for details). A
maximum
temperature
gradient
ΔT
of
~ 4.5
K
, depicted in
Fig.
4g,
was estimated based on these Seebeck coefficients and this
lies
in the general
validity
range
for the analytical power balance in
e
quation
(
1
)
(see Suppl
ementa
ry
note 1
for explicit
calculations
).
Figures 4
a
-
c
show the spectral voltage response of a c
h
romel
-
alumel
structure
(Fig
.
4
a
)
and a bismuth telluride
-
antimony telluride
structure
(Fig
s
.
4
b,
c
). Figure
s
4
a
,
b
show
TE
response
spatially
averaged over a
~400 μm
2
area of the wire
array; these measurements have
larger signal
error bars, but
indicate
a measureable signal
even if the wires are not illuminated
on
ly
at the
TE
junction.
Figure 4
c
shows a
time
-
averaged response
for temporall
y
-
chopped illuminatio
n over
400
periods
for the
same
structure
with
a
tightly focused source illuminat
ing
the TE junction
.
In
Fig
s
.
4
a
-
c
, spectral
features of the voltage
signal
are seen to
parallel the
spectral
absorption
. For
example, in
Fig
.
4c,
we can see a voltage signa
l is prod
uced with a FWHM of around
20 nm.
Small
discrepancies between absorption and voltage spectra are likely due to the
sensitivity of
GMR
structures to illumination incidence
angle
(see Supplementary Fig. 7).
9
A
lumel and
chromel
have
larger thermal c
onductivities
than bismuth telluride or
antimony telluride
,
giving
a lower
ΔT
upon illumination
(see e
quation
(
1
)
),
and
have
smaller
Seebeck coefficient
s
, resulting in a
peak potential of 35 μV under
7.92
μW
illumination
for
alumel
-
chromel
,
comp
ared with a
peak of 800 μV for
bismuth telluride
-
antimony te
lluride
under
the same illumination
.
The
structures
shown in Fig
.
4
b
-
c
are predicted to
exhibit
a
~
4
K
peak
temperature gradient
for
an
800
μV
TEV
,
assuming the above
-
mentioned
Seebeck coe
fficients
for bism
uth telluride and
antimony telluride
.
In Fig
ure
4d w
e
indicate
the responsivity
of bismuth telluride
–
antimony telluride
structures
as a function of wavelength
,
t
he noise spectral density
(
Fig
.
4
e)
, and noise equivalent
power
(
Fig
.
4
f)
.
Compared to a si
milar
graphene photothermoelectric
structure
6
(
with reference
to incident light), our structure has
a larger maximum responsivity, over 119 V/W,
with a similar
noise equivalent power range of
2.5
-
4.8 nW/Hz
1/2
.
The
noise spectral density
, with a
range
of
300
-
320
nV/Hz
1/2
,
could be further decreased
by reducing
the
wire array
resistance and better
controlling the environment (
e.g.,
eliminating noise due to temperature fluctuations from
convection).
Assuming a
spot s
ize
equal to the
detector area, this gives a maximum selective
detectivity (
D*
) of 6.05 x 10
5
cm
-
Hz
1/2
/W
, or detectivity (
D
) of
3.92 x 10
8
Hz
1/2
/W.
The
responsivity of these
structure
s could be increased further in a number of ways, including
through the
rmopiling,
optimizing the
TE
materials (e.g.
increasing
S
in high
-
ZT tellurides by
substrate heating during deposition or doping to i
ncrease the Seebeck coefficient
35,36
), or th
r
ough
altering any of the parameters
described in equation (1), such
as
measuring in vacuum to
eliminate convective loss and/or suspending the wires to eliminate conductive losses to the
substrate.
Measurements of the r
esponse time
under chopped illumination yielded
time constants
of
152.77
μ
s
±
3.05 μs and 153.38
μs
±
3.25 μs during heat up and cool down, respectively
(see
Fig
s
. 4h,
i)
. This corresponds to a
10%
-
90%
rise time of ~337 μs, or almost 3 kHz
, which is
a
fast enough response for many detection and imaging applications.
Th
is
respon
se
t
ime could be
further
reduced by use of smaller TE
structures
that
decrease the overall heat capacity
while
maintaining high
absorptivity
.
We
note that resonant nanophotonic TE structure design could be extended to
a variety of
TE configurations and res
onant
nanophotonic
structures
,
several of which are illustrated
in
Fig.
10
5
, including
the
GMR
structure
s in Fig
.
5a
and
a
thermopile
configuration
designed
to increase
the
TEV responsivity
in Fig. 5b
.
F
or
example,
a 25 wire bismuth telluride
-
antimony tellur
ide
thermopile
structure with a responsivity of 100 V/
W per thermocouple under 8 μW of
illumination
would
create a 20 mV signal
, with
no change in response time and a decrease in
noise
equivalent power
.
A
ddition of a backreflector below the dielectric lay
ers
could be
employed
to
alter the
waveguide
mode profile
,
resulting in a perfect absorber
geometry
(Fig. 5c)
.
Plasmonic
bow
-
tie
antenna
s
37
could
also
be
design
ed
to concentrate
illumination
at
a
TE
junction
(Fig. 5d)
, and resonant nanoparticle
plasmonic structures
could be used to induce
wavelength
-
specific
resonant absorption in
a
n unpatterned
thin
plan
ar
TE
sheet
, as
depicted
in
Fig.
5
e
.
Finally
, TE materials could be incorporated
in an even broader array
of
resonant
absorber
design
s
38
-
41
,
e.g.,
a
split ring resonator
perfect absorber
42
resonantly exciting
a thin TE junction
,
illustrated in Fig. 5f
.
Acknowledgements
This work was supported
primarily
by US Department of Energy (DOE) Office of
Science grant
DE
-
FG02
-
07ER46405
.
S.K. acknowledges support by a Samsung Scholarship.
The auth
ors thank
K. Schwab for discussions.
Author contributions
K.W.M. and H.A.A. conceived the ideas. K.W.M., S.K
performed the simulations. K.W.M.
fabricated the samples. K.W.M.,
S.M.
and D.F
. performed measurements and
K.W.M., S.M.
performed
data analysis. K
.W.M.
,
H
.
A
.
A
.
and S.M.
co
-
wrote the paper, and H.A.A. supervised
the project.
Competing financial interests
The authors declare no competing financial interests.
Methods
STRUCTURE
FABRICATION
11
The
TE
hyperspectral detectors were fabricated as follows.
On top of the waveguide layer of
100 nm thick SiN
x
membrane (Norcada
NX7150C
), the 50 nm SiO
2
spacer layer was deposited
via PECVD (Oxford Instruments System 100 PECVD) at 350°C with 1000 mTorr pressure, with
flows of 710 sccm NO
2
and 170 sccm 5% SiH
4
in
N
2
.
The structures were written via electron beam lithography (Raith EBPG 5000+ Electron Beam
Writer) in a series of aligned writes, followed by deposition and liftoff. For all of the writes, a
bilayer electron beam resist consisting of 50 nm 950 PMMA A
2 on 200 nm 495 PMMA A4 was
spun on top of the SiO
x
spacer layer. Each layer was baked for 5 minutes at 180°C in ambient
conditions after spinning.
The order of structure fabrication was first alignment markers, then the bismuth telluride
(or
chromel)
s
tructure half, then the antimony telluride
(or alumel)
structure half, followed by
contacts for wire bonding. The alignment markers and contacts were written with a dosage of
2100
-
2300 μC/cm
2
, and a beam current of 10
-
50 nA. The resist was developed in a
room
temperature mixture of 1:3 methyl isobutyl ketone:IPA for 50 seconds, submerged in IPA, and
dried with N
2
. Using electron beam evaporation (Lesker Labline E
-
Beam Evaporator), 3
-
5 nm of
Ti was deposited, then 60
-
70 nm of Au. Liftoff was performed by
agitation in 70°C acetone for
30 minutes, followed by an IPA rinse.
The bismuth telluride and antimony telluride structures were written with the same dosage and a
beam current of 500 pA. They were developed in 4°C 1:3 methyl isobutyle ketone:IPA for 60
seconds, submerged in IPA, and dried with N
2
. Bi
2
Te
3
and Sb
2
Te
3
stoichiometric sputter targets
(Stanford Materials) were used in a house
-
modified sputterer (Lesker). Base pressures were in
the 10
-
6
Torr range, process pressure was 30 mTorr, gas flow was
100 sccm Ar, and the power
was 40 W RF to sputter 40 nm of each material. Liftoff was performed in the manner described
above.
Alumel (
Ni/Mg/Al/Si 95/2/2/1 wt%
, VEM) and chromel (
Ni/Cr 90/10 wt%
, VEM)
sputter targets were used with base pressure 3 mTorr,
20 sccm Ar, and 500 W DC.
EXTINCTION MEASUREMENTS
Extinction measurements were done at room temperature using a house
-
built setup including a
2W supercontinuum laser (Fianium), a monochromator, and a silicon photodiode (Newport).
Transmission measuremen
ts were taken using a lock
-
in (Stanford Research systems Model
SR830 DSP Lock
-
In Amplifier) with a chopper and current amplifier (HMS Elektronik current
amplifier model 564). Extinction was calculated as 1
–
transmi
ttance
-
reflect
ance
.
POTENTIAL MEASUR
EMENTS
Voltage measurements were done at room temperature with a voltage amplifier (Signal Recovery
Model 5113 pre
-
amp) and a volt meter (Keithley 6430 sub
-
femtoamp remote source meter).
Voltage signals were normalized to incident power, and interpolated
using the verified relation
that voltage scales linearly with incident power. Space averaged data was taken by scanning x
versus y versus voltage over the
structure
for each wavelength and averaging a fixed set of pixels
in the excited region, subtracted
from a background voltage measurement off the
structure
. This
allowed for adjustments in case of sample or beam drift. Time averaged data involved locating
the beam at a place on the
structure
which produced maximum voltage for that wavelength, and
12
usin
g a chopper and oscilloscope with a voltage amplifier to measure hundreds of data points for
each wavelength.
SIMULATIONS
Simulations were done us
ing Lumerical FDTD Solutions
43
,
COMSOL Multiphysics
44
with RF
and Heat Transfer Modules
, and
rigorous coupled wave a
nalysis
45
.
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Figure 1 | Nanophotonic power flow and guided mode resonance design.
a
, Illustration of
t
he power flow in a TE plasmonic absorbing nanstructure.
b
, Conceptual design of
thermoelectric plasmonic wavelength detector. Light illuminates the junction of the
thermoelectric wires and is absorbed, heating the junction and producing a thermoelectric
voltage.
c
, Enlarged portion of the wire junctions in
b
. Wires sit on a suspended waveguide
composed of 50 nm SiO
2
/100 nm SiN
x
. This plasmonic grating/waveguide structure with 40 nm
high and 60 nm wide wires with a 488 nm pitch create the absorption pro
file shown in
e
.
d
,
False color SEM of a fabricated alumel
-
chromel detector, with gold contacts (50 μm scale bar).
Inset is the junction between bismuth telluride
-
antimony telluride wires in the same geometry
(500 nm scale bar). Fabrication is described
in Methods.
f
, Conceptual design for a
hyperspectral detector pixel. By tuning the wire pitch, the absorption peak can be shifted across
a several hundred nm range. By having an array of detectors of different pitches, incident light
can be decomposed
by wavelength.