In the format provided by the authors and unedited.
1
Supplementary Material for
Resonant Thermoelectric Nanophotonics
Kelly W. Mauser, Seyoon Kim, Slobodan Mitrovic, Dagny Fleischma
n, Ragip Pala, Keith
Schwab, and Harry A. Atwater
Supplementary Notes
Supplementary Figure 1 | Thermopile and wire length analysis.
a
, Absorption spectra used in
simulations for
b,c,e,f
.
b
, Responsivity for a structure with 50 μm long wires and 27 μm
long pads, as a
function of number of wires in
a thermopile configuration. The
entire structure is illuminated and
responsivity is calculated relat
ive to power striking the wire
area. The pads are assumed to have a 20%
absorption, independent of wavelength.
c
, Noise equivalent power (NEP) for the thermopiles in
b
,
assuming Johnson noise as the noise spectral density using simu
lated average temperatures.
d
,
Temperature difference between the edge of the pad and the cent
er of the wires versus power density for
different wire lengths. Pad sizes remain constant with dimensions of 50 μm by 27 μm by 50 nm.
e
,
Responsivity as a function of wavelength for the absorption spe
ctrum in
a
, for different wire lengths, relative
to power illuminating the entire structure.
f
, Noise equivalent power corresponding to the responsivity in
e
,
for different wire lengths. Noi
se spectral density is theoreti
cal Johnson noise using simulated average
temperatures for the structures
. Simulation details are given
in Supplementary Note 1.
Resonant thermoelectric nanophotonics
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Ϯ
Supplementary Figure 2 | Concep
tual design of hyperspectral pix
el.
Each thermoelectric structure in the pixel has a different wire pitch, causing each structure to have an
absorption peak that corresponds
to a different wavelength (Fig
. 3). When light of unknown wavelength
content illuminates the pixel, voltages will be produced in eac
h structure depending
on their specific
absorption profiles. Deconvolu
tion of these voltage signals th
rough an algorithm can enable identification
of the unknown wavelengths.
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ϯ
Supplementary Figure 3 | Fano resonance analysis.
a
, Diagram of interaction of bright (broad
resonance) and dark (narrow res
onance) modes in the production
of Fano lineshapes. The bright mode is
the Fabry-Perot resonance of light with k-vector parallel to in
cident illumination. Analysis from Gallinet et
al.
1
.
b
, Full wave simulation of Sb
2
Te
3
wires that are 60 nm wide, 40 nm thick, with a pitch of 431 nm
on a
50 nm SiO
2
/100 nm SiN
x
suspended waveguide, that is fit to the Fano formula (Suppleme
ntary equation
(S6)). Shown are the simulation (dotted orange), the fit of th
e combined Fano formula (black,
Supplementary equation (S6)) between 440 nm and 650 nm, and the
extracted Fano formula of the bright
mode (blue, Supplementary equation (S5)).
c
, The Fabry-Perot resonance (orange) is calculated viva full-
wave simulation as the normalized magnitude of the electric fie
ld at a point on the surface of a bare
waveguide structure. The bright
mode fit (blue) is described i
n
b
. The shift in the Fabry-Perot peak is
associated with the contributions
of the wires to the effective
index of the entire photonic crystal structure.
d
, Experiment versus simulation for 45 nm SiO
2
/100 nm SiN
x
suspended waveguide with Sb
2
Te
3
wires.
Wire thickness is 40 nm, width is 89 nm, and pitch is 511 nm.
Shown are the full wave simulation for this
structure (solid blue), the total Fano function fit (dotted mag
enta) to the full wave simulation with parameters
given in Supplementary Table 2,
and the bright mode (dotted blu
e) extracted from the total Fano fit function,
corresponding to the Fabry-Perot resonance. Also shown are the
measured absorption (solid orange), the
fitted total Fano function to the
measured absorption (dotted y
ellow), and the extracte
d bright mode profile
from the measured extinction (dashed purple).
e
, Extracted bright mode fo
r the experimental (dotted
orange) and simulated (dotted blue) data from
d
, with the simulated electric field magnitude (dotted yellow)
at the surface of the waveguide (
without the wires) due to the
Fabry-Perot resonance. All curves are
normalized to their maximum value in the given wavelength range for ease of comparing resonance peaks.
The experimental, simulated, and
Fabry-Perot peaks align reason
ably well.
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κ
Supplementary Figure 4 | Dependence of absorption spectra on in
cident illumination angle and wire
thickness.
a
, Measured absorption spectra for different angles of incidence
. An objective with numerical
aperture 0.14 was used, giving an angular spread even at normal
incidence, producing the side peak at
normal (0°) incident angle.
b
, Full wave simulations of the incident illumination angle depe
ndence of 40 nm
tall, 67 nm wide Sb
2
Te
3
wires with a pitch of 488 nm on a 50 nm SiO
2
on 100 nm SiN
x
waveguide. Even at
1 degree offset, the single peak splits into two.
c
, The dependence of wire thickness on absorption spectra,
with pitch of 488 nm. The absorpt
ion asymptotes to its maximum
value for wire heights around 40 nm.
b
c
a
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Supplementary Figure 5 | Thermoe
lectric dielectric functions.
a,c
, Dielectric functions of Bi
2
Te
3
from
300-1000 nm (
a
) and 2-31 μm (
c
).
b
, Dielectric function of Sb
2
Te
3
from 300-2000 nm.
a
b
c
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Supplementary Figure 6 | Focused versus unfocused, spatially un
iform light responsivity and noise
characteristics.
Focused (blue, 60 μm by 5 μm spot size,
e
) and unfocused, spatially uniform (orange, 120
μm by 100 μm spot size,
d
) illumination incident on Bi
2
Te
3
-Sb
2
Te
3
structures at given angles off normal
incidence, with ±1° error. A 5× objective with numerical apert
ure 0.14 was used for both the focused and
spatially uniform illumination data collection.
a
, The input power used to calculated responsivity in the case
of uniform illumination was only
the power that illuminated the wires (a 50 × 50 μm
2
area). The spatially
uniform illumination spot was 120 μm by 100 μm, and completely
covered the wires and pads of the
structure. Noise s
pectral density,
b
, was measured under the power spectrum shown in Supplementary
Fig. 9. Higher noise spectral density in focused light was lik
ely due to back currents from uneven heating
in the structure, discussed furt
her in Supplementary Note 6.
c
, Noise equivalent power was found to be
lower for spatially uniform illu
mination than for focused illum
ination, due to higher responsivity values
combined with lower noise values for spatially uniform illumina
tion.
d
, Black circle illustrates uniform
illumination of structure.
e
, Focused illumination used in
a-c
, Fig. 4d.
f
, Focused illumination in Fig. 4c.
d
e
f
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Supplementary Figure 7 | Chrome
l-alumel structure results.
Thermoelectric potential (TEV) and
absorption results for a chromel-alumel structure with the same
dimensions as that of the Bi
2
Te
3
-Sb
2
Te
3
structures. The stru
cture is under 70.92
μW illumination, or 3
0.4 W/cm
2
incident power density. Data points
are taken as the focused beam is moved across the junction of t
he detector (over a ~400 μm
2
area). All
data points are aver
aged together for a given wavelength.
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Supplementary Figure 8 | Responsivity from thermal simulations
with current and state-of-the-art
thermoelectrics. a-c
, Simulated absorption spectra for wires of the dimensions of t
he experimental Bi
2
Te
3
-
Sb
2
Te
3
structures at 1, 5, and 10 degrees off normal incidence.
d-l
, Responsivity calculated from thermal
simulations using absorption to guide power input at different
angles off normal incidence. 20% absorption
in the pads was assumed independent of wavelength. Simulated a
bsorption from
a-c
, thermal properties
and Seebeck coefficient of state-of-the-art thermoelectirc mate
rials, given in Supplementary Note 10, were
used in
d-f
. Simulated absorption from
a-c
, thermal properties given in Supplementary Note 1 and average
Seebeck coefficient of our materials (242 μV/K for Sb
2
Te
3
and -84 μV/K for Bi
2
Te
3
, see Supplementary Note
8) was used in
g-i
to calculate responsivity. Experimental absorption from Fig. 4
a, thermal properties from
Supplementary Note 1 and average Seebeck coefficient of our mat
erials (above) was used in
j-l
to
calculated responsivity. Deta
ils of thermal simulations are gi
ven in Supplementary Note 1.
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Supplementary Figure 9 | Laser power on wires.
Laser power illuminating the wire region as a function
of wavelength for focused illumi
nation (blue) and uniform illum
ination (orange).
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Supplementary Figure 10 | Resona
ntly excited nanophotonic therm
oelectric structures. a-d,
Conceptual images of the guided mode resonance structures in a
thermopile configuration (
a
), a gold
resonant bowtie antenna focusing the electric field on a thermo
electric wire junction (
b
), a perfect absorber
design on top of a thermoelectric junction (
c
), and a split ring resonator absorber with a thermoelectric
junction as a backreflector (
d
).
e-f
, Full wave simulations of the st
ructures above, with electric
field |
E
|
normalized by incident electric field |
E
0
|. Excitation wavelengths are 631 nm, 660 nm, 1,648 nm, and 1,710
nm, respectively. Scale bars for
e-f
are 2 μm, 200 nm, 300 nm, and 50 nm, respectively.
i,j
, Thermal
simulations of the resonant bowtie antenna and perfect absorber
design, respectively. The perfect absorber
array covers a 10 μm by 10 μm square in the center of a suspend
ed, thermoelectric junction on top of a
SiN
x
membrane. The “cold” ends of the thermoelectric materials sit
on a 100 nm SiN
x
/200 nm Au/20 μm
SiO
2
substrate. The Au layer acts as a high thermal conductivity h
eat sink to conduct heat away from the
“cold” ends of the thermoelectric materials. Both simulations
were performed in vacuum. The scale bars
in
i,j
, are 500 nm and 10 μm, respectively. The absorbed power in
i,j
, are 7.9 μW and 23 μW, respectively.
More details can be found in Supplementary Note 1,11 and Supple
mentary Figs. 11,12.
k
, Simulated
responsivity of the thermopiled
thermoelectric structure shown
in
a,e
, for 8 and 16 wire thermoelectric
junctions in series. More det
ails can be found in Supplementar
y Fig. 1.
l
, Simulated responsivity of the
resonant bowtie absorber.
m,n
, Simulated responsivities as
a function of incident angle of t
he perfect
absorber and split ring resonator
absorber, respectively. Furt
her details for calculations of
l-n
can be found
in Supplementary Fig. 11. In
k
-
n
, the combined Seebeck coefficient of the thermoelectric materi
als is
assumed to be 326 μV/K.
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Supplementary Figure 11 | Bowtie and other absorber designs.
a,b,c
Absorption cross-section or
absorption for the resonant bowti
e absorber, perfect absorber,
and split ring resonator absorber described
in Supplementary Note 1.
d,e,f
Temperature differences between
the hot and cold sides of the
thermoelectric materials as a function of power absorbed for th
e bowtie, perfect absorber, and split ring
resonator absorber described in Supplementary Note 1.
g,h,i
, Noise equivalent power (NEP) lower bound
as a function of wavelength for t
he bowtie, perfect absorber, and split ring resonator absorber described in
Supplementary Note 1. Details of calculations are given in Sup
plementary Note 11. Breifly, responsivity
results are shown in Supplementary Fig. 10k-n, and noise spectr
al density is calculated using theoretical
Johnson noise, assuming the measured resistivity of our Bi
2
Te
3
and Sb
2
Te
3
materials at room temperature.
j,
Thermal simulation of bowtie structure with absorbed power of
7.9 μW. Maximum temperature is ~330
K, but a smaller scale was used to show temperature differences
better. Scale bar is 20 μm and inset scale
bar is 500 nm.
k
, The same thermal simulation as in
j
is shown, but with the full temperature scale bar.
The outline of the bowtie is given in blue dotted line. Scale
bar is 500 nm.
l
, Thermal simulation for split
ring resonator perfect
absorbers utilizing
a thin membrane to l
ower thermal heat loss to the substrate. Total
absorbed power is 23 μW. Scale
bar is 10 μm. Further details
are given in Supplementary Note 1 and
Supplementary Fig. 12.
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Supplementary Figure 12 | Perfect absorber and split ring reson
ator thermal simulation design. a,
Diagram of thermal simulation desi
gn for a perfect absorber and
a split ring resonator thermal simulation
corresponding to data in Supplementary Fig. 10j,m,n and Supplem
entary Fig. 11e,f,h,i,l. The split ring
resonator design has a 50 nm thick SiN
x
membrane with 60 nm of thermoelectric material above it, which
serves as a backreflector in the optical design. The perfect a
bsorber has a 100 nm thick SiN
x
membrane
and 100 nm thick TE materials. It u
ses a 50 nm thick layer of
gold as the backreflector in the 10 μm by 10
μm center absorber patch. The 200 nm gold above the silica inc
reases thermal conduction of heat from
the cold end of the device (i.e. acts as a heat sink), and any
other thermally conductive material would
serve this purpose well. Thermal simulations involved a volume
tric heat influx into the centrally located
SRR or cylinder absorbers in the array (this assumes absorption
near the edges of the arrays would be
worse).
b
, Thermal simulation of perfect absorber with a total absorbed
power of 23 μW. The split ring
resonator thermal profile was sim
ilar (see Supplementary Fig. 1
1l).
a
b
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Supplementary Figure 13 | XRD data.
XRD data of 100 nm of Bi
2
Te
3
(left) and 50 nm Sb
2
Te
3
(right) show
very little crystallinity, as s
puttered in experiments. Two-di
mensional diffraction image frames were
collected with frame
centers set to 20, 4
0, 60 and 80 degrees in 2Ɵ, from right to left, and then merged.
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Supplementary Figure 14 |
XPS survey scans.
Sb
2
Te
3
(top) and Bi
2
Te
3
(bottom) samples.
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Supplementary Figure 15 | Compositional analysis.
Detailed XPS data and fits for bismuth telluride
peaks (
a-b
) and antimony telluride peaks (
c-d
) for our samples.
a
, Three components are visible in Bi 4f
levels: the major components are Bi
2
O
3
, and Bi
2
Te
3
(157.1 eV and spin-orbit pair at + 5.3 eV), with a small
amount of elemental bismuth (156.6 eV).
b
, Te 3d level in bismuth
-telluride is mostly TeO
2
and Bi
2
Te
3
(582.3 eV, SO-splitting of 10.4 eV).
c
, Sb 3d levels show that most of the surface of antimony-tellur
ide is
oxidized (Sb
2
O
3
), much more so than the bismut
h-telluride, with a measurable S
b
2
Te
3
component (538 eV).
d
, Te 3d levels in antimony-tellu
ride show the telluride, an oxi
de and elemental Te peaks.
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Supplementary Table 1
. Comparison of experimental dimensions and illumination angle
(Pitch
s
, Width
s
,
Ɵ
s
) with
best-fit simulation dimensions, illumination angle (Pitch
f
, Width
f
, Ɵ
f
) and scaling factor
corresponding to Fig. 3d in the main text.
Absorption
curve
Pitch
s
(nm)
Width
s
(nm)
Ɵ
s
(deg)
Pitch
f
(nm)
Width
f
(nm)
Ɵ
f
(deg)
Scaling
i
567
97
0.5
560
97
0.5
0.71
ii
566
91
0.5
560
90
0.5
0.66
iii
511
119
0.5
507
102
0.6
1.06
iv
509
98
0.5
507
87
0.6
0.87
v
511
89
0.5
507
82
0.6
0.76
vi
452
131
1
455
102
1
0.99
vii
452
101
1
455
87
1
0.87
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