Supporting Information
Development of Compact and Robust Mid-Infrared Spectrometer by using
Silicon/Air Hyperspectral Filter
Taeyoon Jeon,
Amirhossein Nateghi,
William Max Jones, Changsoon Choi,
Juan Pablo Cardenas, Charles
Ross and Axel Scherer*
Applied Physics and Materials Science, California Institute of Technology, Pasadena, CA 91125, United
States
*Email : etcher@caltech.edu
1. Measurement of refractive index of a-Si
The IR ellipsometry data is collected by using the J.A. Woollm IR-VASE Mark II spectroscopic
ellipsometer at three different angles, 55°, 65°, and 75°. The optical constants of the a-Si film were modeled
using 11 Gaussian oscillators along with a Kramers-Kronig consistent Sellmeier function using the WVASE
data analysis software. The native SiO
2
thickness on the Si wafer was predetermined and fixed in the model,
while the a-Si and surface oxide layer thicknesses were allowed to vary. The mean squared error was less
than 3, resulting in an excellent agreement between the measured and model-generated spectroscopic
ellipsometry data.
Figure S1. Measurement data of refractive index of a-Si deposited by using PECVD
2. Si/air filter fabrication
Fabrication procedure of Si/Air filter is described in Figure S2. Silicon and silicon dioxide (SiO
2
) layers
with
thickness are deposited by PECVD on top of silicon wafer (Figure S2A-1). Dot patterns were
λ
0
/4
n
푖
made by photolithography using S1814 photoresist on the Si/SiO
2
multilayer surface. The 300 nm
chromium (Cr) was then deposited and lift-off was performed to create a Cr hardmask with a hole pattern
on the surface of the Si/SiO
2
stack (Figure S2A-2). The multilayer stack of Si/SiO
2
was etched through
using SF
6
and C
4
F
8
plasma (Figure S2A-3). Then, after removing the Cr layer, the etched holes are filled
with SU-8 photoresist. The additional photolithography using UV light is performed to crosslink SU-8 in
the etched holes (Figure S2A-4). These SU-8 posts support free standing Si layers after etching SiO
2
layers.
The SiO
2
layers are etched out by dipping sample into the HF solution to form a Si/air mirror (Figure S2A-5).
Finally, the two silicon/air mirror sections are combined by placing two different thickness PDMS spacers
on the side portions of the silicon/air mirror with the desired thickness of the cavity length (Figure S2A-6).
Cross-sectional view of silicon/air mirror is shown in Figure S3.
The thickness of the Si/Air mirror (two pairs of silicon and air film) is 5.82 μm (each Si layer is 0.66 μm
and air layer thickness is 2.25 μm). And two mirrors thickness is 11.62 μm. Therefore, the PDMS
thicknesses to have a cavity gap between the two mirrors of about 3
μm
to 8
μm
are 14.62
μm
(11.62 μm +
3
μm)
and 19.62
μm
(14.62 μm + 3
μm).
These PDMS thicknesses can be prepared precisely by controlling
spin speed of spin-coating of PDMS precursor on the wafer. And after curing the PDMS, cut a small piece
of the PDMS membrane and transfer it to one of the mirrors as shown in Figure S2E.
Figure S2. (A) Fabrication procedure of Si/Air filter. (B) SEM image of number 3 step. (C) SEM image of
number 4 step. (D) SEM image of number 6 step. (E) Photographic image of two Si/Air mirrors. One has a
PMDS spacer. (F) Schematic diagram showing the thickness of PDMS on one mirror. (G) Measuring the
thickness of two PDMS films using Filmetrics.
Figure S3. Tilted SEM image of Si/air mirror.
3. Modeling of Si/air transmittance property.
The filter transmittance optical property can be calculated by using matrix multiplication of each interfaces
and phase accumulation on each layers. The boundary condition matching at interface of layer (
i
) and layer
(
j
) for S-polarization is obtained like following equation by assuming = (Figure S4A)
μ
i
μ
j
[
퐸
퐴
퐸
퐵
]
=
1
2
[
1
+
푛
푖
cos
휃
푖
푛
푗
cos
휃
푗
1
―
푛
푖
cos
휃
푖
푛
푗
cos
휃
푗
1
―
푛
푖
cos
휃
푖
푛
푗
cos
휃
푗
1
+
푛
푖
cos
휃
푖
푛
푗
cos
휃
푗
]
[
퐸
퐶
퐸
퐷
]
=
I
푖,푗
[
퐸
퐶
퐸
퐷
]
where and are refractive index and incident of angle in layer i.
푛
푖
휃
푖
Phase accumulation in layer (
j
)
[
퐸
퐶
퐸
퐷
]
=
[
푒
(
―
푖
푘
푗
푑
푗
)
0
0
푒
(푖
푘
푗
푑
푗
)
]
[
퐸
퐸
퐸
퐹
]
=
D
푗
[
퐸
퐸
퐸
퐹
]
where and are wavenumber and thickness of layer (j)
푘
푗
푑
푗
푘
푗
=
2휋
푛
푗
cos
휃
푗
휆
0
,
푑
푗
=
휆
0
4
,
푛
푖
sin
휃
푖
=
푛
푗
sin
휃
푗
By including the overall matrix multiplication in this system (Figure S4B),
[
퐸
퐴
′
퐸
퐵
′
]
=
I
2,1
D
1
I
1,2
D
2
I
2,3
D
3
I
3,2
D
2
I
2,3
D
3
I
3,2
퐶
I
2,3
D
3
I
3,2
D
2
I
2,3
D
3
I
3,2
D
2
I
2,1
D
1
I
1,2
[
퐸
퐴
′
′
퐸
퐵
′
′
]
=
[
푀
11
푀
12
푀
21
푀
22
]
[
퐸
퐴
′
′
퐸
퐵
′
′
]
,where
and
. Material 1 corresponds to a silicon wafer and has a
C
=
[
푒
(
―
푖
푘
2
푑
푐푎푣푖푡푦
)
0
0
푒
(푖
푘
2
푑
푐푎푣푖푡푦
)
]
퐸
퐵
′
′
=
0
refractive index of 3.4. Material 2 is air (n=1) and 3 is PECVD deposited silicon (n=3.3). Transmission
coefficient is calculated from
and transmittance is
.
1
푀
11
(
1
푀
11
)
2
For P-polarization, changes to
.
I
푖,푗
1
2
[
푛
푗
푛
푖
+
cos
휃
푗
cos
휃
푖
푛
푗
푛
푖
―
cos
휃
푗
cos
휃
푖
푛
푗
푛
푖
―
cos
휃
푗
cos
휃
푖
푛
푗
푛
푖
+
cos
휃
푗
cos
휃
푖
]
Figure S4. (A) Schematic drawing of electric field incoming and outgoing at each interface and layer with
two different polarization S and P. (B) Overall multilayer drawing for filter design. Number 1 is a silicon
wafer, number 2 is air, and number 3 is a PECVD-deposited silicon layer.
4. Investigate Q-factor of filter
Since a tilted cavity filter has a gradual change in cavity length, it is not easy to measure the Q-factor of
the filter from one single point of filter. So, we made a uniform-thickness filter (as shown in Figure S5A)
using the same-thick PDMS film to investigate the optical properties of the filter. In this experiment, a thick
PDMS spacer was used to generate multiple peaks within the free spectral range. The cavity gap is 14
μm.
Optical measurement was performed with an FTIR spectrometer. Figure S5B shows the measured
transmittance spectrum of a uniform cavity filter with 14
μm
cavity gap. This is well matched with the
calculated data in Figure S5C. At the central peak of the free spectral range (1075 cm
-1
), the FWHM value
is about 6.3 cm
-1
. And the peaks on the sides (1388 cm
-1
and 784 cm
-1
) have FWHM values of 10.3 cm
-1
and 9.8 cm
-1
. That is, the Q-factor appears high at the center of the free spectrum. The electric field
enhancement inside the cavity at three different resonant positions is calculated by Comsol and shown in
Figure S5D.
Figure S5. (A) Schematic of optical measurements of a uniform cavity filter. (B) Measured transmittance
data from a uniform cavity filter (14
μm
cavity gap). (C) Calculated transmittance data from the same
structure used in (B). (D) Enhancement of the electric field inside the cavity at three different resonance
peaks.
5.
Calculation of filter property depending on incident angle and polarization
The resonance wavelength shift depending on the cavity length is calculated based on the modeling in
Supporting Information 3. The amount of wavelength shift with different incident angle is shown in Figure
S6. Also, the resonance peak difference between S-polarization and P-polarization depending on incident
angle is shown in Figure S7.
Figure S6. Resonance peak position shift with different incident angle at different cavity lengths.
Figure S7. Resonance peak position difference between S-polarization and P-polarization by changing
incident angle.
6.
Blackbody radiation curve at 1000
°C
The blackbody radiation at 1000 °C calculated by Planck's law is shown in Figure S8. It has a peak at
2.27 μm.
Figure S8. The blackbody radiation at 1000 °C calculated by Planck's law.