Supplementary information for
Accurate Layers Determination of Graphene on Transparent
Substrate Based on Polarization-sensitive Absorption Effect
Peng Wang, Zhi-Bo Liu, Xu-Dong Chen, Fei Xing, Wen-Shuai Jiang, Bin Dong, Wei
Xin & Jian-Guo Tian
The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, Teda
Applied Physics School and School of Physics, Nankai University, Tianjin 300071,
China
S1. Transfer flow chart of exfoliated graphene.
Figure S1｜Transfer process for exfoliated graphene samples1: 1. Graphene
samples on SiO2/Si substrate. 2. PMMA is spin-coated on SiO2/Si substrate. 3. SiO2
layer is etched in hydrofluoric acid. 4. PMMA membrane with graphene samples is
detached in deionized water. 5. PMMA is transferred to the target substrate (quartz
plate). 6. PMMA is dissolved with acetone.
S2. Transfer flow chart of CVD graphene.
Figure S2｜Transfer process for CVD graphene samples2: 1. CVD graphene on
copper foil is planished between two glass slides. 2. The copper foil with graphene is
attached to the PET/Silicone membrane and is exerted pressure for several hours. 3.
The copper foil is etched in FeCl3 solution. 4. The PET/Silicone with graphene is
rinsed in deionized water. 5. Attach the membrane to target substrate (quartz plate)
and give some pressure. 6. Peel off the PET/Silicone membrane and the CVD
graphene is transferred to the new substrate. Step 1 to 6 can be repeated again and
again until the desirable layers number is made.
S3. Theoretical and experimental angle-dependent reflection for graphene of
different layers.
Figure S3｜ Simulation and experimental results showing angle-dependent
reflection for TE and TM polarized light. (a) Simulation of reflectance for TE and
TM polarized light for graphene layer 0L (no graphene), 1L, 5L, and 10L, the critical
angle c  43.2 and experimental angle e  47 (for setup in Fig. 1) are shown
with arrows. (b) The experimental results for TE and TM polarized light, 1L and 10L
graphene.
Fig. S3a and S3b demonstrate the simulated and experimental reflectance for TE
and TM wave with different graphene layers. When the incident angle is larger than
the critical angle ( c  43.2 ) the reflection ( R ) or absorption ( A  1  R ) for TE and
TM polarized light behaves quite differently. In details we can notice that the
reflectance difference ( R  RTE  RTM ) or absorption difference ( A=  R )
increases quickly as the number of graphene layers becomes bigger especially near
the critical angle.
S4. The influence of light spot size on spatial resolution
Figure S4｜ Scanning results for RGO band with differently focused light. (a)
Optical image of reduced graphene oxide (RGO) band and the laser spot focused by
optical lens (f=4 cm). (b) Scanning results along the blue dashed line in (a) using
optical lens (focal length f=4 cm) and 50×objective, respectively. The intensity has
been normalized for ease of comparison. It is clear to see that the spatial resolution is
enhanced by using smaller light spot (focused by 50× objective), the diameter of the
light spot is D  20 μm and D  5 μm for lens and 50× objective, respectively.
S5. Influence of aperture diaphragm on the effective range of angle and spatial
resolution
Figure S5｜ Schematic of TIR under focused light and the scanning curves with
and without diaphragm. (a) The schematic of using diaphragm. Both the effective
angle range and spot size are decreased by using diaphragm, thus the angular accuracy
and spatial resolution are enhanced. (b) Scanning results of RGO band in Fig. S4a
with and without diaphragm. The spatial resolution is improved by decreasing the
effective light spot size.
S6. Influence of graphene interlayer spacing on the results.
Figure S6｜Simulation for 8L, 9L and 10L graphene with different interlayer
spacing. The gap in the simulation is introduced by setting the refractive index of the
medium between two graphene layers to be one (vacuum), so the gap distance is the
thickness of the vacuum layer. The zero gap is an ideal situation, which means the
interlayer spacing can be neglected like that in the natural graphite. As can be seen in
the figure, when the gap increases A drops. We can still determine the number of
graphene layers even with a 2 nm gap, which is much more than the single-layer
graphene thickness (0.335 nm). However, this huge gap will cause wrong layers
determination using AFM, since the height measured by AFM includes the
accumulated gap distance among graphene layers.
S7. Influence of the incident angle and refractive indexes of medium sandwiching
graphene.
Figure S7｜ Simulation results showing the influence of angle and refractive
indexes.
(a) Simulation curves for SiO2/graphene/air structure at different incident
angle, 43.2° (critical angle), 47° (experiment), and 60°,respectively. (b) Simulations
for SiO2/graphene/air, SiO2/graphene/water, and SiO2/graphene/PDMS structures, at
their corresponding critical angles (43.2°, 64.8°, 73.6°, respectively)
Fig. S7a shows the results simulated for SiO2/graphene/air structure at three
different incident angles , 43.2°(critical angle ), 47°(experiment), and 60°, combining
Fig. S3 we can see that A becomes more sensitive to thickness as the incident
angle closes to the critical angle. This phenomenon is due to large and sensitive
layers-dependent absorption of TE polarized light and little absorption of TM
polarized light near the critical angle. Fig. S7b gives the simulation after replacing air
by another commonly used medium, water ( n  1.33 ) and PDMS ( n  1.41 ), the
incident angles are chosen to be the corresponding critical angles (64.8°and 73.6°).
We can clearly notice that when the refractive difference n ( n  nH  nL ) of the
high-index medium and low-index medium becomes smaller (0.47, 0.14, 0.06 for air,
water, PDMS respectively), A becomes larger (0.115, 0.188, 0.278 for monolayer
graphene, respectively). Therefore, we can chose two medium with similar refractive
indexes, and incident angle to be critical angle, then the accuracy wil be largely
improved especially for few-layer graphene ( N  5 ).
References:
1
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(2008).
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X.-D. Chen, Z.-B. Liu, C.-Y. Zheng, F. Xing, X.-Q. Yan, Y. Chen, and J.-G.
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