Supplemental Material
Thermal and Optical Properties of Freestanding Flat and
Stacked Single-Layer Graphene in Aqueous Media
Tu Hong1, Yunhao Cao1, Da Ying1, and Ya-Qiong Xu1,2*
1
Department of Electrical Engineering &Computer Science, Vanderbilt University, Nashville, Tennessee 37235, USA.
2Department
of Physics & Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA.
Fabrication of stacked graphene structure
Single-layer graphene samples were prepared by chemical vapor deposition in the
presence of 10 sccm of methane and 100 sccm of hydrogen on copper foils (Fig. S1a).
Poly(methyl methacrylate) (PMMA) was then spin-coated on top of the graphene (Fig. S1b),
followed by the removal of copper foils by wet etching in iron chloride solution (Fig. S1c). The
graphene was then transferred onto a pre-patterned transparent fused silica substrate with a 3 μmdeep, 3 or 5 μm-wide trench (Fig. S1d) and annealed in Ar at 440 ℃ for 30 min (Fig. S1e),
resulting in a complete removal of PMMA1, 2. The suspended monolayer graphene curled and
stacked during the annealing process as illustrated in Figure S1f. This stacked graphene structure
can survive for a long time at room temperature, with no apparent structure change for several
months. Also, this structure can survive up to 710 K during annealing process and stay as low as
77K for the low-temperature measurements.
Experimental setup
To explore the NIR emission from the graphene structures, a 785 nm (1.58 eV) laser was
expanded and focused by a 40x objective (Olympus, N.A. = 0.6). The emission signal was
filtered by an 850 nm long pass filter (Thorlabs) and collected by a liquid nitrogen cooled InGaAs
detector (OMA-V, Princeton Instruments) in the NIR region (900 - 1600 nm). The NIR emission
mapping was recorded by scanning a nanometer-resolution stage (Mad City Labs) and recording
the emission signal in each position. The emission spectrum was recorded by an Acton SP2300
spectrometer (Princeton Instruments) coupled with the same detector. A calibration lamp of
known temperature (Newport) was used for spectrum intensity calibration. All laser powers were
measured at the objective.
Estimation of graphene thermal conductivity
We estimate the thermal conductivity κ of our graphene samples. The amount of heat Q
transferred over time t through a cross section area S is given by the heat flow equation, 𝜕𝑄/
𝜕𝑡 = −𝜅 ∮ ∇𝑇 ∙ 𝑑𝑆. Because the trench width (> 3 μm) is much larger than the laser spot size (~
0.6 μm), the radial heat flow from the middle of the graphene to its boarders is dominating. In the
case of suspended graphene ribbon, the thermal conductivity can be approximated by3
1 Δ𝑃
𝜅 = 2𝜋ℎ Δ𝑇
(1)
where P is the total absorbed laser power, h = 0.335 nm is the graphene thickness. Previous
studies report that the optical absorption of graphene is 2.3% over a broad spectrum range 4, 5.
Since the interface thermal conductivity between graphene and air is relatively small, we ignore
the thermal radiation into ambient air6, 7. The as-obtained graphene thermal conductivity κ is
(927+560/-518) W m-1 K-1, with error source mainly from the Lorentzian fitting of the Raman
peaks. This result is comparable to recently reported graphene thermal conductivity values by
other groups7-10.
Electrolyte gating of graphene and Fermi level calculation
The graphene structure was sealed in a microfluidic chamber, in which 0.1 mM
phosphate buffered saline (PBS) was used as the electrolyte gate material. A gold electrode was
employed to change the gate voltage. When a gate voltage is applied, an electrical double layer is
formed between the gate material and the graphene. The thickness of this electrical double layer
is given by the Debye screening length, which is in the order of nanometers. At room temperature,
the Debye screen length, d (nm), in aqueous media with ion concentration I (M) is approximated
by11 𝑑 =
0.304
.
√𝐼
Thus, the capacitance C of the system can be obtained by
C=
𝜀𝜀0
𝑑
(2)
where ε = 78.2 and ε0 = 8.854×1012 F/m are the permittivity of the gate material (water) and
vacuum, respectively. The relationship between gate voltage Vg and carrier concentration n in
single-layer graphene is given by12, 13
𝑉𝑔 − 𝑉𝐷𝑃 =
𝐸𝐹
𝑒
+𝜑 =
ℏ𝑣F √𝜋𝑛
𝑒
+
𝑛𝑒
𝐶
(3)
where VDP is the gate voltage at the Dirac point, EF = ℏ𝑣F √𝜋𝑛 is the Fermi energy, vF = 1.0×106
m/s is the Fermi velocity, and φ is the electrostatic potential difference between the gate electrode
and the graphene. In this study, a gate voltage as high as ︱Vg－VDP︱ = 4.5 V was applied at an
ion concentration of 1.0×10-4 M. We obtain a Fermi energy of 0.84 eV and a carrier concentration
n = 5.2×1013 cm-2.
Figure S1. Fabrication flow of freestanding stacked graphene
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