Supplementary Information
Electrical Pulse Fabrication of Graphene Nanopores in Electrolyte Solution
Aaron T. Kuan,1 Bo Lu,2 Ping Xie,3 Tamas Szalay1 and Jene A. Golovchenko1,2a)
1School
of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, 02138, USA
2Department
3Oxford
a)
of Physics, Harvard University, Cambridge, Massachusetts, 02138, USA
Nanopore Technologies, One Kendall Square, 02139, Cambridge, Massachusetts, USA
Corresponding author, email: golovchenko@physics.harvard.edu
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Supplementary Information Outline
1. TEM image of suspended graphene membrane
2. Electrical pulse characteristics
3. Correlation between enlargement steps and pore size
4. Pore characteristics
5. Finite element models
6. TEM imaging of electrical pulses fabricated nanopores
7. RAMAN characterization of graphene
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1. TEM image of suspended graphene membrane
(a) TEM micrograph of a suspended graphene
membrane. >50% of the graphene surface area is
atomically clean. (b) Electron diffraction of suspended
graphene membrane. The single hexagonal diffraction
pattern indicates that the suspended membrane is
Fig. S1: TEM image of suspended graphene
single-layer, single-grain graphene.
2. Electrical pulse characteristics
Pulses were supplied by an HP 8110A pulse generator using the
50Ω to 10kΩ output impedance setting and 10 ns rise time. A 5V,
250 ns input pulse (blue trace) was measured using a 10kΩ/50Ω
voltage divider (exponential rise and fall presumably due to ~2 pF
of parasitic capacitance). The response of a suspended graphene
membrane device to such a pulse was measured across a 50Ω
terminating resistor (green trace), showing an RC charging time
constant of about 30 ns. The device can be approximated by the
Fig. S2: Voltage Pulse Characteristics
equivalent circuit shown in the diagram. The voltage drop across the membrane during the pulse is Vin –
Vout(t). This measurement shows that the membrane is charged to the full voltage (Vout ≈ 0) for most of
the duration of the 250 ns pulse.
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3. Correlation between enlargement steps and pore size
Fig. S3 shows the change in diameter due to standard enlargement pulses (5V 250 ns), ΔDE, plotted as a
function of the calculated pore diameter before the pulse. Spearman’s rank-order correlation coefficient
(rs) was used to quantify the correlation, giving rs = 0.03, with
an associated p-value of 0.38 (n = 702). These data suggest
that the changes in diameter due to enlarging pulses are
independent from the pore diameter, which was an assumption
made in the simple Monte Carlo simulation in Fig 2b.
Fig. S3: Correlation between ΔDE and Pore
Diameter
4. Pore Characteristics
Fig. S4a shows IV curves of a graphene membrane before and after fabrication of a 5.5 nm nanopore.
After fabrication, a marked increase in linear conductance is observed. Generally, this conductance is
stable over periods of time as long as several days.
Fig. S4b shows the noise power spectrum of the
same nanopore with 100 mV applied bias. The
noise is dominated by a 1/f-like component. The red
line is a 1/f fit to the data. There is large sample-tosample variation in the 1/f noise (up to an order of
Fig. S4: Pore Characteristics
magnitude). The source of this 1/f noise is still unknown.
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5. Finite element model
An axisymmetric finite element model of the pore was built using
the COMSOL Multiphysics software (COMSOL, Inc.) to predict
open pore currents and DNA translocation blockages (Fig. S5) for
various pore diameters and thicknesses. The model included
electrostatics and fluid dynamics (coupled Poisson-Boltzmann and
Navier-Stokes equations)5. Uncoated graphene membranes were
modeled as an insulating membrane of thickness T = 0.6 nm6.
Coated graphene membranes used T = 4.1 nm (0.6 nm + 2L, Fig.
Fig. S5: Finite element model
S4), and the DNA was modelled as an insulating, charged rod 2.3
nm in diameter7. The predicted current blockage is the difference between the open pore current and the
current with DNA. The color map in the images shows the magnitude of the current density (5 nm
diameter, 3 M KCl, 200 mV bias).
6. TEM imaging of electrical pulse fabricated nanopores
Direct TEM imaging of pulse-fabricated graphene nanopores was very difficult and was not achieved
reliably enough to serve as a precise verification of pore sizes. Contamination during drying of the
sample, in air, and under the electron beam often obscured the pores. Locating small pores was difficult
because the contrast of the pore edges is no stronger than the patterns of surface contamination on the
graphene. Moreover, standard TEM electron energies (80-200kV) can create or enlarge pores in
graphene during the search process1,2. For larger pores, the pore can sometimes be successfully imaged,
but the accuracy of pore size measurements is limited due
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to the complications just mentioned. Fig. S6 shows a suspended
membrane containing a single ~10 nm pore, which is near the middle of
the aperture and approximately circular.
7. Raman characterization of graphene
Direct Raman characterization of the samples used in this study was not
feasible because the silicon nitride adds a large background to the Raman
signal and the areas of suspended graphene (~100 nm) are much smaller
than a Raman laser spot size (~3 µm). However, we performed Raman
analysis of graphene transferred to SiO2. Figure S7a shows a typical
Fig. S6: TEM image of
electrical pulse fabricated pore
Raman spectrum, showing the characteristic graphene
G and 2D bands. Figures S7b and S7c show spatial
maps of the 2D/G and D/G ratios, respectively. These
images suggest that there are local areas of defective
and/or multilayer graphene throughout the sample,
but the majority of the sample is single layer, good
quality graphene. Therefore, it is likely that most
small-area suspended graphene membranes are single
layer and defect free, as observed in our experiments.
Fig. S7: (a) Raman spectrum of graphene on SiO2,
showing D, G, and 2D bands. (b) Raman scan image
showing 2D/G ratio. (c) Raman scan image showing
D/G ratio. Color scale on images is a linear scale where
white indicates the largest value and black the smallest.
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