Field Effect and Local Gating in Nitrogen‐Terminated Nanopores (NtNP) and Nanogaps (NtNG) in Graphene

Abstract

Functionalization of electrodes is a wide‐used strategy in various applications ranging from single‐molecule sensing and protein sequencing, to ion trapping, to desalination. We demonstrate, employing non‐equilibrium Green′s function formalism combined with density functional theory, that single‐species (N, H, S, Cl, F) termination of graphene nanogap electrodes results in a strong in‐gap electrostatic field, induced by species‐dependent dipoles formed at the electrode ends. Consequently, the field increases or decreases electronic transport through a molecule (benzene) placed in the nanogap by shifting molecular levels by almost 2 eV in respect to the electrode Fermi level via a field effect akin to the one used for field‐effect transistors. We also observed the local gating in graphene nanopores terminated with different single‐species atoms. Nitrogen‐terminated nanogaps (NtNGs) and nanopores (NtNPs) show the strongest effect. The in‐gap potential can be transformed from a plateau‐like to a saddle‐like shape by tailoring NtNG and NtNP size and termination type. In particular, the saddle‐like potential is applicable in single‐ion trapping and desalination devices.

Full text

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Field effect and local gating in nitrogen-terminated
nanopores (NtNP) and nanogaps (NtNG) in
graphene
Ivana Djurišić1, Miloš S. Dražić1, Aleksandar Ž. Tomović1, Marko Spasenović2, Željko
Šljivančanin3, Vladimir P. Jovanović4 and Radomir Zikic1,5*
1Institute of Physics, University of Belgrade, Pregrevica 118, 11000 Belgrade, Serbia.
2Center of Microelectronic Technologies, Institute of Chemistry, Technology and Metallurgy,
University of Belgrade, Njegoševa 12, 11000 Belgrade, Serbia.
3Vinča Institute of Nuclear Sciences, University of Belgrade, Mike Petrovića Alasa 12-14, 11000
Belgrade, Serbia.
4Institute for Multidisciplinary Research, University of Belgrade, Kneza Višeslava 1, 11000
Belgrade, Serbia.
5NanoCentre Serbia, Nemanjina 22-26, 11000 Belgrade, Serbia.
KEYWORDS graphene, nanogap, nanopore, DFT+NEGF, field effect, termination

2
ABSTRACT: Single-molecule biosensing, with a promise of being applied in protein and DNA
sequencing, could be achieved using tunneling current approach. Electrode-molecule-electrode
tunneling current critically depends on whether molecular levels contribute to electronic
transport or not. Here we found employing DFT and Non-Equilibrium Green’s Function
formalism that energies of benzene molecular levels placed between graphene electrodes are
strongly influenced by electrode termination. Termination-dependent dipoles formed at the
electrode ends induce in-gap field effect that is responsible for shifting of molecular levels. We
show that the HOMO is closest to Fermi energy for nitrogen-terminated nanogaps (NtNGs) and
nanopores (NtNPs), promoting them as strong candidates for single-molecule sensing
applications.
Single-molecule probing by tunneling currents is often a method of choice for biomolecule
sensing applications, most prominent being next-generation real-time single-molecule DNA and
protein sequencing [ 1,2]. Tunneling current is extremely sensitive to position of a molecule
placed in the nanogap between two nanoelectrodes and to its composition. Discrimination
between molecules is based on variations of the tunneling current induced by interaction of a
molecule traversing the nanogap with electrodes. The molecule-electrodes interaction will
strongly depend on the choice of the electrodes [ 3, 4], as it may improve transport properties
through molecules placed between them by inducing resonant transport – highest
occupied/lowest unoccupied (HOMO/LUMO) molecular levels contribute to the current.
Tunneling current may vary several orders of magnitude depending on whether molecular levels
participate in the transport or not. Resonant transport is commonly accomplished by passivation
of electrodes either through weak interaction between the molecule and electrodes (hydrogen
bonding or Van der Waals) [ 5,3,6] and/or by electrode interface dipoles induced electrostatic
field [ 7,8].
Particularly important material for single-molecule probing applications is graphene [
1,2,9,10,11]: it is atomically thin which significantly increases resolution of devices; it can be
utilized for transversal electrodes; it is impenetrable to ions and thus can be used as a membrane

3
with nanopore; it is easily produced and integrated into devices. Most commonly, graphene
edges are passivized (functionalized, terminated) with hydrogen atoms, however different
terminations of graphene both simple (single atom passivation, nitrogen or hydrogen) [ 3,12,13]
and more complex, with different recognition molecules [ 4,6,14] were used in order to achieve
resonant transport.
In our previous study we have found strong in-gap field effect generated by dipoles formed at
the ends of nitrogen-terminated carbon-nanotube electrodes in a DNA sequencing device [ 8].
Here, in this study we investigate the field effect in graphene nanogaps and nanopores. The
influence of X-terminated (X = N, H, F, S, Cl) semi-infinite graphene nanogap on the position of
highest occupied molecular orbital HOMO of the benzene molecule in respect to Fermi energy
EF was first explored. We showed that the position of HOMO level of the molecule in respect to
EF is mainly determined by in-gap electrostatic potential which is formed as a consequence of
termination-induced dipoles. It is found that N termination is most favorable in the sense that it
drives molecular HOMO level closest to EF compared to other investigated terminations. We
also showed that N-terminated grapehene nanopore should increase the energy levels of a
molecule placed in the pore by the same mechanism.
Calculations for empty nanogaps with different terminations and benzene molecules in such
gaps were performed using density functional theory (DFT) coupled with non-equilibrium
Green’s functions (NEGF) within TranSIESTA package [ 15]. Positions of X (X=N, H, F, S, Cl)
atoms that terminate graphene nanogaps are shown in Figure 1a. The distance between two
graphene sheets, excluding termination is fixed at 11.7 Å (arrow in Figure 1a). Geometry of
benzene molecule perpendicular (⊥) to the plane of the electrodes is given in Figure 1b, while
parallel (||) orientation is given in Figure S1 in Supporting Information (SI). The central region,

4
also called the scattering region or the extended molecule is marked with dashed red rectangle
(Figure 1b). Bulk electrodes are represented by six rows of carbon atoms. Unit cell for DFT
calculations of N-terminated graphene nanopore within SIESTA package [ 16] is presented in
Figure 1c.
Figure 1. a) Geometry of X-terminated graphene gaps: X=N, H, F, S, Cl. Arrow indicates the
fixed distance between C atoms adjacent to termination atoms. b) N-terminated gap with benzene
molecule in perpendicular (⊥) orientation. Dashed red line marks the central region (the
scattering region or the extended molecule). c) Geometry of N-terminated graphene nanopore
(NtNP). Red, green and blue arrows indicate x, y and z directions, respectively.
For both SIESTA and TranSIESTA the basis set was double zeta polarized for all atoms, the
exchange-correlation functional was approximated with the Perdew-Burke-Ernzerhof (PBE)
functional [ 17], core electrons were described with Troullier-Martins norm-conserving
pseudopotentials [ 18] and the mesh cutoff value was 170 Ry for the real-space grid. Charge
excess per atom was obtained from Hirshfeld population analysis. Geometries of benzene

5
molecule and X-termination atoms at the edges of graphene electrodes and graphene nanopores,
were relaxed using SIESTA. For electrode and scattering region calculations in TranSIESTA we
used 1×9×64 and 1×9×1 k-points, respectively. Electrostatic potential energy profiles of N and
H-terminated graphen nanopores were also calculated using GPAW code [ 19] based on the real
space projector augmented waves method [ 20,21]. Grid spacing for the wavefunction
representation was 0.15 Å, exchange-correlation functional was PBE within generalized gradient
approximation and only the Γ-point Brillouin-zone sampling was used. The electronic states
were occupied according to a room-temperature Fermi-Dirac distribution.
The energy difference EHOMO⊥(X), obtained from TranSIESTA, between molecular HOMO
energy of benzene placed between X-terminated electrodes and Fermi energy EF depends on
termination X (Figure 2a and Figure S2a in SI). No matter the orientation of benzene molecule
(perpendicular or parallel) within the nanogap, HOMO energy is closest to EF for N termination;
then F, H, S and Cl terminations follow, respectively.
Figure 2. a) Energy of HOMO level with respect to Fermi energy, EHOMO⊥(X), for
perpendicularly oriented benzene (see Figure 1b) in the nanogaps with different terminations (N-

6
black, F-blue, H-red, S-olive and Cl-violet). b) In-gap electrostatic potential energy Ep(X) along
midline in z direction in electrode plane for X-terminated gaps obtained from TranSIESTA. c)
Comparison of EHOMO⊥(X) (solid orange diamonds) and Ep(X) (solid blue circles) in the center of
the gap for different terminations. Empty blue circles correspond to Ep(X) values in the center of
the gap shifted for -2.1 eV.
Next we calculate, from TranSIESTA, electrostatic potential energy Ep for X-terminated empty
graphene gaps, whose profiles (along midline in z direction in electrode plane) are given in
Figure 2b. The values of Ep in the center of the gap shifted for -2.1 eV vary in the same way as
EHOMO⊥ with termination X (Figure 2c). Thus, the position of the molecular HOMO energy is
primarily determined by the electrostatic potential of empty gap: we will define this as field
effect similar to the one in solid-state electronics with the difference that here no gate electrode is
needed. From the application viewpoint the most favorable is to use N-terminated nanogaps
(NtNGs), as molecular HOMO is brought closest to Fermi energy for nitrogen termination. This
termination is expected to provide the strongest current signals at lowest possible voltages if no
strong interaction (hybridization) between molecule and the electrodes is present [ 8].
The largest value of the difference between HOMO and Fermi energies of benzene is for Cl
termination (~4.1 eV), which is less than molecular energy gap (~5.2 eV). Thus, in situations
where HOMO energy variation with the type of termination is smaller than molecular gap, one
may expect this rule of thumb: EHOMO will be closest to EF for N- and then follow F-, H-, S- and
Cl-terminations, respectively. However, nothing can be said a priori about the exact value of
EHOMO with respect to EF, as it may vary from molecule to molecule.

7
Similarly, in the case of parallel orientation of benzene, the position of HOMO energy with
respect to EF, EHOMO||, is mainly determined by the values of electrostatic potential energy Ep in
the center of the empty gap (Figure S2b in SI). However, there is notable upshift of values of
EHOMO||(X) when compared to EHOMO⊥(X) for all terminations except H-termination (Figure S2a
in SI), where EHOMO||(H) = EHOMO⊥(H). This is expected from the point of view of coupling
between benzene and termination atoms: in both cases of orientation there is negligible coupling.
If we take charging of the molecule (Figure S3 in SI) and charge redistribution between
termination atoms and benzene (Figure S4 in SI) to be the measure of the coupling, then
coupling is much stronger in parallel than in perpendicular orientation for all terminations except
H termination. Combined effect of local change of electrostatic potential due to charge
redistribution, as well as charging of the molecule (negative charge rises energy) leads to upshift
of HOMO level in the case of parallel orientation (Figure S2 in SI).
We will now show, using a simple model, that termination-dependent in-gap electrostatic
potential energy, i.e. the HOMO shift, originates from dipoles formed at the interfaces of
graphene sheets [ 8], as depicted in Figure 3. From TranSIESTA Hirshfeld population analysis,
dipoles are seen as negative charge accumulated on N-termination row, while positive charge is
located on the adjacent row of C atoms (Figure 3a), for the exemplar case of empty N-terminated
graphene nanogap. The presence of benzene in the gap does not significantly alter charge
distribution and dipole orientations in graphene (Figure S5 in SI).
Simple model for calculation of electrostatic potential energy consists of four homogeneously
linearly charged lines (Figure 3b). Each line represents one row of atoms (blue – termination,
green – adjacent C atoms) of graphene sheet. Position and length of a line correspond to position
of row of atoms and the distance between the first and the last atom of a row, respectively.

8
Linear charge densities λ(C) and λ(X) were derived as total charge excess in one graphene row
calculated from Hirshfeld analysis divided by the distance between the first and the last atom of
that row. Calculated in-gap electrostatic potential energy along midline in z direction in the plane
containing linear charges for different terminations is given in Figure 3c. Our model shows good
qualitative agreement with results obtained from TranSIESTA calculation for empty gap (Figure
2b), except for F termination. The reason for this discrepancy is that for F termination there is
significant contribution to Ep from second row of C atoms counting from termination (Figure S5
in SI). If we take the model with six lines of charges (Figure S6 in SI) better qualitative
agreement is obtained. The simple model implies that the electrostatic potential energy
calculated from TranSIESTA emanates from dipoles, i.e. that the field effect comes from local
gating induced by properly chosen termination of graphene sheet.
Figure 3. a) Hirshfeld charge excess Q for each row of atoms of gap-forming N-terminated
graphene sheets at zero bias (solid black line). The dipole arises in the N (blue) and the adjacent
C (green) atom rows. Arrows indicate the orientation of dipoles. b) A model of four
homogenously linearly charged lines represents corresponding rows of atoms (blue –
termination, green – adjacent C atoms) belonging to graphene sheets. Total charge residing on
the line is equal to total charge excess of corresponding row. Position and length of a line

9
correspond to position of and distance between the first and the last atom of a row, respectively.
c) Electrostatic potential energy (Ep) calculated from the four-line model for different
terminations along dashed red line in b), which lies in y-z plane.
The model may indicate how the variation of charge within dipoles can influence the
electrostatic potential energy, i.e. HOMO level shift. For a “symmetric” dipole,
λ
(X) = -
λ
(C),
the field effect is stronger for a larger dipole moment (Figure S7a in SI). Negative
λ
(X) (solid
lines in Figure S7a in SI) produces positive electrostatic energy and a molecule placed in the
nanogap would experience a positive shift of energy levels (Figure S7c in SI). The opposite is
true for
λ
(X) > 0 (dotted lines in Figure S7a in SI). The “asymmetric” dipole case
λ
(X) ≠ -
λ
(C)
is more realistic description of X-terminated graphene. Electrostatic potential energy will be
positive (negative) whenever the total charge,
λ
(X) +
λ
(C), of the dipole is negative (positive),
irrespective of orientation of interface dipole (Figure S7b,c in SI). The larger the total charge of
the dipole (asymmetry) the larger the field effect (Figure S7c in SI). The gap size and the
distance between dipole-forming lines can also influence the behavior of the energy, but to lesser
extent.
We demonstrated that the field-effect and local gating are the most favorable for N-terminated
graphene nanogaps (NtNG). Now we will show that field effect is also present in N and H-
terminated graphene nanopores (NtNP in Figure 1c and HtNP in Figure S8 in SI). Electrostatic
potential energy Ep obtained from SIESTA calculation for NtNP is presented in Figure 4a: in the
nanopore Ep is positive implying the shift of molecular HOMO level towards Fermi energy if a
molecule is placed in the NtNP. The results for Ep of NtNP is in good agreement with the one
obtained using GPAW code (Figure 4b). Additionally, by analogy with results of calculations for

10
terminated nanogaps, the values of Ep in the HtNP are lower than in NtNP as expected (Figure
4b). As in NtNG case, the charge distribution obtained from Hirdhfeld analysis in SIESTA at the
N termination and next-neighbor C atoms of the NtNP (Figure 4c) is responsible for the hat-
shaped potential energy: N atoms bear negative, while next-neighbor C atoms carry positive
charge, forming a ring of radially oriented dipoles. Induced electron density for NtNP obtained
using GPAW (Figure S9 in SI) supports the result of Hirshfeld analysis. Hat-shaped potential can
be obtained from a model of two linearly charged rings (Figure 4d), which is in good qualitative
agreement with both SIESTA and GPAW calculations.
Figure 4. a) 3D profile (top panel) of electrostatic potential energy Ep in y-z plane of NtNP
(Figure 1c) and its profile (bottom panel) along the midline (dashed line in top panel) in z

11
direction in the same plane obtained from SIESTA. b) Electrostatic potential energy along the
same line as in a) for NtNP and HtNP obtained using GPAW. c) Hirshfeld charge excess q for
each atom in NtNP from Figure 1c: N atoms (blue balls), their next-neighboring C atoms (green
balls) and the rest of C atoms (grey balls). Projections of charge to q-y plane are given for N and
neighboring C atoms. d) Electrostatic potential energy profile obtained from two linearly charged
rings along the axis defined by their diameter. Total charge residing on rings is equal to total
charge excess of N and C atoms from c).
This local-gating field effect in NtNGs and NtNPs could improve operation of single-molecule
biosensing devices based on transversal current by lowering their operating voltages as
molecular HOMO should be drawn closer to EF. If one applies NtNGs, transversal tunneling
current measured is on the order of nA or less and expected ratio between resonant (molecular
HOMO contributes to electric current) and non-resonant (no molecular levels contribute to
electric current) current would be much larger than 1. In applications with NtNPs one measures
in-plane current that is on the order of μA [ 11,13]. Inclusion of molecular HOMO in transport
only slightly affects in-plane current (the ratio between resonant and non-resonant current is
expected to be close to but different than 1) however such small variation should be measurable
due to its magnitude [ 11].
We have shown that N termination of graphene nanogaps tends to shift HOMO level of the
molecule closest to EF when compared to F, H, S and Cl terminations. This behavior is a
consequence of in-gap field effect which arises from interface dipoles formed by graphene sheet
termination. In-gap field effect due to local gating by termination is also demonstrated for N-
terminated graphene nanopores. From practical standpoint this means that is more likely that
resonant transport will be achieved for lower values of applied voltage. We therefore suggest that

12
for molecular biosensing based on electric transport measurements one should use N-terminated
graphene nanogaps and nanopores as they could be achieved through room-temperature edge
functionalization in mild NH3 plasma [ 22].
ACKNOWLEDGMENT
This work was supported by the Serbian Ministry of Education, Science and Technological
Development through projects 171033 and 41028. We gratefully acknowledge financial support
from the Swiss National Science Foundation (SCOPES project No.52406) and the FP7-NMP,
project acronym nanoDNAsequencing, GA214840.
ABBREVIATIONS
DFT, density functional theory; NEGF, Non-Equilibrium Green’s Function; NtNP, nitrogen-
terminated nanopores; NtNG, nitrogen-terminated nanogaps; HOMO, highest occupied
molecular orbital; LUMO, lowest unoccupied molecular orbital.
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ASSOCIATED CONTENT
Supporting Information. The following files are available free of charge.
Supporting Information (PDF)
Corresponding Author
Radomir Zikic radomir.zikic@ncs.rs

S-1
Supporting Information
Field effect and local gating in nitrogen-terminated
nanopores (NtNP) and nanogaps (NtNG) in
graphene
Ivana Djurišić1, Miloš S. Dražić1, Aleksandar Ž. Tomović1, Marko Spasenović2, Željko
Šljivančanin3, Vladimir P. Jovanović4 and Radomir Zikic1,5*
1Institute of Physics, University of Belgrade, Pregrevica 118, 11000 Belgrade, Serbia.
2Center of Microelectronic Technologies, Institute of Chemistry, Technology and Metallurgy,
University of Belgrade, Njegoševa 12, 11000 Belgrade, Serbia.
3Vinča Institute of Nuclear Sciences, University of Belgrade, Mike Petrovića Alasa 12-14, 11000
Belgrade, Serbia.
4Institute for Multidisciplinary Research, University of Belgrade, Kneza Višeslava 1, 11000
Belgrade, Serbia.
5NanoCentre Serbia, Nemanjina 22-26, 11000 Belgrade, Serbia.

S-2
Figure S1. N-terminated gap with benzene molecule in parallel (||) orientation. Dashed red line
marks the central region.
Figure S2. a) Position of benzene HOMO level for perpendicular (⊥) and parallel (||) orientation
and different terminations of graphene (N-black, F-blue, H-red, S-olive and Cl-violet). b)
Comparison of EHOMO||(X) (solid orange squares) and Ep(X) (solid blue circles) in the center of
the gap for different terminations X. Empty blue circles correspond to Ep(X) values in the center
of the gap shifted for -2.1 eV.

S-3
Positions of benzene HOMO level for perpendicular (⊥) and parallel (||) orientations and
different terminations are given in Figure S2a. For all terminations HOMO energies are closer to
Fermi energy EF in the case of parallel orientation, except H for which EHOMO||(H)=EHOMO⊥(H).
This upshift of HOMO level is a result of coupling between termination atoms and benzene
molecule. Coupling leads to charge redistribution between termination atoms and benzene,
which results in the charging of the molecule (Figure S3).
Figure S3. Hirshfeld charge excess residing on the benzene molecule for perpendicular (open
red diamonds) and parallel (empty black squares) orientation and different terminations.
Charge residing on the benzene molecule for || and ⊥ orientation is given in Figure S3. For ⊥
orientation benzene molecule is electroneutral for N, F and H, while for S and Cl-termination
there is some charge residing at the molecule. This is expected as C-S and C-Cl bond lengths are
larger than for other terminations (Figure 1a). In the case of || orientation, charging, i.e. coupling
exists for all terminations expect H termination (Figure S3).

S-4
Hirshfeld charge excess distribution for the case of N-terminated gap is given in Figure S4a.
Charge distribution is perturbed at the nearest termination atoms when benzene molecule is
introduced in the gap (Figure S4b,c). In perpendicular orientation, as consequence of negligible
coupling, charge residing at benzene molecule is zero while nearest termination atoms are only
slightly perturbed. In the case of parallel orientation (Figure S4c) the situation is drastically
different: most of the charge redistribution is between benzene molecule and nearest atoms of
termination.
Figure S4. Hirshfeld charge excess per atom given in 10-3 e for graphene gaps: a) empty, b) with
benzene molecule in perpendicular and c) parallel orientation.

S-5
Figure S5. Sum of atomic charge excesses residing at each row (eight atoms along y axes) of
XtNG, obtained from Hirshfeld population analysis for X-terminated empty gaps (top panel) and
gaps containing benzene molecule in perpendicular (middle panel) and parallel (bottom panel)
orientation.
Figure S6. a) A model of six homogenously linearly charged lines represent corresponding rows
of atoms (blue – termination, green – first and red – second row of C atoms) belonging to
graphene sheets. Total charge residing on the line is equal to total charge of corresponding row.

S-6
Position and length of a line correspond to position and distance between first and last atom of a
row, respectively. c) Electrostatic potential energy (Ep) calculated from the six-line model for
different terminations along dashed red line in b), which lies in x-y plane.
Figure S7. Electrostatic potential energy Ep of four-line model (Figure 3b) for a) symmetric
dipole model, i.e.
λ
(X) = -
λ
(C), and b) asymmetric dipole model i.e.
λ
(X) ≠ -
λ
(C). In a)
λ
(C)
carries charge from -0.3 e to +0.3 e. In the left panel of b)
λ
(C) is positive (+0.2 e) and
λ
(X)

S-7
varies from -0.05 e to -0.9 e, while in the right panel
λ
(C) is negative (-0.2 e) and
λ
(X) varies
from +0.05 e to +0.9 e. c) In the symmetric case (
λ
(X) = -
λ
(C), left panel), negative
λ
(X) (green
circles) raises in-gap potential energy (upward arrow), while positive
λ
(X) decreases the energy
(downward arrow). In the asymmetric case (right panel), the sign of total charge
λ
(X) +
λ
(C)
determines whether the Ep is rising (
λ
(X) +
λ
(C) < 0) or lowering (
λ
(X) +
λ
(C) > 0). The effect is
more pronounced (larger arrows) for larger
λ
(X) (blue circles).
Figure S8. Geometry of H-terminated nanopore used in GPAW [ 1] calculations (H atoms are in
yellow, while C atoms are grey).
Figure S9. Isocontour plot of N-induced electron density upon the edge of graphene nanopore
was passivated with nitrogen. Red and yellow isocontours correspond to the charge accumulation
and depletion, respectively.

S-8
REFERENCES
1.
Enkovaara, J. et al., Electronic structure calculations with GPAW: a real-space
implementation of the projector augmented-wave method. J. Phys. Condens. Matter 22
,
253202 (2010).