Two-Dimensional GrapheneâGold Interfaces Serve as Robust

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Two Dimensional Graphene-Gold Interfaces Serve as Robust Templates for Dielectric Capacitor Tamiru Teshome, and Ayan Datta ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b09360 • Publication Date (Web): 15 Sep 2017 Downloaded from http://pubs.acs.org on September 19, 2017

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ACS Applied Materials & Interfaces

Two Dimensional Graphene-Gold Interfaces Serve as Robust Templates for Dielectric Capacitor Tamiru Teshome and Ayan Datta* Department of Spectroscopy, Indian Association for the Cultivation of Science, 2A and 2B Raja S. C. Mullick Road, Jadavpur – 700032, Kolkata, West Bengal, India. Email: [email protected]

ABSTRACT: The electronic structures of novel heterostructures namely graphene-Au van der Waals (vdW) interfaces have been studied using Density Functional Theory. The dispersion-corrected PBE-D2 functionals is used to describe the phonon spectrum and binding energies. Ab-initio molecular dynamics simulations reveal that the van der Waals framework is preserved till 1200K. Beyond T = 1200K a transition of the quasiplanar Au into 3D-cluster like structure is observed. A dielectric capacitor is designed by placing 1-4 hexagonal boron nitride monolayers between graphene and Au conductive plates. Charge separation between the Au and graphene plates is carried out under the effect of an external field normal to the graphene-h-BN-Au interface. The gravimetric capacitances are computed as C1 = 7.6 µF/g and C2 = 3.2 µF/g for h-BN bilayer with the Au-graphene heterostructures. The capacitive behavior shows strong deviations from the classical charging models and exemplifies the importance of quantum phenomenon at short contacts, which eventually nullifies at large interelectrode distances. The graphene-Au interface is predicted to be an exciting van der Waals heterostructure with a potential application as dielectric capacitor. KEYWORDS: Nanoscale Dielectric effects, Energy storage, Electric field, van der Waals solids, 2D materials. such heterostructures14,17-19 is yet to be unambiguous-

1. Introduction

ly determined.14

Two-dimensional materials have attracted great attention amongst both experimental and theoretical scien-

Large-scale, continuous graphene monolayers grown

tists in recent years due to their large surface to vol-

without interruptions can be synthesized on several

ume ratios, novel electronic, thermal and chemical

metal surfaces. Interestingly, due to lattice mismatch

properties1-5 that might help in fabricating new devic-

between the underlying substrate and graphene, moiré

es.6-8 Under ambient atmospheric situations, the per-

patterns can be formed.20-22 N’Diaye et al. have

fect hexagonal lattice in graphene contains defects

shown that graphene moire on Ir(111) serves as a

and out-of-plane buckling9 and impurities10 that

template for forming superlattices of several mono

would typically alter the band-structure. These effects

dispersed nanoclusters.23-27

become particularly relevant on surfaces since cova-

In the context of energy storage conventional (elec-

lent bonding between them cause large perturbations

trostatic) and electrochemical or electrochemical

.11-16 The electron-hole separation length-scales for 1

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double layer capacitors, are being widely used.28, 29 In

direction to avoid interaction between neighboring

the trade-off between power and storage, electrostatic

images. A Monkhorst-Pack grid with 5 × 5 × 1 k-

capacitors are superior. Nanoscale capacitors can

point mesh was used for the structural relaxations and

have energy densities which are much higher than

15 × 15 × 1 k-point meshes were used for optimiza-

their conventional analogues.30-34 Mixed metal ox-

tion, optical spectra and band structure calculations of

ides35 polymers36 and carbon nanotubes37,

have

the graphene-Au interface. The cutoff energy for the

Contem-

plane-wave basis is set to be 500 eV, and the struc-

porary studies on several 0D, 1D and 2D materials

tures are relaxed till a residual force cut-off of 0.001

have focused on understanding the dielectric behavior

eV/Å. For each h-BN intercalated structure (n=1-4),

in the nanoscale.41-43

the structures were individually optimized. Dipole

39, 40

been used to fabricate supercapacitors.

38

corrections were utilized to overcome spurious peri-

In this article, we investigated novel two-dimensional

odic images.53 Charges separation into the plates was

graphene-Au interface in the applications to dielectric

achieved by an external electric field=1.0 V/Å. The

capacitors. A novel dielectric capacitor is fabricated

phonon calculations are carried out using the PHO-

with a graphene-Au van der Waals (vdW) hetero-

NOPY code54 combined with density functional per-

structure wherein one to few layers of h-BN is inter-

turbation theory (DFPT) method in VASP to verify

calated between the conducting plates. The graphene-

the vibrational stability of the Au-graphene vdW het-

Au van der Waals interface is predicted to be an ex-

erostructures. Ab-initio molecular dynamics (MD)

citing hybrid van der Waals material for device appli-

simulation was performed for 10 ps with a time step

cations.

of 1.0 fs over the range of temperatures, T = 300, 500, 800, 1200, 1600 and 1800 K to gauge the stabil-

2. Computational Details

ity of the heterostructure.

Calculations are performed using the density functional theory (DFT) using the projector augmented plane-wave method within the Vienna Ab-initio Sim-

3. Results and Discussion

ulation Package.44 We carried out calculations with

3.1 Structures and Stability

LDA,45 PW91,46,47 PBE,48 and PBEsol49 GGA func-

The optimized graphene-Au interface in its primitive

tionals. Moreover, since gold was not included in the

consists in its unit cell a 2 × 1 graphene lattice con-

list of the elements in the initial DFT-D2 implementa-

stants and 1 × 1 Au lattice with a = 2.64 Å and b =

tion50 we have used C6 = 40.62 J nm6 mol−1 and

4.52 Å. This hybrid unit cell is a hexagonal graphene

r(vdW) = 1.772 Å for Au.51-52 Rest of the parameters

lattice with a = b = 2.46 Å (Fig. 1(a)) and unit cell of

were used from VASP as defaults. Vacuum regions

Au monolayer consisting of two Au-atoms with a =

with the thickness of 25 Å were placed along the z2


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2.83 Å and b = 4.71 Å (Fig. 1(b)). This results in a

dispersion interactions. It is worthwhile to mention

small lattice mismatch (∆ = 0.042 Å) which being

that strong orbital interaction between Ru(0001) and

quite small does not significantly affect the purpose

graphene can reduce the interlayer distance to as low

of the present study. Two-dimensional Au monolayer

as 0.145 nm57. Within the heterostructure, the calcu-

is predicted to have a hexagonally close packed

lated bond length of graphene is 1.48 Å which is 0.02

(HCP) arrangement which agrees well with previous

Å longer than freestanding of graphene and Au-Au

55

reports. Hence, 2D gold can be safely claimed to be

bond length is 2.6 Å shorter than freestanding of 2D

an exciting planar system like square-planar carbon.56

Au (2.75 Å). To confirm the dynamical stability (at

On the basis of our calculations, the equilibrium dis-

T=0 K) of such new materials, phonon calculations

tance between the two layers is 3.42 Å (Fig. 1(c)).

are essential. The phonon frequencies predicted by

This estimate compares well with graphene-Ir(111)

the PBE-D2 for freestanding graphene and 2D Au

27

surface distance=0.34 nm, and also interlayer dis-

monolayer are shown in Fig. 2(a) and Fig. 2(b), re-

tance in graphite (0.334 nm) as expected for weak

spectively.

Figure 1: The two dimensional optimized structures for (a) free standing graphene, (b) hexagonally close packed (HCP) 2D Au monolayer and (c) 2D graphene-gold interface. the high symmetry lines, ᴦ– к– м– ᴦ (Fig. 2(c)). The

Clearly 2D Au is predicted to be vibrationally stable. Furthermore, the HCP motifs that maximize the Au-

lack of the negative frequencies in the first 2D Bril-

Au bonds, and result in an evenly distributed coordi-

louin zone for PBE-D2, LDA and PW91functionals

nation within the 2D plane can improve its stability.

shows that the graphene-Au interface is dynamically

This is in agreement with the general view that rela-

stable. However, for the PBE-D3 and PBEsol func-

tivistic effects58 which result in aurophilic interactions 59

are essential to describe the chemistry of gold.

tionals, one observes small imaginary frequencies (υ

The

= 55.28 cm-1 and 38.08 cm-1, respectively), indicating

dynamical stability of the graphene-Au interface is

that the graphene-Au interface becomes dynamically

calculated using phonon spectra which is located at 3 ACS Paragon Plus Environment


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unstable under such dispersion-correlation functionals

graphene and 2D Au monolayer, respectively. The

(Figure S1). Hence, those structures were reoptimized

binding energy calculated for graphene-Au hetero-

by relaxing along those phonon modes to remove the

structures are (in eV) -1.82, -1.26, -0.34, -1.39 and -

vibrational unstability. Clearly, the vdW layered

1.12 at PBE-D2, PBE-D3, PBEsol, LDA and PW91

structures are indeed preserved for these functionals

levels of theory, respectively for an interlayer dis-

as well.

tance 3.42 Å as shown in Fig. 3(a). The stability of Au-graphene can be gauged by comparing the bind-

To further test the stability of graphene-Au interface,

ing energy for other similar 2D vdW layers. For bi-

the binding energy was computed as

layer graphene, the AA and AB configurations have

E E / E E

binding energies as 11.5(9) and 17.7(9) meV/atom,

where E /, E and E are the ener-

respectively.60

gies of the graphene/Au heterostructures, freestanding

Figure 2: Phonon dispersion curves of PBE-D2 in (a) pure graphene, (b) 2D Au monolayer, (c) graphene-Au interface and (d) an interlayer spacing effects between graphene and Au in graphene-Au heterostructures. Γ (0, 0, 0), K (1/3, 1/3, 0), M (1/2, 0, 0) and Γ (0, 0, 0) indicate the high symmetry points along the first Brillouin zone. In MoS2/MoSe2 heterostructures for which binding 61

energetically preferred over the AA stacking -0.186

∆E = -

eV.62 β-GaS/GaSe and ε- GaS/GaSe heterostructures

0.1 eV – -0.2 eV. For the graphene/h-BN, the AB

have binding energies are -0.132 eV and -0.314 eV,

stacking configuration with -0.24 eV is found to be

respectively.63 Evidently, the higher binding energy of

energy have been reported experimentally,

4 ACS Paragon Plus Environment

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the graphene-Au heterostructure interface vis-à-vis

temperatures corresponds to the formation of defects

MoS2/MoSe2 or GaS/GaSe is encouraging and might

in the hexagonal closed packed structure of Au atoms.

be observed in experiments. For the molecular

With further increase in temperature, beyond T =

dynamics simulations a 4 × 6 supercell was used

1800 K, a transition of quasiplanar Au layer into a

under periodic boundary conditions. The simulations

three dimensional (3D) structure is observed. Similar

were run at T = 300 K, 500 K, 800 K, 1200 K, 1600

2D → 3D transition has been reported in the context

K and 1800 K (Figure S2). The average separation

of small pure and doped Au-clusters.64 In spite of the

distances between graphene and Au layers are 3.35 Å,

large structural transformations in the Au-layer, no

3.48 Å, 7.55 Å, 9.37 Å, 9.58 Å and 10.74 Å at 300 K,

significant reorganization of the graphene matrix is

500 K, 800 K, 1200 K, 1600 K and 1800 K, respec-

observed in the temperature range within simulations.

tively. Such increasing interlayer distance at elevated

Figure 3: (a) Binding energy with respect to the interlayer distance calculated using PBE-D3, PBE-D2, PBEsol, LDA and PW91 functionals. (b) Time evaluation of interlayer distance and running average of graphene-Au interlayer distance for 18 ps over 300 K and (c) Normalized probability histogram of dihedral angle (in degrees). Figure 2(d) and Figure 3(a) shows that weak vdW

The average interlayer distance equilibrates at 〈d〉

interactions result is stability of the Au…Gn inter-

3.35 Å. Figure 3(c) shows the normalized probability

face. Figure 3(b) represents the average interlayer dis-

distribution of average dihedral angles in the Au-

tance between graphene and Au for 18 ps at 300 K.

layer. The average dihedral angle, 〈ɸ〉 ≈ 2 degrees 5



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which clearly indicates that the Au-layer remains

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5d-states. Additionally, the Fermi level is dominated

planar at T 300 K within the Au-graphene het-

by the 6p, 5d and 6s-states of Au with the 6p state

erostructures.

contributing maximally.55 Hybridization also occurs between the 5d and 6s states which is a consequence

3.2 Electronic Structures of graphene-Au Interface

of the relativistic stabilization of its outermost 6s or-

To understand the electronic properties of this hybrid

bital. Relativistic effects also improve s-d hybridiza-

system, we have computed the projected density of

tion (Figure S3). Basically, the length-scale for CT

states and band structures of freestanding graphene,

across a graphene-Au interface is controlled by the

Au and 2D graphene-Au interface. The partial densi-

Au (d-orbitals) – graphene (π-orbitals) interactions as

ties of states (PDOS) analyses show that below the

shownin Fig. 4(a) (contribution of graphene and Au

Fermi energy, the dominant population is from Au

in Fig. 4(b) and 4(c), respectively).

Figure 4: Partial density of states (PDOS)

using PBE-D2 for (a) graphene-Au interface, (b) graphene

contribution and (c) 2D Au monolayer contribution at 1E2 = 1.0 V/Å applied on the systems. The imaginary part of dielectric function of optical spectra polarization of light perpendicular to (d) graphene, (e) 2D Au monolayer and (f) graphene-Au interface. The optical spectra of freestanding graphene, 2D Au

illustrated in Fig. 4(d-f), respectively. Our calcula-

monolayer and the hybrid graphene-Au interface are

tions of absorption spectrum are based on random6


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phase approximation (RPA). Freestanding graphene

absorption for visible and UV light compared to free-

shows σ → σ* transition in the polarization of light

standing graphene and 2D Au monolayers, especially

perpendicular to graphene with two peaks at 11.02

in energy range ~2-10 eV as shown in Fig. 4(f). This

and 14.46 eV (see Fig. 4(d)). In the case of 2D Au

is due to the charge transfer and interlayer coupling of

monolayer the optical spectrum is shown in Fig. 4(e)

π and d-orbitals that induce overlap of electronic

which due to s-d orbitals mixing shows peak maxima

states and new optical transitions arise. Clearly, the

at 8.65 eV for polarization of light perpendicular to

Au-C interactions tune the electronic structure. We

2D Au monolayer. The graphene-Au interface exhib-

have computed the band structures as presented in

its a wider optical spectrum range and more intense

Fig. 5(a-d) which indicate a metal-like behavior.

Figure 5: Band structure for (a) freestanding graphene, (b) p-state of graphene in graphene-gold interface (red 12 = color), (c) graphene-Au interface and (d) d-state of Au contribution in graphene-Au interface (blue color) at E 1.0 V/Å applied on the systems. The band structure of freestanding graphene and 2D

upward shift 0.6 eV and down ward shift -1.2 eV, as a

Au monolayer and their contributions in graphene-Au

result of CT of 0.086 electron or σ = +0.27 C/m2

interface are presented in Fig. 5(b) and Fig. 5(d), re-

where area of graphene-Au is given by 5.12 ×10-20

spectively. Interestingly, the π-bands of graphene get

m2) with an electric field 1.0 V/Å applied. In absence

modified by the Au atoms. They undergo a uniform

of an electric field being applied to the graphene-Au 7



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heterostructure interface, the Dirac cones of π and π*

can enhance capacitance by reducing the separation, d

in graphene are located at 0.6 eV and -0.2 eV, respec-

between the plates wherein d is limited by the electric

tively (Figure S4(b) and Figure S4(c)). The charge

discharge occuring through the dielectric medium.

density distribution gives comprehensive and effec-

One can offer improved performance of carrier sepa-

tive clue on the nature of chemical bonding. The val-

ration in graphene-Au interface by varying the inter-

ance electrons of C tend to transfer towards the top

layer distance between graphene and Au. We ob-

site in HCP of Au atoms for the graphene-Au creating

served that quantum size effects dominate the capaci-

charge transfer states and electron localization. This

tance at very low separation as shown in Fig. 6(a) and

is evident from the partial charge density of highest

the accumulation of charges on the plates in Fig. 6(b).

occupied molecular orbital (HOMO) and lowest un-

The energy stored in the capacitor, 34 as calculated as 34 56, 312 8 39 56, 312 1.08 39 56, 312 08

occupied molecular orbital (LUMO) in the graphene-

Where 39 56, 312 1.08 and 39 56, 312 08 are the total

Au interface (Figure S6(a) and Figure S6(b)).

energy obtained by an electric field and without elec-

3.3 Dielectric Capacitor

tric field, respectively.71 The charge density differ-

As a consequence of charge transfer, holes are donat-

ence illustrated that charges are localized on Au at-

ed from the metal to graphene that makes it a p-type

oms graphene to Au charge-transfer. This can be un-

material. Interestingly, under an external electric field

derstood from the Bader's analysis on charge density

of 1.0 V/Å, the charge transfer increases yet the ge-

grid 0.084 electrons and 0.045 electrons localized on

ometries remain unaffected. In the Au graphene inter-

C atom and Au atom, respectively without an electric

face, the Dirac cone due to the π-states of graphene

field applied (Figure S6(d)). The integral charge den-

gets shifted up and down while the d-orbitals arising

sity differences between graphene-Au and its compo-

from Au-states are located in between the π and π* of

nents are further calculated as

graphene (see Fig. 5(b) – Fig. 5(d)). A transfer of

Δρ>z@ A ρB >x, y, z@dxdy A ρD >x, y, z@dxdy

0.086 electrons shifts the Fermi level by -1.2 eV

A ρ >x, y, z@dxdy

when for an electric field normal to the graphene-Au

where ρ9 >E, F, G@ , ρH >E, F, G@ and ρIJ >E, F, G@ are the

interface. The computation shows that the surplus electrons are accommodated on Au atoms while the

total charge density graphene-Au, graphene and Au

same amounts of electrons are depleted from gra-

monolayer, respectively. Both charge transfer as well

phene. Such electron transfer results in the formation

as Au-graphene chemical interactions result in charge

of an electric double layer with a potential step. One Table 1: The number of intercalated h-BN layers in the Au-Gn interface, interlayer distance between graphene and Au, d(in Å); primitive unit cell mass, m (g x10-22); computed dielectric constants of h-BN, k; CT between 8 ACS Paragon Plus Environment

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the graphene and Au plates; Ec (eV); plane-average electrostatic potential difference between graphene and Au, ∆Vz (in V); gravimetric capacitance in mF/g computed using C1, C2 and C3. The values in brackets for C3 are those obtained by the dielectric constant h-BN bulk, k = 5.25. ∆Mz

C1

C2

C3

0.059

2.8

1.8

2.1

(6.7) 2.97

0.082

0.062

3.7

7.6

3.2

(3.8) 1.89

3.52

0.057

0.055

2.7

3.7

2.7

(2.6) 1.77

3.89

0.045

0.048

3.6

2.4

1.4

(1.9) 1.54

n

d

m

k

|Q|

Ec

1

5.6

6.3

2.31

0.037

2

8.6

7.1

2.56

3

11.4

7.9

4

14.3

8.7

redistribution. Such interactions play a crucial role in

charge separation between plates. In the present case,

dipole formation on metal surfaces.65, 66

an external electric field is applied normal to the

Since, the electronic properties of graphene are not

plane in order to separate charges as illustrated in Fig.

affected by interfaced h-BN layers and the lattice-

7(a). Two disconnected conducting plates namely Au-

matching of ‘n’ h-BN with graphene and 2D-Au layer

layer and graphene are separated by three h-BN lay-

71

is excellent , they form efficient capacitors. It has

ers results in a robust capacitor with efficient charge

been shown that both experimentally67 and theoreti-

separation (Fig. 7(b)). Another prerequisite for a good

cally68-70 that several layers of h-BN can be fabricated

photoelectric heterostructures material is a large built-

on graphene. Freestanding single-layer h-BN is a

in electric field to drive charge carriers and separate

large band gap insulator with Eg ~ 4.6 eV. We calcu-

the electrons and holes efficiently. We model a capac-

lated the band structure of monolayer and multilayers

itor with separated charged plates of positive and

h-BN (n = 1 – 4) and they provide an excellent die-

negative charges when an external electric field ap-

lectric medium within the graphene and Au interface

plied =1.0 V/Å is applied in the presence of three h-

(Figure S7- Figure S9). The capacitance of a capaci-

BN layers between graphene-Au interface as present-

tor depends upon the area of the conductors (gra-

ed in Fig. 7(b). On account of this good separation (d

phene-Au) and the interlayer distance between gra-

= 14.3 Å) the lifetime of photogenerated carriers can

phene and Au. Hence, it is important to achieve

be effectively prolonged.



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Figure 6: (a) Energy stored Ec at different interlayer distance between graphene and Au, (b) charges on plates 12 = 1.0 V/Å was applied perpendicular to graphene-Au for the calculating energy stored Ec and |Q|. Notes that E charge |Q|. The integrated charge density difference under differ-

increase the number of h-BN between the plates, C1

ent external field is calculated according to the for-

increases till n = 2 and then decreases to 2.4 µF/g for

mula

n = 4. The gravimetric capacitors in terms of potential difference C2 is definition as, C2 = Q/m∆Uz where ∆Uz

∆ρNO A ρ>P12QR@ >x, y, z@dxdy A ρ>P12 QS@ >x, y, z@dxdy

is the plane-average potential difference. The external

where ρ>P12QR@ >E, F, G@ and ρ>P12QS@ >E, F, G@ are the

electric field can also reinforce the built-in electric

charge densities of graphene-Au nanocomposite at (x,

potential from graphene to Au layer as they are in the

y, z) point with and without external electric field

same direction. We calculated capacitance (mass-

strength, respectively. At 312T 1.0 U ⁄Å clear locali-

scaled) in primitive unit cell from the expression, C1

zation of positive and negative charges are observed

= Q2/2mEc, where |Q| the charge separation, m repre-

on graphene and Au layer respectively (Fig. 7(b)).

sents the mass in the primitive unit cell and Ec the en-

We obtain an electrostatic potential difference of 2.7

ergy stored in the capacitor. As shown in Fig. 8 (blue

V as seen in Fig. 7(c). To understand the charge in-

line), C1 = 7.6 µF/g for h-BN monolayer in between

side the graphene-Au interface, we plotted the aver-

the two plates. Similar to C1, C2 also has maxima at n

age in-plane total electrostatic drop ∆Uz (Figure S9

= 2; C2 = 3.2 µF/g. We further calculated the capaci-

(a-d)) for n = 1 - 4. We calculated the maximum grav-

tor using the classical Helmholtz relation Fig. 8 (pink

imetric capacitance for n = 2 as C1 = 7.6 µF/g. As we

line). 10


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Figure 7: (a) Dielectric capacitor with three h-BN monolayers between the graphene and Au plates, (b) the charge density difference negatively charged (graphene) and positively charged (Au plates), and (c) Schematic description of plane-averaged electrostatic potential, ∆Uz. The isosurface values are taken as 4.27 x 10-6 elec-

trons/bohr3. Pink and yellow represents excess and depleted electrons, respectively. (YZ

[\]^_ ` I ab

@. It is evident that C3 ∝ 1/d, (see val-

ues for ‘n’ in Table 1) as the interlayer distance between graphene and Au increases, C3 decreases. 4. Conclusion In summary, we have performed calculation with five exchange-correlation functionals to study the stable 2D graphene-Au interface with hexagonal close packed lattice. Our calculations indicate that the graFigure 8: Variation of the dielectric capacitance with

phene binds to 2D Au monolayer with an interlayer

respect to the number of h-BN layers. C1 (blue line)

spacing of 3.42 Å and with binding energy of about -

computed based on the energy stored in the capacitor,

1.82 and -1.39 eV at PBE-D2 and LDA, respectively.

Ec; C2 (red line) using the plane-average ∆Vz; C3 using

As the interlayer distance increases the binding ener-

the classical Helmholtz formula when kbulk = 5.25

gy decreases and it tends to zero value. PBE-D2 gives

(green line) and calculated values of kv=0║ (kv=0,⊥) for

the most stable structure which is confirmed by phonon calculation. We observe that charge-transfer

‘n’ = 1 - 4 (pink line).

might be driven by applying an electric field normal We used our computed dielectric constants for esti-

to the graphene-Au interface. The absence of dynam-

mating the capacitance (C3) as well as used the bulk

ic instability is shown by the lack of negative fre-

dielectric constant value (k = 5.25) for h-BN

quencies f in the first 2D Brillouin zone. Molecular dynamics simulations show that the heterostructure is able to maintain its planarity till T = 1200 K. The ca11



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Page 12 of 17

pacitance in graphene-Au systems can be increased

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