# Silicene and Germanene: A First Principle Study of Electronic Structure and Effect of Hydrogenation-Passivation

**ABSTRACT** Using first principle calculations we have explored the structural and electronic properties of silicene (silicon analogue of graphene) and germanene (germanium analogue of graphene). The structural optimization reveals that buckled silicene and germanene are more stable than their planar counterparts by about 0.1 and 0.35 eV respectively. In comparison to planar graphene (buckling parameter Δ = 0 Å) the germanium sheet is buckled by 0.737 Å and silicene by 0.537 Å but both have similar electronic structure with zero band gap at K point as that of graphene. Further we investigated the effects of complete hydrogenation on these materials by considering different geometrical configurations (chair, boat, table and stirrup) and found that chair-like structure has the highest binding energy per atom in comparison to other structures. Hydrogenated silicene (silicane) shows an indirect band gap of 2.23 eV while hydrogenated germanene (germanane) possess a direct band gap of 1.8 eV.

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RESEARCH ARTICLE

Copyright © 2014 American Scientific Publishers

All rights reserved

Printed in the United States of America

Journal of

Computational and Theoretical Nanoscience

Vol. 11, 1–8, 2014

Silicene and Germanene: A First Principle

Study of Electronic Structure and Effect of

Hydrogenation-Passivation

Shyam Trivedi1?2?∗, Anurag Srivastava1, and Rajnish Kurchania2

1Advanced Materials Research Group, Computational Nanoscience and

Technology Lab ABV-IIITM, Gwalior 474010, India

2Department of Physics, Maulana Azad National Institute of Technology (MANIT), Bhopal 462051, India

Using first principle calculations we have explored the structural and electronic properties of silicene

(silicon analogue of graphene) and germanene (germanium analogue of graphene). The structural

optimization reveals that buckled silicene and germanene are more stable than their planar counter-

parts by about 0.1 and 0.35 eV respectively. In comparison to planar graphene (buckling parameter

? = 0 Å) the germanium sheet is buckled by 0.737 Å and silicene by 0.537 Å but both have similar

electronic structure with zero band gap at K point as that of graphene. Further we investigated the

effects of complete hydrogenation on these materials by considering different geometrical config-

urations (chair, boat, table and stirrup) and found that chair-like structure has the highest binding

energy per atom in comparison to other structures. Hydrogenated silicene (silicane) shows an indi-

rect band gap of 2.23 eV while hydrogenated germanene (germanane) possess a direct band gap

of 1.8 eV.

Keywords: Silicene, Germanene, Hydrogenation, First Principle, Electronic Structure, Binding

Energy.

1. INTRODUCTION

Graphene, a two dimensional honeycomb structure of car-

bon atoms has been extensively studied in the last few

years because of its novel electronic properties. Since it is

difficult to incorporate graphene in today’s silicon based

electronic industry, much interest has been generated by

other group IV elements like silicon and germanium in

theoretical study.1?2Germanene still remains a hypotheti-

cal material although ultrathin Ge nanobelts bonded with

nanotubes have been fabricated and characterized by Han

et al.3Silicene stripes have been experimentally grown

over Ag (110)4?5and on zirconium diboride substrate.6Ear-

lier density functional theory (DFT) studies have shown

that buckled hexagonal sheets of silicon and germanium

are more stable than their planar arrangements.7This indi-

cates that barring carbon all group IV elements have a ten-

dency to avoid sp2hybridization. Corrugated structures of

Si and Ge are promising materials in the design of field

effect transistors as application of vertical electric fields can

open and control the band gaps.8?9Because of low buck-

led structure and greater spin orbit coupling, silicene can

∗Author to whom correspondence should be addressed.

also be an important material for spintronics as Quantum

spin Hall Effect in silicene has been reported by Liu et al.10

Hydrogen-passivated graphene (graphane) has attracted

much attention in theoretical studies because of drastic

changes in band gaps that occur upon hydrogenation.11

It has been synthesized in laboratory and the hydrogena-

tion process is shown to be reversible thereby making

it a potential candidate for hydrogen storage.12Safe and

efficient storage of hydrogen is a concern and various

nanomaterials have been explored computationally so that

hydrogen storage with high gravimetric and volumetric

density becomes a reality.13Hydrogenation of carbon and

SiC nanotubes and their subsequent use in hydrogen stor-

age have also been extensively studied in theory.14–16The

structure and electronic properties of different geometri-

cal configurations of graphane (chair, table and boat) have

been theoretically investigated by AlZahrani et al.17finding

a direct band gap of 3.9 eV and a buckling parameter

of 0.46 Å. A new isomer of graphane having stirrup-

like structure is also explored by Bhattacharya et al.18

Osborn et al.19have studied the geometry and energetics

of partially hydrogenated silicene and found that adsorp-

tion energy of hydrogen on silicene increases with the

hydrogenation ratio. Zhang et al.20have investigated the

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Trivedi et al.

properties of half and fully hydrogenated chair-like struc-

tures of silicene and reported that the former acts like a

ferromagnetic semiconductor. Houssa et al.21have explored

the electronic properties of hydrogenated silicene and ger-

manene using many body perturbation methods and found

that germanane has a direct average energy gap of 3.2 eV.

In view of above, we thought it pertinent to explore the

understanding of structural and electronic behaviour of sili-

con/germanium sheets and calculate the binding energies of

different hydrogenated crystal geometries in order to inves-

tigate the change in bandstructure and density of states due

to hydrogenation.

2. COMPUTATIONAL DETAILS

Structural optimization and calculations were performed

using DFT based ab-initio approach implemented in

Atomistix Toolkit-Virtual Nanolab (ATK-VNL) provided

by Quantumwise.22Local Density approximation (LDA)

with Perdew and Zunger23type parameterization and

generalized-gradient approximation (GGA) with Perdew–

Burke–Ernzerhof (PBE) parameterization24were used as

Fig. 1.

(? kept at 0.537 Å). (c) Energy variation with bond length for planar germanene for fixed lattice a = 4?130 Å (d) Energy variation with lattice for

buckled germanene (? kept at 0.737 Å).

(a) Energy variation with bond length for planar silicene for fixed lattice a = 3?910 Å. (b) Energy variation with lattice for buckled silicene

exchange correlation functionals along with double zeta

single polarized basis sets. Self-consistent force opti-

mizations were performed till Hellmann-Feynman force

between the atoms and the associated stress of the lattice

became less than 0.0025 eV/Å and 0.005 eV/Å3respec-

tively. The hexagonal ‘c’ parameter was kept very large

(42.32 Å) so that inter layer periodic interactions can be

treated as negligible. For Brillouin zone integration a mesh

of 21×21×1k-points were used. A mesh cut off of 600 eV

was found to be sufficient for the convergence of the plane

wave function for both silicene and germanene crystals.

Monkhorst-Pack scheme25using a k-point grid of 11×

11×1 was chosen for calculation of density of states of

both silicene and germanene.

3. RESULTS AND DISCUSSION

3.1. Silicene and Germanene

To perform the structural analysis of planar silicene,

hexagonal graphene crystal structure was taken into

consideration and in-plane atomic bond length of Si

Si

2

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Silicene and Germanene: A First Principle Study of Electronic Structure and Effect of Hydrogenation-Passivation

was varied from 2.10 Å to 2.35 Å for each of the lat-

tice parameter ranging from 3.75 Å to 4.0 Å. The total

energy was calculated for each configuration using both

LDA-PZ and GGA-PBE exchange correlation methods.

The lattice parameter at which minimum energy and stable

bond length for planar silicene is obtained was selected.

At this fixed value of lattice, energy variation as a func-

tion of bond length is plotted for planar silicene as

shown in Figure 1(a). Here we have shown energy curves

corresponding to GGA-PBE method only. To investigate

the buckled structure of silicene one of the atom was made

out of plane initially by 0.5 Å and optimization routine was

run till minimum force and lattice stress condition is met.

Corresponding to the minimum obtained energy, the bond

length and buckling parameter of the crystal (?=0?537 Å)

was calculated. In Figure 1(b) we have shown the energy

variation with lattice for buckled silicene crystal. A similar

procedure was used for analysis of planar and buckled ger-

manene and the corresponding energy curves are shown in

Table I.

Lattice parameter, bond length, total energy, band gap and buckling parameter for different arrangements of silicene and germanene.

Properties

SILICENE

a (Å)Bond length (Å)Total energy (eV) Band gap (eV) Buckling parameter ? (Å)

Planar

LDA-PZ3?87

3?84532

3?83033

2?24

2?2133

−355?94100

GGA-PBE

Buckled

LDA-PZ

3?912?252

−358?21300

3?804

3?8557

3?83126

3?80832

3?82031

3?85

3?88120

0?554

0?4426

0?5330

0?4431

0?4432

0?537

0?54019

2?265

2?2477

2?2477

−356?0390

GGA-PBE2?287

2?29819

−358?30

2?132

Hydrogenated (chair-like)

LDA-PZ3?826

3?82031

3?876

3?88420

2?327

−388?4222?031

1?233

2?227

2?3620

0?733

0?7231

0?727

0?73619

GGA-PBE2?353

2?35919

−391?262

GERMANENE

Planar

LDA-PZ

GGA-PBE

Buckled

LDA-PZ

4?01

4?13

2?31

2?383

−559?351

−561?735

0

0

0

0

3?938

3?8907

4?031

3?94234

3?96835

4?034

0?691

0?7131

0?63534

0?64535

0?737

2?376

2?3317

−559?6520

GGA-PBE

Hydrogenated (chair-like)

LDA-PZ

2?443

−562?0850

3?8762?37

−591?4631?875

1?531

1?812

0?782

0?6931

0?821GGA-PBE3?9082?401

−594?308

Figures 1(c)–(d). Looking at the total energy values (for

GGA-PBE) listed in Table I and energy curves of Figure 1

we note that the buckled structure of both silicene and

germanene is more stable than its planar arrangement by

0.1 eV and 0.35 eV respectively, this is in agreement with

earlier predictions.7The phonon dispersion calculations

performed by Cahangirov et al.26also shows that planar

structure is not stable.

For comparative understanding the structure, band dia-

gram and Fermi velocities of silicene, germanene and

graphene are shown in Figure 2. Since they all are metal-

lic in nature having zero band gap with linear dispersion

at the K point, their Fermi velocities can be calculated

through the E–k curve by using the following relationship:

vf=1

?

dE

dk

(1)

where h is the reduced Planck’s constant. The calculated

Fermi velocity of graphene and silicene is of the order of

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Fig. 2.

Structure, bandstructure with Fermi velocities of silicene germanene and graphene.

106and 105m/s respectively while velocity in germanene

lies somewhere in the middle. This result is in confirmation

with Refs. [26 and 27]. At low values of energy, electrons

in these structures behave like massless Dirac-fermions.

Fermi velocity in silicene is less than half of the value

reported for graphene.28Theoretical calculations on effec-

tive electron mass in quantum wells, wires and superlat-

tices have been performed by Bose et al.29The higher the

Fermi velocity the lower is the effective mass of electrons

moving through the periodic structure. Since graphene is

sp2hybridized, the coupling between the nearest neigh-

bour atoms is very strong and electrons can easily tunnel

from one atom to another which may explain the larger

velocities of electrons in graphene compared to silicene

and germanene.

The band structure of graphene, buckled germanene,

planar and buckled silicene are quite similar but for pla-

nar germanene the Dirac point is slightly raised above the

Fermi level (shown in Fig. 3) making it poorly metallic

in character. This kind of ‘raised’ K-point band structure

for planar germanene was also reported in Refs. [2,26].

Fig. 3.

Bandstucture of planar germanene.

However on structural transformation from planar to buck-

led, this crossing point shifts down to Fermi level.

Germanene structure is more buckled than silicene.

The buckling parameter for silicene was calculated to be

0.537 Å and for germanene it was 0.737 Å (GGA results).

Our results of buckling parameter of silicene are in agree-

ment with Ding and Ni30but slightly higher than the val-

ues reported in Refs. [26,31, and 32]. This may be due

to the difference in the underlying methods of the tool

used for performing simulation. The bond lengths, buck-

ling parameter and band gaps are listed in Table I along

with values obtained in previous works. The bond lengths

in silicene and germanene are longer in comparison to

graphene because of large size of Si and Ge atoms.

Silicon has a preference towards sp3hybridization than

sp2. Figure 4(a) shows sp2hybridized silicon in a planar

Fig. 4.

hybridization.

(a) sp2hybridized planar silicene (b) buckled silicene having sp3

4

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Silicene and Germanene: A First Principle Study of Electronic Structure and Effect of Hydrogenation-Passivation

Fig. 5.

silicene/germanene.

Various geometricalconfigurationsfor hydrogenated

structure similar to graphene. The lobes of each atom are

perpendicular to the plane of the silicon sheet and this

results in formation of ? bonds with the nearest neigh-

bours leading to conducting nature of the sheet. However

in a buckled sp3hybridized structure shown in Figure 4(b)

the lobes of neighbouring atoms point in opposite direc-

tions so the ? bonds can only be formed with the second

nearest neighbour rather than the first nearest neighbour.

The sp2hybridized orbitals get slightly dehybridized into

sp3-like orbital which causes weakening of ? bonds lead-

ing to buckled structure of silicene. The same reason

could be accounted for buckled structure of germanene as

well.

Table II.

geometries of silicene and germanene.

Binding energy and bond lengths of different hydrogenated

SILICANE configurationsB.E (eV/atom)Si Si bond length (Å)

Table

Chair

Boat

Stirrup

GERMANANE

configurations

Table

Chair

Boat

Stirrup

4?426

4?71

4?639

4?528

2.333

2.353

2.346, 2.416

2.331, 2.364

Ge

Ge Bond

length (Å)

2.524

2.401

2.4, 2.489

2.419, 2.429

B.E (eV/atom)

3?768

4?069

4?019

3?904

3.2. Effect of Hydrogen-Passivation

To analyse the role of hydrogenation we considered four

different geometries of full-hydrogenated structures of sil-

icene and germanene as shown in Figure 5. The band gap

is calculated for the arrangement which has highest bind-

ing energy. The table structure has all the hydrogen atoms

attached on one side of the sheet. The chair and the boat

conformer has H atoms alternating in (1up-1down) and

(2up-2down) fashion on either side of Si-plane (or Ge-

plane) respectively. The stirrup-like model has three con-

secutive H atoms of each hexagon alternating on both sides

of sheet (3up-3down). The binding energy in eV/atom for

each of these configurations has been calculated (using

Fig. 6.

(b) germanane.

Optimized structure of chair like configuration for (a) silicane

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Trivedi et al.

Fig. 7.

Bandstructure of (a) silicane and (b) germanane.

GGA) by the following relation:

B?E =E?config?−nE?C?−mE?H?

?n+m?

where E(config) is the total energy of the geometry under

consideration. E?C? and E?H? are the total energies of

single carbon and hydrogen atom respectively, while n and

m are the number of carbon and hydrogen atoms respec-

tively in a unit cell under consideration.

The binding energies and bond lengths for all four con-

figurations are listed in Table II which clearly indicates

that the chair conformer is the most stable of them fol-

lowed by the boat arrangement. Two different Si

(2)

Si bond

Fig. 8.

(a) DOS for germanene (b) projected DOS for hydrogenated germanene (c) DOS for silicene (d) projected DOS for hydrogenated silicene.

lengths exist in the stirrup structure. The bond between

silicon atoms which have hydrogen atoms lying over the

plane of hexagon (3-up) has a length of 2.364 Å and those

which contain hydrogen atom lying below the plane of

hexagon (3-down) has a length of 2.331 Å. In the same

way the boat arrangement also has two bond lengths.

The optimized structure (with GGA values) of chair-like

arrangement of silicane and germanane is shown in

Figure 6. Hydrogenation of the silicene and germanene

sheets causes the Si

Si and Ge

increase in comparison to the normal sheet structure.

The bond angles are very much close to tetrahedral angle

109.5?showing that sp3-like arrangement is preferred for

Ge bond lengths to

6

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Silicene and Germanene: A First Principle Study of Electronic Structure and Effect of Hydrogenation-Passivation

these hydrogenated structures. The calculated Si

Si

H bond lengths in silicane are 2.353 Å and 1.51 Å

respectively along with a vertical buckling of 0.727 Å, a

good agreement with Ref. [19]. Germanane gets buckled

by 0.821 Å and as expected its bond length, buckling

parameter are greater in magnitude in comparison to that

of silicane. In general the buckling parameter for silicene

and germanene increase due to hydrogenation and the

structure becomes more stable.

Hydrogen passivation leads to a remarkable change

in the band structure as compared to ideal silicene and

germanene (Fig. 7). A band gap opens up considerably

turning them into semiconductor materials. Silicane has

an indirect band gap of 2.23 eV between ? and M point

while germanane has direct band gap of 1.8 eV at ? point.

The opening of band gap due to hydrogenation is also

reflected in density of states shown in Figures 8(a)–(d).

For germanene the density of states starts to rise beyond

the Fermi level and it has distinct features both in occupied

and unoccupied energy regions. In the occupied region

germanene has a sharp peak at Ef−2 eV while in the

unoccupied region large states are available particularly

at Ef+3?94 eV, Ef+2?78 eV and Ef+0?71 eV. Upon

hydrogen passivation of germanene the ? and ?∗states are

removed and a finite band gap opens. Figure 8(b) shows

the projected density of states for germanane. A strong

peak is present at Ef−3?9 eV and Ef−4?09 eV in the

occupied region contributed mainly by H s and Ge p states.

In the unoccupied range large density of states are avail-

able at Ef+3?28 eV and Ef+3?91 eV largely because of

the contribution from Ge p, Ge d and H s states. Similarly,

silicane also shows an opening of band gap in Figure 8(d)

along with peak DOS at Ef+3?87 eV and Ef−3?98 eV

in the unoccupied and occupied region respectively, con-

tributed by Si p and H s states.

Si and

4. SUMMARY AND CONCLUSION

We have performed a step by step structural and band gap

analysis of sheets of silicon and germanium finding that

buckled structure is energetically more favourable than the

planar one. The band structure of buckled silicene and

germanene is similar to that of graphene. The chair-like

hydrogenated arrangement has the highest binding energy

in comparison to boat, table and stirrup structures. Silicene

and germanene show a metal to semiconductor transfor-

mation upon hydrogenation which is evident from band

gap opening and change in density of states. DFT calcu-

lations generally underestimate the bandgap by 30–50%36

but it can be safely estimated that the correct band gap

in silicane is less than that of graphane lying in 3.5–4 eV

range and for germanane it is close to 3 eV making it a

suitable material to be used in optoelectronic devices oper-

ating in blue-violet range of electromagenetic spectrum. In

future these Quantum-Confined Optoelectronic Materials37

may prove to be useful for the emerging nanoelectronic

industry.

Acknowledgments: Shyam Trivedi is thankful to the

Ministry of Human Resource Development (MHRD),

Government of India for GATE scholarship and also to the

Advanced Materials Research Group, ABV-IIITM Gwalior

for providing infrastructural support.

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