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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Trivedi et al.
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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Trivedi et al.
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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