Structures and electronic properties of si nanowires grown along the [1 1 0] direction role of surface reconstruction

Structures and electronic properties of Si nanowires grown along the [110]
direction: Role of surface reconstruction
Toru Akiyama
*
, Kohji Nakamura, Tomonori Ito
Department of Physics Engineering, Mie University, 1577 Kurima-Machiya, Tsu 514-8507, Japan
article info
Article history:
Received 30 May 2008
Accepted for publication 4 August 2008
Available online 9 August 2008
Keywords:
Density functional calculation
Surface energy
Silicon
Nanostructures
abstract
The atomic and electronic structures of silicon nanowires grown along the [110] direction are systemat-
ically investigated using first-principles pseudopotential method. For nanowires whose diameters are
$4 nm, the calculations taking account of various surface reconstructions both with and without hydro-
gen atoms on nanowire facets demonstrate that the reconstruction on nanowire facets is strongly depen-
dent on hydrogen chemical potential
l
H
. The nanowire terminated by H atoms is stabilized for high
l
H
whereas the pristine nanowire is favorable for low
l
H
. The nanowires with partially hydrogenated facets

also appear within a certain
l
H
range. Peculiar features in the electronic structure caused by facet edges
are found in both pristine and partially hydrogenated nanowires.
Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction
Semiconductor nanowires (NWs) are recently paid much atten-
tion as potential building blocks for nanoelectronic and photonic
devices. Silicon NWs (Si NWs) are in particular attracting great
interest due to their compatibility with conventional Si-based
technology. Furthermore, they are scientifically of interest and
importance for a prototype of nanoscale materials to study effects
of quantum confinement, dimensionality, and orientation. So far, Si
NWs of diameters below 10 nm have been synthesized by solution
techniques [1], oxide-assisted catalyst-free method [2–4], and me-
tal-catalytic vapor–liquid–solid (VLS) method [5–8].
More recently, Si NWs fabricated by means of Au nanocluster-
catalyzed VLS method using the chemical vapor deposition (CVD)
have been shown to be the controlled growth of molecular-scale
Si NWs [7]: the high-resolution transmission electron microscopy
(HRTEM) has shown that Si NWs are single crystal with little or
no visible amorphous oxide down to diameters as small as 4 nm.
Furthermore, it have been shown that, importantly, the smallest-
diameter NWs are grown primarily along the [110] direction while
the NWs with large diameter are grown along the [111] direction.
The HRTEM has also observed the hexagonal nanowire shape
which consists of {001} and {111} facets. On the other hand, re-
cent theoretical investigations have investigated the effect of the
nanowire size on the electronic properties for Si NWs terminated

with hydrogen in an idealized symmetric dihydride structure [9–
11]. Zhao et al. investigated the size and orientation dependence
on the structural, electronic, and optical properties of hydrogen-
passivated Si NWs with diameter up to 4.2 nm and found that
quantum confinement becomes significant for diameter less than
2 nm, where the dielectric function exhibits strong anisotropy
and new low-energy absorption peaks start to appear in the imag-
inary part of the dielectric function for polarization along the wire
axis [9]. Vo et al. also clarified the effects of surface reconstruction
on the opto-electronic properties for dihydride and monohydride
cases on the {0 0 1} facets [10]. In spite of these findings, there still
remain matters to debate about effects of surface reconstruction
both on {001} and {111} facets of Si NWs: since the reconstruction
could depends on temperature and pressure of hydrogen ambient
during and after the fabrication process in the CVD, it is expected
that various surface reconstructions including those in clean sur-
faces exhibit on the nanowire facets. Due to higher surface–volume
ratio in thin NWs compared to those in thick or bulk phase, effect
of surface reconstruction could be crucial on the electronic proper-
ties of thin NWs.
In this paper, effects of surface reconstruction on structural and
electronic properties of Si NWs grown along the [110] direction
are systematically investigated based on total energy electronic
structure calculations. In particular, we focus on the surface recon-
struction of nanowire facets in Si NWs with diameter of $4nm,
which have been successfully fabricated by the CVD. The relative
stability among NWs with various surface reconstructions is deter-
mined based on the calculated formation energy depending on
hydrogen chemical potential which represents temperature and
pressure effects of hydrogen ambient. Furthermore, effects of sur-

face reconstruction of nanowire facets on the electronic structures
are examined from the calculated band structures and wave func-
tion characters. We find that the reconstruction on nanowire facets
is strongly dependent on hydrogen chemical potential
l
H
and Si
0039-6028/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.susc.2008.08.002
* Corresponding author. Tel.: +81 59 232 1211x3978; fax: +81 59 231 9726.
E-mail address: (T. Akiyama).
Surface Science 602 (2008) 3033–3037
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journal homepage: www.elsevier.com/locate/susc
NWs with partially hydrogenated facets appear within a certain
l
H
range. We further propose that peculiar features in the electronic
structure caused by facet edges could be realized in both pristine
and partially hydrogenated nanowires.
2. Calculation procedure
All calculations have been performed within the generalized
gradient approximation in density functional theory (DFT) [12].
We use norm-conserving pseudopotentials [13] and the conju-
gate-gradient technique [14,15] both for the electronic structure
calculation and for the geometry optimization. In the optimized
geometries the remaining forces acting on the atoms are less than
5.0 Â 10
À2

Ry/Å. The valence wave functions are expanded by the
plane-wave basis set with a cutoff energy of 10 Ry which gives
an enough convergence of total energy to discuss the relative sta-
bility. We employ a supercell in which a nanowire is placed with
its facets being separated by $7 Å from those of adjacent NWs.
1
Two atomic-layers are employed to simulate the periodicity along
the [110] direction.
2
Eight k-points are used in the integration over
one-dimensional Brillouin zone.
We construct hexagonal nanowire models whose diameters are
$3.7 nm according to the following procedure: First, we have con-
firmed a possible nanowire shape using Wulff’s theorem [16] in
which the ratio of surface energy to the distance from the centre
of crystal to the surface is constant. Assuming that nanowire facets
during the growth consist of clean surface, we have obtained that
the ratio of the distance for {0 01} facet to that for {111} facet is
1.03 [17]. This value can be satisfied by taking hexagonal shape
considered in this study. Next, we have determined the nanowire
size which reproduces the diameter fabricated by the CVD [7].
The diameter of nanowire model is 3.7 nm, which is comparable
to the experimental value of 4 nm. Therefore, it is expected that
clean surface will appear on the nanowire facets during the growth
condition. However, surface Si atoms can be terminated with H
atoms after the growth by changing hydrogenation conditions.
Considering such situations, we here consider both pristine and
hydrogen terminated NWs. We adopt asymmetric dimers with
p(2 Â 1)-type structure for pristine {00 1} facets, and monohydride
and dihydride configuration for H-terminated {001} facets [18].

For pristine {111} facets, we take account of two types of (2 Â 1)
surface, such as buckling structure [19] and
p
-bonded chain [20]
configurations, because recent calculations for flat Si(111) surfaces
have shown that the
p
-bonded structure is unstable compared to
the buckling structure when the width of dangling bonds is less
than three top-layer atoms in the ½11

2 direction [21]. These calcu-
lated results indicate a plausibility of the buckling structure as a
relevant surface reconstruction on {111} facets with finite flat sur-
face area. The dimers, adatoms, and stacking faults (DAS) model
[22] for the (7 Â 7) structure is excluded in the present study be-
cause such reconstruction requires more surface areas. For H-ter-
minated {111} facets, the (1 Â 1) structure is considered.
The relative stability of Si NWs is determined using the forma-
tion energy E
f
[18] written as
E
f
¼ E
tot
À n
Si
l
Si

À n
H
l
H
þ n
H
e
z
; ð1Þ
where E
tot
is the total energy of nanowire in the supercell,
l
Si
(
l
H
)is
the chemical potential of an Si (H) atom, n
Si
(n
H
) is the number of Si
(H) atoms, and e
z
is the zero-point energy of Si–H vibrations. The
value of
l
Si
is equal to that in bulk Si and the zero of

l
H
is taken
to be the chemical potential at which the formation energy of
SiH
4
is equal to zero. The value of e
z
is taken to be 0.21 eV which
corresponds to the zero-point energy per H atom in SiH
4
. We also
estimate the temperature at 1 atom of partial pressure of H
2
from
the standard partition function, within the harmonic approxima-
tion, including both rotational and zero-point vibrational energies
[23].
3. Results and discussion
Fig. 1a shows the calculated formation energy per Si–H unit as a
function of H-chemical potential for various structures. The calcu-
lated formation energy indicates that the energetically lowest
structure depends on
l
H
. For
l
H
lower than À0.81 eV, the pristine
nanowire with

p
-bonded chain on {111} facets and p(2 Â 1) sur-
face on {001} facets, shown in Fig. 2a, is the most favorable struc-
ture. This structure is found to be stable compared to the pristine
nanowire with buckling structure (pristine: {111}-(2 Â 1) buckling
in Fig. 1) by 0.12 eV/Si–H pair, which is comparable to the energy
difference between the buckling and
p
-bonded chain structures
on flat Si(111) surface (0.13 eV/1 Â 1 cell). The appearance of
p
-
bonded chain implies that the stability of {111} facets is similar
to that in clean Si(111) surface.
3
In contrast, for
l
H
higher than
À0.75 eV, H-terminated nanowire on both {00 1} and {111} facets
is stabilized. As shown in Fig. 2d, this completely H-terminated
nanowire consists of monohydride configuration on {0 0 1} facets
and (1 Â 1) H-terminated surfaces on {111} facets: the NWs with
dihydride facets are not found as stable configurations over entire
l
H
range considered in this study, although recent calculations have
shown that Si NWs with canted dihydride NWs could appear for high
l
H

[10]. Since in flat Si(001) surface monohydride configuration is
stable over wide H-chemical potential range and dihydride structure
is favorable in the limit range [18], it is reasonable to conclude that
dihydride {001} facets might appear in the limited condition.
In addition to these structures, we found that partially H-termi-
nated structures are stabilized in the narrow
l
H
range. Fig. 1b
shows the formation energy between low and high
l
H
where pris-
tine and completely H-terminated NWs are stabilized, respectively.
Only {001} facets are hydrogenated for À0.81 <
l
H
< À0.78 eV
(Fig. 2b) and {1 1 1} facets are hydrogenated for À0.78 <
l
H
<
À0.75 eV (Fig. 2c). Since the number of adsorbed hydrogen atoms
in the former structure (12 atoms in the unit cell) is smaller than
the number in that in the latter one (24 atoms in the unit cell),
these partially hydrogenated structures can be interpreted as inter-
mediate structures between pristine and completely hydrogenated
structures. The estimated temperature range for partially hydroge-
nated NWs is 530–570 K, implying that partially hydrogenated
NWs can be formed in such narrow temperature range. However,

due to the very small energy difference, it can be expected that
these NWs coexist in this temperature range.
The analysis of the electronic structure for stable NWs clarifies
that the surface reconstruction on nanowire facets crucially affects
the electronic structure. Fig. 3 shows the Kohn-Sham band struc-
ture of stable NWs. In the case of NWs which possess nanowire fac-
ets without H atom, as shown in Fig. 3a–c, surface related
1
For the flat Si(111) surfaces, the validity of surface separation has been checked
by using slab geometry with 7–12 Å thick vacuum region. We found that the surface
energy and positions of surface atoms of Si(111)-(2 Â 1)
p
-bonded chain surface are
identical within 0.01 eV and 0.01 Å, respectively.
2
Although the size of unit cell along the [110] direction is insufficient to obtain the
most stable c(4 Â 2) reconstruction on Si(001) surfaces, the energy difference
between p(2 Â 1) and c(4 Â 2) is found to be negligible compared with the energy
differences discussed in the paper (the calculated energy difference is within 0.01 eV/
1 Â 1 cell). Therefore, the relative stability depending on hydrogen chemical potential
could be the same as those using larger supercells.
3
The result is different from the relative stability between the buckling and
p
-
bonded chain structures in Ref. [21]. This is because the geometry of top-layer Si
atoms on nanowire facets are different from that in Ref. [21]. There are boundaries
between the (2 Â 1) with
p
-bonded chain and (1 Â 1) structure along the ½ 1


10
direction in the nanometer-scale Si(1 11) surface while no boundary exists on top-
layer Si atoms of
p
-bonded chain-like structure on {111} facets of Si NWs.
3034 T. Akiyama et al. / Surface Science 602 (2008) 3033–3037
electronic states appear around the band gap. In the pristine nano-
wire, as shown in Fig. 3a, both localized electronic states caused by
p
-bonded chains on {111} facets (arrows in Fig. 3b) and dangling
bonds of p(2 Â 1) surface on {001} facets (arrows in Fig. 3c) are
formed. In addition, the electronic states originating from the
nanowire edges between adjacent {111} facets are formed near
the Fermi level at the zone boundary (arrowheads in Fig. 3b).
Due to these electronic states, it is expected that pristine and
{001} facets hydrogenated NWs exhibit semimetallic character.
This is quite different from the metallic and semimetallic behav-
iour proposed in Si NWs along the [001] direction [24]. Since both
p
-bonded chain and p(2 Â 1) reconstructions on Si(111) and
Si(001), respectively, exhibit semiconductor behaviour, such elec-
tronic structures are typical for NWs containing pristine facets
edges.
In order to clarify the origin of semimetallic character, we ana-
lyze the character of wave functions in the {0 0 1} facets hydroge-
nated nanowire shown in Fig. 2b. Fig. 4a and b show the contour
plots of wave functions for symmetrically equivalent two highest
occupied (HO) and four lowest unoccupied (LU) states, respec-
tively. By comparing the distribution of wave functions for the

p
-
bonded chain on Si(111) surface (insets of Fig. 4), we find that
the wave functions of the doubly-degenerate HO states and four
LU states correspond to the
p
-like bands of edge atoms and the
Fig. 1. Calculated formation energies of NWs grown along the [110] direction for various surface reconstructions as a function of hydrogen chemical potential. (a) Formation
energy over wide temperature range and (b) that for narrow range where partially hydrogenated structures are stabilized (represented by vertical dotted lines). Dashed lines
denote metastable structures. The temperature of H
2
-gas temperature at 1 atom is also shown.
Fig. 2. Cross-sectional views of (a) pristine, (b) {111} facets hydrogenated, (c) {001} facets hydrogenated, and (d) completely H-terminated NWs. Open and filled circles
represent Si and H atoms, respectively. The six-membered rings which constitute nanowire edges between adjacent {111} facets are represented by grey areas in (a) and (b).
T. Akiyama et al. / Surface Science 602 (2008) 3033–3037
3035
p
*
-like bands on {111} facets, respectively. This is because nano-
wire edges between adjacent {1 11} facets consist of six-membered
ring (grey area in Fig. 2a and b) while surface atoms of normal
p
-
bonded chain on {111} facets belong to seven-membered ring:
the difference in atomic configuration causes the suppression of
lattice relaxation for edge atoms. Indeed, the
p
*
-like bands for
the edge atoms are located $0.2 eV above the

p
-like bands for
the edge atoms, implying that the suppression of lattice relaxation
results in the weakness of surface bound states. As a result, the en-
ergy of
p
-like bands on nanowire edge becomes close to the
p
*
-like
bands on {111} facets. We note, however, that more elaborate cal-
culations beyond DFT calculations, such as GW approximation
[25], should be required to exclude the possibility that such a semi-
metallic behaviour comes from the limitation of DFT calculation.
For completely H-terminated nanowire, as shown in Fig. 3d, the
surface related electronic states are completely eliminated around
the band gap. More importantly, the gap energy (0.94 eV) is large
compared to that in bulk Si (0.74 eV) and the direct band gap char-
acter is found. The band structure of monohydride nanowire is
qualitatively consistent with the calculated results for Si NWs with
dihydride surface in the previous calculations [9–11]. As explained
in the previous study [9,10], this character can be understood in
terms of the projection of energy band in bulk Si and confinement
effect: the confinement decreases the energy of HO states and in-
creases the energy of the LU states, but the magnitude of the en-
ergy shift depends on their effective masses. Due to the large
effective mass along the longitudinal direction of the LU states lo-
cated at $85% along
C
to X in bulk Si, which is projected at the

C
-
point for NWs grown along the [110] direction, the energy shift of
the projected LU states becomes small, resulting in the direct band
gap character.
4. Summary
We have investigated atomic and electronic structures of silicon
NWs along the [110] direction based on first-principles pseudopo-
tential calculations. For atomic structure, we found that partially
hydrogenated NWs as well as H-terminated and pristine NWs
can be formed depending on hydrogen chemical potential. The
existence of the nanowire edges between different nanowire facets
causes the stabilization of
p
-bonded chain on {111} facets, which
results in the appearance of partially hydrogenated NWs with
p
-
bonded chain configuration. We have also confirmed the direct
band gap character with larger gap energy than bulk value for com-
pletely hydrogenate nanowire, consistent with previous theoreti-
cal studies. Surface related electronic states caused by nanowire
facets appear for pristine and partially hydrogenated NWs result
in semimetallic nature different from flat surfaces. This semimetal-
lic nature originates from the suppression of lattice relaxation for
edge atoms which results in the weakness of surface bound states.
Although the size dependence on the structural and electronic
properties have been left in the present study, the calculated re-
sults imply that over wide range of the nanowire diameter the
reconstruction on nanowire edge crucially affects the structural

Energy (eV)
Energy (eV)
Energy (eV)
Energy (eV)
-1
0
1
X
-1
0
1
X
-1
0
1
X
-1
0
1
X
ΓΓ ΓΓ
abcd
Fig. 3. Energy bands of (a) pristine, (b) {111} facets hydrogenated, (c) {001} facets hydrogenated, and (d) completely H-terminated NWs. The zero of energy is set to the
Fermi level. Arrows in (b) and (c) represent the surface related electronic states due to
p
-bonded chain on {111} facets and dangling bonds on p(2 Â 1) surface of {001} facets,
respectively. Arrowheads in (b) indicate the electronic states related to
p
-bonded chain of nanowire edges between adjacent {111} facets. The calculated gap energy in bulk Si
is 0.73 eV.

Fig. 4. Cross-sectional views of the wave functions at zone boundary of (a) two highest occupied and (b) four lowest unoccupied states in the {0 01} facets hydrogenated
nanowire. The density of isosurfaces is 1.5 Â 10
À3
e/Å
3
. The wave functions of
p
- and
p
*
-like bands on Si(111)-(2 Â 1) surfaces are also shown on the inset of (a) and (b),
respectively.
3036 T. Akiyama et al. / Surface Science 602 (2008) 3033–3037
and electronic properties of Si NWs grown along the [110]
direction.
Acknowledgements
This work was supported in part by Grant-in-Aid for Scientific
Research from JSPS under Contract No. 18560020. Codes used in
this work are based on Tokyo Ab-initio Program Package (TAPP).
Computations were performed at RCCS (National Institutes of Nat-
ural Sciences) and ISSP (University of Tokyo).
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[23] The temperature is estimated using the relationship
l
H
2
¼Àk
B
T lnðf
trans

Â
f
rot
 f
vib
Þ, where f
trans
¼ k
B
T=fp
H
2
ð2pmk
B
T=h
2
Þ
3=2
g; f
rot
¼ T=ð2h
r
Þ, and f
vib
=
{1 À exp(Àh
m
/k
B
T)}

À1
are the partition functions for the translational,
rotational, and vibrational motions, respectively (p
H
2
is the pressure of H
2
gas, m is the mass of an H
2
molecule,
m
is the frequency, and h
r
= 85.4 K). See, Y.
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T. Akiyama et al. / Surface Science 602 (2008) 3033–3037
3037