Theoretical investigations on the formation of wurtzite segments
in group III–V semiconductor nanowires
Tomoki Yamashita *, Kosuke Sano, Toru Akiyama, Kohji Nakamura, Tomonori Ito
Department of Physics Engineering, Mie University, 1577 Kurima-Machiya, Tsu, Mie 514-8507, Japan
Available online 6 February 2008
Abstract
Structural trends in group III–V semiconductor nanowires (NWs) are systematically investigated based on Monte-Carlo simulations using our
empirical potential calculations. The calculated NW stacking sequences for the selective area growth demonstrate that the averaged periodicity
between wurtzite segments, which is independent of the NW size, decreases with increasing ionicity of semiconductors f i. It is also found that the
periodicity is affected by the nucleus size of NWs: The calculated periodicity in InP (InAs) NWs with the nucleus size consisting of � 10 atoms are
0.76 (0.86) nm, reasonably consistent with the experimentally reported one. On the other hand, the nucleus size to reproduce the experimentally
reported periodicity in GaAs NWs is estimated to be more than 70 atoms. These results thus imply that the nucleus size as well as f i is of
importance in determining the averaged periodicity between wurtzite segments.
# 2008 Elsevier B.V. All rights reserved.
PACS : 81.07.Bc; 81.10.�h; 61.46. +w
Keywords: Nanowires; Monte-Carlo simulation; Rotational twins; Nucleus size; Ionicity
www.elsevier.com/locate/apsusc
Available online at www.sciencedirect.com
Applied Surface Science 254 (2008) 7668–7671
1. Introduction
One-dimensional nanostructures such as semiconductor
nanowires (NWs) are expected to play a key role in future
nanotechnology due to their potential application as building
blocks in electronics and optoelectronics. In particular,
NWs of group III–V materials have attracted much
attention because of their specific optical properties
and are expected to be applied to light-emitting diodes
[1–3], photodetectors [4,5] and lasers [6–8]. Hence,
considerable efforts have been devoted to fabricate these
NWs by employing various methods such as metal-organic
vapor-phase epitaxy and molecular beam epitaxy. It is
experimentally known that there are some structural
characteristics different from bulk crystals. Observation by
high resolution transmission electron microscopy (HRTEM)
has revealed that group III–V NWs fabricated by the
selective area metal-organic vapor-phase epitaxy (SA-
MOVPE) often include wurtzite (W) segments in the zinc
* Corresponding author. Tel.: +81 59 232 1211x3978; fax: +81 59 231 9726.
E-mail address: [email protected] (T. Yamashita).
0169-4332/$ – see front matter # 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.apsusc.2008.01.135
blende (ZB) structure. This results in the formation of
rotational twins in GaAs NWs at 750 �C [9], 4H-like
structure in InAs NWs at 540 �C [10] and W structure in InP
NWs at 600 �C [11]. Despite these experimental findings, the
systemization for the propensity to incorporate W segments
in NWs grown by the SA-MOVPE has been rarely carried out
at present.
In our previous study, the relative stability between ZB and
W structures in group III–V NWs has been successfully
investigated based on an empirical interatomic potential
calculations [12]. The relative stability can be explained in
terms of the ionicity of semiconductors f i. We have also
investigated the formation of rotational twins in InP NWs
grown along the [1 1 1] direction by the vapor–solid–liquid
(VLS) reaction and by the SA-MOVPE based on a Monte-
Carlo (MC) simulations using our empirical potential [13].
The results imply that the nucleus formation at the top of
growing NW crucially affects the W segments formation. In
this study, we extend our approach to group III–V NWs
fabricated by the SA-MOVPE to clarify the chemical trends
for the incorporation of W segment formation systematically.
We discuss the span between W segments in terms of the
nucleus size and f i.
Fig. 1. Calculated stacking sequences of InAs NWs with diameter of 50 nm
obtained by the MC simulations at 540 �C for (a) Nnc=10, (b) Nnc=30, (c)
Nnc=50, and (d) Nnc=70. Light and dark regions correspond to the stacking
sequences of ZB structure along the [1 1 1] direction. Boundaries between light
and dark regions represent the W-type stacking sequence corresponding to
rotational twins. The calculated periodicity between W segments is obtained
from the distance between these boundaries.
T. Yamashita et al. / Applied Surface Science 254 (2008) 7668–7671 7669
2. Computational methods
Since the stacking sequences corresponding to the W
stacking sequence (ABAB� � � ) can be incorporated in the ZB
stacking sequence (ABCABC� � � ) along the [1 1 1] direction,
there are many types of stacking sequence available along this
direction. In order to determine the stacking sequence of double
layer under the crystal growth, we perform MC simulations by
employing our empirical potential calculations. In the
calculation procedure, we first calculate the NW cohesive
energy of double layer for various stacking sequences using a
six double-layer unit cell. The NW cohesive energy is obtained
by using our empirical interatomic potential which is given by
E ¼ E0 þ DEW� ZB (1)
E0 ¼1
2
X
i; j
Vi j (2)
where E0 is the NW cohesive energy calculated by Kohr–Das
Sarma type empirical interatomic potential Vi j within the
second nearest neighbors [14–16]. DEW� ZB is the energy
difference between W and ZB structures in the bulk form,
which is caused by the electrostatic interaction [17]. Here, we
use the energy difference between W and ZB structures in the
bulk form obtained from ab initio calculations [18]. The values
of f i and DEW� ZB used in this study are listed in Table 1. Using
Eq. (1), the relationship between stacking sequence and cohe-
sive energy is obtained.
Next, we consider a NW model with hexagonal shape which
can minimize the surface dangling bonds in the ZB structure
[13]. Although the fabrication of NWs with anisotropic side
facets is reported [10], we consider NWs consisting of 500
double layers with isotropic flat (1 1 0)-like facets as a
representative of the NW models. We then calculate their
cohesive energies by summing the cohesive energy of each
double layer obtained by using Eq. (1). Considering that the
nuclei formation is one of the key processes to determine the
crystal strucure in epitaxial growth, we here take account of the
influence of the critical nuclei formation on the stacking
sequence preference by evaluating the energy difference in the
MC step. The energy difference DEnc is calculated by the
energy of nucleus, which is given by
DEnc ¼ NncðEf � EiÞ (3)
Table 1
The ionicity f i used in this study and energy difference DEW� ZB (meV/atom)
between wurtzite and zinc blende structures for group III–V compound
semiconductors in the bulk form obtained by ab initio calculations [18]
GaSb AlSb InSb GaAs AlAs InAs
f i 0.15 0.16 0.19 0.218 0.221 0.29
DEW� ZB 9.9 9.5 8.2 8.3 8.2 5.3
GaP AlP InP AlN GaN InN
f i 0.295 0.298 0.35 0.69 0.74 0.83
DEW� ZB 5.8 5.7 3.4 �13 �12.7 �15.5
where Nnc is the number of atoms consisting the nuclei. Ef and
Ei are the cohesive energies before and after the replacement in
the MC step, respectively. We assign the two dimensional
nucleation at the top layer of growing NW, which could be
applied to the crystal nucleation in the SA-MOVPE [13]. In the
present study, we consider different size for Nnc (=10, 30, 50,
and 70) to clarify effects of nucleus size on the W segment
formation.1
The MC simulations are performed for NWs ranging from
1.4 to 80 nm to confirm the size dependence of W segment
formation in the SA-MOVPE. In the MC scheme, a randomly
chosen double layer is replaced by another randomly chosen
double layer which can be stacked in the host layers using
Eq. (3). The stacking sequence preference during NW growth is
assigned to the equilibration by the MC step.
3. Results and discussion
Fig. 1 displays the calculated stacking sequence of InAs
NWs for the SA-MOVPE by the MC simulations. Here, we find
that the averaged periodicity P between W segments in group
III–V NWs with diameters ranging from 10 to 80 nm is
independent of the NW size. As shown in the light and dark
contrasts shown in Fig. 1, P increases as the nucleus size
becomes large. This is because the energy difference in Eq. (3)
becomes large for Nnc with large number of atoms. The large
energy difference results in taking the ZB stacking sequence
1 Effects of the polarity along the growth direction might be included in the
size of critical nuclei.
T. Yamashita et al. / Applied Surface Science 254 (2008) 7668–76717670
which is stable in the bulk form. It should be noted that the
calculated stacking sequence well reproduces the experimen-
tally reported TEM image. Especially, the stacking sequence
using Nnc=10 (Fig. 1(a)) agrees well with the TEM image of
InAs NW with diameter of 60 nm [10].
Fig. 2 shows the periodicity P as a function of the ionicity f i
in 12 compound NWs at (a) 540 �C, (b) 600 �C, and (c) 750 �C,
which corresponds to the growth temperatures of InAs, InP, and
GaAs NWs, respectively[10,11,13]. It is found that for all
temperatures P decreases as f i increases except nitride NWs
(AlN, GaN, and InN NWs). Since f i is larger than the critical
ionicity f ci (= 0.455) [17] for nitride NWs, they always take the
W structure as seen in the bulk phase. For the other NWs, the
decrease in P can be interpreted as the energy difference
Fig. 2. Calculated periodicities between W segments in 12 compound NWs as
functions of f i obtained by the MC simulations at (a) 540 �C, (b) 600 �C, and
(c) 750 �C. Diamonds, circles, triangles, and squares represent the periodicities
obtained using Nnc=10, 30, 50, and 70, respectively. The values estimated from
the experimental results [9–11] are also plotted by asterisks. The values of f i are
determined to reproduce the results obtained from ab initio calculations (see,
Table 1).
between W and ZB structures, because the energy difference is
large for small f i. Experimentally, the value of P in InAs NWs
at 540 �C is about 0.70 nm [10]. The calculated P using the
nucleus size of 10 atoms is 0.86 nm, reasonably agree with the
experimental value. Therefore, it is implied that the nucleus
size to reproduce the experimental value is � 10 atoms as
shown in Fig. 2(a). For InP NWs, it is reported that InP NWs
fabricated at 600 �C takes W structure (P = 0.66 nm) [11] while
P using the nucleus size of 10 atoms is 0.76 nm in our
calculation. Although the calculated results shows that W
segments are randomly incorporated in ZB sequence, this imply
that the nucleus size to reproduce the experimental value is also
� 10 atoms (Fig. 2(b)). For GaAs NWs, in contrast, the
experimental value of P in GaAs NWs at 750 �C is estimated to
be more than 10 nm [9]. This value corresponds to the
calculated P using the nucleus size of 70 atoms (9.2 nm).
Therefore, the nucleus size in GaAs NWs could be more than 70
atoms as shown in Fig. 2(c).
In order to verify the validity of the nucleus size obtained in
this study, we estimate the critical nucleus size using simple
approach [19], where the radius of critical nuclei rc is expressed
as
rc ¼bas
Dm(4)
Here, b is the step free energy, as the surface area per atom in
solid phase, and Dm the chemical potential difference
between solid and gas phase. The calculated step formation
energy obtained from the linear combination of structural
motifs [20] and the chemical potential of gas phase estimated
from quantum chemical approach [21] are used for b and
Dm, respectively. The calculated values of rc are 3.8, 6.2,
and 33 A, which correspond to Nnc=6, 15, and 515 for
InAs, InP, and GaAs, respectively. The values of Nnc are
qualitatively consistent with those obtained by the simple
estimation.
4. Conclusion
We have clarified the structural trends in group III–V
semiconductor nanowires (NWs) based on a Monte-Calro
simulations using our empirical interatomic potential calcula-
tions. We have found that the averaged periodicity between W
segments for the SA-MOVPE decreases with increasing f i. We
have also found that the periodicity is affected by the nucleus
size of NWs: The calculated periodicity in InP (InAs) NWs
with the nucleus size consisting of � 10 atoms are 0.76 (0.86)
nm, reasonably consistent with the experimentally reported
one. On the other hand, the calculated periodicity in GaAs NWs
is estimated to be more than 70 atoms. These results thus
suggest that the nucleus size as well as f i is important factor in
determining the averaged periodicity between wurtzite
segments. Although the obtained results should be checked
from various aspects including validity of NW model, our
approach using the MC simulations is feasible to clarify the
formation of wurtzite segments in NWs.
T. Yamashita et al. / Applied Surface Science 254 (2008) 7668–7671 7671
Acknowledgments
This work was supported in part by Grant-in-Aid for
Scientific Research from JSPS under contracts No. 18560020.
Computations were performed at RCCS (National Institute of
Natural Sciences) and ISSP (University of Tokyo).
References
[1] K. Haraguchi, T. Katsuyama, K. Hiruma, K. Ogawa, Appl. Phys. Lett. 60
(1992) 745.
[2] X. Duan, Y. Huang, Y. Cui, J. Wang, C.M. Lieber, Nature 409 (2001) 66.
[3] M.S. Gudiksen, L.J. Lauhon, J. Wang, D.C. Smith, C.M. Lieber, Nature
415 (2002) 617.
[4] H. Kind, H. Yan, B. Messer, M. Law, P. Yang, Adv. Mater. 14 (2002) 158.
[5] J. Wang, M.S. Gudiksen, X. Duan, Y. Cui, C.M. Lieber, Science 293
(2001) 1455.
[6] M. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind, E. Weber, R. Russo,
P. Yang, Science 279 (1998) 208.
[7] J.C. Johnson, H.-J. Choi, K.P. Knutsen, R.D. Schaller, P. Yang, R.J.
Saykally, Nat. Mater. 1 (2002) 106.
[8] X. Duan, Y. Huang, R. Agarwal, C.M. Lieber, Nature 421 (2003) 241.
[9] J. Motohisa, J. Noborisaka, J. Takeda, M. Inari, T. Fukui, J. Cryst. Growth
272 (2004) 180.
[10] K. Tomioka, J. Motohisa, S. Hara, T. Fukui, Jpn. J. Appl. Phys. 46 (2007)
1102.
[11] P. Mohan, J. Motohisa, T. Fukui, Nanotechnology 16 (2005) 2903.
[12] T. Akiyama, K. Sano, K. Nakamura, T. Ito, Jpn. J. Appl. Phys. 45 (2006) 275.
[13] K. Sano, T. Akiyama, K. Nakamura, T. Ito, J. Cryst. Growth 301/302
(2007) 862.
[14] K.E. Kohr, S. Das Sarma, Phys. Rev. B 38 (1988) 3318.
[15] T. Ito, K.E. Kohr, S. Das Sarma, Phys. Rev. B 40 (1989) 9715.
[16] T. Ito, J. Appl. Phys. 77 (1995) 4845.
[17] T. Ito, Jpn. J. Appl. Phys. 3 (1998) 1217.
[18] C.-Y. Yeh, Z.W. Lu, S. Froyen, A. Zunger, Phys. Rev. B 45 (1992) 12130.
[19] M. Ohring, The Material Science of Thin Films, Academic Press, San
Diego, 1992, p. 41.
[20] S.B. Zhang, A. Zunger, Phys. Rev. B 53 (1996) 1343.
[21] Y. Kangawa, T. Ito, Y.S. Hiraoka, A. Taguchi, K. Shiraishi, T. Ohachi,
Surf. Sci. 507–510 (2002) 285.