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: yamashita06@nd.phen.mie-u.ac.jp (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).

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