Nano Express

# Probability of twin formation on self-catalyzed GaAs nanowires on Si substrate

Masahito Yamaguchi*, Ji-Hyun Paek and Hiroshi Amano

Author Affiliations

Department of Electrical Engineering and Computer Science, Nagoya University, C3-1 Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan

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Nanoscale Research Letters 2012, 7:558  doi:10.1186/1556-276X-7-558

 Received: 14 July 2012 Accepted: 22 September 2012 Published: 8 October 2012

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### Abstract

We attempted to control the incorporation of twin boundaries in self-catalyzed GaAs nanowires (NWs). Self-catalyzed GaAs NWs were grown on a Si substrate under various arsenic pressures using molecular beam epitaxy and the vapor-liquid-solid method. When the arsenic flux is low, wurtzite structures are dominant in the GaAs NWs. On the other hand, zinc blende structures become dominant as the arsenic flux rises. We discussed this phenomenon on the basis of thermodynamics and examined the probability of twin-boundary formation in detail.

##### Keywords:
GaAs nanowire; Molecular beam epitaxy; Vapor-liquid-solid; Twin boundary; Supersaturation; Wurtzite; zinc blende

### Background

III-V compound semiconductor nanowires (NWs) have been attracting significant attention as fundamental structures of novel optical and electronic devices. Especially, vapor-liquid-solid (VLS) NWs grown on Si substrates have been investigated for optoelectronic integrated circuits [1,2].

Previously, we succeeded in growing self-catalyzed GaAs NWs on Si substrates using molecular beam epitaxy (MBE)-VLS method which is a combination of MBE and VLS method [3]. However, twin boundaries formed in the NWs during growth. The occurrence of twin boundaries is controlled by various methods such as control of supersaturation, growth temperature, and diameter [4-8]. To control the twin boundaries, we focused on the pressure of arsenic because self-catalyzed GaAs NW growth was nearly independent of Ga pressure, and arsenic flux plays an important role in the growth mechanism [3]. In addition, arsenic solubility in Ga solution is very low [9]. This means that the degree of supersaturation depends on arsenic pressure only.

### Methods

Self-catalyzed GaAs NWs were grown on a (111)Si substrate by MBE-VLS method. The growth temperature was 580°C. When the arsenic flux varied from 5.0×10−6 to 1.9×10−5 Torr, the diameter and the length of the obtained GaAs NWs varied from 90 to 30 nm and 0.5 to 3.5 μm, respectively. We have previously discussed the tendency of the diameter and length to depend on the arsenic flux [3]. The obtained NWs were observed by transmission electron microscopy (TEM).

### Results and discussion

TEM images of GaAs NWs are shown in Figure 1. In the case of low arsenic flux (5.0 × 10−6 Torr), wurtzite (WZ) structures are dominant as shown in Figure 1a. On the other hand, when the arsenic flux is high, Figure 1c shows that segments between the twin boundaries become large, and zinc blende (ZB) structures are dominant. The segment size follows the time between successive twin-crystal nucleation events. Furthermore, distribution of the segment sizes is exponential from a stochastic point of view [10].

Figure 1. TEM images of NWs grown under various arsenic fluxes. (a) 5.0 × 10−6, (b) 7.0 × 10−6, and (c) 1.9 × 10−5 Torr.

Figure 2 shows the distribution histogram of the segment sizes obtained from Figure 1. We assume a segment size of x and fitted the histogram with an exponential curve of the form exp (x/a) to estimate the expectation value of segment α. The estimated expectation values were 1.1 and 6.5 monolayers at arsenic fluxes of 7.0 × 10−6 and 1.9 × 10−5 Torr, respectively. The reciprocal of the expectation value α−1 is equivalent to the probability of occurrence of twin-crystal nucleation. The probabilities were approximately 90% (7.0 × 10−6 Torr) and 15% (1.9 × 10−5 Torr). The dependence of the probability on the arsenic flux is in good agreement with [11] and [12].

Figure 2. Histogram and distribution of segment size obtained from Figure1. Arsenic fluxes are (a) 7.0 × 10−6 and (b) 1.9 × 10−5 Torr. Solid lines are exponential fitting curves.

To understand these phenomena, we calculate the degree of supersaturation and estimate the probability of twin-boundary formation, following the procedure presented by Glas [13]. The degree of supersaturation Δμ is as follows:

Δ μ = μ Ga L + μ As L 2 μ GaAs (1)

where μGaAs is the half chemical potential of GaAs crystal nucleation; μGaL and μAsL are the chemical potentials of liquid gallium and liquid arsenic, respectively. We assume that the arsenic adatom was liquid arsenic existing on the gallium droplet. However, μGaL and μAsL include an interaction between gallium and arsenic in pure gallium and arsenic chemical potentials μGapL and μAspL, respectively. Therefore, μXL (X = Ga or As) is given by

μ X L = μ X pL + R T ln a X L (2)

where R is the gas constant, T is the growth temperature, and a L X is the activity of X in the liquid phase. At T0 = 298.15 K, when we adopt an enthalpy per mol in the X, the solid phase of hX,0pS, the degree of supersaturation Δμ is given by

Δ μ = R T ln a Ga L + R T ln a As L + μ Ga L h Ga, 0 pS + μ As pL h As, 0 ps 2 μ GaAs 0.5 h Ga, 0 pS 0.5 h As, 0 pS . (3)

All terms except the enthalpies depend on the growth temperature. The third, fourth, and fifth terms are the differences between the chemical potential and enthalpy of the pure gallium droplet, arsenic droplet, and GaAs crystal. Their values are tabulated in the paper of Ansara et al. [14]. The first and second terms are concerned with interactions in the alloy. They are denoted by the atomic concentration cX and the interaction parameter for gallium and arsenic ωGa,As as follows:

R T ln a Ga As L = R T ln c Ga As + c As Ga 2 ω Ga , As = R T ln c Ga As + c As Ga 2 V Ga V As c Ga V Ga + c As V As δ Ga δ As 2 1.256 × 10 5 χ Ga χ As 2 V Ga V As (4)

where VGa(As), χGa(As), and δGa(As) are the molar volume in the liquid phase, Pauling electronegativity, and Hildebrand solubility parameter, respectively. From these equations, we can obtain the relational expression for the supersaturation dependence on growth temperature and arsenic concentration in the gallium droplet.

Figure 3 shows the supersaturation as a function of the arsenic concentration in the gallium droplet at 580°C. In this calculation, the supersaturation per atom Δμ/NA, where NA is Avogadro's number, is adopted. In Figure 3, the equilibrium arsenic concentration is approximately 0.06% at Δμ/NA = 0. This value is in fair agreement with the arsenic concentration of approximately 0.1% in the gallium droplet at 580°C [9]. Therefore, when the arsenic concentration is positive because of an oversupply of arsenic atoms greater than 0.06%, GaAs VLS growth may occur.

Figure 3. Supersaturation as a function of arsenic concentration in gallium droplet at 580°C.

From supersaturation Δμ/NA, we can obtain the probability of twin-boundary formation. When arsenic adatoms on the gallium droplet surface diffuse to the three-phase boundary of vapor, liquid, and solid phases, we assumed that the GaAs crystal nucleus would be formed into a rhombus shape with side length r at the vertex of the nanowire top surface. Figure 4 shows the growth model. When the ZB and WZ structures form, the amount of Gibbs free energy change in this growth system is given by

Δ G ZB WZ = 3 r 2 h Δ μ 2 Ω N A + 2 r h γ SL,ZB WZ + ζ γ SV,ZB WZ γ LV sin β + 3 r 2 2 γ SN (5)

where Ω is the solid volume of the Ga-As pair (4.51 × 10−29 m3), h is the height of crystal nucleus, β is the contact angle of the droplet, γLV (γSN) is the interface energy between the droplet and the vapor phase (between the crystal nucleus and the NW top surface), and γSL,ZB(WZ) and γSV,ZB(WZ) are the interface energies of the GaAs ZB (WZ) crystal nucleus top and side surfaces. Obviously, h is the (111) GaAs lattice spacing, which is 0.32639 nm. γSV,ZB and γSV,WZ are the surface energies of (1-10)GaAs and (11-20)GaAs, which are 0.62 and 0.54 J/m2, respectively [15]. The interface energy γLV depends on temperature, and we use the following relation: γLV = 0.708 − 0.66 × 10− 4 × (T − 303) (J/m2) [16]. If the crystal nucleus is ZB, γSN = 0. On the other hand, in the case of the WZ crystal nucleus, γSN is 0.023 (J/m2), which is half of the GaAs stacking fault energy [17]. We assumed that the contact angle β is 45° [18]. Since the NW side surface has a certain asperity, we adopted the parameter ζ (0 < ζ < 1). Therefore, the maximum ΔGZB(WZ) * and the critical nucleus of Equation 4 for r are obtained as follows:

Δ G ZB WZ * = 2 h 2 γ SL,ZB WZ + ζ γ SV,ZB WZ γ LV sin β 2 3 h Δ μ Ω N A γ SN (6)

r ZB WZ * = 2 h γ SL,ZB WZ + ζ γ SV,ZB WZ γ LV sin β 3 h Δ μ Ω N A γ SN (7)

Figure 4. Growth model adopted in the calculation.

At steady state, it is known that the probability of crystal nucleation JZB(WZ) is proportional to the SZB(WZ) region, where a crystal nucleus can form, and Zeldovich factor ZZB(WZ)[19]. The relation is given by

J ZB WZ Z ZB WZ S ZB WZ exp Δ G ZB WZ * k T (8)

where k is the Boltzmann constant, S ZB WZ = 3 3 r ZB WZ * 2 , and the Zeldovich factor is

Z ZB WZ = 3 h Δ μ Ω N A γ SN / 2 π k T 1 / 2 (9)

Therefore, the probability of twin-crystal nucleation P is

P = J WZ J ZB + J WZ = Z WZ S WZ exp Δ G WZ * k T Z ZB S ZB exp Δ G ZB * k T + Z WZ S WZ exp Δ G WZ * k T (10)

This equation indicates that the probability depends on the growth temperature and arsenic concentration. When we assume that ζ is 0.8 at 580°C, the relation between the probability P and arsenic concentration cAs is shown in Figure 5. As the droplet arsenic concentration increases with increasing arsenic flux, the probability of twin-crystal nucleation decreases. This phenomenon agrees with the experimental results.

Figure 5. Relation between the probability of the twin-crystal nucleus and arsenic concentration at 580°C (ζ= 0.8).

By using the probability of twin-crystal nucleation in Figure 2, we can calculate the arsenic concentration and supersaturation per atom. When the arsenic fluxes are 7.0 × 10−6 and 1.9 × 10−5 Torr, the arsenic concentrations are 0.11% and 0.38%, and the supersaturations per atom are 53 and 143 meV, respectively. These supersaturation values are smaller than those of Au-catalyzed GaAs NWs (230 to 1,570 meV) [20]. This difference might be due to the difference in the side facet surface. Glas et al. adopted the {111} and {1-100} facets in the ZB and WZ structures in their calculations, respectively. In addition, there might be a difference in the diffusion length between gold and gallium droplets. From the obtained arsenic concentration, we estimate the critical nucleus. When the arsenic fluxes are 7.0 × 10−6 and 1.9 × 10−5 Torr, the critical nuclei of ZB (WZ) are 1.1 (0.3) and 0.4 (0.1) nm, respectively. This means that the increase of arsenic flux decreases the critical nucleus and increases the growth rate. In the case of high arsenic flux, the size difference between critical ZB and WZ nuclei is small compared with the case of low arsenic flux. This means that the ZB structure appears easily as the arsenic flux increases. Therefore, we could improve the comprehension of the growth mechanism in the self-catalyzed GaAs NWs. This comprehension might support a technological feasibility of a novel device like twin-plane 1D superlattices [21].

### Conclusions

Self-catalyzed GaAs NWs were grown on a (111)Si substrate by MBE-VLS method under various arsenic fluxes. From the TEM observations, we found that the segment size between the twin boundaries depends on the arsenic flux. In order to understand this phenomenon, we attempted to calculate the degree of supersaturation and estimate the probability of twin-boundary formation. When the supersaturation increased with increasing arsenic flux, the size difference between the critical ZB and WZ nuclei decreased. As a result, the ZB structures were easier to obtain as the arsenic flux increased. This qualitatively explained the experimental results and the high probability of the incorporation of twin boundaries.

### Abbreviations

GaAs: gallium arsenide; MBE: molecular beam epitaxy; NW: nanowires; Si: silicon; TEM: transmission electron microscope; VLS: vapor-liquid-solid; WZ: wurtzite; ZB: zinc blende.

### Competing interests

The authors declare that they have no competing interests.

### Authors’ contributions

MY conceived, designed, and coordinated the study and drafted the manuscript. JP carried out the experiments and calculations and helped draft the manuscript. HA participated in the coordination of the study. All authors read and approved the final manuscript.

### Authors’ information

MY is an associate professor, JP is a graduate school student, and HA is a professor at the Department of Electrical Engineering and Computer Science, Nagoya University.

### Acknowledgments

This study was partly supported by the Grant-in-Aid for Scientific Research (KAKENHI) No. 23510148 of the Japan Society for the Promotion of Science (JSPS) and ‘Tatematsu Foundation.’ Nagoya University Venture Business Laboratory is gratefully acknowledged for allowing the use of facilities.

### References

1. Mårtensson T, Svensson CPT, Wacaser BA, Larsson MW, Seifert W, Deppert K, Gustafsson A, Wallenberg LR, Samuelson L: Epitaxial III−V nanowires on silicon.

Nano Lett 2004, 4:1987-1990. Publisher Full Text

2. Roest AL, Verheijen MA, Wunnicke O, Serafin S, Wondergem H, Bakkers EPAM: Position-controlled epitaxial III–V nanowires on silicon.

Nanotechnology 2006, 17:S271-S275. Publisher Full Text

3. Paek JH, Nishiwaki T, Yamaguchi M, Sawaki N: Catalyst free MBE-VLS growth of GaAs nanowires on (111)Si substrate.

phys stat sol (c) 2009, 6:1436-1440. Publisher Full Text

4. Dubrovskii VG, Sibirev NV, Cirlin GE, Bouravleuv AD, Samsonenko YB, Dheeraj DL, Zhou HL, Sartel C, Harmand JC, Patriarche G, Glas F: Role of nonlinear effects in nanowire growth and crystal phase.

Phys Rev B 2009, 80:205305.

5. Shtrikman H, Popovitz-Biro R, Kretinin A, Heiblum M: Stacking-faults-free zinc blende GaAs nanowires.

Nano Lett 2009, 9:215-219. PubMed Abstract | Publisher Full Text

6. Johansson J, Dick KA, Caroff P, Messing ME, Bolinsson J, Deppert K, Samuelson L: Diameter dependence of the wurtzite-zinc blende transition in InAs nanowires.

J Phys Chem C 2010, 114:3837-3842. Publisher Full Text

7. Moewe M, Chuang LC, Dubrovskii VG, Chang-Hasnain C: Growth mechanisms and crystallographic structure of InP nanowires on lattice-mismatched substrates.

J Appl Phys 2008, 104:044313. Publisher Full Text

8. Cirlin GE, Dubrovskii VG, Samsonenko YB, Bouravleuv AD, Durose K, Proskuryakov YY, Mendes B, Bowen L, Kaliteevski MA, Abram RA, Zeze D: Self-catalyzed, pure zincblende GaAs nanowires grown on Si(111) by molecular beam epitaxy.

Phys Rev B 2010, 82:035302.

9. DeWinter JC, Pollack MA: Ga-As liquidus at temperatures below 650°C.

J Appl Phys 1985, 58:2410-2412. Publisher Full Text

10. Johansson J, Karlsson LS, Svensson CPT, Mårtensson T, Wacaser BA, Deppert K, Samuelson L, Seifert W: Structural properties of <111>B -oriented III-V nanowires.

Nature Mater 2006, 5:574-580. Publisher Full Text

11. Joyce HJ, Gao Q, Tan HH, Jagadish C, Kim Y, Fickenscher MA, Perera S, Hoang TB, Smith LM, Jackson HE, Yarrison-Rice JM, Zhang X, Zou J: Unexpected benefits of rapid growth rate for III−V nanowires.

Nano Lett 2009, 9:695-701. PubMed Abstract | Publisher Full Text

12. Spirkoska D, Arbiol J, Gustafsson A, Conesa-Boj S, Glas F, Zardo I, Heigoldt M, Gass MH, Bleloch AL, Estrade S, Kaniber M, Rossler J, Peiro F, Morante JR, Abstreiter G, Samuelson L, Fontcuberta i Morral A: Structural and optical properties of high quality zinc-blende/wurtzite GaAs nanowire heterostructures.

Phys Rev B 2009, 80:245325.

13. Glas F: Chemical potentials for Au-assisted vapor–liquid–solid growth of III-V nanowires.

J Appl Phys 2010, 108:073506. Publisher Full Text

14. Ansara I, Chatillon C, Lukas HL, Nishizawa T, Ohtani H, Ishida K, Hillert M, Sundman B, Argent BB, Watson A, Chart TG, Anderson T: A binary database for III-V compound semiconductor system.

Calphad 1994, 18:177-222. Publisher Full Text

15. Yamashita T, Akiyama T, Nakamura K, Ito T: Theoretical investigation on the structural stability of GaAs nanowires with two different types of facets.

Physica E 2010, 42:2727-2730. Publisher Full Text

16. Hardy SC: The surface tension of liquid gallium.

J Cryst Growth 1985, 71:602-606. Publisher Full Text

17. Takeuchi S, Suzuki K: Stacking fault energies of tetrahedrally coordinated crystals.

phys stat sol (a) 1999, 171:99-103. Publisher Full Text

18. Chatillon C, Chatain D: Congruent vaporization of GaAs(s) and stability of Ga(l) droplets at the GaAs(s) surface.

J Cryst Growth 1995, 151:91-101. Publisher Full Text

19. Markov IV: Crystal Growth for Beginners: Fundamentals of Nucleation, Crystal Growth and Epitaxy. Singapore: World Scientific; 2003.

20. Glas F, Harmand JC, Patriarche G: Why does wurtzite form in nanowires of III-V zinc blende semiconductors.

Phys Rev Lett 2007, 99:146101. PubMed Abstract | Publisher Full Text

21. Tsuzuki H, Cesar DF, Rebello De Sousa Dias M, Castelano LK, Lopez-Richard V, Rino JP, Marques GE: Tailoring electronic transparency of twin-plane 1D superlattices.

ACS Nano 2011, 5:5519. PubMed Abstract | Publisher Full Text