Vertical or Horizontal: Understanding Nanowire Orientation and

Article pubs.acs.org/JPCC

Vertical or Horizontal: Understanding Nanowire Orientation and Growth from Substrates Y. Y. Cao and G. W. Yang* State Key Laboratory of Optoelectronic Materials and Technologies, Institute of Optoelectronic and Functional Composite Materials, Nanotechnology Research Center, School of Physics & Engineering, Sun Yat-sen University, Guangzhou 510275, Guangdong, People's Republic of China ABSTRACT: We have established a theoretical model to address quantitatively the temperature-dependent growth of nanowire orientation and growth from substrates upon the vapor−liquid−solid (VLS) process by introducing thermal fluctuations. It was found that there is a critical temperature, depending on the Gibbs free energy of the nanowire nucleus, and that the nanowires with higher critical temperature tend to align horizontally to the substrate. Moreover, nanowires are vertically aligned on the substrate, or their growth direction is angled from the substrate, varying between 90 and 40°, if the critical temperature is lower. The critical temperatures of nanowires can be enormously dissimilar, which accounts for the fact that growth directions can be modulated by temperature. The developed theory explains the findings from a recent set of experiments on the temperature-dependent orientation of nanowires grown by the VLS process. These investigations concluded that thermal fluctuations play a crucial role in the VLS nanowire growth, and the preferred nanowire growth directions can be produced by temperature regulation, which would provide useful physical criteria in other types of experiments.

1. INTRODUCTION As promising materials, semiconductor nanowires have become the focus of intensive research due to their unique applications in mesoscopic physical chemistry and fabrication of nanoscaled devices. It is generally accepted that nanowires provide a good system to investigate the dependence of electronic and thermal transport, or even mechanical properties, on dimensionality and size reduction. Further, nanowires are expected to play an important role as both interconnects and functional units in fabricating electronic, optoelectronic, electrochemical, and electromechanical devices at the nanometer scale.1 Up to now, vapor-phase synthesis is probably the most extensively explored approach to prepare all kinds of semiconductor nanowires, and the vapor−liquid−solid (VLS) process seems to be the most successful for growing nanowires.2−6 This process was originally developed by Wagner and co-workers in the 1960s to produce micrometer-sized silicon whiskers7 and has been recently re-examined by Lieber et al. for synthesizing onedimensional nanostructures such as nanowires and nanorods from a rich variety of inorganic materials.8 However, the commonly grown out-of-plane nanowire geometry imposed by the VLS process appears as an obstacle to the current planar processing technology of microelectronic and optoelectronic devices.9,10 To control the growth direction of nanowires from the substrate, for example, vertically- or horizontally aligned, we need a deep understanding of the basic physical chemistry involved in the VLS process. Generally, a typical VLS process starts with the dissolution of gaseous reactants into nanoscaled liquid droplets in the presence of a catalyst metal. Once the liquid droplet is supersaturated with the metal, nanowire nucleation and growth will © 2012 American Chemical Society

start to occur at the solid−liquid interface. This growth is thus induced and dictated by the liquid droplets, and the radial size remains largely unchanged during the entire process.2 Meanwhile, growth directions of nanowires are determined by the surface free energy from the perspective of the energy theory based on thermodynamics.11,12 From this view, each liquid droplet serves as a soft template to strictly limit the lateral growth of nanowires. Therefore, previous theoretical treatments of the VLS nanowire nucleation and growth have been based on the energy theory of thermodynamics.7,13−15 As an important characteristic, the nanowire direction can be affected by growth conditions, such as substrate orientation and materials.14,16 Recently, reports have shown that this growth direction depends on temperature,10,16−21 implying that thermal effects underlie the growth mechanism. However, the above-mentioned energy theories completely neglect thermal fluctuations because high entropic gains of the (thermodynamically extensive) interface would lead to various stable states.22,23 It is thus essential to develop a new theoretical treatment that includes thermal effects to understand these temperaturedependent growth characteristics. In this contribution, we have established a theoretical model to address quantitatively the temperature-dependent growth via the VLS process by introducing the effect of thermal fluctuations. Interestingly, we find that the critical temperature depends on the Gibbs free energy of the nanowire nucleus, and there is a correlation between nanowire growth direction Received: November 7, 2011 Revised: February 22, 2012 Published: February 23, 2012 6233

dx.doi.org/10.1021/jp210659g | J. Phys. Chem. C 2012, 116, 6233−6238

The Journal of Physical Chemistry C

Article

where t(α) factors in the volume of the nucleus. On the basis of Tan’s model,13 Δgv0 is defined as Δgv0 = −(RcT)/(Vm) ln(C/(Ceq)), in which T, Rc, and Vm are temperature, gas constant, and mole volume of the nanowires. C and Ceq are the respective material concentrations of the nanowires on the solid and liquid lines of the eutectic catalyst−nanowire phase diagram. Hence, the total Gibbs free energy is

and critical temperature. Moreover, we find that nanowires would be vertically aligned from the substrate or angled between 90 and 40° if their critical temperature is lower. The range of critical temperatures leading to different growth directions is broad, which explains why nanowire orientation and growth can be modulated by temperature. Finally, we explain the findings of a recent set of experiments on the temperaturedependent directions of GaAs or CdSe nanowires grown using the VLS process.10−13,16−21 Additionally, these investigations provide useful information for controllable growth of nanowires upon the VLS process.

σ ⎞ ⎛1 G = σnv R2s(α) + ⎜ Δg v0 − nv ⎟R3t(α) ⎝2 R ⎠

Accordingly, we obtain the formation energy for unit area of nucleus

2. THEORETICAL MODEL Previous research have shown that the growth direction of nanowires depends on the orientation of the nanowire nucleus in the VLS process,11,12,24,25 as illustrated in Figure 1. Here, we

1

σnv s(α)R2 + Δg v0t(α)R3 G 2 V= = 1 S̅ [s (α) + s2(α)]R2 2 1

focus on the stability of the nucleus. By consideration of the thermal effect, the nucleus surface would oscillate and become unstable. In fact, thermal fluctuations mostly affect this surface, displacing it from thermal equilibrium and altering its surface energy; thus, growth direction can be changed thermally. For the study, we first calculated the energy of formation energy per unit area for nanowire nucleation as a function of direction. The Gibbs free energy of formation, including contributions from surface (Gs) and volume (Gg), can be expressed as (1)

If a cluster of atoms condenses around the catalyst on the substrate, the surface energy difference can be given as Gs = [(σsn − σsv )s1 + (σcn − σcv )s2 + σnv s3]R2

(2)

where σsn, σsv, σcn, σcv, and σnv are the interface energy of the substrate−nucleus, the substrate−vapor, the catalyst−nucleus, the catalyst−vapor, and the nucleus−vapor, respectively. R is the radii of the nucleus; s1(α) and s2(α) are, respectively, the interface area factor of substrate−nucleus and catalyst−nucleus, whereas s3(α) is the surface area factor of the nucleus; α gives the angular orientation of the nucleus to the original substrate direction. On the basis of the balance condition of forces, we obtain σsn − σsv = σnv cos θ2 and σcn − σcv = −σnv cos θ0, in which θ2 is the contact angle between substrate and nucleus, whereas θ0 is the contact angle between catalyst and nucleus. Here we choose s(α) = s1(α) cos θ2 − s2(α) cos θ0 + s3(α), hence Gs = σnvR2s(α). According to nucleation thermodynamics and the Kelvin equation,24 the Gibbs energy for volume can be expressed as Gg =

⎛ 1 0 σnv ⎞ 3 ⎜ Δg ⎟ R t (α ) − ⎝2 v R ⎠

(5)

The unit area energy is important in making sense of oneparticle systems in the following. On the basis of the condition for critical nucleus formation, (∂G)/(∂R) = 0, if the atomic cluster transforms into a critical nucleus, we can calculate the radius of the critical nucleus, R* = −(4/3)((σnv)/(Δgv0))((s(α)−t(α))/(t(α))). Given different directions, the morphology of the nucleus would change. Figure 2 illustrates the variety of nuclei with different shapes and orientations. To compare the different orientations, we simply take Figure 2a as the origin. Parts b−e of Figure 2 show the nucleus with different angles α to the original substrate direction. The complement (μ/2) − α is the angle between nanowire and substrate. However, there is a critical angle αc, as seen in Figure 2c, that if exceeded the morphology of the nucleus would change dramatically. Hence, the surface and volume factors of the nucleus would have different expressions as α varies. If α < αc, the area and volume factors can be expressed as s1 = π sin2 θ2, s2 = π sin2 θ0, s3 = 2π(cos θ2 − cos θ0), and t(α) = (4/3)π((cos3 θ0 − cos3 θ2 − 3cos θ0 + 3cos θ2)/4). If α > αc, the area and volume factors turn out to be a little complicated; the interface area factor of the substrate-nucleus becomes s1(α) = (((b2+L2)2)/(4L2))[π − arcsin((2bL)/(b2+L2))] − ((b(b2 − L2))/(2L)), and the catalyst−nucleus interface area factor can be expressed as s2(α) = (((b2+a2)2)/(4a2))[π − arcsin((2ba)/(b2+a2))]− ((b(b2 − a2))/(2a)), in which L = ((cos θ3 − cos θ0)/ (sin α)) = ((cos θ1 cos2 α − cos θ0)/(sin α)) + sin θ2, b = (sin2 θ0 − ((cos θ1 − cos θ0)2)/(tan2 α))1/2 and a = sin θ0 + (cos θ1 − cos θ0)/(tan α). Additionally, the surface area factor of the nucleus can be expressed as s3(α) = ∫ θθ00−2α ((b′2+a′2)/ (a))[α − arcsin((2b′a′)/(b′2+a′2))]Rdθ. The volume factor is t(α) = ∫ θθ00−2α {((b′2+a′2)2)/(4a′2) [π−arcsin((2b′a′)/(b′2+a′2))] − ((b′(b′2−a′2))/(2a′))}Rdθ, where b′ = (sin2 θ − ((cos θ1 − cos θ)2)/(tan2 α))1/2 and a′ = sin θ + ((cos θ1 − cos θ))/(tan α). Given the area and volume factors in eqs 1−5, we obtain the angle dependence of the energy per unit area for the nucleus. To explore the thermal stability of the nucleus, we consider thermal fluctuations on its cross-sectional boundaries; the radii of these cross sections r fluctuate with polar coordinate, 0 ≤ θ ≤ 2π. The boundaries are allowed to oscillate with elastic energy (k/2)r2 and interact via a local potential V. On the basis

Figure 1. Schematic illustration of nucleus with various directions and the nanowires grown from the nucleus correspondingly. The arrows on the nucleus are the orientation directions.

G = Gs + Gg

(4)

(3) 6234



Article

Figure 2. Schematic illustration of nanowire nucleus with various directions. Taking (a) as the initial state of the orientation of nucleus. The dashed line in (b−e) is the substrate position with the initial direction of nucleus, and the angle α between the substrate and the dashed line shows the various direction of nucleus. The angle α in (c) is the critical angle αc, which is the demarcation point of two different morphology of nucleus.

of the energy associated with these surface fluctuations, the partition function can be expressed as Ζ(β) =

∫ ∏ [dr]e

−β

∫0

2π

The equipartition energy for free oscillators is contained in the coefficient in front of the trace, in which λ is the linear density of oscillators and can be expressed as λ = K/k, where K is the microscopic spring constant. Because r = R sin θ2, the Hamiltonian can be re-expressed as

d θ[(k /2)r 2 + R * 2V /2]

r

(6)

where β = 1/kBT. Moreover, if the boundaries are infinitely stiff, the integral in eq 6 turns into a limit circles r(θ) = r*, where r* = R* sin θ2 is obtained from the critical radii associated with the minimum in nucleus energy. The integral in the exponent of eq 6 is the energy of the cross-sectional surface of the nucleus incorporating more importantly thermal fluctuations. We assume a system of just one radius r as a single particle since the fluctuations only depend on r. Thus the integrand in the exponent is the single-particle energy under our assumptions. By introducing the density matrix and the standard transformation,26−29 eq 6 can be written as the trace ⎛ 2π ⎞2πλ ⎡ ⎛ 4π ⎞⎤ Ζ(β) = ⎜ ⎟ Tr ⎢exp⎜ − 2 Ĥβ⎟⎥ ⎠⎦ ⎝ βk λ ⎠ ⎣ ⎝ R*

Ĥβ = −

d2

4βk sin 2 θ2 dR2

+

β 4 R* V 4

(9)

We can obtain its lowest bound eigenstate from Ĥ βψβ(r) = Eβψβ(r). Thus, the probability for the cross-sectional radius of the nucleus is p(r) = |ψβ(r)|2. If the Hamiltonian Ĥ β has no bound state, the probability p(r) would be constant. The equipotent probability for various radii leads to an unstable nucleus; as long as the probability p(r) is not constant, the nucleus has a stable regime. However, with the existence of a bound state in Ĥ β, we can deduce whether p(r) is constant or not.22 Therefore, nucleus stability can be judge by the existence of a bound state in a suitable one-particle Hamiltonian operator. The potential in eq 9 depends linearly on the radius of the nucleus. For general linear potentials, the energy spectrum would change from being discrete to continuous without restriction from the rigid wall at the lowest potential. Hence, the bound state is not always existed with a linear potential. Considering the radius of a nucleus is always positive valued,

(7)

in which the temperature-dependent Hamiltonian can be expressed as β R *2 d2 Ĥβ = − + R *4 V 2 4βk dr 4

R *2

(8) 6235



Article

the potential in eq 9 has only a maximum finite potential; meanwhile, the lower bound of the potential is infinite. The linear potential cannot ensure a bound state is present; i.e., the nucleus is not always stable. Here we solve the problem by the quantization rules in the Wentzel−Kramers−Brillouin approximation.30 The classic allowed range, which is used in the quantization rules, is from zero to infinitely great in theory. However, nucleus sizes are finite in practice and restricted necessarily by catalyst size.13,25 By adding a size limitation to the classically allowed range, the limits of integration in the quantization rules turn out to be 0 ≈ Rm, with Rm the maximum radius of the nucleus. Accordingly, we can obtain a critical temperature corresponding to the disappearance of the lower bound eigenstate as Tc =

−Δg v0kt(α) 4 3/2 R m R *sin θ2 3π s1(α) + s2(α)

(10) 2

We can obtain the elastic constant as k = ((Y)/(1−υ))ε , where Y, υ, and ε are Young’s modulus, Poisson’s ratio, and strain for the nanowires. The critical temperature determines the stability of nucleus: if T > Tc, there are no bound states, thus no stable nucleus, whereas if T < Tc, the nucleus is stable as the Hamiltonian has at least one bound state and from the nucleus a nanowire can form and grow. From eq 10, the largest radius plays an important role in the critical temperature. We could obtain a stable nucleus at higher temperatures by enlarging the catalyst size. Interestingly, we have obtained the critical temperature from the potential energy. Leaving aside the effect of nucleus size, the potential depends on surface and volume factors through introducing the identity cos θ2 = cos θ1 cos α. In our analysis above, these factors are determined by angle α so that the critical radius of the nucleus is also a function of α. Considering the dependence of Δgv0 upon temperature, we define Δgv0 = TΔgT0 , where ΔgT0 is assumed constant. Accordingly, we can relate the critical temperature to the growth direction α Tc(α) =

Figure 3. (a) The potential energy of GaAs nucleus with various angle α. The lowest point is the critical angle. (b) The potential energy of nucleus vs the radii. The real line and dashed line represented the nucleus with α = αc − 10° and α = αc + 30°, respectively.

α, trends in the potential stay the same. As the radius increases, the potential decreases and determines a maximum radii which we choose as 25 nm.18,21 On the basis of this trend in potential, we can obtain the critical temperature by integration. Assume the parameters in eq 10 are all constants except the maximum of radii Rm. We normalize all other parameters to focus on the Rm dependence of the critical temperature plotted in Figure 4.

⎛ 16σnv ⎞2/3 ⎜ ⎟ Rm ⎝ 9π ⎠

⎧ ⎫1/3 ⎪ [s(α) − t(α)]2 ⎪ k 2 2 ⎨− ⎬ (1 − cos θ1 cos α) 0 ⎪ ⎪ t(α)[s1(α) + s2(α)] ⎭ ⎩ ΔgT (11)

The nucleus will have various angle-dependent critical temperatures Tc(α) and will be stable if the growth temperature is below that critical temperature; nanowires will preferentially grow along that direction at the exclusion of other directions.. Hence, we have deduced a temperature-dependent growth direction for nanowires.

3. RESULTS AND DISCUSSION Taking the growth of GaAs nanowires on the Si substrate as an example, we check the validity of the above model. Figure 3a shows the potential of the nucleus as a function of angle α. Because different α leads to different nucleus morphologies, the potential energy is different. The radial dependence of the potential, used in the integral to obtain the critical temperature, is shown in Figure 3b. The two different lines illustrate the nucleus with α > αc and α < αc, respectively. Despite a varying

Figure 4. The critical temperature of the stability of nucleus vs the maximum radii of nucleus. 6236



Article

some nanowires grew vertically to the substrate, and some inclined at about 35.3°. At higher temperatures, planar nanowires grew. Cai et al.20 reported temperature-dependent growth directions of ZnSe nanowires. The nanowires were inclined at 55° from the GaAs (001) substrate at 530 °C. If the growth temperature is lowered to 390 °C, nanowires are predominantly vertical to the substrate but haphazardly inclined about this angle. Another experiment report18 described Si nanowires grown on a Si(111) substrate at temperatures between 450 and 600 °C. Also, yields of vertical nanowires would decrease with increasing temperature. Zhang et al.19 reported on GaAs nanowire growth from a GaAs [311]B substrate. The vertical or inclined nanowires were grown at temperatures lower than 460 °C. If the growth temperature is increased to 500 °C, they found that all nanowires grew laterally on the substrate. All these experiments are in agreement with our conclusions; in other words, the direction of nanowires can be modulated by temperature, growth tending to be planar at higher temperatures and stable with smaller α at lower temperatures. Additionally, we provide a detailed comparison of our model predictions with experimental data as follows. By use of the GaAs nanowires grown on Si (001) substrates as an example to make this comparison, we plot eq 11 without normalizing the parameters as a diagram for the nanowire growth as shown in Figure 5b. In our calculations, the interface energy density of GaAs vapor is chosen to 13.75 ev/nm2,31,32 and the Poisson’s ratio and Young’s modulus are 0.31 and 85.9GP,33 respectively. The critical temperature in Figure 5b has a similar trend with α as that in Figure 5a. The nanowires with various angles can only be stable under the temperature lower than the critical temperature. From the experiments,17 the GaAs nanowires are angled at about 35° (about 65° in our model) from the Si (001) substrate at 580 °C. However, the nanowires are oriented randomly when the growth is at lower temperatures on the same substrate. Therefore, the experimental data agree well with our theoretical results. This agreement between theory and experiment suggests that thermal fluctuations play a crucial role in the nanowire growth upon the VLS process. Accordingly, modulating temperature leads to various growth directions of nanowires, which provides useful information to be exploited in other experiments. The orientation of the substrate plays also an important role in the VLS nanowire growth. In the experiments,20 nanowires are grown along the ⟨110⟩ direction both on GaAs (001) and GaAs (110) substrates at 530 °C. The nanowires are inclined at angle 55° from the GaAs (001) substrate, whereas these are vertical when the growth is on the GaAs (110) substrate. Lowering the temperature to 390 °C, the growth angles are still different on the two substrates, although both grow along the ⟨111⟩ direction. The same situation is also present in CdSe nanowires grown on GaAs (001) and GaAs (110) substrates.21 Identically, inclined angles for GaAs nanowires grown on a Si (001) surface is about 35° and becomes 90° when grown on a Si (111) surface.17 Meanwhile, the GaAs nanowires grown on GaAs (100),10 GaAs (111),34 and GaAs (311)19 are also different in the directions. All these experiments demonstrate the influence of substrate orientation on nanowire growth direction, and lowering energy drives this preferential growth.14 Thus, altering substrate orientation provides an alternative means to control nanowire growth while maintaining temperature.

However, the maximum in the nucleus radius is determined by the catalyst size. Thus, by enlarging catalyst size, stable nanowires at higher temperatures can duly be obtained. Furthermore, the nucleus angle α dictates growth direction: if α = 0°, the nanowires are grown vertically to the substrate, whereas for α = 90° planar nanowires are formed. The angle dependence of critical temperature is plotted as the solid line in Figure 5a based on eq 11. At temperatures below the critical

Figure 5. (a) The critical temperature as functions of the angle α, which denotes the growth direction of nanowires. (b) The critical temperature of GaAs nanowires with the angle α. Nanowires can grow in the region below the critical temperature line. The experimental data (■) are from ref 17.

line, the nanowires grow at a preferential direction. An undulation appears curiously if α is smaller than about 50°. In the temperature range below the value of the dashed line in Figure 5a, all nanowires with α smaller than 50° have a certain probability of occurring; hence, at lower temperatures, nanowires grow in haphazard directions. However, if the temperature is above those represented by this dashed line, stable nanowires form at increasingly greater angle α as temperature increases, becoming more planar-aligned in the process. Because the material parameters enter as a morphological factor, the deductions we have obtained above are universal. These deductions were compared with some nanowire common systems. In an experiment,10 temperature was modulated to change the GaAs nanowire growth direction on GaAs (100) substrate. Nanowires grown at low temperature are cluttered; 6237



Article

(25) Wang, C. X.; Wang, B.; Yang, Y. H.; Yang, G. W. J. Phys. Chem. B 2005, 109, 9966−9969. (26) Kleinert, H. Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets; World Scientific: Singapore, 2006. (27) Feynman, R. P. Statistical Mechanics; Westview Press: Boulder, 1998. (28) Alerhand, O. L.; Berker, A. N.; Joannopoulos, J. D.; Vanderbilt, D.; Hamers, R. J.; Demuth, J. E. Phys. Rev. Lett. 1990, 64, 2406−2409. (29) Poon, T. W.; Yip, S.; Ho, P. S.; Abraham, F. F. Phys. Rev. Lett. 1990, 65, 2161−2164. (30) Fermi, E. Notes on Quantum Mechanics; University of Chicago Press: Chicago, 1995. (31) Földi, P.; Kálmán, O.; Benedict, M. G.; Peeters, F. M. Phys. Rev. B 2006, 73, 155325. (32) Guyer, J. E.; Barnett, S. A.; Voorhees, P. W. J. Cryst. Growth 2000, 217, 1−12. (33) Zhao, J. H.; Ryan, T.; Ho, P. S.; McKerrow, A. J.; Shih, W. Y. J. Appl. Phys. 1999, 85, 6421−6424. (34) Harmand, J. C.; Tchernycheva, M.; Patriarche, G.; Travers, L.; Glas, F.; Cirlin, G. J. Cryst. Growth 2007, 301, 853−856.

4. CONCLUSION In summary, we have developed a theoretical model to address quantitatively the influence of temperature on growth direction of nanowires upon the VLS process by taking into account within a quantum mechanics framework thermal fluctuation. The energy potential of the nanowire nucleus and the Hamiltonian determine the relationship between critical temperature and growth direction. Interestingly, our theoretical predictions are consistent with various experiments. Our theory not only brings out many new interesting findings about this growth process but also hints at important ways to control growth directions of nanowires.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant No. U0734004).

■

REFERENCES

(1) Xia, Y.; Yang, P.; Sun, Y.; Wu, Y.; Mayers, B.; Gates, B.; Yin, Y.; Kim, F.; Yan, H. Adv. Mater. 2003, 15, 353−389. (2) Ross, F. M. Rep. Prog. Phys. 2010, 73, 114501. (3) Mohammad, S. N. J. Appl. Phys. 2010, 107, 114304. (4) Kikkawa, J.; Ohno, Y.; Takeda, S. Appl. Phys. Lett. 2005, 86, 123109. (5) Sundaresan, S. G.; Davydov, A. V.; Vaudin, M. D.; Levin, I.; Masler, J. E.; Tien, Y.-L.; Rao, V. M. Chem. Mater. 2007, 19, 5531− 5537. (6) Leung, Y. P.; Liu, Z.; Hark, S. K. J. Cryst. Growth 2005, 279, 248− 257. (7) Wagner, R. S.; Ellis, W. C. Appl. Phys. Lett. 1964, 4, 89−90. (8) Morales, A. M.; Lieber, C. M. Science 1998, 279, 208−211. (9) Fan, H. J.; Werner, P.; Zacharias, M. Small 2006, 2, 700−717. (10) Fortuna, S. A.; Wen, J. G.; Chun, I. S.; Li, X. L. Nano Lett. 2008, 8, 4421−4427. (11) Schmidt, V.; Senz, S.; Gosele, U. Nano Lett. 2005, 5, 931−935. (12) Wang, C. X.; Hirano, M.; Hosono, H. Nano Lett. 2006, 6, 1552−1555. (13) Tan, T. Y.; Li, N.; Gosele, U. Appl. Phys. Lett. 2003, 83, 1199− 1201. (14) Schwarz, K. W.; Tersoff, J. Phys. Rev. Lett. 2009, 102, 206101. (15) Glas, F.; Harmand, J. C.; Patriarche, G. Phys. Rev. Lett. 2007, 99, 146101. (16) Fortuna, S. A.; Li, X. L. Semicond. Sci. Technol. 2010, 25, 024005. (17) Ihn, S. G.; Song, J. I.; Kim, T. W.; Leem, D. S.; Lee, T.; Lee, S. G.; Koh, E. K.; Song, K. Nano Lett. 2007, 7, 39−44. (18) Schmid, H.; Björk, M. T.; Knoch, J.; Riel, H.; Riess, W. J. Appl. Phys. 2008, 103, 024304. (19) Zhang, G. Q.; Tateno, K.; Gotoh, H.; Nakano, H. Nanotechnology 2010, 21, 095607. (20) Cai, Y.; Sou, S. K.; Chan, Y. F.; Su, D. S.; Wang, N. Small 2007, 3, 111−115. (21) Shan, C. X.; Liu, Z.; Hark, S. K. Appl. Phys. Lett. 2007, 90, 193123. (22) Nisoli, C.; Abraham, D.; Lookman, T.; Saxena, A. Phys. Rev. Lett. 2009, 102, 245504. (23) Nisoli, C.; Abraham, D.; Lookman, T.; Saxena, A. Phys. Rev. Lett. 2010, 104, 025503. (24) Liu, Q. X.; Wang, C. X.; Xu, N. S.; Yang, G. W. Phys. Rev. B 2005, 72, 085417. 6238


Vertical or Horizontal: Understanding Nanowire Orientation and

Recommend Documents