NANO LETTERS
Diameter-Dependent Growth Direction of Epitaxial Silicon Nanowires
2005 Vol. 5, No. 5 931-935
Volker Schmidt,* Stephan Senz, and Ulrich Go1 sele Max Planck Institute of Microstructure Physics, Weinberg 2, D-06120 Halle, Germany Received March 10, 2005; Revised Manuscript Received March 24, 2005
ABSTRACT We found that silicon nanowires grown epitaxially on Si (100) via the vapor−liquid−solid growth mechanism change their growth direction from 〈111〉 to 〈110〉 at a crossover diameter of approximately 20 nm. A model is proposed for the explanation of this phenomenon. We suggest that the interplay of the liquid−solid interfacial energy with the silicon surface energy expressed in terms of an edge tension is responsible for the change of the growth direction. The value of the edge tension is estimated by the product of the interfacial thickness with the surface energy of silicon. For large diameters, the direction with the lowest interfacial energy is dominant, whereas for small diameters the surface energy of the silicon nanowire determines the preferential growth direction.
The ongoing miniaturization of electronic devices together with the limitations of optical lithography has triggered worldwide interest in the field of nanowires in general and silicon nanowires in particular.1 These inherent 1D, selforganized structures combine high crystalline quality with good controllability of both length and diameter. To make use of these properties, growing silicon nanowires epitaxially on a suitable substrate seems to be the most promising way of realizing a high density of integrated devices based on nanowires. One parameter of crucial importance in this context, especially for epitaxially grown nanowires, is the crystallographic growth direction. In this letter, we report on experiments demonstrating that the growth direction of epitaxially grown silicon nanowires changes with decreasing diameter of the nanowires from the 〈111〉 to 〈110〉 direction, as had similarly been observed for nonepitaxial silicon nanowires.2 A model is proposed to explain this phenomenon. It has been known since the mid 1960s3 that silicon nanowires grown by chemical vapor deposition with gold as a catalyst and diameters greater than 100 nm tend to grow in the 〈111〉 direction. In addition, growth in the 〈110〉 direction,4,5 the 〈112〉 direction,6,7 and rarely in the 〈100〉 direction8,9 has also been reported in the literature. We investigated silicon nanowires that were grown epitaxially10 on a silicon (100) substrate. The nanowires were produced by UHV chemical vapor deposition using diluted silane as a precursor gas. Gold served as a catalyst, which was deposited at room temperature as a film of 0.3 nm thickness and annealed at 400 °C for 10 min. Growth takes place at a temperature of 400 °C and at a silane partial pressure of 10 Pa. Figure 1a shows a typical top-view SEM image of a sample. It exhibits three different kinds of nanowires. First, * Corresponding author. E-mail:
[email protected]. 10.1021/nl050462g CCC: $30.25 Published on Web 04/08/2005
© 2005 American Chemical Society
the ones pointing at (18.4° with respect to the horizontal or vertical image axis of Figure 1a are shown. As depicted schematically in Figure 1c, these nanowires are unambiguously 〈112〉-oriented. The 〈110〉-oriented nanowires are the second group that can be identified. These are growing at (45° with respect to the horizontal image axis (Figure 1b). Furthermore, one can immediately recognize that their diameter is relatively small. As for the third kind, the ones observed horizontally or vertically in the projection plane, the situation is more complicated. Considering the schematic drawings shown in Figure 1c and d, it is apparent that these could either be 〈211〉- or 〈111〉-oriented, so in this case we get a mixed distribution. But if we assume that the number density is identical for the different possible 〈112〉 directions, we can deduce the pure 〈111〉 distribution by subtracting the 〈112〉 contribution obtained in the beginning. In addition, sometimes a kinking of the nanowires is observed. As an example, one nanowire changing its growth direction from 〈110〉 to 〈111〉 or 〈112〉 is marked in Figure 1a with a yellow arrow. The observation of this transition of the growth direction supports our model presented later in this text. For a better understanding of the spatial orientation of the nanowires, a schematic 3D side view of the different growth directions is shown in Figure 2. Here, parts a and c of Figure 2 show the four possible 〈110〉 or 〈111〉 growth directions, respectively. In Figure 2b, the 12 possible 〈112〉 growth directions are displayed. We obtained the resulting size distributions of the 〈110〉-, 〈112〉-, and 〈111〉-oriented nanowires by analyzing top-view SEM images, and these are depicted in Figure 3. Here it can be seen that for diameters smaller than 20 nm the 〈110〉 direction is preferred. However, for diameters greater than 30 nm the 〈111〉 direction becomes dominant. Especially by considering the relative proportion of the different directions,
Figure 1. (a) Top-view scanning electron micrograph of nanowires grown on a silicon (100) substrate. (b) Schematic top-view image of 〈110〉-oriented nanowires grown on a (100) substrate of the same orientation as in part a. (c) Schematic top-view image of 〈112〉-oriented nanowires grown on a (100) substrate of the same orientation as in part a. (d) Schematic top-view image of 〈111〉-oriented nanowires grown on a (100) substrate of the same orientation as in part a.
shown in the inset of Figure 3, it becomes apparent that a transition between the 〈111〉 and the 〈110〉 orientation takes place at a crossover diameter dc ) 2rc of approximately 20 nm. In the diameter range around this crossover diameter, the 〈112〉 orientation is also present, but because it appears only in this intermediate range, it will not be discussed in detail in the course of this letter. These size distributions agree surprisingly well with the results of Wu et al.2 for nonepitaxial silicon nanowire growth, which is interesting from a nucleation point of view. Their nanowires, grown on amorphous SiO2, experienced totally different nucleation conditions, so the substrate properties cannot account for the diameter dependence of the nanowire growth direction. A possible explanation for this diameter dependence of the growth direction will be presented in the following discussion. Silicon nanowire growth can be explained by the vaporliquid-solid mechanism as proposed by Wagner and Ellis.3 The first step in their model is that silane is cracked catalytically at the surface of the liquid gold-silicon eutectic droplet. Silicon then diffuses through the droplet and freezes out at the liquid-solid interface, producing the silicon nanowire. Because growth takes place only at the liquidsolid interface, it is obvious that the growth direction is also determined by the properties of this interface. In a thermodynamical model, interfaces are usually assumed to be atomically abrupt.11 In reality, this is not the case. On both sides of an Au/Si-Si interface, a certain transition region12 extending over a few atomic layers was simulated. Consequently, a description of the liquid-solid interface between the Au/Si eutectic droplet and the silicon nanowire has to include all of the contributions that arise in this transition region. This means that in our case we have to consider six different contributions: the bulk energy of silicon, the bulk 932
energy of the Au/Si eutectic droplet, the interfacial tension of the liquid-solid interface, the line tension of the triple phase line (vapor-Au/Si-Si),11 the surface tension of the droplet, and the surface tension of the silicon nanowire. These six contributions are depicted schematically in Figure 4. Fortunately, because we are interested in the energy difference of two growth directions, we can concentrate on the contributions that are growth-direction-dependent. This means that the two bulk energies and the surface tension of the Au/Si eutectic droplet can be neglected. In addition, we disregard the contribution of the line tension because there are indications that its absolute value is negligibly small.13 Consequently, there are two growth-direction-dependent terms remaining. First is the interfacial energy itself, given by the product of the interfacial area A with the corresponding liquid-solid interfacial tension σls. Second is the silicon surface tension contribution from the edge of the interface. This term is proportional to the circumference L with a proportionality constant , for which we want to use the term edge tension. This edge tension ) σs∆z is given by the product of the silicon surface tension σs with ∆z, the interfacial thickness on the silicon side (Figure 4). Thus the edge tension, being proportional to the surface tension, differs from the thermodynamic line tension, which by definition is the residual energy contribution not comprising the surface tension. The free energy F of a 〈111〉-oriented interface can now be expressed in terms of the edge tension and the interfacial tension: F ) L + σlsA
(1)
Concerning the geometry of the nanowires, we assume that 〈111〉-oriented ones have a regular hexagonal cross section with r being the distance from the center to one corner. Nano Lett., Vol. 5, No. 5, 2005
the radius r of the nanowire as the corner-to-center distance of a regular hexagon having the same circumference as the nanowire in question. The liquid-solid interface is assumed to be flat and perpendicular to the growth direction. Dividing equation 1 by L and introducing the geometrical parameter a ) AL-1r-1, which is independent of the radius of the nanowire, the free energy per circumference f ) F/L of a 〈111〉-oriented nanowire can be expressed as f ) ∆zσs + aσlsr
(2)
This means that f as a function of r is given by a straight line with y-axis intercept ∆zσs and a slope that is proportional to the interfacial tension of the liquid-solid interface. Keeping in mind the definition of r, a similar expression holds for f ′, the interfacial energy per circumference of a 〈110〉-oriented nanowire f ′ ) ∆zσ′s + a′σ′lsr
(3)
where a′, σ′ls, and σ′s are the geometrical parameter, the interfacial tension, and the surface energy of a 〈110〉-oriented nanowire. For reasons of simplicity, it is assumed here that ∆z takes the same value for both orientations. In the case in which σs > σ′s and a′σ′ls > aσls, the functions f and f ′ are crossing at a crossover radius rc given by
Figure 2. (a) Schematic side view of 〈110〉-oriented nanowires grown on a (100) substrate. The viewing direction is [1h1h1h]. (b) Schematic side view of 〈112〉-oriented nanowires grown on a (100) substrate. The viewing direction is [1h1h1h]. (c) Schematic side view of 〈111〉-oriented nanowires grown on a (100) substrate. The viewing direction is [1h1h1h].
Figure 3. Number density versus diameter for different growth directions. (Inset) relative proportion of the different growth directions.
Because 〈110〉-oriented nanowires have surface planes of different orientation, the hexagonal cross section of the 〈110〉 nanowires is not regular. Therefore, in this case we define Nano Lett., Vol. 5, No. 5, 2005
σs - σ′s rc ) ∆z a′σ′ls - aσls
(4)
This is depicted schematically in Figure 5, where f and f ′ are shown as a function of radius r. It becomes immediately clear that minimizing the energy with respect to the growth direction results in 〈110〉-oriented nanowires for radii smaller than rc. For radii greater than rc, the 〈111〉 direction is energetically more favorable. The reason is that for large diameters the direction with the lowest liquid-solid interfacial energy is dominant, whereas for small diameters the surface energy of the silicon nanowire determines the preferential direction of growth. To verify this result, estimates of the interfacial and surface tensions have to be found. Consider the interfacial and surface properties of 〈111〉oriented nanowires. The geometrical parameter a ) AL-1r-1 of the hexagonal {111} liquid-solid interface is 0.43. (A circular interface would give a ) 0.5.) The interfacial tension can be calculated using Young’s equation provided that the contact angle, the surface tension of the gold-silicon eutectic droplet, and the surface energy of silicon are known. A droplet surface tension of 0.85 J‚m-2,14 a silicon 〈111〉 surface energy of approximately 1.25 J‚m-2,15,16 and a contact angle of 137° 17 then yields an interfacial tension of σls ) 0.62 J‚m-2. Concerning the surface tension of 〈111〉-oriented nanowires, we assume that the nanowire is hexagonal having 933
Figure 4. Schematic of a liquid-solid interfacial region.
Table 1. Summary of Parameters Determining rc
Figure 5. Schematic of the free energy per circumference as a function of the radius of both 〈110〉- and 〈111〉-oriented nanowires.
six {110} surface planes. The surface tension can be found by assuming that the surface energy of a certain plane is roughly proportional to the corresponding density of dangling bonds.18 This estimate results in a surface tension that is
x3/2 larger than-2 the surface tension of a {111} plane, giving
σs ) 1.53 J‚m . The same argument can be used to find an estimate for the interfacial tension σ′ls of the liquid-solid interface of a 〈110〉-oriented nanowire, which then gives σ′ls ) 0.76 J‚m-2. It is assumed that the interface is flat and perpendicular to the growth direction because our TEM investigations showed no evidence for V-shaped interface morphology, in contrast to what has been observed by Wu et al.2 Interestingly, the increase of the interfacial area by such a V-shaped morphology would amount to the same factor x3/2 by which the {110} interfacial tension is larger than the {111} interfacial tension. To evaluate the surface tension σ′s of the silicon surface of a 〈110〉-oriented nanowire, one has to take into account that two of the six surface planes are {100} and four are {111} planes.19 The relative area proportion (1.59) of the {111} planes to the {100} planes can be used together with the Wulff theorem to calculate σ′s ) 1.28 J‚m-2. This means that the surface energy σ′s of a 〈110〉-oriented nanowire is only slightly higher than the surface energy of a silicon {111} plane (1.25 J‚m-2). From the geometry of the nanowire cross section given by Ma et al.,19 a geometrical parameter a′ ) 0.39 can be deduced. A summary of all of these parameters is shown in Table 1. The parameter ∆z, the thickness of the interface, is estimated to be ∆z ≈ 1 nm. Together with the estimates for the surface and interfacial tensions, equation 4 leads to a crossover radius of rc ≈ 10 nm. This value fits very well to the corresponding crossover diameter of 20 nm based on the 934
〈111〉 orientation
〈110〉 orientation
a ) 0.43 σls ) 0.62 J‚m-2 σs ) 1.53 J‚m-2
a′ ) 0.39 σ′ls ) 0.76 J‚m-2 σ′s ) 1.28 J‚m-2
experimental results shown in Figure 3. It should be emphasized here that the crossover radius strongly depends on the relative magnitude of the interfacial and surface tensions so that small changes in the surface tension might alter the value of the crossover radius substantially. This sensitivity with respect to the interfacial and surface energies implies that the technologically most interesting 〈100〉 growth direction (desirable for a combination of conventional CMOS microelectronics on (100) wafer surfaces with high-density vertical 〈100〉-oriented nanowires) might be achieved by a modification of the respective energies. The 〈112〉 direction has not been considered in any detail, but we expect that the model could be extended straightforwardly, provided that the required parameters were available. In conclusion, we have shown that epitaxially grown silicon nanowires of diameter greater than 40 nm prefer the 〈111〉 direction whereas wires with diameters of less than 20 nm are mostly 〈110〉-oriented. This change of the growth direction has been explained by considering the free energy of the silicon nanowire, which is influenced by both an edge tension term and an interfacial tension term. An estimate provides a crossover diameter of 20 nm, in agreement with experimental data. References (1) AdV. Mater. 2003, 15, Special Issue: One-Dimensional Nanostructures. (2) Wu, Y.; Cui, Y.; Huynh, L.; Barrelet, C. J.; Bell, D. C.; Lieber, C. M. Nano Lett. 2004, 4, 433. (3) Wagner, R. S.; Ellis, W. C. Appl. Phys. Lett. 1964, 4, 89. (4) Givargizov, E. I.; Sheftal, N. N. J. Cryst. Growth 1971, 9, 326. (5) Cui, Y.; Lauhon, L. J.; Gudiksen, M. S.; Wang, J.; Lieber, C. M. Appl. Phys. Lett. 2001, 78, 2214. (6) Givargizov, E. I. J. Cryst. Growth 1975, 31, 20. (7) Ozaki, N.; Ohno, Y.; Takeda, S. Appl. Phys. Lett. 1998, 73, 3700. (8) Lew, K.-K.; Reuther, C.; Carim, A. H.; Redwing, J. M.; Martin, B. R. J. Vac. Sci. Technol., B 2002, 20, 389. (9) Sharma, S.; Sunkara, M. K. Nanotechnology 2004, 15, 130. (10) Schmidt, V.; Senz, S.; Go¨sele U. Appl. Phys. A 2005, 80, 445. (11) Rowlinson, J. S.; Widom, B. Molecular Theory of Capillarity; Dover Publications Inc.: Mineola, NY, 2002.
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(12) Kuo, C.-L.; Clancy, P. Surf. Sci. 2004, 551, 39. (13) Getta, T.; Dietrich, S. Phys. ReV. E 1998, 57, 655. (14) Naidich, Y. V.; Perevertailo, V. M.; Obushchak, L. P. Zh. Fiz. Khim. 1975, 49, 1554. (15) Zhang, J.-M.; Ma, F.; Xu, K.-W.; Xin, X.-T. Surf. Interface Anal. 2003, 35, 805. (16) Jaccodine, R. J. J. Electrochem. Soc. 1963, 110, 525.
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